THREE ESSAYS ON DEPENDENT PANELS: EMPIRICAL EVIDENCE

A DISSERTATION SUBMITTED TO THE GRADUATE DIVISION OF THE

UNIVERSITY OF HAWAI‘I AT MANOA IN PARTIAL FULFILLMENT OF THE

REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

IN

ECONOMICS

AUGUST 2014

By

Qianxue Zhao

Dissertation Committee:

Carl S. Bonham, Chairperson

Byron Gangnes

Peter Fuleky

Sumner La Croix

David S. McClain

Keywords: cross-sectional dependence, panel unit root test, panel estimator

Dedication

I dedicate my dissertation work to my family.

ii

Acknowledgements

I own many thanks to all those professors who instructed me to the best of their knowledge

and made this dissertation possible, especially my committee members: Professor Carl S.

Bonham, Professor Peter Fuleky, Professor Byron Gangnes, Professor Sumner La Croix,

and Professor David S. McClain.

My deepest gratitude is to two professors from whom I learn most. I first want to thank

Professor Carl S. Bonham, one of my advisors and the chairperson, who introduced me to

the fascinating area of dependent panel techniques. My indebtedness to professor Bonham

is also due to his supports of various softwares for all my projects and his effective guidance

on conducting empirical researches.

I am also indebted a lot to Professor Peter Fuleky, my other advisor, who introduced

me to the programing language R and helped me become acquainted with it. I also benefit

from Professor Fuleky in studying many other economic packages, econometrical methods

and writing skills.

I also want to thank professor Luigi Ventura, my co-author from University of Rome,

for providing me the opportunity of working jointly with him.

I would like to thank the Department of Economics in University of Hawaii, the Hung

Fellowship and the University of Hawaii Economic Research Organization (UHERO) for

providing financial supports throughout the years.

Finally, I own my greatest debt to my grand parents, my parents, my sister, my dog

back home and my forever-love husband. It is their strong love that backs me up in difficult

times. I cannot be what I am now without it.

iii

Abstract

The assumption of cross-sectionally independent units in the panel data may fail due to

common shocks and spillover effects. This dissertation mainly deals with the issue of cross-

sectional dependence when conducting empirical researches. This objective is accomplished

by utilizing advanced panel methods. This dissertation consists of three empirical stud-

ies exploring the improvements in econometric methods to investigate three different yet

equivalently interesting topics.

The first essay contributes to the literature of tourism studies. It is the first paper to

account for cross-sectional dependence when estimating the tourism demand elasticities.

Using a quarterly panel of 48 states on the mainland of the US form 1993Q1 to 2011Q2, I

found that the conventional estimation method is unable to control for unobserved common

factors in the variables appropriately. As a result, it leaves common factors that are non-

stationary in the regression errors and causes counter-intuitive estimations. To solve the

problem of cross-sectional dependence, I use advanced methods for dependent panel and

reestimate the tourism demand elasticities for Hawaii.

In the second essay, I study the degree of consumption smoothing through international

markets using a annual panel of 158 countries during the year of 1970 to 2010. To estimate

the degree of consumption smoothing, I compare different methods of separating the com-

mon and the idiosyncratic shocks from observed data. I show that the conventional method

fails to control for aggregate shocks completely. I reestimate the degree of consumption

smoothing with the statistically defensible CCE estimators.

In the last essay, I re-examine the degree of gasoline market integration in the US,

accounting for both cross-sectional dependence and structural breaks. I test for the law of

iv

one price (LOP) within state-level retail gasoline markets. To deal with the adverse effects

of cross-sectional dependence and structural breaks on the residuals of the LOP regression

model, I propose a hybrid panel unit root test. Using the hybrid method, I fail to find a

constant cointegrating relationship between state gasoline prices and the national average

price in the US.

v

Contents

Acknowledgements iii

Abstract iv

List of Tables viii

List of Figures x

1 Essay 1: Estimating Demand Elasticities in Non-Stationary Panels: TheCase of Hawaii’s Tourism Industry 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Tourism Demand Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Methodology Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 Common Correlated Estimator . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.4.1 CCE Estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.5 Panel Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.5.1 Cross-Section Dependence Test . . . . . . . . . . . . . . . . . . . . . 91.5.2 Panel Unit Root Tests . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.6 Data and Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 111.6.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.6.2 Empirical Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.7 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141.7.1 Pre-test for Unit Root in Variables . . . . . . . . . . . . . . . . . . . 141.7.2 Estimations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

1.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.8.1 Income . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171.8.2 Price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.9 Robustness Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201.9.1 Other Substitute Price . . . . . . . . . . . . . . . . . . . . . . . . . . 20

1.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 Essay 2: Common Correlated Effects and International Risk-sharing 262.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2 Regression Equation for International Risk-sharing . . . . . . . . . . . . . . 27

2.2.1 Theoretical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.2 Empirical Model in the Literature . . . . . . . . . . . . . . . . . . . 292.2.3 Empirical Model in this Paper . . . . . . . . . . . . . . . . . . . . . 30

2.3 The Common Correlated Effect Estimator . . . . . . . . . . . . . . . . . . . 322.3.1 Common Correlated Effect Estimator . . . . . . . . . . . . . . . . . 32

vi

2.3.2 Relationship to Consumption Risk-sharing . . . . . . . . . . . . . . . 352.4 Empirical Strategy and Data . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4.1 Roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362.4.2 Cross-sectional Dependence Test and Panel Unit Root Test . . . . . 372.4.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.5 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.5.1 Variable Test and Residual Diagnostic Test . . . . . . . . . . . . . . 392.5.2 Estimation for the Overall β . . . . . . . . . . . . . . . . . . . . . . 482.5.3 The Change of the Overall β Over Time . . . . . . . . . . . . . . . . 492.5.4 Individual β . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3 Essay 3: How Integrated are US Gasoline Markets: An Empirical Testwith Cross-sectional Correlation and Structural Breaks 573.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.2 Examination of the Degree of Gasoline Market Integration . . . . . . . . . . 593.3 Empirical Strategy for the Test for the LOP . . . . . . . . . . . . . . . . . . 62

3.3.1 The Regression Model . . . . . . . . . . . . . . . . . . . . . . . . . . 623.3.2 A Hybrid Unit Root Test . . . . . . . . . . . . . . . . . . . . . . . . 64

3.4 Data and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663.4.1 Main Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673.4.2 Test of the LOP based on Relative Prices . . . . . . . . . . . . . . . 76

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

Appendix A 82A.1 Additional Tables for Essay 1 . . . . . . . . . . . . . . . . . . . . . . . . . . 82A.2 Additional Tables for Essay 2 . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Appendix B 86B.1 Additional Figures for Essay 1 . . . . . . . . . . . . . . . . . . . . . . . . . 86

Appendix C 89C.1 The Comparison Between the Pooled Estimator and the Mean Group Estimator 89

Appendix D 91D.1 Univariate Test for the Presence of Structural Breaks in the Time Series . . 91D.2 Univariate Test for a Unit Root with Structural Breaks . . . . . . . . . . . 92D.3 Panel Test for Unit Roots with Structural Breaks and Common Factors . . 94

Bibliography 97

vii

List of Tables

1.1 Raw Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.2 Test for additive outliers in individual variable . . . . . . . . . . . . . . . . 19

1.3 Tests for Individual Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.4 Panel Estimates Comparison, CCE and OLS . . . . . . . . . . . . . . . . . 20

1.5 Residual Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

1.6 Panel Estimates Comparison, CCE and FMOLS . . . . . . . . . . . . . . . 22

1.7 Robustness Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.1 Tests for Individual Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.2 Residual Diagnostic Tests, Weighted Averages . . . . . . . . . . . . . . . . . 41

2.3 Residual Diagnostic Tests, Simple Average . . . . . . . . . . . . . . . . . . . 44

2.4 Mean Group Coefficient Estimates for Sub-Samples . . . . . . . . . . . . . . 50

2.5 The Effect of Financial Liberalization . . . . . . . . . . . . . . . . . . . . . 52

2.6 CCEMG Coefficient Estimates for Sub-Samples, in Sub-Periods . . . . . . . 52

2.7 Homogeneous test for individual CCE estimates . . . . . . . . . . . . . . . . 53

2.8 Country-Specific Coefficient Estimates . . . . . . . . . . . . . . . . . . . . . 54

2.9 Comparison of country-specific coefficient estimates (continued) . . . . . . . 55

3.1 Possible Results for the LOP Test . . . . . . . . . . . . . . . . . . . . . . . 64

viii

3.2 Tests for Individual Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 67

3.3 Reference Table for States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

3.4 Test for break in individual log (price) . . . . . . . . . . . . . . . . . . . . . 71

3.5 Test for break in individual OLS residuals . . . . . . . . . . . . . . . . . . . 73

3.6 Diagnostic tests for OLS residuals . . . . . . . . . . . . . . . . . . . . . . . 74

3.7 Diagnostic tests for OLS residuals, excluding Hawaii and Alaska . . . . . . 75

3.8 Test for break in individual log relative price (price) . . . . . . . . . . . . . 77

3.9 Diagnostic tests for relative price level . . . . . . . . . . . . . . . . . . . . . 78

3.10 Diagnostic tests for relative price level, excluding Hawaii and Alaska . . . . 80

3.11 Estimated Dates of Break in Common Factors . . . . . . . . . . . . . . . . . 81

A.1 State Code and Regional CPI . . . . . . . . . . . . . . . . . . . . . . . . . . 82

A.2 State Code and Regional CPI, continued . . . . . . . . . . . . . . . . . . . . 83

A.3 Sub-Sample Country Group . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

A.4 Sub-Sample Country Group, continued . . . . . . . . . . . . . . . . . . . . . 85

ix

List of Figures

1.1 The roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2 Time plots of standardized logarithms of variables and the cross-sectionalaverages (in red) from 1993Q1 to 2012Q1. . . . . . . . . . . . . . . . . . . . 15

1.3 Time plots of standardized FMOLS and CCE residuals. . . . . . . . . . . . 18

2.1 The roadmap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.2 Distribution of the γci,c and γyi,y loading coefficient estimates in the first-stageequations of CCE, see equations (2.23) and (2.24). . . . . . . . . . . . . . . 42

2.3 Distribution of the γyi,c and γci,y loading coefficient estimates in the first-stageequations of CCE, see equations (2.23) and (2.24). . . . . . . . . . . . . . . 43

2.4 Distribution of correlation coefficients Corr(ξcit, cit− ct) and Corr(ξyit, yit− yt). 45

2.5 Scaled estimates of idiosyncratic components (left), ξcit and ξyit and the cross-sectionally demeaned variables (right), cit − ct and yit − yt. . . . . . . . . . 46

2.6 Estimates of idiosyncratic components, ξcit and ξyit, and the cross-sectionallydemeaned variables, cit − ct and yit − yt for representative countries. . . . . 47

2.7 Distribution of country specific coefficient estimates for long-run and short-run. 56

3.1 Flow chart for empirical strategy of panel unit root test . . . . . . . . . . . 65

3.2 Individual state-level gasoline prices and Break date (vertical line) . . . . . 69

B.1 Distribution of individual coefficient estimates. . . . . . . . . . . . . . . . . 86

B.2 Distribution of individual coefficient estimates. . . . . . . . . . . . . . . . . 87

B.3 Distribution of individual coefficient estimates. . . . . . . . . . . . . . . . . 88

x

Chapter 1

Essay 1: Estimating Demand Elasticities in Non-Stationary

Panels: The Case of Hawaii’s Tourism Industry

1.1 Introduction

Since the early 20th century, the tourism industry has expanded considerably together with

the development of worldwide economy. Along with this expansion, studies of tourism in

terms of explaining tourism demand started to flourish. Two major objectives of these

studies are to quantify the effects from determinants of tourism demand and to forecast

future tourism demand (Song and Li, 2008).

Due to data availability, early empirical studies of tourism demand often used time

series data from a single origin-destination pair. To avoid spurious regressions, studies have

paid special attention to the unit root and the cointegration properties of the data. As a

consequence, these studies applied advanced methods, such as the autoregressive distributed

lag model (ADLM)(Song et al., 2003), the error correction model (ECM)(Kulendran and

Wilson, 2000; Kulendran and Witt, 2003; Lim and McAleer, 2001), the vector autoregression

(VAR) model (Song and Witt, 2006) or the vector error correction model (VECM) (Allen

et al., 2009). However, estimations from the literature vary widely and their use in forecast

and policy-making are limited.

As data availability grew across regions, there was a trend to utilize panel data. Panel

datasets have many advantages over time series datasets: it provides richer information

with variations in both temporal and cross-sectional dimensions (Song and Li, 2008); and

it can overcome the problem of multicollinearity and lack of degrees of freedom. Yet,

the assumption of independent cross-sectional units in conventional panel techniques does

not always hold for macroeconomic studies due to the presence of common shocks and/or

spillover effects. Without adequately dealing with cross-sectional dependence, regression

results will be misleading (Westerlund and Urbain, 2011).

There is a strand of literature aiming at solving the cross-sectional dependence in panel

estimations (Kapetanios et al., 2011; Pesaran, 2007; Pesaran and Tosetti, 2011). However,

these cutting-edge methodologies have not yet been considered in the tourism economics

literature and I try to fill this gap in this paper. In this paper, I estimate tourism demand

elasticities for US visitors who travel to Hawaii, accounting for the possibility of cross-

1

sectional interdependence caused by non-stationary common factors.

The rest of this paper is organized as follows: Section 2 illustrates a theoretical tourism

demand model and summarizes estimated values from the literature. Section 3 goes over ex-

isting methods in estimating tourism demand. Section 4 and 5 discuss econometric method-

ologies used for unit root test and panel estimation. Section 6 explains the data and presents

the empirical strategy. Section 7 illustrates both results of unit root tests and regressions.

Section 8 discusses the economic meaning of estimated values. Then in Section 9, some

robustness tests are reported. Finally, this paper concludes in Section 10.

1.2 Tourism Demand Model

According to the demand theory, the budget line for a tourist is determined by his income

and the price of goods and services. Specifically, the demand for aggregate tourism flows

from origin i to destination j can be expressed as

Dij = f(Yi, Pi, Pj , Ps) , (1.1)

where Dij is the tourism demand in destination j by consumers from origin i; Yi is the level

of income at origin i; Pi is the price of goods and services at origin i; Pj is the price of

tourism goods and services at destination j; Ps is the price of tourism products at competing

destinations of place j (Bonham et al., 2009).

In most international tourism studies, the domestic destination is assumed to be a sub-

stitute for the destination abroad; thus, the price level in the origin place is considered

as a proxy for Ps (Witt and Witt, 1995). Similarly, to examine the tourism demand of a

domestic destination, the price level at the origin in this paper is assumed to be a proxy for

the price of the substitute Ps.1 As a result, equation (1.1) becomes

Dij = f(Yi, Pi, Pj) , (1.2)

Assuming a homogeneous demand function, tourism demand can be written as a function

of real income, and relative price level

Dij = f

(YiPi,PjPi

). (1.3)

In the literature, the most popular measurement for tourism demand Dij is the number

of visitors from the origin to the destination (Li et al., 2005; Song and Li, 2008); alternative

measurements include tourist expenditures and tourist nights spent (Witt and Witt, 1995).

Besides the dependent variable, the choice for measurements of Yi varies with the purpose of

traveling. Witt and Witt (1995) recommended including private consumption or disposable

1This is a strong assumption. But it may be possible if one believes that local travels within the originarea may substitute for travels to the destination place.

2

personal income to explain and predict holiday visits, and a more general income measure,

such as national income, for business travel. With regard to the choice for Pj , two price

variables are widely used in the literature: the cost of travel to the destination and the cost

of living at the destination.

Some researchers go beyond explanatory variables Yi and Pj mentioned above. For

example, Yap and Allen (2011) examined the potential effects of variables such as consumer

perceptions about the future of the economy, household debt, and the number of hours

worked in paid jobs. Meanwhile, other studies included dummy variables for special events

such as Olympic games, policy changes, or natural disasters (Falk, 2010; Kuo et al., 2009).

Estimated elasticities from the tourism demand model are often used to forecast tourism

demand in the future and to provide insight to policymakers. Therefore, the accuracy

of estimations are undoubtedly important. Even with a consensus in modeling tourism

demand, empirical studies found a wide range of estimated values of coefficients. Witt and

Witt (1995) reported from a summary of 30 years’ worth of international tourism demand

studies that income elasticity ranges from 0.4 to 6.6 with median value of 2.4. In addition,

Crouch (1995, 1996) found that nearly 5% of the estimates were negative while conventional

opinion indicates that income elasticity should be between one and two. Such large variation

in estimated elasticities therefore limits the value of these empirical studies in policymaking

and future prediction.2

Similarly, for transportation cost, estimations of price elasticity range from -0.04 to -4.3,

with median value -0.5 in Witt and Witt (1995), and values vary between 0.11 and -1.89

in Crouch (1995). For cost at the destination, price elasticity ranges from -0.05 to -1.5,

with median value -0.7 in Witt and Witt (1995), and about 29% of the estimates reviewed

in Crouch (1995, 1996) have positive estimates. Moreover, counterintuitive results are

found for other explanatory variables. For example, Yap and Allen (2011) found a positive

relationship between domestic tourism demand and working hours in Australia; Aslan et al.

(2009) obtained a positive relationship between earthquakes and tourism demand. Crouch

(1995, 1996) investigated a vast number of factors that might cause differences among

studies. By applying meta-analysis to all studies, the varying methods used in estimation

was found to be significant for inter-differences of estimated coefficients.

1.3 Methodology Development

The development of estimating methodology enables us to obtain more precise measures

for income and price elasticities in the tourism demand model. Due to the lack of adequate

data from multiple countries, early tourism demand studies relied on time series data from a

single pair of countries. Applications of the conventional time series approach are diversified:

2In these studies, income elasticity with a negative value and values less than one are respectivelyexplained by the arguments of “inferior” tourism destination and the necessity of traveling to adjacentdestinations, such as short-haul international trips from the US to Canada.

3

ranging from exponential smoothing to vector autoregressive and error correction models

(Li et al., 2005; Witt and Witt, 1995). Recently, some alternative quantitative tools, such as

artificial neural networks, fuzzy time series, and genetic algorithms, have also been applied

in the tourism literature. (For a comprehensive survey of recent developments in tourism

demand modeling, see Song and Li (2008).) However, a time series dataset may not be

sufficient to provide enough variations for estimating the parameter of interest. For example,

Bonham et al. (2009) found that “the income elasticity in the just-identified US demand

relationship is implausibly large and estimated quite imprecisely.”

Fortunately, there is a way to obtain a better estimate of the interested parameters

by taking advantage of panel data. The advantage of panel data over time series data

is straightforward: with variations in both cross-sectional and time dimensions, a shorter

size in the time dimension can be compensated by the cross-sectional dimension to ensure

enough variations, and vice versa. As more data became available and econometric tools

advanced, a trend to exploit the richness of panel data emerged in the tourism literature

(Seetaram and Petit, 2012; Song and Li, 2008). Song and Li (2008) noted an increasing

passion for panel methods in literature after reviewing recent methodological development of

tourism demand studies. Moreover, Song et al. (2012) suggested that “future studies should

pay more attention to the dynamic version of panel data analysis and to more advanced

estimation methods.”

One popular model used in many panel tourism studies (for example, Garın-Munoz and

Montero-Martın (2007), Aslan et al. (2009), Garın Munoz (2007), Naude and Saayman

(2005), Habibi et al. (2009), Kuo et al. (2009), and Brida and Risso (2009)) is a dynamic

model proposed by Morley (1998). It is widely used in tourism demand studies due to

its capability to account for the habit persistence of tourists. In this dynamic model, the

first lag of the dependent variable is included on the right hand side of tourism demand

equation. Due to the inclusion of lagged dependent variable, estimation from traditional

method (OLS, Random effects or Fixed effects) is inconsistent. To obtain consistent es-

timations, many studies assume that autocorrelation is within two periods and make use

of the proposed method from Arellano and Bond (1991), which uses historical dependent

variables as instruments.

With the awareness of unit roots in and co-integration relationship among variables,

Seetanah et al. (2010) examined the inbound tourism to South Africa using a panel of 38

origin countries in a gravity model. They found that all variables are non-stationary based

on the Im et al. (2003) panel unit root test and were able to reject the null hypothesis

of no cointegration at 5 % level when using the cointegration test proposed in Pedroni

(1999). Therefore, they estimated their tourism model by using the fully modified OLS for

heterogeneous panels developed by Pedroni (1999, 2001) to eliminate the likely endogeneity

of the regressors and serial correlation.

All conventional panel estimation techniques and the recently developed approach in

4

Arellano and Bond (1991) as well as the FMOLS are based on the assumption of cross-

sectional independence. Yet, empirical studies in macroeconomics (for example, Baltagi and

Moscone (2010) and Holly et al. (2010)), and results presented in this paper for the tourism

demand in Hawaii, show that cross-sectional dependence is very likely to be present. Cross-

sectional dependence occurs as a result of both simultaneous impacts on individual regions

from common shocks (for instance, business cycle) and spillover influences from regions

nearby, and it is very common for a panel of national or regional data. Mathematical proof

and simulations in theoretical studies (Kapetanios et al., 2011; Pesaran, 2006; Phillips and

Sul, 2003) found that neglecting cross-sectional dependence results in substantially biased

estimators and suffers from size distortions even with large N, T.

One way to account for cross-section correlation is through the spatial model, which

has been used in existing studies (for example, Baltagi and Moscone (2010)). To model

cross-sectional correlation, the error term in the regression model is assumed to follow a

certain type of spatial process with pre-specified weights.3 In many empirical work, the

choice for the weighting matrix is subjective, and it is usually based on the inverse of the

distance across units. From an economic perspective, the distance alone may not capture the

magnitude of the dependence between units completely and correctly, and the geographic

distance cannot fully represent the economic distance. Therefore, tourism demand studies

explored cross-sectional correlation in a more general way. Early studies have used seemingly

unrelated regressions (SUR) to deal with cross-sectional correlation (Allen and Yap, 2009;

Ledesma-Rodriguez et al., 2001; Yap and Allen, 2011). The GLS type transformation to

purge cross-sectional dependence from a SUR model is only satisfactory when the time

dimension is larger than the cross-sectional dimension.

For a dynamic panel model with autoregressive process, Phillips and Sul (2003) sug-

gested to use a common time effect with individual-specific loadings to model cross-sectional

dependence. This is justified by the fact that common shocks might cause co-movements

between multivariate time series. However, in the proposed methodology, the series of

the common time effect is restricted to have variance one and mean zero for identifica-

tion. Moreover, the iterative procedure of obtaining unbiased estimator is valid only when

cross-sectional dimension is large while the number of time periods is relatively small.

Similar to Phillips and Sul (2003), another approach to model the cross-sectional de-

pendence is to use a common factor structure. Common factors are frequently discussed

in international finance and macroeconomics where each individual region may be subject

to national or global shocks such as business cycles, technological innovations, oil crises or

national fiscal and monetary policies. For instance, Beck et al. (2009) investigated the co-

movement of inflation variables for both regions across Euro area and 11 metropolitan areas

in the US. By applying the principal components analysis, they found that there are at least

three common components shared among individual series, which explain a large portion

3For detail discussion of spatial model, see Chudik et al. (2011); Pesaran and Tosetti (2011).

5

(up to 80 %) of the variance of the data. However common shocks will cause cross-sectional

dependence of variables in the estimated model, violating the identically-independent dis-

tribution assumed in the conventional panel estimation techniques, and consequently will

cause problem in the estimation procedures.

Cross-sectional dependence in the panel cannot be dealt in a satisfactory way in clas-

sic estimators. To solve this problem, Pesaran (2006), Bai et al. (2009), and Kapetanios

et al. (2011) recently proposed some innovative methods. By using a factor structure,

recent development in econometric theory makes it possible to model the cross-sectional

dependence through a vector of unobserved common factors. Pesaran (2006) modeled the

cross-sectional dependence among units via a vector of unobservable stationary common

factors. To eliminate the cross-sectional dependence, he augmented the simple OLS re-

gressions with cross-sectional means of dependent and independent variables. The panel

estimation procedures provided in Bai et al. (2009), and Kapetanios et al. (2011) capture

cross-sectional dependence via even non-stationary common factors. By making use of a

factor model, they model the heterogeneity of cross-sectional interdependence for individ-

uals through differentiated loading parameters of common factors. Compared with early

solutions to the issue of cross-sectional dependence, the spatial model and the method in

Phillips and Sul (2003), the factor model is more applicable because it allows for a more gen-

eral type of serial correlation of variables (even non-stationary properties) and unit-specific

influence of common shocks. In the following section, I will focus on the panel estimation

technique that utilizes such factor structure from Pesaran (2006) and Kapetanios et al.

(2011).

1.4 Common Correlated Estimator

It is common for researchers to augment income and price variables in equation (1.3) with

deterministic variables such as time trends to capture evolving consumer tastes, secular

growth, or decline in an industry; a constant term to account for destination amenities

such as natural assets or other factors that are time invariant; dummies to account for

one-time events such as terrorism, natural disasters, major sporting events, and oil crises;

seasonality; or changes in data definitions or collection methods. These types of events, if

otherwise neglected, might lead to bias in the estimated parameters (Bonham et al., 2009).

The method described in this section deals with such deterministic effects the same way as

it deals with unobserved common factors such as business cycles, technological shocks, or

policy changes. As a result, I do not need to subjectively select deterministic proxies for

these events.

The long-run relationship compatible with the theoretical tourism demand model (1.3)

can be written in the following log-linear form,

yit = αi + β′ixit + uit , i = 1, 2, . . . , N , t = 1, 2, . . . , T , (1.4)

6

where yit = log(Dij,t), xit =

(log

(Yi,tPi,t

), log

(Pj,tPi,t

))′. Coefficient βi represents the

elasticity of demand with respect to the regressors xit.

Following Pesaran (2007) and Kapetanios et al. (2011), I model the dynamics and the

common unobserved factors in the error terms uit. In particular, I assume that uit has the

following structure

uit = γ ′ift + εit , i = 1, 2, . . . , N , t = 1, 2, . . . , T , (1.5)

in which ft is an m× 1 vector of unobserved common effects. εit are the individual-specific

(idiosyncratic) errors assumed to be distributed independently of xit and ft, but they can

be weakly dependent across i, and serially correlated over time. The parameter vector of

the slope coefficients, βi, is heterogeneous across units. But in order to assess the overall

effects of the demand determinants, I will focus on the estimation of its average value.

Assuming a random coefficient model, βi = β + wi, where wi ∼ IID(0,Vw), the overall

demand elasticities are β = E(βi).

The vector xit could be correlated with unobserved common factors, ft, and generated

as

xit = ai + Γ′ift + vit , i = 1, 2, . . . , N , t = 1, 2, . . . , T , (1.6)

where ai is a k × 1 vector of individual effects, Γi is a m× k factor loading matrix, vit are

the specific components of xit distributed independently of the common effects and across

i, but assumed to follow general covariance stationary processes. A valuable feature of the

model is that the error term, uit, is allowed to be correlated with the regressors, xit, through

the presence of the factors, ft, in both. The assumption of stationary εit implies that if ft

contains unit root processes then yit, xit, and ft must be cointegrated.

1.4.1 CCE Estimators

To estimate demand elasticity, β, I use the Common Correlated Effects (CCE) estimator of

Pesaran (2006), which asymptotically eliminates cross-sectional dependence from the errors.

Because the error term uit, contains non-stationary common factors that are correlated with

the regressors, conventional estimators of the model in (1.4) are biased. Pesaran (2006)

suggested using cross-sectional averages of yit and xit to deal with the effects of unobserved

factors. Kapetanios et al. (2011) proved that the CCE estimators are consistent regardless

of whether common factors ft, are stationary or non-stationary. They have further shown

that the CCE estimator of the mean of the slope coefficients β, is consistent for any number

of factors. Moreover, Pesaran and Tosetti (2011) showed later that results for the CCE

estimator hold even when the loading coefficients, γi and/or Γi, are zero (or in other words,

under the case of weak cross-sectional dependence). The good performance of the CCE

estimator sharply contrasts with the principal component approach of Bai et al. (2009),

7

which requires an estimate of the number of factors, and was shown to be more biased than

the CCE estimators in Westerlund and Urbain (2011).

For each individual unit, the CCE estimator for βi is

βi = (X ′iMXi)−1X ′iMyi , (1.7)

where Xi = (xi1,xi2, . . . ,xiT )′, yi = (yi1, yi2, . . . , yiT )′, and M = IT −H(H ′H)−1H ′ with

H = (ι, X, y), where ι is a T×1 vector of ones, X is a T×k matrix of cross-sectional means

of the k regressors, and y is a T × 1 vector of the cross-sectional mean of the dependent

variable.

The CCE estimator is equivalent to the Ordinary Least Squares (OLS) estimator applied

to an auxiliary regression that is augmented with cross-sectional means of all variables

in the regression, containing individual-specific loading coefficients of the cross-sectional

averages. Thus, the CCE estimator of the βi coefficients captures the effect of the demand

determinants after controlling for co-movement across units. By allowing for heterogeneous

loadings, γi and Γi, the CCE estimator allows for differentiated effects on individual units

of common factors.

To get the mean value of individual slope coefficients, Pesaran (2006) proposed two

estimators. The CCE mean group estimator (CCEMG) is a simple average of individual

CCE estimators, βi, defined by

βCCEMG =1

N

N∑i=1

βi , (1.8)

The estimator for the variance of βCCEMG is given by

V ar(βCCEMG) =1

N(N − 1)

N∑i=1

(βi − βCCEMG)(βi − βCCEMG)′ . (1.9)

When the slope coefficients, βi, are homogeneous across units, efficiency gains can be

achieved by pooling observations over cross section units. Pesaran (2006) developed a

pooled estimator as

βCCEP = (

N∑i=1

X ′iMXi)−1

N∑i=1

X ′iMyi , (1.10)

with variance

V ar(βCCEP ) =1

NΨ∗−1R∗Ψ∗−1 , (1.11)

where

Ψ∗ =1

N

N∑i=1

X ′iMXi

T, (1.12)

8

and

R∗ =1

N − 1

N∑i=1

(X ′iMXi

T)(βi − βCCEMG)(βi − βCCEMG)′(

X ′iMXi

T) . (1.13)

For the CCE estimator, unobserved common factors are assumed to be captured by

cross-sectional means. As long as the residuals are stationary, the CCE pooled (CCE-P)

and the CCE mean-group (CCE-MG) estimators are both consistent under the random

coefficient model assumption (Pesaran and Smith, 1995). Furthermore, with the help of

Monte Carlo simulations, Pesaran and Tosetti (2011) showed that the CCE method is still

able to provide consistent estimation in the presence of many types of cross-sectional depen-

dence: strong dependence (for example, due to common factors) and/or weak dependence

(for example, spatial correlation).

Compared to other approaches, the CCE estimator has many advantages. First of

all, the factor structure can stand for a variety of types of cross-sectional dependence.

Thus, CCE estimator is especially useful when the real type of cross-sectional dependence

is unknown. Second, the validity of CCE estimator does not require ex ante information

about the unobserved common factors, and it also allows the factors to contain unit roots

and to be correlated with the regressors. Finally, the CCE estimator offers good finite

sample properties (Kapetanios et al., 2011; Westerlund and Urbain, 2011), and is relatively

simple to implement.

1.5 Panel Data Analysis

1.5.1 Cross-Section Dependence Test

Without cross-sectional dependence, conventional estimators can provide valid estimates.

Therefore, the necessity for the CCE method is implied by the existence of cross-sectional

dependence. A pre-test for cross-sectional dependence in variables can provide insight for

the best method.

Pesaran (2004) proposed a cross-sectional dependence (CD) test which is applicable to

a variety of cases. The CD test is based on the average of pairwise correlations of individual

units

CD =

√2T

N(N − 1)(N−1∑i=1

N∑j=i+1

ρij) ∼a N(0, 1) , (1.14)

where ρij is the estimate of correlation between units yi and yj . Specifically,

ρij = ρji =

∑Tt=1 yityjt

(∑T

t=1 y2it)

1/2(∑T

t=1 y2jt)

1/2. (1.15)

9

It is shown in Pesaran (2004) that the CD test is valid whether or not the individual series

contains unit roots and the rejection of the null hypothesis of cross-sectional independence

will inform the presence of the cross-sectional dependence.

1.5.2 Panel Unit Root Tests

Breitung and Pesaran (2008) classified panel unit root tests into two generations. Methods

in the first generation assume that individual series are cross-sectionally independent. In

contrast, procedures in the second-generation relax this restrictive assumption and capture

the cross-sectional dependence through a factor structure. Using Monte Carlo simulation,

Gengenbach et al. (2006, 2010) showed that the dependence across units will cause size

distortion in panel unit root tests if it is overlooked. Therefore, if cross-sectional dependence

is found, a second-generation panel unit test is more desirable.

Several panel unit root tests accounting for the cross-sectional dependence have been

recently proposed in the literature. The PANIC test of Bai and Ng (2004) requires an

estimation for the number of common factors as an input and is based on the consistent

estimation of the unobserved components from the principal component analysis. Then, it

tests for unit roots in both components separately. To test for unit roots in the common

component, Bai and Ng (2004) suggested implementing the ADF test if the number of

common factor is estimated to be one and a rank-type unit root test for multiple common

factors.

Pesaran (2007) proposed a test for unit roots in the idiosyncratic component. In his

paper, the cross-sectional dependence is modeled through an unobservable common factor.

To deal with the shared common factor, he augmented each individual regression for the

standard ADF test with cross-sectional averages of lagged level and first-differences of the

series been tested. The covariate ADF test based on the augmented regression is then

implemented to each panel individual unit. Since Pesaran showed that individual statistics

from the covariate ADF test are independent from each other, he then derived the statistics

for the panel unit root test, CIPS, by averaging the covariate ADF test statistics computed

for each unit following Im et al. (2003). According to Gengenbach et al. (2010), the CIPS

test of Pesaran (2007) has higher power than the PANIC tests for testing a unit in the

idiosyncratic component.

However, it is important to note that the test in Pesaran (2007) misses unit roots

in the common component (Gengenbach et al., 2010) because it deals with cross-sectional

dependence by an orthogonal projection of the data on cross-sectional means. Consequently,

a unit root test for common factors is still required in order to draw a conclusion about the

unit root in a panel dataset.

The approach proposed by Sul (2009) uses the cross-sectional mean as the proxy for the

common factors and proposes a covariate unit root test with recursive mean adjustment

(CRMA) to test the null hypothesis that the common factors are integrated of degree one.

10

The proposed method for testing a unit root in common factors does not require estimation

of the number of common factors as in Bai and Ng (2004). More importantly, it is shown in

Sul (2009) and Gengenbach et al. (2010) that for unit root test for common factors, CRMA

test has similar size and power properties to Bai and Ng (2004).

In this paper, the test for unit roots in a panel dataset consists of two parts: the first,

which tests for unit roots in the idiosyncratic component from Pesaran (2007) and the

second, which tests for unit root in the common component from Sul (2009) and Bai and

Ng (2004). The panel is non-stationary if the null hypothesis of unit root is not rejected in

either component, and is stationary when both components are found to be I(0).

1.6 Data and Empirical Strategy

In this paper, I estimate the demand elasticities for tourism from the U.S. Mainland to

Hawaii. I use the number of visitors arriving to Hawaii (V IS) as my measure of tourism

demand and the total real personal income by state (Y ) as the income variable in the model.

My selection of the income variable is mainly owing to Witt and Witt (1995) as the authors

suggest to use personal income or disposable income for leisure travel, which accounts for

the majority (over 70%) of tourists’s purpose of visiting Hawaii. In addition, I include both

the transportation cost (airfare: PAIR) and the hotel room rate (PRM) as a proxy for

the cost of the trip. The nominal variables are deflated using the consumer price index at

the origin (CPI), so that prices enter the model in relative terms. Formally, one of the

estimated models (denoted as Model 2) in this paper is

log V ISit = αi+β1i log

(Yit

CPIit∗ 100

)+β2i log

(PAIRitCPIit

∗ 100

)+β3i log

(PRMt

CPIit∗ 100

)+uit .

(1.16)

In this regression, the hotel room rate at the destination is independent of trip origins and

therefore can be considered as an observed common factor. As already demonstrated, the

CCE method is based on an orthogonal projection onto proxy of all common factors (both

observed and unobserved). Therefore, the inclusion of the room rate should not have any

substantial effect on the CCE estimation of other coefficients. I verify this argument by

also estimating an alternative model below (denoted as Model 1) that does not include the

room rate.

log V ISit = αi + β1i log

(Yit

CPIit∗ 100

)+ β2i log

(PAIRitCPIit

∗ 100

)+ uit . (1.17)

1.6.1 Data

I obtained tourist arrivals by state from the first quarter of 1993 through the first quarter

of 2012 from annual reports of the Department of Business, Economic Development and

Tourism (DBEDT), Hawaii Visitors and Convention Bureau (HVCB), and Hawaii Visitor

11

Bureau (HVB). With the exception of year 1995 and year 1997, the data is available at the

monthly frequency. For the year 1995 and year 1997, I interpolated the annual values using

the pattern calculated from monthly data of all other years. The data of the total personal

income was collected from the Bureau of Economic Analysis (BEA). Airfares were obtained

from the DB1B Market database of the Bureau of Transportation Statistics (BTS), which

offers a 10% random sample of all domestic trips in a given quarter. To avoid the effect of

outliers, I calculated the median airfare per quarter for each state. The hotel room rate series

was obtained from Hospitality Advisors LLC. The consumer price index (CPI) was obtained

from the Bureau of Labor Statistics (BLS). Since the CPI series are only reported at the

metropolitan level, I assigned the values from a specific metropolitan statistical area to a

given state (see Table A.1 and A.2 for more information). In addition, because CPI series

are reported at monthly, bi-monthly and semiannual frequencies, I linearly interpolated the

low frequency series to approximate their values at the highest (monthly) frequency. For

my analysis, I converted all data to quarterly frequency and seasonally adjusted all series

using the X-12 ARIMA method. I excluded Delaware and the District of Columbia due to

the lack of airfare data. The raw data is summarized in Table 1.1.

Franses and Haldrup (1994) pointed out that additive outliers might produce spurious

stationarity, so the Dickey-Fuller unit root test will over-reject the null of unit-root. To

avoid the effect of outliers, I followed the procedure suggested by Perron and Rodrıguez

(2003) to remove additive outliers in all series entering the regression model. Results are

summarized in Table 1.2.

1.6.2 Empirical Strategy

The roadmap is illustrated as Figure 1.1. After removing outliers from each series, I pre-test

each variable for cross-sectional dependence by following Pesaran’s (2004) CD test. To test

for a unit root in the common component of variables, I implement the CRMA test from

Sul (2009). The rejection of the null hypothesis will indicate the presence of a stationary

common component. For the idiosyncratic component, I use the CIPS test from Pesaran

(2007), which will imply stationarity under alternative hypothesis. In addition, I compare

coefficient estimates from the OLS method and the FMOLS method to the CCE method,

with the former two serving as illustrations of the case when cross-sectional dependence

is neglected. Particularly, the FMOLS estimation is supposed to be valid since it aims at

avoiding spurious regression.

Moreover, for each regression, I use the panel unit root test on regression residuals as

the test for a cointegration relationship. In particular, I obtain the residuals of both the

OLS and FMOLS methods based on the following model,

uit = yit − αi − β′xit , (1.18)

12

Step  1    Pre-­‐test  of  variables  

Test  for  cross-­‐sec1onal  dependence  (CD):    H0:  cross-­‐sec/onal  independence  

In  the  common  component  (CRMA)  

In  the  idiosyncra1c  component  (CIPS)  

Test  for  unit  root:  H0:  unit  root  

Step  2  Model  es1ma1on  

Step  3  Residual  diagnos1c  test  (Test  for  cross-­‐sec1onal  

dependence  and  unit  root)  

reject  

Conven1onal  method  (OLS,  FMOLS):  ignoring  

cross-­‐sec/onal  dependence    

Advanced  method  (CCE):  dealing  with  cross-­‐sec/onal  dependence  

Figure 1.1: The roadmap

13

where αi and β are estimated coefficients. Because the common factors in the variables are

ignored during these estimation process, they are likely to be left in the regression residuals,

uit.

In contrast, the CCE method is designed to get rid of unobserved common factors by

cross-sectional averages. Therefore, the CCE residuals, obtained by εit from equation (1.5),

is free of common factors. Nevertheless, it may still contain some weak cross-sectional

dependence which cannot be captured by common factors.

To account for cross-sectional dependence in residuals, I implement the following diag-

nostic tests for all regression residuals. The first diagnostic test is the CD test. Rejection

of the CD test will indicate the presence of common factors, which is further confirmed

by applying the approach in Bai and Ng (2002) to estimate the number of common fac-

tors. Since there is a tendency to overestimate the number of common factors (Gengenbach

et al., 2010), I only choose the minimum number estimated from all information criteria.

If there are any common factors detected in residuals from OLS and FMOLS, I will apply

the CRMA test in Sul (2009) or the test in Bai and Ng (2004) to examine common unit

root. For idiosyncratic components, I rely on the test of Pesaran (2007). On the other

hand, if there is any common factor detected in CCE residual, I argue that the factor is

probably due to some high degree of spatial correlation (or in other words, it is the weak

dependence discussed in Pesaran and Tosetti (2011)). Thus, I only apply the panel unit

root test in Pesaran (2007), which controls for cross-sectional dependence and tests for unit

root in idiosyncratic components.

1.7 Results

1.7.1 Pre-test for Unit Root in Variables

As results in Table 1.3 indicate, I reject the null hypothesis of cross-sectional independence

in all the variables. Furthermore, plots in Figure 1.2 graphically illustrate the existence of

the cross-sectional dependence in each variable. In each plot, there is a common movement

shared across units. Specifically, these common trends represent common shocks that affect

all individual series at the same time. For instance, the level of income in all states are

affected by the global economic recession in 2008-2010, causing a decline in all real income

series in the same period. Similarly, the crude oil price impacts the price level of airfare

in all states, which induces a co-movement of real airfare series. Interestingly, the cross-

sectional mean of individual series, highlighted in red, seems to be a good indicator of the

co-movement.

The presence of these common trends also points out that the appropriate panel unit

root tests should take into account the cross-sectional dependence among units. Therefore,

I implement Sul (2009)’s CRMA statistics to test for a unit root in the common component

of each variable. Since variables are I(1) when the common component and/or the idiosyn-

14

1995 2000 2005 2010

−4

−2

02

4

time

in lo

gs

log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)log of arrivals and cross−sectional means(red)

1995 2000 2005 2010

−2

−1

01

2

time

in lo

gs

log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)log of income and cross−sectional means(red)

1995 2000 2005 2010

−3

−2

−1

01

23

time

in lo

gs

log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)log of airfare and cross−sectional means(red)

1995 2000 2005 2010

−3

−2

−1

01

23

time

in lo

gs

log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)log of room rate and cross−sectional means(red)

log(V ISit)log

(Yit

CPIit∗ 100

)

log

(PAIRitCPIit

∗ 100

)log

(PRMt

CPIit∗ 100

)

Figure 1.2: Time plots of standardized logarithms of variables and the cross-sectional aver-ages (in red) from 1993Q1 to 2012Q1.

15

cratic component has a unit root, results in Table 1.3 indicate that I cannot reject the null

hypothesis of non-stationarity for any of the variables.

1.7.2 Estimations

I estimate equation (1.16) and (1.17) by both CCE and OLS estimators. For the CCE

method, I obtain the average effect of explanatory variables both by the pooled estimator

and the mean-group estimator. The estimation results are shown in Table 1.4.

As suggested, estimates of the income elasticity and the price elasticity (for airfare and

room rate, respectively) from the CCE method have expected signs. When comparing

CCE estimations between two model specifications (with and without lodging prices), the

estimates for the income and the airfare elasticity are similar. As explained, this is because

the hotel room rate in Hawaii is a common factor across states, which will be controlled

implicitly in the CCE estimation of Model 1. In contrast, the OLS estimators have an

unexpected sign on hotel room elasticity and a much smaller income elasticity compared to

the CCE estimations.

Residual diagnostic test of these regressions are in Table 1.5. It indicates that there

seems to be some cross-sectional dependence in both the OLS and the CCE residuals. The

information criteria for estimating the number of common factors from Bai and Ng (2002)

further suggest that with the exception of the CCE residuals from the pooled regression of

Model 1, there is no common factor found in the residuals of the CCE method. As common

factors in the regression are shown to be well controlled in the CCE method, I relate the

single factor in CCE residuals from the pooled regression of Model 1 to a high degree of

weak dependence. Therefore, I only report unit root test results from Pesaran (2007).

For the OLS regression, a single common factor is found in residuals of all specifications.

Thus, I use both the ADF test on the estimated common factor and the CRMA test on the

cross-sectional mean to test for a unit root in the common component. Because the null

hypothesis of a unit root cannot be rejected, the common component of the OLS residuals

is non-stationary. This result combined with unit root tests for idiosyncratic components

in Table 1.5 suggests that the OLS estimates are invalid because they are spurious. By

contrast, the CCE regressions are valid as residuals are stationary according to CIPS test

from Pesaran (2007).

The first panel of Table 1.6 compares the CCE estimates of Model 2 (with lodging

price) to the fully modified ordinary least squares (FMOLS) estimates commonly used

in the tourism literature (Seetaram and Petit, 2012). Same as the OLS estimates, the

FMOLS estimation of room price elasticity has a wrong sign. Because both the OLS and

the FMOLS methods ignore common factors, such as global shocks, in the variables, the

parameter estimates partly associate business cycle fluctuations in arrivals with business

cycle fluctuations in room prices. Therefore, the positive room rate elasticity may capture

the fact that the common factors in these two variables are positively correlated.

16

The middle pane of Table 1.6 presents unit root tests in the FMOLS residuals using

the conventional methodology. The tPP , and tADF are the Pedroni (1999, 2004) tests for

the null hypothesis of no-cointegration based on the Phillips and Perron t-statistics, and

the augmented Dickey Fuller t-statistic, respectively. Both tests assume cross-sectional

independence, and both reject the null of no cointegration. Thus, the conventional Pedroni

test leads to the acceptance of FMOLS results.

However, Pesaran’s (2004) CD test in the last pane rejects the null hypothesis of cross-

sectional independence, suggesting that the conventional tests are misleading due to their

disregard of common factors in the residuals. This is further proved by the procedure in

Bai and Ng (2002) and Sul (2009). In particular, the result of Bai and Ng (2002) indicates

that there is one common factor in the FMOLS residuals. In addition, Sul (2009)’s CRMA

statistic, which tests for unit roots in the common factors, fails to reject the null of a unit

root in the FMOLS residuals, implying that the FMOLS estimates are still spurious. In

Figure 1.3, I illustrate the comparison between the individual series of the CCE residuals

and the FMOLS residuals. In this figure, some co-movement can be clearly seen in the

FMOLS residuals.

In sum, the rejection of unit root in the residuals of CCE regressions, εi,t from equation

(1.5), suggests that CCE estimations are not spurious, implying that the observed variables

and the unobserved factors are cointegrated with the cointegrating vector given by the CCE

estimates (Kapetanios et al., 2011).

1.8 Discussion

1.8.1 Income

The estimated average income elasticity of tourism demand from the U.S. mainland to

Hawaii is slightly greater than unity, implying that travel to Hawaii is likely to be regarded

as a luxury good.4 Although Hawaii is a domestic tourism destination for US visitors, its

far distance from the mainland likely makes a trip to Hawaii very income elastic.

The CCE estimates of the income elasticity presented in this paper are similar to the

value of 0.996 in Nelson et al. (2011), which included some observed and deterministic

common factors in their model, such as oil prices and a non-linear time trend. However,

it is much lower than 3.5 found in Bonham et al. (2009) who estimated a VECM with

cointegrating relationships identified as supply and demand relations.5

4As illustrated in Figure ??, income elasticity estimates for individual units can be both positive andnegative, but most of them are positive and clustered around unity. Moreover, t test of the overall incomeelasticity indicates that the value is not significantly different from 1. Specifically, in Model 1 of Table 1.4,the t statistics for the null hypothesis of β1 = 1 from CCE-MG and CCE-P are 0.52 and 1.22, respectively;in Model 2, the t statistics for the null hypothesis of β1 = 1 from CCE-MG and CCE-P are 1.04 and 1.57,respectively.

5As noted in Section 1.4, the CCE estimator controls for global trends in the panel, and in general

17

Table 1.1: Raw DataVariable Source Frequency Seas. Adj.

Visitor Arrivals (VIS) HTA M NoPersonal Income (Y) BEA Q YesMedian Roundtrip Airfare (PAIR) BTS Q NoAverage Daily Room Rate (PRM) HA M NoConsumer Price Index (CPI) BLS M, BM, S NoNote: Visitors Arrivals (VIS) excludes estimated in-transit passengers, returning Hawai’i residents

and intended residents from airline passenger counts. I obtained monthly visitor arrivals for 1993-

1994 from HVCB, for 1996-1998 form HVB, for 1999-2010 from DBEDT, and for 2011-2012 from

HTA. For 1995 and 1997 only annual visitor arrivals are available, so I estimate the monthly series

by interpolation. The CPI series for the states are approximations based on data available for

metropolitan areas and geographic regions.

Acronyms: HVCB - Hawaii Visitors and Convention Bureau; HVB - Hawaii Visitor Bureau; HTA -

Hawaii Tourism Authority; DBEDT - Hawaii Department of Business, Economic Development and

Tourism; BEA - Bureau of Economic Analysis; BTS - Bureau of Transportation of Statistics; HA

- Hospitality Advisors, LLC; BLS - Bureau of Labor Statistics; M - Monthly; BM - Bi-Monthly; Q

- Quarterly; S - Semiannual.

1995 2000 2005 2010

−4

−2

02

4

time

in lo

gs

residual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmolsresidual from fmols

1995 2000 2005 2010

−4

−2

02

4

time

in lo

gs

residual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rateresidual from mean group estimator, with room rate

FMOLS residuals CCE residuals

Figure 1.3: Time plots of standardized FMOLS and CCE residuals.

18

Table 1.2: Test for additive outliers in individual variableVariable critical level No. of series tested Additive outliers ? No. of series with outliers

log V IS 0.01 48 yes 28

log YCPI 0.01 48 yes 4

log PAIRCPI 0.01 48 yes 20

log PRMCPI 0.01 22 no 0

Note: The regression model is illustrated in equation (1.16).

Table 1.3: Tests for Individual Variablesvariables y x1 x2 xa3CD 155.35∗ 285.51∗ 193.23∗ 130.12∗

CRMA -1.13 -0.45 -0.66 -0.03

Note: y = log(V IS), x1 = log(

YCPI ∗ 100

), x2 = log

(PAIRCPI ∗ 100

), x3 = log

(PRMCPI ∗ 100

). The

null hypothesis of the CD statistic is cross-sectional independence. The CRMA statistic tests for

unit roots in the cross-sectional mean; the null hypothesis is unit root; the lag length is chosen by

the BIC. Statistical significance at the 5% level or lower is denoted by ∗.a: I use 22 series to implement the test.

In addition, although Crouch (1996) found that the omission of a price variable might

cause a positive bias in income elasticity, I find that results from the CCE method are only

marginally affected by dropping the variable of room rate from the model. This is because

the CCE estimator controls for the omitted price variable via proxies.

1.8.2 Price

Results in this paper indicate that the tourism demand for Hawaii is inelastic with respect

to airfare. If airfare increases by 10%, arrivals to the state are expected to fall by a little

more than 2%. Again, this value is fairly close to -0.211, the airfare elasticity estimate of

Nelson et al. (2011). The estimated hotel room price elasticity suggests that tourists are

more responsive to changes in room rates than to fluctuations in airfare. Particularly, a

10% drop in the hotel room rate is expected to generate 12% higher visitor arrivals, over

five times more than a corresponding drop in airfare. Facing a $1000 airline ticket and a

daily price of $200 for a double occupancy room, a couple on a ten-day trip has to split

their budget evenly between airfare and accommodation.

The difference between airfare and room rate elasticities could also be explained by a two

stage decision making process undertaken by travelers: in the first stage they choose a desti-

nation from a range of competing locations, and in the second stage, they pick their flights.

The idea of two-stage decision-making process is related to the idea of multi-stage decision-

produces different results than conventional estimators of time series data lacking a cross-sectional dimension.

19

Table 1.4: Panel Estimates Comparison, CCE and OLS

Model1 Model 2Coefficient CCE-MG CCE-P OLS-MG CCE-MG CCE-P OLS-MG

β1 1.09∗ 1.18∗ 0.62 1.20∗ 1.27∗ 0.29β2 -0.32∗ -0.36∗ -0.35 -0.23∗ -0.26∗ -0.39β3 -1.23∗ -1.20∗ 0.56Note: Regression equations are illustrated in equation (1.16) and (1.17). Statistical significance at

the 5% level or lower is denoted by ∗. Since the OLS regression is invalid, I do not report the level

of marginal significance for OLS coefficient estimates.

making process discussed in Strotz (1957), who describes this process as first deciding how

to allocate a budget among several groups of goods and then making independent spending

decisions within the groups. Applying this idea to tourism, Syriopoulos and Thea Sinclair

(1993), and Song et al. (2012) all discuss the multi-stage decision-making process and Bon-

ham and Gangnes (1996), Nicolau and Mas (2005) and Eugenio-Martin and Campos-Soria

(2011) base their models on it. When deciding whether to make a trip to Hawaii, it is likely

that tourists first choose the destination among a group of competing locations, which may

be affected by promotional activities, such as free nights or the attracting package from

hotels. In the next stage, tourists select their favorite flights to the chosen destination by

minimizing their cost. As a result, the effect on tourism demand of changes in room rate

price is greater than the effect of changes in the airfare level.

1.9 Robustness Test

The criticism that the population growth might drive both aggregate income and aggregate

visitors can be avoided via the implementation of CCE estimator.6 This is because the

unobserved common factors shared by the number of visitors and total income is controlled

by the augmented cross-sectional means. Alternatively, population can be controlled by

transforming variables to per-capita terms. In tourism literature, there are many papers

specifying the tourism demand model in per-capita terms. However, this type of specifica-

tion constrains the elasticity of population to be one if a log-linear model is employed (Witt

and Witt, 1995).

1.9.1 Other Substitute Price

In the previous section, the model assumes that traveling to places near the origin is a

substitute for traveling to Hawaii. This assumption may be questionable since the moti-

vation for traveling to Hawaii is quite different from visiting places nearby. Considering

6As discussed in Witt and Witt (1995), including population as an additional explanatory variable mayalso induce multicollinearity problem.

20

Table 1.5: Residual TestsModel1 Model 2

CCE-MG CCE-P OLS-MG CCE-MG CCE-P OLS-MG

CD-3.32∗ -3.72∗ 87.81∗ -3.09∗ -3.75∗ 68.09∗

NO. of CF0 1 1 0 0 1

CIPSlag=1 -27.80∗ -24.49∗ -16.16∗ -28.76∗ -25.95∗ -14.52∗

lag=2 -21.26∗ -17.78∗ -10.31∗ -22.94∗ -19.73∗ -8.80∗

lag=3 -20.03∗ -16.88∗ -7.96∗ -22.69∗ -19.42∗ -6.69∗

lag=4 -15.58∗ -11.92∗ -4.73∗ -19.25∗ -14.59∗ -3.57∗

ADF— — -1.17 — — -1.17

CRMA— — -1.70 — — -1.55

Note: The null hypothesis of the CD statistic is cross-sectional independence. No. of common

factors is estimated following Bai and Ng(2002). The CIPS statistic is the cross-sectional average

of individually CADF(p) statistics. For the CIPS statistics the null hypothesis is that all series

are non-stationary; the alternative hypothesis is that some series are stationary; the maximum lags

of CIPS is set equal to T 1/3 = 4, which determines the lag length for all units in panel for their

individual Covariate ADF test. The ADF test is for the estimated single common factor. The

CRMA statistic tests for unit roots in the cross-sectional mean; the lag length is chosen by the

BIC. Statistical significance at the 5% level or lower is denoted by ∗.

21

Table 1.6: Panel Estimates Comparison, CCE and FMOLS

Model 2

Coefficient CCE −MG CCE − P FMOLS

β1 1.20∗ 1.27∗ 0.34∗

β2 -0.23∗ -0.26∗ -0.37∗

β3 -1.23∗ -1.20∗ 0.52∗

FMOLS Residual Diagnostics

First Generation tPP tADF-6.90∗ -4.65∗

SecondGeneration CD NO. of CF tADF CRMA68.93∗ 1 -1.13 -1.56

Note: Regression equation is illustrated in equation (1.16). FMOLS is Pedroni’s (2001)

fully modified OLS estimator for heterogeneous cointegrated panels. CCE-MG and CCE-

P are the mean group and pooled common correlated effects estimators of Pesaran (2006).

tPP , and tADF are the Pedroni (1999, 2004) cointegration tests based on the Phillips

and Perron t statistics, and the augmented Dickey Fuller t statistic, respectively. CD is

Pesaran (2004)’s cross-sectional independence test, and CRMA is Sul (2009)’s unit root

test for the common factors and the lag length was chosen by the BIC. NO. of CF is

the number of common factors estimated following Bai and Ng (2002), and tADF is the

standard ADF test implemented to the estimated single common factor following Bai and

Ng (2004). Lag length is determined by BIC. Statistical significance at the 5% level or

lower is denoted by ∗.

22

that Hawaii is famous for its seaside attractions, I choose another competing destination of

Hawaii - Miami, Florida. This makes more sense as both destinations attract US domestic

visitors with its beaches and sunny weather.

Specifically, I include another price variable, the airfare price to Miami, Florida, into

the regression equation (1.16) as a proxy for a substitute price. I select the airfare price

to Miami by three different ways: the median airfare to Miami International Airport, the

median airfare to Fort Lauderdale-Hollywood International Airport and the median airfare

to either airport. Estimation results are summarized in Table 1.7. Compared to estimation

for equation (1.16) in Table 1.5 and Table 1.6, estimates of income and price elasticity

only change slightly. The elasticity for substitute price measured in airfare to Miami is not

significant at 5% level for most regressions.7

1.10 Conclusion

Regional macroeconomic variables are likely to be affected by non-stationary common fac-

tors, which will lead to inconsistent and biased estimates if it is ignored. In this paper,

I explore the factor structure of regional variables in a tourism demand model, test the

series for common and idiosyncratic unit roots, and estimate tourism demand elasticities

by controlling for non-stationary common factors. To my knowledge, this is the first paper

in the tourism literature that accounts for non-stationary common factors in the data.

I apply the CCE estimators proposed by Pesaran (2006) and Kapetanios et al. (2011) to

a tourism demand model for Hawaii. The common factors controlled in the CCE method

could be population, business cycle and others. Using quarterly data spanning the period

from the first quarter of 1993 to the first quarter of 2012, I obtain income elasticity slightly

over unity, fairly high hotel room price elasticity, but relatively low airfare elasticity. A

sound explanation of these estimates is provided in the discussion section.

Although the CCE method has many merits, such as its easy implementation and its

availability under a variety of cross-sectional dependence, this paper still has room for

improvement. First of all, from a policy standpoint, it would be interesting to examine the

differentiated elasticities in segmented markets according to criteria such as geographical

segment, or income levels. By contrast, this paper treats the US mainland as a single

market, ignoring the differences in the behavior of tourist from different regions. Thus,

future research can be more concentrated on estimations in different markets.

Secondly, the log-linear constant elasticity demand model might be a misspecification of

demand behavior. According to Witt and Witt (1995), the popularity of the log-linear model

stems from its convenience in thinking in terms of elasticities and its superior empirical

7Of course, it may be more reasonable to state that the competing destination of Hawaii for US visitorsmight be Caribbean. Alternatively, I may follow Song et al. (2003) which uses tourist arrivals weighted CPIfrom a group of competing destinations as measure for substitution price. However, due to the lack of properdata, I leave this question for future work.

23

Table 1.7: Robustness TestsIncluding Substitution Price

airfare to mia-int airfare to fort-laud airfare to either airportCoefficient CCE-MG CCE-P CCE-MG CCE-P CCE-MG CCE-P

β1 1.16∗ 1.15∗ 1.14∗ 1.14∗ 1.18∗ 1.16∗

β2 -0.22∗ -0.26∗ -0.24∗ -0.24∗ -0.24∗ -0.24 ∗

β3 -1.27∗ -1.28∗ -1.73∗ -1.49 ∗ -1.50∗ -1.38∗

β4 0.03 0.08∗ 0.04c 0.06c 0.05 0.10∗

CD-3.18∗ -3.78∗ -2.98∗ -3.83∗ -2.96∗ -3.80∗

NO. of CF0 0 0 0 0 0

CIPSlag=0 -32.49∗ -31.41∗ -32.51∗ -31.60∗ -32.51∗ -31.69∗

lag=1 -29.05∗ -26.52∗ -29.72∗ -27.21∗ -29.40∗ -26.70∗

lag=2 -23.31∗ -20.36∗ -24.41∗ -20.54∗ -23.90∗ -20.33∗

lag=3 -23.37∗ -19.82∗ -24.76∗ -20.11∗ -23.76∗ -19.03∗

lag=4 -18.53∗ -14.36∗ -20.43∗ -15.63∗ -19.36∗ -13.93∗

Note: Regression equation is log V ISit = αi + β1i log(

Yit

CPIit∗ 100

)+ β2i log

(PAIRit

CPIit∗ 100

)+

β3i log(

PRMt

CPIit∗ 100

)+ β4i log

(PAIR−MIAit

CPIit

)+ uit. PAIR −MIAit is the airfare from mainland

states to Miami, Florida. The null hypothesis of the CD statistic is cross-sectional independence.

No. of common factors is estimated following Bai and Ng (2002). The CIPS statistic is the cross-

sectional average of individually CADF(p) statistics. Statistical significance at the 5% level or lower

is denoted by ∗. Statistical significance at the 10% level or lower is denoted by c.

24

results in terms of “correct” coefficient signs and model fit. Alternatively, when market

share is modeled, a semi-log functional form is generally specified. This is another area to

explore in future work.

Finally, the demand for the tourism in Hawaii may have changed during the past two

decades. Therefore, the tourism demand model with constant elasticities may be misspeci-

fied. To account for the change in the demand elasticity, a future extension of this study is

to examine the presence of structural breaks in the coefficients of tourism demand model.

25

Chapter 2

Essay 2: Common Correlated Effects and International

Risk-sharing

2.1 Introduction

Consumption is an integral part of everyday life and people pay attention to the level of

their consumption over time. Generally, consumers are risk averse; variation in their con-

sumption resulting from income shocks make them worse off. In order to avoid undesirable

welfare loss caused by fluctuations in consumption and obtain a relatively steady amount

of consumption from year to year, consumption smoothing activities must be considered.

With adequate consumption smoothing, consumers can insure themselves against unex-

pected shocks to their income and avoid large variation in their consumption. Within an

economy, consumers can rely on formal institutions such as charities, and private insurance

or on informal mechanisms such as loans from neighbors, friends and relatives (Cochrane,

1991) to insure against idiosyncratic shocks to their income and wealth. Similarly, in an

integrated world economy, residents of different countries can brace themselves against

country-specific shocks through international market: different countries can trade goods,

services and financial assets with each other to smooth country-specific shocks.

Under perfect international risk sharing, consumption is smoothed because idiosyncratic

risk in the income is diversified away. The theoretical implication of perfect risk sharing

states that individual consumption is independent of idiosyncratic income shocks and fol-

lows aggregate consumption only. However, in reality, perfect consumption smoothing may

fail due to incomplete financial and real markets, and limited participation in risk-sharing

activities.

Early papers such as Cochrane (1991), Mace (1991) and Obstfeld (1994) have derived

the regression model for empirical examinations of consumption smoothing. Based on the

same theoretical model, most of the later empirical studies on international risk sharing

test whether or not the idiosyncratic fluctuation in consumption is independent of the

idiosyncratic fluctuation in income. In such empirical test, the correct measurement of

idiosyncratic fluctuations in consumption and income is crucial. Yet, existing studies largely

neglect this important detail.

In this paper, I demonstrate that the conventional methods of controlling for the effects

26

of common shocks in consumption and income regression impose some ad-hoc homogeneity

assumptions. In addition, I propose a different method to isolate idiosyncratic fluctuations

in consumption and income. In particular, the proposed method deals with aggregate shocks

in the same way as in the Common-Correlated Effect (CCE) Estimator of Pesaran (2006)

and Kapetanios et al. (2011). Based on diagnostic tests, I show that the new method can

deal with aggregate shocks more appropriately than conventional methods.

With a panel of 158 countries over 40 years, I test for the implication of full risk sharing,

i.e., the idiosyncratic fluctuation in consumption is independent of idiosyncratic fluctuation

in income. Results from the CCE-type regression are compared with conventional regression

models. I find that: first, by using the CCE estimator, the regression residual is cross-

sectionally independent and stationary; second, loading coefficients of aggregates obtained

from the CCE estimator suggest that restrictions imposed in conventional regressions are

incorrect and may lead to spurious regressions; third, according to the homogeneity test of

coefficients across units, the degree of consumption risk sharing and the speed of adjustment

vary across countries.

This paper also contributes to the literature by examining the effect of globalization on

consumption risk sharing. Based on the CCE estimations, I estimate the degree of consump-

tion risk sharing in both pre-globalization and post-globalization sub-periods.1 Although

there is substantial removal of capital controls in the post-globalization period, I do not

find empirical support for an improvement of consumption risk sharing during the period

of financial globalization.

The following section is constructed as follows: In Section 2, I discuss the empirical

regression following the conventional method and the one following the CCE method. In

Section 3, I illustrate how the CCE method works and its relationship with the consumption

risk sharing regression. I describe the empirical strategy and data for this paper in Section

4, and report empirical results in Section 5.

2.2 Regression Equation for International Risk-sharing

2.2.1 Theoretical Model

In an economy with a single good and N countries, each country has a finitely lived repre-

sentative agent that makes decision about consumption under uncertainty, represented by

state-date event, st. At a given st, country i receives an endowment of good, eist and realizes

output Yst .

The representative agent in country i aims to maximize the discounted life-time utility

1The era of globalization refers to a period with increasing in cross-border trade and financial flows (seeKose et al. (2008), for instance).

27

as (Mace, 1991; Obstfeld, 1994) :

maxCi,0,Ci,st

(U i(Ci,0) +T∑t=1

ρti∑st

πstUi(Ci,st)) , i = 1 . . . N, (2.1)

Here, U i is the utility function function, and Ci,0, Ci,st are the consumption decisions. In

addition, T is the time horizon, ρi is the time preference coefficient for the agent in country

i and πst is the probability of date-event st. In such economy, countries can trade Arrow-

Debreu securities, which has the price of qst for the date-event st, payoff 1 if the date-event

st happens and 0 otherwise.

With budget constraints at time t = 0 and t = s, which are (Ci,0 +∑

stqstYst) = ei0 and

(Ci,st = eist + Yst), equation (2.1) is equivalent to

maxYst

(U i(ei0 −∑st

qstYst) +T∑t=1

ρti∑st

πstUi(eist + Yst)) , i = 1 . . . N. (2.2)

The solution to this maximization problem is obtained by taking first-order derivative with

respect to Yst , which leads to,

U i′(Ci,0)qst = ρtiπstU

i′(Ci,st). (2.3)

With the risk-aversion coefficient µi, a CRRA utility, U i(Ci,st) =C

1−µii,st

1−µi , is assumed. Further

assuming that U i′(Ci,0) is normalized to unity, equation (2.3) can be written as,

qst = ρtiπstC−µii,st

. (2.4)

Taking the logarithm transformation of equation(2.4), individual consumption satisfies,

log qst = t ∗ log ρi + log πst − µi logCi,st . (2.5)

When we equalize the left hand side of equation (2.5) for country i and j, it shows that the

consumption series in country i is correlated with the consumption in country j,

logCi,st =t(log ρi − log ρj)

µi+µjµi

logCj,st (2.6)

or

logCi,st = aijt + bij logCj,st (2.7)

Where aijt =t(log ρi−log ρj)

µiand bij =

µjµi

.

Because equation (2.5) also holds for an appropriately defined aggregate consumption,

28

the right hand side variables from equation (2.7) can be replaced by the aggregate con-

sumption and leads to,

logCit = ait + bi logCwt (2.8)

where Cit is a measure for country i’s consumption, Cwt is an aggregate measure of con-

sumption. Equation (2.8) implies that under a complete market, individual consumption

should move with aggregate consumption only. Moreover, it also implies that the logarithm

of individual consumption should not be influenced by any other idiosyncratic variables net

of the effects from aggregate consumption.

2.2.2 Empirical Model in the Literature

In the literature, the following regression is used as an empirical test for the null hypothesis

of perfect risk sharing,

logCit = αi + bc,i logCw,t + βi(log Yit − by,i log Ywt) + εit, (2.9)

where Yit is the country i’s income, Ywt is the aggregate income, and as a result, (log Yit −by,i log Yw,t) is considered to be the idiosyncratic income or output shock. Because country’s

consumption follows the aggregate consumption and is independent of idiosyncratic income

with perfect risk sharing, existing studies test two implied hypotheses of bc,i = 1 and βi = 0.

Others test the implication of prefect risk sharing by first differencing variables in equation

(2.9) in order to avoid the unit root in the regression and misleading inference of coefficients,

for instance Mace (1991).

The regression in levels emphasizes the co-movement between relative consumption and

income in the long-run while the regression in log differences applies for short-run. As argued

in Artis and Hoffmann (2012), there are many advantages when looking at a regression at

lower frequency. First and foremost, Lucas (1987) recognized that the welfare gain by

eliminating transitory variation in income is negligible, whereas there will be a susbstantial

benefit if idiosyncratic shocks are persistent. Secondly, regressions at higher frequency

(i.e., business frequency) is likely to be affected by the changes in the relative contribution

of permanent and transitory shocks to consumption. As consumption reacts primarily

to permanent shocks in income, the smaller volatility of the business cycle due to the

Great Moderation may offset the effect of financial globalization in terms of consumption

smoothing.

In equation (2.9) or its counterpart when using log-differenced variables, βi acts as a test

for the null hypothesis of perfect risk-sharing either in the long-run or in the short-run. In

particular, because the value of β is zero under the null hypothesis of perfect risk-sharing,

the rejection of the null of βi = 0 indicates the lack of perfect risk sharing. Moreover, βi

measures the transmission of idiosyncratic income to idiosyncratic consumption, as a result,

its value is also a measure for the degree of risk-sharing. A smaller value of βi suggests a

29

higher degree of risk sharing.

Following such implication of the coefficient βi, many existing studies directly test

whether or not the idiosyncratic income has significant effect on idiosyncratic consump-

tion. To accomplish this test, idiosyncratic consumption and income must be isolated from

observed data.

Existing literature (for example, Cochrane (1991), Asdrubali et al. (1996), Sorensen

and Yosha (1998), Crucini (1999)) often impose bc,i = 1, by,i = 1 and subtract aggregate

consumption (income) from individual consumption (income) to approximate measures of

idiosyncratic fluctuations. The imposed value for bc,i and by,i is derived assuming perfect

risk sharing and homogeneity in the discount factor ρ and the risk-aversion coefficients µ.

As a result, the regression models are:

logCit − logCw,t = αi + β(log Yit − log Yw,t) + εit, (2.10)

∆ logCit −∆ logCw,t = αi + β(∆ log Yit −∆ log Yw,t) + εit (2.11)

As shown, these assumptions lead to the absence of individual-specific effect of logCw,t and

log Yw,t, which implicitly assumes that aggregate fluctuation will have the same magnitude

of effect across countries.

In most papers based on Equation (2.10, 2.11), cross-sectional means of logCit and

log Yit are used to proxy for the aggregates, logCwt and log Ywt, respectively. As a result,

equation (2.10) and (2.11) are equivalent to regressions with cross-sectionally demeaned

variables (denoted as DEM in this paper). In addition, as no individual βi is allowed,

the assumption of a constant degree of consumption smoothing across country is imposed

in equation (2.10, 2.11). To allow for individual country’s heterogeneity, the fixed effect

estimator is used in most panel studies (denoted as DEM-FE).2

2.2.3 Empirical Model in this Paper

As noticed, there are some assumptions maintained in DEM-FE regressions. In the first

place, to obtain the idiosyncratic fluctuation in consumption, the DEM-FE regression as-

sumes identical and constant relative risk aversion coefficient µi across countries. Specifi-

cally, equation (2.7) shows that bc,i = µwµi

. Therefore, when µi is identical across units, i.e.,

µi = µj = µw, the loading coefficient bc,i in equation (2.9) is equal to one under the null

2Some studies (for example Asdrubali et al. (1996), Lewis (1997), Sorensen and Yosha (1998), andFratzscher and Imbs (2009)) replace this explicit cross-sectional demeaning with an implicit approach whichincludes a time dummy in the pooled regression to control for the effect of common trend in variables:

logCit = αi + dt + β log Yit + εit , (2.12)

where dt is a time dummy. Mathematically, the empirical estimation strategy for equation (2.12) with timedummies is the same as the regression with demeaned variables.

30

of perfect consumption smoothing. When perfect consumption smoothing is absent, the ef-

fect of aggregate fluctuation varies across countries, regardless of the value of risk aversion

coefficient. Additionally, when the attitude toward risk differs across countries, equation

(2.7) implies that the coefficient bc,i is individual-specific even under the situation of per-

fect consumption smoothing. In either case, imposing bc,i = 1 to obtain the idiosyncratic

consumption is likely to cause misspecification.

As for the idiosyncratic income, the coefficient for the effect of aggregate income, by,i

is also restricted to be one based on a similar homogeneity assumption as consumption.

Although it is reasonable to keep this assumption for a group of similar countries, it may

lead to the misspecification of the model when the group of countries under analysis is very

different from each other in terms of their productive and financial structures, regulations,

or participations in international trade. Especially in the case of a large and heterogeneous

panel used in this paper, it is more reasonable to relax the homogeneity assumption on the

loading coefficient and allow for country-specific influence of aggregate shocks.

Some studies, Pierucci and Ventura (2010) for instance, relax the assumptions on bc,i,

by,i and lead to regression equations as below (denoted here as Partial Pre-Filtering, or

PPF). But, these studies may be plagued by another problem.

log Y idioit = log Yit − by,i log Yw,t, (2.13)

logCidioit = logCit − bc,i logCw,t, (2.14)

logCidioit = αi + β log Y idioit + εit (2.15)

In particular, the way that both DEM and PPF regressions deal with aggregate shocks

implicitly assumes that the fluctuation in output is exogenous to consumption. As equa-

tion (2.13) illustrates, the idiosyncratic income is obtained by only removing the aggregate

income, log Yw,t. Similarly, in equation (2.14), the idiosyncratic consumption is extracted

from the data after controlling the aggregate consumption, logCw,t.

However, the assumption of uncorrelated consumption and output may fail due to rea-

sons other than market incompleteness (Becker and Hoffmann, 2006). One example will

be the non-separability between consumption and leisure in the utility function (Backus

et al., 1992). As a result, equation (2.10, 2.11) and (2.13 to 2.15) may be misspecified as it

neglects the possible correlation between fluctuations in consumption and income. Obstfeld

(1994) examined the effect of consumption from both aggregate consumption and aggregate

output for G-7 countries. Despite the high correlation between aggregate consumption and

output, the author still concluded that for France, Germany and Japan, consumption is

more correlated with aggregate output than with aggregate consumption.

31

Finally, there is another homogeneity assumption imposed in the existing test. Most

existing literature disregard heterogeneity in the coefficient β and estimate the overall β

from the fixed effect estimator. Pooling can bring efficiency gain when there is high degree of

homogeneity across individual units, otherwise, the ignored heterogeneity in the coefficient

of interest may lead to small sample bias in the estimation (See appendix for detailed

discussion about the pooled and mean-group estimator as in Coakley et al. (2001)). Given

a mix of over 100 countries in this paper, I also relax the assumption of a fixed β across

units and use the cross-sectional average of individual βi as a measure for the overall effect

(denoted as MG in this paper).

In this paper, I propose a different method to obtain measures of idiosyncratic fluctu-

ations in consumption and income. Recalling equation (2.9) above and rearranging terms,

the equation for risk-sharing test with fewest number of restrictions will be,

logCit = αi + γCi logCw,t + βilogYit + γYi logYw,t + εit , (2.16)

When cross-sectional means are used as proxy for aggregate series, equation (2.16) coincides

with a Common-Correlated-Effect (CCE) estimator for dependent panel regressions which

will be discussed in the following section.

2.3 The Common Correlated Effect Estimator

2.3.1 Common Correlated Effect Estimator

Pesaran’s (2006) common correlated effects (CCE) estimator, which deals with dependen-

cies across units in heterogeneous panel, is an ideal tool for an estimation with idiosyncratic

effects. The CCE estimator accomplishes this task because it accounts for common factors,

such as global business cycles or common shocks, allows for individual-specific effects of

these factors, and produces consistent coefficient estimates based on idiosyncratic fluctua-

tions in the data.

Specifically, the CCE estimator asymptotically eliminates the cross-sectional depen-

dence in a panel regression by augmenting it with cross-sectional means of variables in the

regression. Considering the following regression with panel dataset:

xit = αi + βizit + uit , i = 1, 2, . . . , N , t = 1, 2, . . . , T , (2.17)

where zit is a k× 1 vector of observed individual-specific regressors for the ith cross section

unit at time t. The dynamics and the unobserved common factors are modeled in the error

terms uit. In particular, uit is assumed to have the following structure

uit = γ ′ift + εit , (2.18)

32

where ft is an m× 1 vector of unobserved common effects with individual specific loading

vector γi. εit are the individual-specific (idiosyncratic) error, assumed to be distributed

independently of zit and ft. However, the εit are allowed to be weakly dependent across i,

and serially correlated over time.

The CCE estimator is based on the assumption that the regressor, zit, is generated as

zit = Ai + Γ′ift + vit , (2.19)

where Ai is the individual time-invariant effect, and Γi is a m × 1 loading vector for the

effect from common factors. The idiosyncratic component vit is distributed independently

of the common effects and across i. The error term in equation (2.17), uit, is allowed to

be correlated with the regressor, zit, through the presence of common factors in both, and

failure to account for this correlation will generally produce biased estimates of parameters

of interest.

Pesaran (2006) suggested using cross section averages of both regressant and regressors

to deal with the effect of unobserved factors. The CCE estimator is defined as,

βi = (z′iMzi)−1z′iMxi , (2.20)

where zi = (zi1, zi2, . . . , ziT )′, xi = (xi1, xi2, . . . , xiT )′, and M = IT − H(H ′H)−1H ′ with

H = (ι, z, x), and ι is a T × 1 vector of ones. z is a T × 1 matrix of cross-sectional means

of zit, and x is a T × 1 vector of cross-sectional means of the dependent variable.

While Pesaran (2006) derived the CCE estimator for stationary variables and factors,

Kapetanios et al. (2011) proved that the CCE estimator is consistent whether or not the

common factors, ft, are stationary. In the latter case, xit, zit, and ft are cointegrated if εit

(in equation 2.18) is stationary. The authors also showed that under a random coefficient

model, βi = β+ωi, where wi ∼ IID(0,Vw), both the individual and the mean of the slope

coefficient CCE estimates are consistent for any number of unobserved factors. To estimate

the mean value of the slope coefficient, two estimators are proposed. The CCE mean group

estimator (CCEMG) is a simple average of individual CCE estimators, βi,

βCCEMG =1

N

N∑i=1

βi . (2.21)

When slope coefficients, βi, are homogeneous, efficiency gains can be achieved by pooling

33

observations over cross section units, and the pooled estimator (CCEP) is defined as,3

βCCEP = (N∑i=1

y′iMyi)−1

N∑i=1

y′iMci . (2.22)

More specifically, the CCE estimation can be reconsidered as a two-stage procedure. In

the first stage, common effects are filtered out from the data by regressing each variable on

the cross-sectional averages of all variables in the model,

cit = αi,c + γci,cct + γyi,cyt + εcit , (2.23)

yit = αi,y + γci,y ct + γyi,yyt + εyit , (2.24)

where γci,c and γyi,c in equation (2.23) denote the individual-specific effect from aggregate

consumption and income, on individual consumption respectively; γci,y and γyi,y in equation

(2.24) capture the influence of aggregates on individual income, respectively. In the second

stage, the CCE estimate of an individual βi is obtained by regressing the residual εcit,

capturing idiosyncratic variation in consumption on the residual εyit, which captures the

idiosyncratic variation in income. Alternatively, βCCEP is obtained from a pooled regression

of εcit on εyit.

Although the CCE estimator admits both simple and weighted cross-sectional averages

in the M matrix, unequal weights may distort the inference if they overstate the importance

of outliers in the cross-sectional distribution of the data. For example, if a variable of interest

is in per capita terms, each country could be weighted by its population share, so that the

aggregate becomes a global per capita measure,

N∑i=1

(Cit ∗ wit) = Ct, wit =Nit

Nt, i = 1, 2, . . . , N , t = 1, 2, . . . , T , (2.25)

where C stands for consumption per capita, and N stands for population. This weight-

ing scheme overweighs countries with a large population. If some of these countries are

atypical, inferences will be distorted. Specifically, if the proxies for the common factors are

biased towards outliers, the CCE procedure will not be able to eliminate cross-sectional

dependence in the panel. Furthermore, most macroeconomic time series, such as consump-

tion and income, require a log-transformation before being fed to linear models. Such a

non-linear transformation will affect the location of the aggregate measure relative to the

distribution of the individual country level variables, and further distort inferences. In a

large panel dataset used in this paper, the size of population may not be a good weight

for consumption (income) per capita following all reasons mentioned above. Thus, simple

3In the CCEP, observations are pooled after a unit-by-unit orthogonal projection onto the cross-sectionalmeans. That is, the CCEP estimator allows for idiosyncratic loadings, γi, Γi, while estimating a commonslope coefficient for the variable of interest, β.

34

cross-sectional means entering the M matrix might be more appropriate to help handle

unobserved common factors.

2.3.2 Relationship to Consumption Risk-sharing

To examine the degree of international risk-sharing, empirical analysis requires control of

common shocks from individual variables and regressing idiosyncratic consumption on id-

iosyncratic income,

cidioit = αi + βiyidioit + uit , i = 1, 2, . . . , N , t = 1, 2, . . . , T , (2.26)

where cidioit , yidioit are idiosyncratic consumption and idiosyncratic income, respectively. With

the help of advanced techniques, aggregate shocks in individual consumption (income) can

be approximated by unobserved common factors. To be more specific, a particular country’s

observed income series, yit can be decomposed into two unobserved components. By defini-

tion, the common component can be captured by common factors, ft, and its contribution

to individual country’s observed income is measured by the factor loadings, λi,y,

yit = λ′i,yft + ξyit , (2.27)

where λi,y allows countries to be heterogeneous in terms of their sensitivity to global shocks.

The term λ′i,yft yields the amount of fully diversified income for country i, and the balance,

ξyit = yit − λ′i,yft, is the idiosyncratic component of observed income.

To control for common factors in both consumption and income and obtain the es-

timated coefficient for idiosyncratic variations, cross-sectional averages of both variables

can be incorporated in the regression following the CCE method from Pesaran (2006) and

Kapetanios et al. (2011), which leads to:

cit = αi + βiyit + γci ct + γyi yt + uit . (2.28)

Here cit and yit are observed individual consumption and income series in logarithm trans-

formation, and γci and γyi are the individual specific loading coefficients from aggregate

measures, respectively. Because Pesaran (2006) already showed that βi and the mean value,

β, can be consistently estimated by the augmented regression above, coefficient estimates

reflect the effect of income on consumption after controlling for common factors in the data.

Equation (2.28) takes the same functional form as equation (2.16) derived in the pre-

vious section, suggesting that the estimated coefficient βi from equation (2.16) measures

the transmission of idiosyncratic income to idiosyncratic consumption. This is because the

augmentation of aggregate consumption and income can proxy the common movement of

variables in the regression and help to isolate the idiosyncratic variations. It will be il-

35

lustrated later in the results section through some diagnostic tests that residuals from the

augmented regression are cross-sectionally independent. By contrast, DEM-type and PPF-

type regressions leave common factors in the regression residual which leads to a spurious

regression.

2.4 Empirical Strategy and Data

2.4.1 Roadmap

In this paper, I examine the degree of international risk-sharing in the long run using the

CCE method as equation (2.16) or (2.28). The CCE method allows me to handle all types

of aforementioned heterogeneity. To show that conventional demean (DEM) and partial

pre-filtering (PPF) methods have problems in dealing with aggregate shocks appropriately,

I perform residual diagnostics to each type of regression. As the roadmap (Figure 2.1)

illustrates, I first test for cross-sectional dependence in regression residuals using the CD

statistics proposed by Pesaran (2004). This is because cross-sectional dependence might

be present in regression residuals if the regression cannot appropriately control aggregate

shocks in the variables. Next, when the CD test rejects the null hypothesis of cross-sectional

independence, I use unit root tests that take into account cross-sectional dependence to

avoid distorted size and power discussed in Banerjee et al. (2004) and Gengenbach et al.

(2010). In particular, for the unit root test, I apply the CRMA test of Sul (2009) to test

for a unit root in common factors of the residual, and test for unit roots the idiosyncratic

component using the CIPS statistics of Pesaran (2007). As a robustness check of the

residual diagnostic test, I apply the same empirical procedure to a shorter sample which

excludes observations of the most recent recession.

For CCE regression, I also examine the degree of risk-sharing in the short-run using an

Error Correction Model (ECM) when the residual from the long-run regression is stationary,

and the equation for ECM under CCE estimator is:4

∆cit = βSRi ∆yit+Υci∆ct+Υy

i∆yt−κi(cit−1−αi−βLRi yit−1−γci ct−1−γyi yt−1)+eit (2.29)

To measure the mean value of the slope coefficient in the sample, I report βCCEMG

calculated by averaging individual βi. I compare estimations of CCEMG regression with

two alternatives: DEMFE and DEMMG. As discussed in Section 2 and 3, I suggest a

different method to obtain idiosyncratic consumption and income instead of using demeaned

4To estimate this model, I follow the two-stage estimation procedure from Engle and Granger (1987).In the first step, the long-run equilibrium relationship between common factors, idiosyncratic income andconsumption is estimated and the deviation is captured by the regression residual as (cit−1−αi−βLRi yit−1−γci ct−1 − γyi yt−1). In the second stage, the speed at which this equilibrium error is corrected, κ, can then beestimated along with the extent of risk sharing in the short run, βSR.

36

variables, a common approach in the literature. Moreover, I also relax the assumption of

a common coefficient β across countries. The comparison between DEMFE, DEMMG and

CCEMG will shed light on the relative merits of CCE method with such large panel data.

In addition to the mean effect for the whole sample, I also look at the subsample’s mean

effects. For each subsample, I further look at the change in the extent of risk sharing over

the past forty years to examine whether globalization has led to an increase in interna-

tional consumption smoothing. Finally, I examine individual estimates of βi and discuss

individual’s degree of risk-sharing.

2.4.2 Cross-sectional Dependence Test and Panel Unit Root Test

The international risk sharing hypothesis postulates that individual consumption and out-

put series across countries follow a similar pattern. The presence of common patterns across

countries can be tested by the cross-sectional dependence (CD) statistic of Pesaran (2004).

The test is based on the pairwise correlation of individual units, and has been shown to

have good finite sample properties in heterogeneous panels. Moreover, it is shown that the

CD test is valid regardless of whether individual series have unit roots. The statistic for

the CD test is:

CD =

√2T

N(N − 1)(

N−1∑i=1

N∑j=i+1

ρij) ∼a N(0, 1) , (2.30)

where ρij is the estimate of correlation between units i and j. Specifically,

ρij = ρji =

∑Tt=1 yityjt

(∑T

t=1 y2it)

1/2(∑T

t=1 y2jt)

1/2, (2.31)

where ys,t for s = i, j are individual series. The null hypothesis for the CD test is cross-

sectional independence, and the rejection suggests cross-sectional correlation.

Breitung and Pesaran (2008) classified panel unit root tests into two generations. The

first generation tests assume cross-sectional independence of individual series, while proce-

dures in the second-generation overcome this drawback by capturing cross-sectional depen-

dence through a factor representation. Using Monte Carlo simulations, Gengenbach et al.

(2006, 2010) showed that the dependence across units will cause size distortion in panel

unit root if it is overlooked. Thus, it is more desirable to use the second-generation panel

unit test when the null hypothesis of the CD test is rejected.

Several panel unit root tests that account for cross-sectional dependence have been

recently proposed in the literature. With the help of a factor structure, panel unit root test

can be implemented by testing for unit root in the common component and the idiosyncratic

component separately. The panel is found to be non-stationary if a unit root is found in

either component and stationary, if both components are stationary.

Pesaran (2007) proposes a test for unit root in the idiosyncratic component. To deal

37

Step  1  Pre-­‐test  of  variables  

Test  for  cross-­‐sec1onal  dependence  (CD):    H0:  cross-­‐sec/onal  independence  

In  the  common  component  (CRMA)  

In  the  idiosyncra1c  component  (CIPS)  

Test  for  unit  root:  H0:  unit  root  

Step  2  Model  es1ma1on  

Step  3  Residual  diagnos1c  test  

(Test  for  cross-­‐sec1onal  dependence  and  unit  root)  

reject  

Advanced  method    (CCE):  

 relaxing  homogeneity  assump/ons  

Conven1onal  methods  (DEM  and  PPF):    

with  homogeneity  assump/ons  

Figure 2.1: The roadmap

38

with cross-sectional correlation, the author first augmented individual standard ADF re-

gressions with cross-sectional averages of lagged levels and first-differences of the series been

tested. Then, he applies the covariate ADF test based on the augmented regression to each

individual series in the panel. Because individual covariate ADF test statistics are shown to

be independent from each other, he derives a panel test statistics, the CIPS, by averaging

individual statistics as in Im et al. (2003).

Because Pesaran’s (2007) CIPS test, which only focuses on the idiosyncratic component,

controls cross-sectional dependence through an orthogonal projection of the data on the co-

variates, it overlooks unit roots in common factors (Gengenbach et al., 2010). Therefore,

the unit root test for common factors is also required.

The approach proposed by Sul (2009) uses the cross-sectional mean as proxy for the

average of unobserved common factors and implements a covariate unit root test with

recursive mean adjustment (CRMA) to test the null hypothesis that the common factors

are integrated. The test for unit root in cross-sectional average overcomes the estimation of

the number of common factors required in other methods such as Bai and Ng (2004). Sul

(2009) and Gengenbach et al. (2010) showed that for the unit root test of common factors,

CRMA test has good size and power properties.

2.4.3 Data

In this paper, I use annual data from the Penn World Tables, version 7.1, released in

November 2012 (Heston et al. (2012)).5 This is a comprehensive dataset, covering more

than 170 countries over a fairly long time span. To maximize the number of countries with

continuously available data in the panel, I select the period from 1970 to 2010. All values are

expressed in US dollars, so as to make comparisons across countries and time feasible. From

the Penn World Tables, I collect the following variables: purchasing power parity (PPP)

converted GDP per capita at 2005 constant prices (Laspeyres), PPP-converted consumption

per capita at 2005 constant prices, and population.

2.5 Empirical Results

2.5.1 Variable Test and Residual Diagnostic Test

Considering the fact that individual consumption and income are both affected by common

shocks such as global crisis and world-wide technological change, it may be more reasonable

to use second generation panel unit root tests to examine the time series properties for each

variable. Pre-tests for logarithm transformed real consumption per capita and real GDP per

capita are summarized in Table 2.1. Both the CD test and the estimation for the number

5Analyzed series from Penn World Tables are comparable to those in other datasets. For example,growth rates of real GDP and real final consumption almost perfectly match those in the last release of theWorld Bank’s World Development Indicators.

39

of common factors indicate that there is cross-sectional interdependence for both series due

to the presence of common factors. Moreover, unit root tests on the common component

(CRMA) and the idiosyncratic component (CIPS) suggest that both series in log-level are

integrated of degree one.

To examine the degree of international risk sharing using non-stationary variables, the

first thing is to ensure that the residuals are stationary. Table 2.2 and 2.3 display residual

diagnostic tests for all three types of regressions: the CCE estimation, the estimation with

demeaned variables (DEM), and the PPF estimation. We run each regression with data

both in levels and in first-differences. Results in Table 2.2 are obtained when the global

shock is approximated by population weighted cross-sectional averages, whereas those in

Table 2.3 are based on cross-sectional averages with equal weights. Additionally, the lower

panels of both tables illustrate residual tests from regressions with a truncated sample

excluding the recent Great Recession. The extra column in Table 2.3 is the result for the

ECM model, described in equation (2.29).

The rejection of the CD test for residuals in all DEM and PPF regressions indicates

that these methods are not able to fully control cross-sectional dependence in the regres-

sion. This problem also remains for the case of CCE regression when the common trend

is approximated by population weighted cross-sectional averages. The latter result may be

explained by the fact that in such a large sample, some countries with a large population are

not typical in terms of common risks. Hence, population weights are inappropriate when

obtaining the approximation of common factors for real GDP per capita and consumption

per capita. From the residual diagnostic test, only the CCE estimation with simple averages

is statistically defensible.

As discussed, in contrast to the CCE method, the widely-used DEM method imposes

homogeneity assumption on individual’s link to aggregate shock and obtain the idiosyncratic

consumption (income) by simple cross-sectional demeaning. It has been shown in Table 2.2

and 2.3 that the simple demeaning leaves a unit root in the regression residuals. Here, I

include some visual comparisons between the idiosyncratic fluctuation obtained from the

CCE method and from the DEM method, to provide some intuition for the problem of

cross-sectional demeaning. Figure 2.2 illustrates the distribution of self-loading coefficients

γci,c and γyi,y in the first stage of CCE regressions (equation (2.23) and (2.24)). It reveals

that these loading coefficients vary sharply across countries and they are not all equal to

one, the value imposed by the DEM-type regression. Similarly, Figure 2.3 illustrates the

distribution of the cross-loading coefficients γyi,c and γci,y. They are not all equal to zero,

the value imposed by both DEM-type and PPF regressions. These loading coefficients

estimated from the data indicate that the values imposed in DEM-type fluctuation may

cause misspecification of the idiosyncratic fluctuations in consumption and income. Thus,

the DEM approach is incapable of filtering out the common factors from the panels.

In addition, Figure 2.4 visualizes the correlation between the idiosyncratic components

40

Table 2.1: Tests for Individual Variables

Levels DifferenceslogC log Y ∆ logC ∆ log Y

CD 253.45∗ 239.37∗ 22.93∗ 43.33∗

No. of CF 1 1 1 1CRMA 2.11 2.08 -3.92∗ -3.21∗

CIPS(4) -0.32 1.87 -9.72∗ -7.78∗

Note: Pesaran’s (2004) cross-sectional independence test (CD) follows a standard normal distribu-

tion. No. of CF denotes the estimated number of common factors in the panel following Bai and

Ng (2002). The 5% critical value for Pesaran’s (2007) panel unit root test (CIPS) is -2.06. The lag

length for the CIPS test is set to T 1/3 = 4. The 5% critical value for Sul’s (2009) unit root test for

the cross-sectional means (CRMA) is -1.88. The lag length for the CRMA test is determined by

the Bayesian Information Criterion with maximum 4 lags. Statistical significance at the 5% level or

lower is denoted by ∗.

Table 2.2: Residual Diagnostic Tests, Weighted Averages

Full Sample: 1970-2010

DEM PPF CCE DEM∆ PPF∆ CCE∆

CD 10.11∗ 6.76∗ 5.06∗ 17.24∗ 9.12∗ 3.80∗

CRMA -1.62 -1.57 -1.45 -4.69∗ -5.56∗ -4.97∗

CIPS(4) -3.31∗ -9.67∗ -7.39∗ -9.35∗ -8.83∗ -10.33∗

Truncated Sample: 1970-2007

DEM PPF CCE DEM∆ PPF∆ CCE∆

CD 11.00∗ 7.58∗ 5.55∗ 14.60∗ 6.33∗ 4.14∗

CRMA -1.78 -1.45 -1.15 -4.20∗ -4.55∗ -3.64∗

CIPS(4) -4.25∗ -8.83∗ -6.35∗ -7.31∗ -7.62∗ -8.79∗

Note: CCE and CCE∆ are the common correlated effects estimates for the data in log-levels and

in log-differences, respectively. DEM and DEM∆ are estimates from a cross-sectionally demeaned

regression with the data in log-levels and in log-differences, respectively. PPF and PPF∆ are

estimates from a partially pre-filtered regression with the data in log-levels and in log-differences,

respectively. ECM is the error correction model under CCE, equation (2.29). See note in Table 2.1.

41

CCE loading, individual cons on cross−sectional mean of cons

loading factor

Fre

quen

cy

−10 −5 0 5 10 15

05

1015

20

CCE loading,df, individual cons on cross−sectional mean of cons

loading factor

Fre

quen

cy

−5 0 5 10 15

05

1015

2025

3035

CCE loading, individual rgdp on cross−sectional mean of rgdp

loading factor

Fre

quen

cy

−10 −5 0 5 10 15

05

1015

20

CCE loading,df, individual rgdp on cross−sectional mean of rgdp

loading factor

Fre

quen

cy

−2 0 2 4

05

1015

γci,c γci,c

γyi,y γyi,y

Data in log-levels Data in log-differences

Figure 2.2: Distribution of the γci,c and γyi,y loading coefficient estimates in the first-stageequations of CCE, see equations (2.23) and (2.24).

42

CCE loading, individual rcons on cross−sectional mean of gdp

loading factor

Fre

quen

cy

−10 −5 0 5 10 15

05

1015

20

CCE loading,df, individual cons on cross−sectional mean of gdp

loading factor

Fre

quen

cy

−4 −2 0 2 4 6 8

05

1015

2025

30

CCE loading, individual rgdp on cross−sectional mean of cons

loading factor

Fre

quen

cy

−10 −5 0 5 10 15

05

1015

20

CCE loading,df, individual gdp on cross−sectional mean of cons

loading factor

Fre

quen

cy

−4 −2 0 2 4 6

05

1015

γyi,c γyi,c

γci,y γci,y

Data in log-levels Data in log-differences

Figure 2.3: Distribution of the γyi,c and γci,y loading coefficient estimates in the first-stageequations of CCE, see equations (2.23) and (2.24).

43

Table 2.3: Residual Diagnostic Tests, Simple Average

Full Sample (1970-2010)

DEM PPF CCE DEM∆ PPF∆ CCE∆ ECMCD 11.28∗ 15.27∗ 0.06 22.86∗ 10.17∗ -0.53 -0.83CRMA -1.74 -0.85 — -6.02∗ -5.45∗ — —CIPS -2.03 -5.13∗ -5.87∗ -8.66∗ -9.32∗ -10.09∗ -10.03∗

Truncated Sample (1970-2007)

DEM PPF CCE DEM∆ PPF∆ CCE∆ ECMCD 12.68∗ 16.41∗ 0.36 23.44∗ 8.74∗ -0.33 -0.48CRMA -1.86 -0.80 — -5.56∗ -5.19∗ — —CIPS -0.13 -3.96∗ -5.75∗ -5.34∗ -6.59∗ -8.36∗ -11.02∗

Note: See note in Table 2.1 and 2.2

based on the CCE first-stage (equation 2.23 and 2.24) and the cross-sectionally demeaned

variables. Again, with full risk sharing and when individual countries are homogeneous

in terms of the risk-aversion, time preference and endowments, a unit loading coefficient

is expected and the idiosyncratic components from the demeaned data will be close to

those from the CCE first-stage. Nevertheless, in the data, the idiosyncratic components

from equation (2.23) and (2.24) are different from the demeaned. According to Figure 2.4,

the correlation between the two types of idiosyncratic components is below 0.80 for most

countries.

Moreover, the misspecified idiosyncratic components from cross-sectional demeaning are

left with trending common factors and will lead to unexpected outcome in the estimation

of international risk sharing. Figure 2.5 compares the idiosyncratic measures from the first-

stage of the CCE method with the demeaned variables for all countries. This figure shows

that both demeaned consumption and income series behave quite differently from the first-

stage residuals of the CCE. In particular, for many countries, the idiosyncratic measures

based on cross-sectionally demeaned variables are trending, which may be either introduced

or not fully removed by the imposed and identical value of the effects of aggregate shocks.

When regressing the trending idiosyncratic consumption on income as in Figure 2.6 for two

representative countries, the trend from both dependent and independent variables is likely

to cause bias in the estimated β for two reasons. First, the trend effect in both variables may

dominate other types of variation and lead to a misleadingly estimated βi for the degree of

international risk sharing. Second, as reported in Table 2.3, there is no cointegration found

between these trending variables and the estimate for β in the long run is spurious.

44

Log Level Consumption

Correlation Coefficient

Fre

quen

cy

0.2 0.4 0.6 0.8 1.0

05

1525

Log Level Income

Correlation Coefficient

Fre

quen

cy

0.2 0.4 0.6 0.8 1.0

05

1020

CORR(ξcit, cit − ct)

CORR(ξyit, yit − yt)

Figure 2.4: Distribution of correlation coefficients Corr(ξcit, cit − ct) and Corr(ξyit, yit − yt).The idiosyncratic components, ξcit and ξyit, are estimated in (2.23) and (2.24), and the cross-sectionally demeaned variables, cit − ct and yit − yt, appear directly in (2.2). All analyzedseries are in log-levels.

45

1970 1980 1990 2000 2010

−3

−2

−1

01

23

Idiosyncratic Consumption

time

1970 1980 1990 2000 2010

−3

−2

−1

01

23

Demeaned Consumption

time

1970 1980 1990 2000 2010

−3

−2

−1

01

23

Idiosyncratic Income

time

1970 1980 1990 2000 2010

−3

−2

−1

01

23

Demeaned Income

time

ξcit in Log-Levels cit − ct in Log-Levels

ξyit in Log-Levels yit − yt in Log-Levels

Figure 2.5: Scaled estimates of idiosyncratic components (left), ξcit and ξyit and the cross-sectionally demeaned variables (right), cit − ct and yit − yt.Estimated in (2.23) and (2.24), and (2.10) respectively. All analyzed series are in log-levels.The estimates are highlighted for two representative countries: Singapore (dash-dotted line)and Cameroon (long-dashed line).

46

1970 1980 1990 2000 2010

−2

−1

01

2

Idiosyncratic Consumption,reprsentative country

time

1970 1980 1990 2000 2010

−2

−1

01

2

Demeaned Consumption,representative country

time

1970 1980 1990 2000 2010

−2

−1

01

2

Idiosyncratic Income,representative country

time

1970 1980 1990 2000 2010

−2

−1

01

2Demeaned Income,representative country

time

ξcit in Log-Levels cit − ct in Log-Levels

ξyit in Log-Levels yit − yt in Log-Levels

Figure 2.6: Estimates of idiosyncratic components, ξcit and ξyit, and the cross-sectionallydemeaned variables, cit − ct and yit − yt for representative countries.Estimated in (2.23), (2.24) and (2.2) respectively. All analyzed series are in log-levels. Theestimates are highlighted for two representative countries: China (solid line) and CentralAfrica Republic (dash-dotted line).

47

2.5.2 Estimation for the Overall β

In this section, I will focus on the discussion of the estimated β from the statistically valid

CCE method. In Table 2.4, I include the CCEMG estimation for the overall β both in the

long-run and in the short-run, as well as the average speed of adjustment from the ECM.

To compare and contrast with results following methods in the literature, I also estimate

two alternative specifications based on DEM-type idiosyncratic fluctuation. Particularly,

the DEMFE refers to a fixed effect estimator for the overall β when the idiosyncratic

consumption and income are obtained by cross-sectionally demeaning. In contrast to the

pooling feature in the fixed effect estimator, the DEMMG refers to a mean-group estimator

using DEM-type fluctuations.

The decision to estimate the overall β from the mean-group estimator instead of the

pooled estimator is based on Coakley et al. (2001), which examines the small sample prop-

erties of different panel estimators: the fixed effect estimator and the mean-group estimator.

By using Monte Carlo simulation, the authors show that when there is a large heterogene-

ity in the slope coefficient of a panel, the mean group estimator will be closer to the true

value of β. In Table 2.4, the sharp divergence between DEMFE and DEMMG for most

sub-groups of countries suggests a negative bias in DEMFE. As explained in the appendix,

this also implies a negative relationship between βi and the variance of demeaned income,

i.e., the country in a particular group with relatively large variation in its income will likely

have a small value of βi. This is consistent with bounded rationality discussed in Browning

and Collado (2001): countries with large variation in income tend to have a large degree of

consumption smoothing.

The valid and consistent CCE estimations provide many valuable results. First, in line

with earlier studies (Artis and Hoffmann, 2008; Becker and Hoffmann, 2006; Leibrecht and

Scharler, 2008), no evidence for perfect international risk-sharing is found, and on average,

consumption tends to be affected by idiosyncratic risks significantly in both short-run and

long-run. Second, the extent of risk-sharing tends to be higher in the short run than in

the long-run. In the long-run, the fraction of uninsured variation in GDP transmitted

to consumption is above 0.80, while it is about 0.70 in the short run. Third, partially

consistent with the findings in Kose et al. (2008), the degree of consumption smoothing is

inversely related to the level of development, both in the long-run and in the short-run.6

This finding is predictable economically since most developed economies have better access

to most risk-sharing channels: the credit and capital market, and international trade.

Finally, the estimates for OECD countries are quite similar to those obtained by Leibrecht

and Scharler (2008): our βLR = 0.68 and βSR = 0.80 fall slightly below their estimates of

about 0.7 and 0.9, respectively. However, the estimated speed of equilibrium-error correc-

6This argument is more obvious by comparing OECD v.s. Non-OECD and Developed v.s. Non-developed.

48

tion, κ = −0.31, deviates from their -0.1 estimate by a larger margin.7 Consequently, the

mean adjustment lag (computed as µ = (1− βSR)/(−κ) based on Hendry (1995) indicates

that in OECD countries an income shock exerts its full effect on consumption within about

a year according to our study, and in about three years according to the results of Leibrecht

and Scharler (2008).

2.5.3 The Change of the Overall β Over Time

Lane and Milesi-Ferretti (2007) has documented the intensity in the degree of financial

globalization for both industrial and developing countries since 1990s. For emerging mar-

kets, the improvement in financial globalization is characterized by the increasing equity

component in the external liabilities and official reserve assets. For major debtors, the debt

liabilities is their major source of the external finance.

By analyzing international risk sharing at low frequency, Artis and Hoffmann (2012)

examine the changes of β in periods of pre-1990 and post-19908 due to increasing financial

liberalization. Based on a fixed effect estimator of DEM-type fluctuation, the authors found

strong evidence of an improvement of international risk sharing in a group of OECD coun-

tries. As a preliminary analysis, I constructed the same dataset as in Artis and Hoffmann

(2012), and repeat their empirical strategy. Considering the problem of DEMFE estimation

discussed before, I conduct the CD test and second generation panel unit root tests for the

residuals. As Table 2.5 shows, the residuals are found to be cross-sectionally dependent and

non-stationary. Moreover, I reestimate their empirical model by relaxing the assumption of

a homogeneous β and by following the CCE method. In contrast to their findings, I could

not find any evidence of improved international risk sharing.

To acquire some insight into the change in the degree of international risk sharing with

the large panel, I follow Artis and Hoffmann (2012) and estimate the empirical model for

two sub-periods: 1970-1989, and 1990-2010. Results are reported in Table 2.6. Since the

1990s, the global financial market has become more integrated due to increasing capital flows

across countries. In principal, consumers can insure themselves against income shocks more

easily in a more integrated financial market. Hence, it is widely accepted that the degree

of international risk sharing should be higher in the period of 1990-2010. Nevertheless,

according to Table 2.6, results across all sub-groups do not suggest any evidence for a higher

degree of international risk sharing. The estimated β coefficient is not significantly lower

in the post-globalization period and this conclusion is robust to different sample groups of

countries. In fact, there are signs of a deterioration in international risk sharing in the EU

subsample.

The lack of the improved consumption risk sharing has been found in other studies.

7Notice, however, that the time period and the country analyzed by Leibrecht and Scharler (2008) aredifferent from ours.

8The dataset used in this paper is obtained form PWT 6.2, which ends in 2004. The two sub-periodsare 1960-1990 and 1990-2004.

49

Table 2.4: Mean Group Coefficient Estimates for Sub-Samples

Country Group βLRDEMFE βSR

DEMFE βLRDEMMG βSR

DEMMG βLRCCEMG βSR

CCEMG κ µWhole Sample1 0.78∗ 0.68∗ 0.85∗ 0.73∗ 0.83∗ 0.71∗ -0.39 0.74

High Income1,2,3,4 0.66∗ 0.74∗ 0.91∗ 0.72∗ 0.82∗ 0.65∗ -0.33 1.06UpperMid Income2 0.87∗ 0.78∗ 0.92∗ 0.74∗ 0.85∗ 0.73∗ -0.41 0.66LowerMid Income2,3 0.76∗ 0.54∗ 0.77∗ 0.67∗ 0.83∗ 0.70∗ -0.42 0.71Low Income 0.81∗ 0.71∗ 0.80∗ 0.77∗ 0.82∗ 0.77∗ -0.44 0.52

OECD3,4 0.81∗ 0.78∗ 0.87∗ 0.76∗ 0.80∗ 0.68∗ -0.31 1.03Non-OECD1 0.77∗ 0.68∗ 0.85∗ 0.72∗ 0.84∗ 0.72∗ -0.42 0.67

Developed1,2,3,4 0.85∗ 0.74∗ 0.87∗ 0.73∗ 0.78∗ 0.65∗ -0.32 1.09Developing1,3 0.78∗ 0.66∗ 0.88∗ 0.73∗ 0.87∗ 0.74∗ -0.41 0.63

EU4 0.87∗ 0.74∗ 0.88∗ 0.76∗ 0.83∗ 0.69∗ -0.34 0.92

Note: Country group definitions follow those used by the World Bank and OECD. βLRDEMFE

and βSRDEMFE are obtained by estimating equation (2.10) and (2.11), respectively. βLR

DEMMG and

βSRDEMMG are obtained by estimating equation (2.10) and (2.11) for each indiviudal, respectively,

and aggregating the βi using equation (2.21). βLRCCE is obtained by estimating equation (2.9) with

data in log-levels; βSRCCE is obtained by estimating the error-correction model in equation (2.29),

and aggregating βi using equation (2.21). κ denotes the estimated speed-of-adjustment coefficient

in the error-correction model. µ denotes the mean adjustment lag computed as µ = (1− βSR)/(−κ)based on Hendry (1995). The β coefficient measures the extent of income shocks transmitted toconsumption. The theory of international risk sharing implies H0: β = 0. Statistical significance atthe 5% level or lower is denoted by ∗.1 indicates that βLR

CCEMG and βLRDEMFE are different at the 10% level of marginal significance.

2 indicates that βLRCCEMG and βLR

DEMMG are different at the 10% level of marginal significance.

3 indicates that βSRCCEMG and βSR

DEMFE are different at the 10% level of marginal significance.

4 indicates that βSRCCEMG and βSR

DEMMG are different at the 10% level of marginal significance.

50

Pierucci and Ventura (2010) failed to conclude that the surge in international financial

liberalization improved long-run risk sharing. Kose et al. (2008) found that only industrial

countries have attained better risk sharing during the recent period of globalization, and that

developing countries have been mostly shut out of these benefits. In their paper, the reason

was imputed to the particular composition of capital flows, with external debt preventing

most emerging economies to efficiently share risks. At last, Bai and Zhang (2012) found that

consumption risk sharing shows little improvement for their whole sample, OECD countries

as well as emerging markets. Bai and Zhang (2012) suggests that it is the existence of

friction in the capital markets that limits the observed increase in capital flow under financial

liberalization. As a result, there is no significant improvement in consumption smoothing

and risk sharing.

2.5.4 Individual β

In this paper, I allow individual-specific coefficient of β in the regression model of consump-

tion smoothing considering the large and heterogenous panel used in this paper. In the

previous discussion about the estimation of the overall β, I attribute the difference between

the fixed effect estimator and the mean-group estimator partially to the heterogeneity in

terms of βi. Here, I provide additional evidence regarding the heterogeneity of βi. The

rejection of Pesaran and Yamagata’s (2008) test of parameter homogeneity in Table 2.7

implies that the heterogeneity of βi is statistically significant.

With the large degree of heterogeneity in βi across countries, it is also interesting to

examine individual βi. I report the estimations of βi in Table 2.8 and 2.9 and plot their

distribution in Figure 2.7. Notably, there is a remarkable heterogeneity in terms of countries’

risk-sharing coefficients, both in the long run and in the short run. This further suggests

that the pooled CCE estimator is less appropriate to measure the mean slope coefficient of

the regression for countries in such large sample.

Since the panel unit root test suggests stationarity in the CCE regression, I also test

for the presence of perfect risk-sharing hypothesis based on individual βi. To account for

heteroskedasticity and autocorrelation in individual regression residuals, I use the Newey

and West (1987, 1994) heteroskedasticity and autocorrelation consistent (HAC) covariance

matrix for the inference of βi.

Accordingly, more than 95% of the βLR and almost 90% of the βSR estimates are

significantly different from zero, indicating a widespread lack of consumption risk sharing.

Moreover, the degree of risk sharing tends to be lower in the long run for most countries.

In particular, 33 of the analyzed countries have 50% higher coefficient estimates in the long

run than in the short run, and over 45 of them appear to exhibit dis-smoothing behavior

(βi > 1) in the long run, whereas only 27 cases in the short run.

51

Table 2.5: The Effect of Financial Liberalization

Period: 1960-1990 Period: 1990-2004

βDEMFE 0.98 0.63CD test -3.74∗ -2.36∗

CIPS -1.65 5.09

Estimations from the Mean-group Estimators

βDEMMG 1.03 0.91βCCEMG 0.93 0.94

Note: Values obtained from βDEMFE are reported in Artis and Hoffmann (2012). All estimations are

significant at 5% level. Pesaran’s (2004) cross-sectional independence test (CD) follows a standard

normal distribution. The 5% critical value for Pesaran’s (2007) panel unit root test (CIPS) is -2.06.

The lag length for the CIPS test is set to T 1/3. Statistical significance at the 5% level or lower is

denoted by ∗.

Table 2.6: CCEMG Coefficient Estimates for Sub-Samples, in Sub-Periods

βLRCCEMG βSR

CCEMG

Country Group 1970-1989 1990-2010 1970-1989 1990-2010Whole Sample 0.82∗ 0.85∗ 0.70∗ 0.68∗

High Income 0.82∗ 0.83∗ 0.66∗ 0.62∗

UpperMid Income 0.88∗ 0.85∗ 0.75∗ 0.75∗

LowerMid Income 0.77∗ 0.85∗ 0.66∗ 0.66∗

Low Income 0.78∗ 0.87∗ 0.76∗ 0.70∗

OECD-AH 0.76∗ 0.78∗ 0.64∗ 0.56∗

OECD 0.80∗ 0.80∗ 0.68∗ 0.64∗

Non-OECD 0.82∗ 0.86∗ 0.71∗ 0.69∗

Developed 0.76∗ 0.80∗ 0.65∗ 0.63∗

Developing 0.85∗ 0.89∗ 0.72∗ 0.73∗

EU1 0.78∗ 0.86∗ 0.64∗ 0.69∗

Note: 1 indicates that the βLR estimates differ between two sub-periods at the 5% level of marginal

significance. See also the Table 2.4 notes.

52

Table 2.7: Homogeneous test for individual CCE estimates

CCELR CCEECM

∆ 69.79∗ 42.53∗

∆adj 72.43∗ 44.18∗

Note: Both ∆ and ∆adj have standard normal distribution. The null hypothesis is homogeneous

coefficient among individuals. ∗ suggests rejection of the null at the 5% level.

2.6 Conclusion

With perfect international risk sharing, the theoretical model implies that idiosyncratic con-

sumption should be independent of idiosyncratic income shocks. Accordingly, a prerequisite

of this test is the isolation of country-specific variation in the data.

In this paper, I show that the cross-sectional demeaning, a commonly used method

of the literature, is generally insufficient to eliminate the cross-sectional dependence in a

panel regression of the international risk sharing test. More importantly, I demonstrate that

the cross-sectional dependence left in the regression residuals leads to common unit roots.

Therefore, I suggest that a more statistically appropriate approach is the CCE methodology

of Pesaran (2006) and Kapetanios et al. (2011) that controls for global trends and allows

for heterogeneous effects across units. To estimate the degree of international risk sharing,

I use a relatively large panel dataset, which has never been considered in the literature.

Given such large number of different countries in the panel, I recommend the use of mean

group estimator for the overall risk sharing coefficient.

In the empirical analysis, I first conduct residual diagnostic tests for all types of regres-

sions and show that only residuals from the CCE method are cross-sectional independent

and stationary. Based on the statistically valid CCE mean group estimations, I measure the

average degree of international risk sharing for different subgroup countries both in the long

run and in the short run from an ECM. Similar to most existing literature, no evidence of

high degree of risk sharing is found. Moreover, I also investigate whether or not the degree

of international risk sharing is higher during the subperiod with more liberalization of inter-

national financial market. Consistent with a few conclusions in Kose et al. (2008) and Bai

and Zhang (2012), my empirical results cannot support the argument of an improvement in

the degree of risk sharing. Finally, I measure the risk sharing coefficient for each individual

country and find a large variation across countries.

53

Table 2.8: Country-Specific Coefficient Estimates

id country βLR βSR κ id country βLR βSR κ1 AFG 0.87∗ 0.95∗ -0.20 ∗ 41 DOM 0.90∗ 1.01∗ -0.21 ∗

2 AGO 2.00∗ 0.62 -0.58 ∗ 42 DZA 1.48∗ 0.24 -0.213 ALB 0.18∗ 0.29∗ -0.22 ∗ 43 ECU 0.71∗ 0.57∗ -0.58 ∗

4 ARG 0.97∗ 1.26∗ -0.19 ∗ 44 EGY 0.68∗ 0.37 -0.33 ∗

5 ATG 0.99∗ 1.58∗ -0.70 ∗ 45 ESP 0.89∗ 0.80∗ -0.32 ∗

6 AUS 0.42∗ 0.12 -0.10 46 ETH 1.10∗ 1.03∗ -0.43 ∗

7 AUT 1.11∗ 0.74∗ -0.35 ∗ 47 FIN 0.81∗ 0.46∗ -0.27 ∗

8 BDI 0.86∗ 0.79∗ -0.52 ∗ 48 FJI 0.64∗ 0.57∗ -0.37 ∗

9 BEL 0.98∗ 0.53∗ -0.35 ∗ 49 FRA 1.02∗ 0.73∗ -0.24 ∗

10 BEN 0.80∗ 0.66∗ -0.22 ∗ 50 FSM 1.03∗ 0.98∗ -0.81 ∗

11 BFA 1.96∗ 1.27∗ -0.52 ∗ 51 GAB 0.34∗ -0.09 -0.56 ∗

12 BGD 1.61∗ 1.10∗ -0.62 ∗ 52 GBR 1.13∗ 0.95∗ -0.55 ∗

13 BGR 1.01∗ 0.85∗ -0.39 ∗ 53 GER 1.16∗ 0.62∗ -0.28 ∗

14 BHR 0.64∗ 0.78∗ -0.42 ∗ 54 GHA 1.00∗ 0.88∗ -0.65 ∗

15 BHS 1.42∗ 1.29∗ -0.36 ∗ 55 GIN 1.56∗ 1.53∗ -0.33 ∗

16 BLZ 1.22∗ 1.11∗ -0.56 ∗ 56 GMB 0.85∗ 0.92∗ -0.35 ∗

17 BMU 1.47∗ 0.90∗ -0.38 ∗ 57 GNB 0.99∗ 0.74∗ -0.50 ∗

18 BOL 0.64∗ 0.86∗ -0.46 ∗ 58 GNQ 0.67∗ 0.72∗ -0.31 ∗

19 BRA 0.83∗ 0.90∗ -0.46 ∗ 59 GRC 0.20 0.49∗ -0.15 ∗

20 BRB 1.59∗ 1.29∗ -0.31 ∗ 60 GRD 0.46∗ 0.69∗ -0.53 ∗

21 BRN -0.90∗ 0.04 -0.57 ∗ 61 GTM 0.86∗ 0.75∗ -0.26 ∗

22 BTN 0.56∗ 0.57∗ -0.41 ∗ 62 GUY 1.15∗ 0.93∗ -0.26 ∗

23 BWA 0.40∗ 0.19∗ -0.34 ∗ 63 HKG 1.22∗ 0.85∗ -0.43 ∗

24 CAF 0.92∗ 0.83∗ -0.45 ∗ 64 HND 1.00∗ 0.19 -0.54 ∗

25 CAN 0.41∗ 0.48∗ -0.18 ∗ 65 HTI 0.97∗ 1.12∗ -0.46 ∗

26 CHE 0.23 0.23∗ -0.32 ∗ 66 HUN 1.02∗ 1.00∗ -0.20 ∗

27 CHL 0.96∗ 0.79∗ -0.22 67 IDN 1.09∗ 0.56∗ -0.27 ∗

28 CHN 1.00∗ 1.01∗ -0.42 ∗ 68 IND 0.95∗ 0.71∗ -0.58 ∗

29 CIV 0.76∗ 0.78∗ -0.48 ∗ 69 IRL 0.64∗ 0.62∗ -0.48 ∗

30 CMR 0.97∗ 0.79∗ -0.40 ∗ 70 IRN 0.59∗ 0.39∗ -0.27 ∗

31 COG 0.46∗ 0.30∗ -0.11 71 IRQ -0.08 0.27∗ -0.86 ∗

32 COL 0.92∗ 0.75∗ -0.40 ∗ 72 ISL 1.25∗ 1.01∗ -0.60 ∗

33 COM 0.40∗ 0.27 -0.38 ∗ 73 ISR 1.08∗ 0.83∗ -0.39 ∗

34 CPV 0.99∗ 0.67∗ -0.13 74 ITA 1.00∗ 0.76∗ -0.53 ∗

35 CRI 0.93∗ 1.13∗ -0.18 75 JAM 0.88∗ 0.80∗ -0.43 ∗

36 CUB 1.16∗ 1.18∗ -0.34 ∗ 76 JOR 1.34∗ 0.68∗ -0.30 ∗

37 CYP 0.87∗ 0.72∗ -0.48 ∗ 77 JPN 0.86∗ 0.63∗ -0.27 ∗

38 DJI 1.25∗ 0.96∗ -0.72 ∗ 78 KEN 1.08∗ 1.41∗ -0.43 ∗

39 DMA 0.62∗ 0.47∗ -0.70 ∗ 79 KHM 0.94∗ 0.97∗ -0.57 ∗

40 DNK 0.53∗ 0.67∗ -0.32 ∗ 80 KIR 0.67∗ 0.47∗ -0.30 ∗

Note: See Table 2.9 below.

54

Table 2.9: Comparison of country-specific coefficient estimates (continued)

id country βLR βSR κ id country βLR βSR κ81 KNA 0.80∗ -0.06 -0.51 ∗ 121 PRT 0.81∗ 0.50∗ -0.49 ∗

82 KOR 0.84∗ 0.78∗ -0.19 ∗ 122 PRY 0.77∗ 0.23 -0.30 ∗

83 LAO 0.85∗ 0.98∗ -0.39 ∗ 123 ROM 0.50∗ 0.61∗ -0.39 ∗

84 LBN 0.84∗ 0.84∗ -0.81 ∗ 124 RWA 0.59∗ 0.20∗ -0.11 ∗

85 LBR 1.15∗ 0.90∗ -0.28 ∗ 125 SDN 1.01∗ 1.43∗ -0.34 ∗

86 LCA 0.70∗ 0.89∗ -0.52 ∗ 126 SEN 0.88∗ 0.50∗ -0.21 ∗

87 LKA 1.10∗ 0.49∗ -0.62 ∗ 127 SGP 0.73∗ 0.46∗ -0.1388 LSO 1.05∗ 0.66∗ -0.35 ∗ 128 SLB 1.04 0.44∗ -0.17 ∗

89 LUX 0.69∗ 0.31∗ -0.26 ∗ 129 SLE 0.67∗ 0.79∗ -0.23 ∗

90 MAC 1.00∗ 0.25∗ -0.11 ∗ 130 SLV 1.32∗ 1.16∗ -0.55 ∗

91 MAR 0.34 0.44∗ -0.50 ∗ 131 SOM 0.95∗ 1.01∗ -0.48 ∗

92 MDG 1.17∗ 0.12 -0.10 132 STP 1.19∗ 1.31∗ -0.63 ∗

93 MDV 0.96∗ 0.66∗ -0.24 ∗ 133 SUR 1.30∗ 1.83 ∗ -0.68 ∗

94 MEX 0.80∗ 0.83∗ -0.19 ∗ 134 SWE 0.67∗ 0.58 ∗ -0.32 ∗

95 MHL 1.34∗ 0.56∗ -0.40 ∗ 135 SWZ 0.40∗ -0.08 -0.66 ∗

96 MLI -0.17 0.00 -0.44 ∗ 136 SYC 1.08∗ 0.89∗ -0.2397 MLT 0.75∗ 0.67∗ -0.13 137 SYR 0.78∗ 0.96∗ -0.20 ∗

98 MNG 0.67∗ 1.09∗ -0.52 ∗ 138 TCD 0.47∗ 0.51∗ -0.1999 MOZ 0.89∗ 0.70∗ -0.44 139 TGO 0.33 ∗ 0.54∗ -0.83 ∗

100 MRT 0.80∗ 0.83∗ -0.49 ∗ 140 THA 0.78∗ 0.61∗ -0.70 ∗

101 MUS 0.84∗ 0.60∗ -0.47 ∗ 141 TON 0.92∗ 0.65∗ -0.56 ∗

102 MWI 0.44∗ 0.54∗ -0.86 ∗ 142 TTO 0.93∗ 0.81∗ -0.77 ∗

103 MYS 0.54∗ 0.96∗ -0.26 ∗ 143 TUN 0.64∗ 0.28∗ -0.53 ∗

104 NAM 1.03∗ 0.88∗ -0.85 ∗ 144 TUR 0.72∗ 0.94∗ -0.38 ∗

105 NER 0.32∗ 0.67∗ -0.62 ∗ 145 TWN 1.12∗ 0.63∗ -0.37 ∗

106 NGA 1.13∗ 1.28∗ -0.45 ∗ 146 TZA -0.04 0.37∗ -0.33 ∗

107 NIC 0.72∗ 0.51∗ -0.36 ∗ 147 UGA 0.97∗ 0.94∗ -0.66 ∗

108 NLD 0.72∗ 0.71∗ -0.18 ∗ 148 URY 1.00∗ 0.95∗ -0.05109 NOR 0.38∗ 0.57∗ -0.26 ∗ 149 USA 0.91∗ 0.74∗ -0.21110 NPL 1.10∗ 1.13∗ -0.48 ∗ 150 VCT 0.74∗ 0.98∗ -0.36 ∗

111 NZL 0.95∗ 0.79∗ -0.36 ∗ 151 VEN 1.02∗ 0.77∗ -0.35112 OMN 1.26∗ 0.53 -0.57 ∗ 152 VNM 0.55∗ 0.77∗ -0.14113 PAK 0.59∗ 0.90∗ -0.49 ∗ 153 VUT 0.78∗ 0.76∗ -0.32 ∗

114 PAN 0.15 0.14 -0.65 ∗ 154 WSM 0.95∗ 0.92∗ -0.67 ∗

115 PER 0.95∗ 0.93∗ -0.36 ∗ 155 ZAF 0.67∗ 0.62∗ -0.38 ∗

116 PHL 0.29∗ 0.30∗ -0.21 ∗ 156 ZAR 0.63∗ 0.21 -0.55 ∗

117 PLW 0.45 -0.89∗ -0.12 157 ZMB 0.88∗ 1.34∗ -0.33 ∗

118 PNG 0.96 0.57 -0.08 158 ZWE 0.24 0.67∗ -0.52 ∗

119 POL 0.93∗ 1.08∗ -0.40 ∗

120 PRI 0.55∗ 0.34∗ 0.01

Note: βLR is obtained by estimating equation (2.28) with data in log-levels. βSR is obtained

by estimating the error-correction model in equation (2.29). κ denotes the estimated speed-of-

adjustment coefficient in the error-correction model. Inference is based on heteroskedasticity and

autocorrelation consistent robust standard errors. Statistical significance at the 5% level or lower is

denoted by ∗.

55

Histogram for beta, LR

Beta

Fre

quen

cy

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

010

2030

40

Histogram for beta, SR

Beta

Fre

quen

cy

−1.0 −0.5 0.0 0.5 1.0 1.5 2.0

010

2030

40

βLR βSR

Figure 2.7: Distribution of country specific coefficient estimates for long-run and short-run.βLR is obtained by estimating equation (2.28) with data in log-levels. βSR is obtained byestimating the error-correction model in equation (2.29).

56

Chapter 3

Essay 3: How Integrated are US Gasoline Markets: An

Empirical Test with Cross-sectional Correlation and

Structural Breaks

3.1 Introduction

Studying commodity prices across regional markets helps determine the extent of spatial

arbitrage and the resulting regional market integration. The degree of integration cross

regional markets produces insight to the effectiveness of policies which target all markets.

For example, when regional markets are well integrated, it implies that a national policy,

such as the Renewable Fuel Standard (RFS) program or the Keystone Pipeline project

will have a similar impact on local prices. Meanwhile, it is also an indication for market

liberalization policy and the market intervention from the government. When regional

markets are spatially integrated with each other, products are efficiently allocated among

markets, suppressing the need for additional government intervention.

Empirical researchers use the law of one price (LOP) to examine the degree of market

integration. The absolute LOP states that a good will sell for the same price across ge-

ographical regions when regional markets are perfectly integrated.1 When the LOP fails,

price changes in one market will not be transmitted on a one-for-one basis to prices in other

geographic markets either instantaneously, or over a number of periods. Thus, regional

prices will tend to diverge from each other in both the short and long run.

Since its deregulation in 1981, the U.S. retail gasoline market has been described as close

to perfectly competitive, suggesting that the LOP may hold. However, many other factors

may prevent the LOP from holding among regional markets. The price of retail gasoline in

a given region is set by the price of crude oil, refinery costs, the cost of transportation and

distribution as well as the cost of selling. Thus, the different structure of each intermediate

industry may affect the spatial relationship between retail gasoline prices over time. For

instance, refineries in different regions use differentiated sources of crude oil. As a result,

changes in the source of crude oil for US refineries (i.e. the decline in the imports from

African) will lead to mixed effects on local regular gasoline prices. Paul et al. (2001) and

1The relative LOP allows for the difference between regional prices in terms of transportation cost andother time invariant factors.

57

Holmes et al. (2013) argued that local gasoline retailers hold some degree of market power

due to factors ranging from the refinery’s purchasing price of crude oil to the demographic

characteristics (Iyer and Seetharaman, 2008; Temple, 1988). Because of these unknown

factors, the degree of spatial market integration for the retail gasoline in the US is unknown

and requires empirical examinations.

The empirical test of the LOP in the market for retail gasoline can be conducted at

different levels. For example, Paul et al. (2001) used data at the Petroleum Administrative

Defense District (PADD) level while Holmes et al. (2013), at the state-level. When state-

level data is used, the price of retail gasoline is influenced by many state-specific factors,

such as regulations on the gasoline content. When state markets are integrated, local

supply shocks may cause not only a price spike in a single state but in all other states as

well. Similarly, the change in federal regulations such as a nation-wide cap on Reid Vapor

Pressure (RVP) of gasoline,2 might influence the price level of gasoline in all states.

To examine the LOP for the gasoline market, some studies use a regression model as,

logPi,t = αi+βi logP ∗t + εi,t. In these studies, testing the LOP is based on hypothesis tests

on the regression coefficients, which examines the presence of an one-to-one relationship

between the regional price and the reference price. Since the price series may contain a

unit root, the test on the coefficient is valid only when the unit root test indicates that the

regression residuals donot have unit roots. To increase the power of the unit root test, panel

methods are used in more recent studies (Dreher and Krieger, 2005; Suvankulov et al., 2012).

However, these studies largely ignore two issues. First, given the fact that regional gasoline

prices are affected by common shocks such as a nation-wide policy change, world-wide

demand decline due to the global recession or a world-wide technological improvement,

the resulting residuals from the model of the LOP test are likely to be cross-sectionally

dependent. Second, the literature also overlooks the presence of structural breaks in the

regression residuals. One potential source of structural breaks in the regression residuals is

the misspecification of the regression model. The regression model used to test for the LOP

in the literature may be misspecified as it ignores changes in the degree of market integration

over time. Structural breaks in the regression residuals will affect the performance of unit

root test (Leybourne et al., 1998; Leybourne and Newbold, 2000; Perron, 1989). Thus,

it will also affect the consequent test on the coefficients. With structural breaks in the

regression residuals, tests of LOP may be misleading.

There are reasons to think that structural breaks in the degree of market integration

may exist. Early papers such as Borenstein et al. (1997), Lewis (2009) and Verlinda (2008)

among others have identified many regional factors that will impact gasoline price dynamics

over time. For instance, it is widely accepted that the rate of change of gasoline prices is

greater when prices are rising than when they are falling (Borenstein et al., 1997; Lewis,

2The policy was implemented in late 1989 and summer 1992, which led to changes in the amount of lightcomponents in gasoline.

58

2011). Thus, it is possible that the degree to which regional gasoline prices are cointegrated

differs in sub-periods. In addition, Lewis (2009) also found that there were long-lasting

geographical differences in retail prices after the supply shock of the Hurricane Rita. In

summary, structural breaks imply that the regression model with constant coefficients —

used to test for the LOP, is misspecified.

In this paper, I examine the degree of market integration across states for retail gasoline

in the US, taking into account two widely neglected issues: cross-sectional dependence and

structural breaks. I demonstrate that the test of the LOP is indeed affected by the issue

of cross-sectional dependence. Therefore, I propose a different panel unit root test to deal

with the resulting size distortion and reduced power discussed in Gengenbach et al. (2010).

In particular, I use a panel unit root test procedure that accounts for structural breaks in a

dependent panel. I first examine whether state-level retail gasoline prices are cointegrated

with the reference price (the national average price level). Then, I test for the LOP by

examining the slope coefficient when the null hypothesis of no cointegration in the first step

is rejected.

This paper is organized as follows: Section 2 discusses the literature that studies the

degree of gasoline market integration where they neglect both common cross-sectional de-

pendence and structural breaks; Section 3 discusses the empirical strategy for studying

the degree of gasoline market integration, with a focus on cross-sectional dependence and

structural breaks; Section 4 discusses the data and results.

3.2 Examination of the Degree of Gasoline Market Integra-

tion

As early as 1980s, there were studies that investigated the spatial relationship between

regional gasoline prices to examine the degree of market integration for gasoline in the US.

Stigler and Sherwin (1985) examined the co-movement of wholesale gasoline prices from

three cities - New Orleans, Chicago, and Detroit - during the period from October 1979

to October 1983. In this paper, they first calculated the correlation between pairs of price

series to quantify the similarity between city-level prices. Because common influences such

as the overall price level or the inflation of the crude oil price, may induce misleadingly

high correlation between individual prices, the authors therefore regressed the gasoline

price in each city on the crude oil price or on a national price level to get rid of these

common effects. Following this, the authors calculated the correlation between residuals

from these regressions for each city. Different from the analysis based on raw prices, these

regressions remove the common effects in the price of city gasoline, leaving behind the

desired price to study the provision of wholesaling services in local market. The authors

claimed that these regression residuals measure the price of wholesaling and are likely to

be equal across relevant geographic markets. As expected, their results show a fairly high

59

correlation between city’s residual series after removing the influence of common influences.

The simple comparison between local prices using correlation may be impaired by unit

roots in the price series. As an alternative to examine the relationship between local prices,

empirical analysis can also test whether these prices are diverging over-time. The co-

movement of local prices over time implies the presence of a long-run equilibrium relation-

ship between prices. From a time series perspective, such relationship between series implies

a cointegrating relationship. Therefore, cointegration techniques can be applied to study

the spatial relationship in gasoline prices. A cointegrating relationship allows testing of the

implication of perfect market integration, the presence of the LOP and the long-run price

parity.

Using two cointegration methods, Paul et al. (2001) studied the long-run price parity

among US retail gasoline markets using data at the Petroleum Administrative Defense

District (PADD) level. To detect the presence of the LOP as a consequence of a high degree

of price competition, they evaluated the price parity during the period between January

1983 and December 1998. They found a cointegrating relationship among PADD level price

series both from the Engle and Granger (1987) two-step method and the Johansen (1988)

rank approach, suggesting a co-movement between PADD-level gasoline prices in the long

run. However as the slope coefficient in the regression of pairs of prices was not equal to

unity, they failed to find the existence of long-run price parity. In other words, according

to their results, perfect market integration does not hold.

The long run price parity implies that relative prices or price differentials are mean-

reverting, or stationary. Therefore, unit root tests on relative prices are used as another

method to examine the LOP. Holmes et al. (2013) focused on the retail gasoline markets

in the US at the state-level. To test for price parity, they applied the Augmented Dickey-

Fuller test (ADF) to test for a unit root in the series of price differentials and calculated

the probability of rejecting of the ADF test in all pairs of state prices. Based on a rejection

rate for ADF tests of more than 95%, they concluded there was a strong support for the

law of one price between state-level markets on the mainland.

To increase the power of unit root tests, methods of panel unit root test were applied

in more recent literature to examine gasoline market integration in other areas. Dreher

and Krieger (2005) suspected the presence of a gasoline price convergence due to the ease

of cross-border purchases of both gasoline and oil products in Europe. They examined

the consequent degree of gasoline market integration using weekly prices of 15 European

countries during January 1994 to May 2004. Using panel unit root test in Maddala and Wu

(1999) and Levin et al. (2002) which include a constant term, Dreher and Krieger (2005)

rejected the null hypothesis of unit roots in a panel of relative price series, suggesting the

presence of a weak form of price parity, i.e., allowing for transportation cost differences.

Moreover, they also tested for the strong version of the LOP by implementing panel unit

root tests without a constant. In this latter case, the null hypothesis of unit roots cannot

60

be rejected.

The drawback of panel unit root tests used in Dreher and Krieger (2005) is discussed

and illustrated in Breitung and Pesaran (2008) and Gengenbach et al. (2010). Breitung and

Pesaran (2008) classified the literature of panel unit root test into two generations. The

first generation tests (for example, Maddala and Wu (1999) and Levin et al. (2002)) assume

that individual series are cross-sectionally independent, while procedures in the second

generation consider individual series to be cross-sectionally correlated with each other. As

a result, the panel data is modeled as a combination of the common component and the

idiosyncratic component. Using Monte Carlo simulations, Gengenbach et al. (2006, 2010)

showed that the dependence across units could cause size distortion and reduced power

in panel unit root tests when overlooked. Hence, if cross-sectional dependence exists in a

panel, the second-generation panel unit test is more desirable.

Accounting for cross-sectional dependence, Suvankulov et al. (2012) studied the LOP

in Canadian retail gasoline markets at the city level from January 2000 to October 2010.

In light of the threshold effect caused by transportation cost on the price differences in

the equilibrium, they tested for unit roots in relative prices using a non-linear panel unit

root test. Since the authors were able to reject the null of unit roots for most cities, they

suggested that the market is well integrated.

Another issue that may affect the test of the LOP and may interact with cross-sectional

dependence is the presence of structural breaks in the series being tested. Similar to the

problem caused by cross-sectional dependence, ignoring structural breaks in a time series

will also have size distortion effects on the unit root test.

To be more specific about the form of structural breaks considered in this paper, here I

assume the data-generating process of an interested series yt as,

yt = dt + ut, (3.1)

ut = αut−1 + vt, (3.2)

with −1 < α ≤ 1, and dt = µ + βt is the trend function of yt. In the trend function,

the intercept µ measures the level of the series, and the slope coefficient β represents the

average growth rate of the series.3 In a time series, the most obvious type of structural

breaks is the structural break in levels (µ) and / or in the growth rate (β). In this paper, I

consider the situation when structural breaks are both in levels and in the growth rate.

Perron (1989) found that the standard Dickey-Fuller (DF) type unit root test cannot

reject the null hypothesis of a unit root if the series tested is a stationary noise component

with a structural break in the slope of the trend function. This occurs because a structural

break in the trend function produces serial correlation properties that are similar to those

of a random walk. On the other hand, Leybourne et al. (1998) and Leybourne and Newbold

3Equivalently, the DGP illustrated in equation (1) and (2) can be rewritten as, yt = αyt−1 + (1−α)µ+αβ + (1 − α)βt+ vt for −1 < α < 1 and yt = yt−1 + β + vt for α = 1.

61

(2000) found that a structural break occurring early (in other words, with small value of

break fraction, τ , where breaking date is defined as (τ ∗ T ) ) in the series will cause an

over-rejection of null hypothesis in standard Dickey-Fuller unit root tests. Such “Converse

Perron Phenomena” happens because the limiting distribution of negative Dickey-Fuller

statistics varies with τ and is not symmetric around the point when τ = 1/2. As a result,

for small τ , the test statistics will take large negative values, leading to frequent rejections

of the null hypothesis. In general, if not taken into account, structural breaks in terms of

parameters in the trend function of a series will lead to misleading conclusions in the unit

root test.

In summary, the test of the LOP in the gasoline market is subject to problems caused

by both cross-sectional dependence and structural breaks. The literature has generally not

devoted much attention to these issues. Regional gasoline prices are likely to be cross-

sectionally correlated due to common shocks such as global economic recessions, or national

technology improvements in the gasoline industry. These unobserved common effects in

regional gasoline prices may result in cross-sectional dependence in the residuals of the

empirical model. Moreover, shocks to individual prices may change the relationship between

prices, affecting the degree of market integration. Failure to consider these changes in the

regression model may result in structural breaks in the regression residuals. To control for

the adverse effect of both cross-sectional dependence and structural breaks on the test of

the LOP, I propose a hybrid method in this paper.

3.3 Empirical Strategy for the Test for the LOP

3.3.1 The Regression Model

Following the literature, I test the LOP based on a regression model of regional prices and

the reference price, represented by

logPi,t = αi + βi logP ∗t + εi,t (3.3)

where logPi,t is the natural logarithmic transformation of price level in region i, and logP ∗t

is the natural logarithmic transformation of the corresponding price level in the reference

region.4 In equation (3.3), the coefficient αi measures the time-invariant difference between

the regional price and the reference price caused by factors such as transportation cost,

tax levels and the commodity’s quality. The coefficient βi measures how the regional price

co-moves with the reference price over time. When regional markets are well integrated, the

LOP holds and there will be a one-to-one relationship between the regional price and the

reference price, i.e., βi = 1. Theoretically, there are two forms of the LOP. The strong form

4Because price series are likely to have exponential growth rate, many existing studies and this paperuse a natural logarithmic transformation of prices in the regression.

62

of the LOP implies that αi = 0 and βi = 1, while the weak form allows αi to be non-zero.

When price series, logPi,t and logP ∗t , contain unit roots, equation (3.3) implies a long-

run equilibrium between logPi,t and logP ∗t when a cointegrating relationship exists. In

the presence of a cointegrating relationship, the LOP can be examined by testing the null

hypothesis of βi = 1.

To investigate the presence of an equilibrium relationship between logPi,t and logP ∗t , I

test for unit roots in a panel of regression residuals, εi,t from equation (3.3). The panel unit

root test on the residuals is subject to the presence of cross-sectional dependence resulting

from common shocks in individual prices. Hence, I consider a factor structure for the

regression residuals εi,t, which is εi,t = γiFt+vit. In such structure, the vector of unobserved

common factors Ft captures the presence of cross-sectional dependence. Meanwhile, the

idiosyncratic component, vit in the factor structure, is cross-sectionally independent. In

the panel of residuals, both Ft and vit may also contain structural breaks. This is because

structural breaks in the intercept and slope coefficients of equation (3.3) may occur; as a

result, the estimated regression model with time-invariant coefficients is misspecified and

structural breaks in the coefficients are left in the regression residuals.

In the case of the US gasoline market, structural breaks in the coefficients of equation

(3.3) are likely given that the degree of gasoline market integration in the US has changed

since the deregulation of gasoline price in the early 1980s. Muehlegger (2006) pointed out

that the US gasoline market became more differentiated because of the introduction of

more stringent and heterogenous federal and state regulations on gasoline content. There

are states that are required to use reformulated gasoline because they failed to meet air

quality standards. As a result, gasoline prices are higher in some states because they are

using gasoline products that have added operating and distribution costs. These regula-

tions lead to more differentiated gasoline products sold in regional markets and reduce the

substitutability of gasoline products between markets. Therefore, they are likely to cause a

change in the degree of market integration across states. Similarly, the closure of refineries,

production disruptions caused by natural disasters and construction of new distribution

systems may lead to permanent structural changes in the gasoline industry and affect the

degree of regional market integration. Yet, the empirical model, equation (3.3), does not

allow for any changes in its coefficients. Neglecting changes in the degree of market integra-

tion in the regression model will consequently result in structural changes in the regression

residuals of equation (3.3), i.e., in both components of the regression residuals εi,t.

The interactive effects from both unit roots and structural breaks on the regression

residuals will adversely affect the LOP test. In Table 3.1, I list four possible results for the

LOP test with both unit roots and structural breaks. Specifically, structural breaks in the

residuals indicate that the LOP regression model as equation (3.3) is misspecified. There-

fore, the LOP implied by this equation does not hold. On the other hand, the presence of

unit roots in the residuals suggests that price series do not have a cointegrating relation-

63

Table 3.1: Possible Results for the LOP Test

In the Residuals With Unit Root Without Unit Root

Structural Breaks LOP fails; Prices are not cointegrating LOP fails; Model is mis-specified

No Breaks LOP fails; Prices are not cointegrating Continue to test coefficients

ship. As a result, the test on the coefficient is invalid. To continue the test of LOP on the

regression coefficient, it requires that both unit roots and structural breaks are absent from

regression residuals.

In sum, the test for unit roots in εi,t is subject to the size distortion and reduced power

caused by both cross-sectional dependence and structural breaks. To deal with these issues,

I propose a hybrid method which combines some advanced unit root tests.

3.3.2 A Hybrid Unit Root Test

To test for unit roots in a panel with cross-sectional dependence and structural breaks,

I follow the second generation panel unit root test produce. I test for unit roots in the

common and the idiosyncratic components separately. The panel is I(0) when unit root

tests on both components reject the null hypothesis of unit roots.

More specifically, as Figure 3.1 illustrates, I first estimate equation (3.3) for each individ-

ual unit separately by OLS and saving the residuals as a panel. Then, I test for the presence

of cross-sectional dependence in the residuals through the CD test in Pesaran (2004) and

through estimating the number of common factors following Bai and Ng (2002). If the null

hypothesis of cross-sectional independence is rejected and the number of common factors

estimated is ≥ 1, I then use principal component analysis (PCA) to separate the common

and the idiosyncratic components in the panel.

I use the procedure of Bai and Carrion-i Silvestre (2009) to test for unit roots in the

idiosyncratic component. As shown in the Appendix, this method eliminates the common

component in the panel by the PCA and focuses solely on the idiosyncratic component.

For the idiosyncratic component, the unknown dates of structural breaks in each series

is estimated from the data and controlled by dummies. With individual-specific dates of

structural breaks in the idiosyncratic component, the method constructs individual modified

Sargan-Bhargava (MSB) statistics that are shown to be cross-sectionally independent. Later

on two panel test statistics are calculated using individual statistics or p values. Since this

method only tests for the unit root in the idiosyncratic component, it overlooks the unit

root in the common component.

The estimated common factors are independent from each other as a result of PCA.

64

T-­‐test  on  coefficients:  

Test  for  the  LOP  in  US  Gasoline  Market  Empirical  Strategy  

!

H0 :" i = 0#i =1

$ % &

Cross-­‐sec/onal  independence  test  of  residuals  

Reject  

Obtain  common  and  idiosyncra/c  components  by  Principal  Component  Analysis  

Not  reject   First  genera/on  panel  unit  root  test  with  considera/on  of  breaks  

Structural  break  test  on  each  factor,  Perron  and  Yabu  (2009)                              (                      No  break    )  

No  break  

Unit  root  test  on  each  factor,  Augmented  Dickey-­‐Fuller  (1976)                

Break  Common  

!

H0 :

Es/mate  

!

logPit = " i + #i logP t +$ it

Idiosyncra/c  Component  

Es/mate  break  points  

Unit  root  test  on  the  idiosyncra/c  component  

No    

Factors  

Reject  

break  

Break  Not  reject  

The  LOP  is  rejected  

Reject  

Not  reject  

Unit  root  test  on  the  idiosyncra/c  component  

Unit  root  test  on  each  factor,  Carrion-­‐I  Silvestre(2009)  

Panel  unit  root  test,  Bai  and  Carrion-­‐I  Silvestre  (2009)  

Save  residuals  

Figure 3.1: Flow chart for empirical strategy of panel unit root test

65

Next, to test for a unit root in the common component, I use univariate unit root tests and

test for a unit root in each of the estimated common factors separately. Prior to conducting

the unit root test, I test for the null hypothesis of no structural breaks in each factor

following Perron and Yabu (2009).5 Because the univariate test method offered in Carrion-i

Silvestre et al. (2009) will have serious size distortions when the series tested does not have

a structural break in the parameters of the trend function, I use the conventional ADF test

when the null hypothesis of no structural breaks cannot be rejected.

The presence of LOP based on equation (3.3) must satisfy two conditions sequentially:

first, there is a cointegrating relationship between prices, i.e., regression residuals do not

have unit roots; second, the β coefficient must be time-invariant and equal to one. When

the null hypothesis of unit root cannot be not rejected for the residuals, no cointegration

is found, implying that prices are diverging from each other in the long run. In contrast,

when unit root tests in both the common and the idiosyncratic components reject the

null hypothesis of unit roots, I conclude that a cointegrating relationship is supported by

equation (3.3) with estimated coefficients. Furthermore, if no structural break is found

in neither the common nor the idiosyncratic components, I continue to examine the LOP

by testing βi = 1. Otherwise, if a structural break is found in either component of the

regression residuals, it suggests that equation (3.3) is misspecified and the LOP does not

hold.

3.4 Data and Results

In this paper, I use data on monthly prices of regular gasoline sales to end users (measured

in dollars per gallon, excluding taxes) for all 50 states in the US.6 The data are available

from the Energy Information Administration (EIA), assembled by the survey form EIA-

782B. To calculate the gasoline price of a particular state, the Form EIA-782B is sent to

a scientifically selected sample of motor gasoline retailers. All sampled firms provide the

volume-weighted average pre-tax price of their sales during a particular month from all

their points of sale within a state. Therefore, the price of gasoline of a particular grade is

equal to the monthly revenue obtained from the sales of that gasoline grade divided by the

corresponding monthly volume. The reported state price is a weighted average of reports

of all the sampled firms.

Although data is available as early as January 1983, all regions have missing values

between July 1987 to December 1988. In addition, the survey was suspended by EIA in

5As explained in the appendix, the rejection of the null indicates that the relevant series contains atleast one structure break.

6Regular gasoline is defined as gasoline having an antiknock index (average of the research octane ratingand the motor octane number) greater than or equal to 85 and less than 88, and it is the most commontype of gasoline used. Moreover, the sales to end users is defined as: Sales made directly to the consumer ofthe product, including bulk consumers, such as agriculture, industry, and utilities, as well as residential andcommercial consumers. For more information, please refer to: http://www.eia.gov/dnav/pet/TblDefs/

pet_pri_allmg_tbldef2.asp

66

2011 due to the FY2011 funding level provided. Because of these reasons, my dataset ranges

from January 1989 to February 2011, which yields a total of 266 time observations for each

state.7 Following O’Connell and Wei (2002) and Suvankulov et al. (2012), the average price

level, log Pt, is chosen as the reference price.

Before estimating the empirical model of the LOP test, I first conduct some pre-tests

for the panel of individual gasoline prices. First, accounting for global shocks, I test for

the presence of cross-sectional dependence in the panel of state-level gasoline prices. The

rejection of the null hypothesis in the CD test suggests that individual log-transformed

gasoline prices are cross-sectionally dependent. As a result, I use panel unit root tests in

the second generation. In particular, the CRMA test of Sul (2009) is used to test for a unit

root in the common components of the panel and the CIPS test of Pesaran (2007) is for

unit root test in the idiosyncratic component. From Table 3.2, results indicate the panel of

logarithmic price is integrated of degree one.

Table 3.2: Tests for Individual Variables

Levels DifferenceslogP ∆ logP

CD 565.88∗ 485.75∗

CRMA -0.65 -6.97∗

CIPS(6) -18.43∗ -34.19∗

Note: Pesaran’s (2004) cross-sectional independence test (CD) follows a standard normal distribu-

tion. The 5 % critical value for Pesaran’s (2007) panel unit root test (CIPS) is -2.06. The lag

length for the CIPS test is set to T 1/3 = 6. The 5% critical value for Sul’s (2009) unit root test for

the cross-sectional means (CRMA) is -1.88. The lag length for the CRMA test is determined by

the Bayesian Information Criterion with maximum 6 lags. Statistical significance at the 5% level or

lower is denoted by ∗.

3.4.1 Main Results

Next, I investigate the LOP by taking into account both cross-sectional dependence and

structural breaks. As a preliminary examination for the presence of structural breaks, I

first test the null hypothesis of no structural breaks for each logarithmic price following the

procedure of Perron and Yabu (2009). Following the method described in the appendix

section D.1, I obtain an estimation for the location of the major structural break in each

price, which is illustrated in the plots of Figure 3.2. In Figure 3.2, I plot logarithmic state

gasoline prices over time. Because states in the West Coast region are shown to have a

7Despite the effort to obtain a balanced panel of data, few sporadic missing values remained: Arkansas(2008 m9, 2009 m8, 2009 m9, 2009 m10); Idaho (2010 m7); Montana (1996 m9, 1999 m4, 2001 m10, 2002m1, 2002 m4); North Dakota (1999 m4); New Jersey (2007 m1); Nevada (1997 m3, 1998 m6, 1998 m12,1999 m4); Oklahoma (1999 m7); Washington (2010 m2). These missing values were proxied using linearlyinterpolated values.

67

different estimated date of structural break than the rest of states, I plot the series in this

area separately.

The upper plot includes gasoline prices for all states except states in the West Coast

region8 and the vertical line is the estimated date of break9 for most states in this area.

The lower plot contains gasoline prices of states in the West Coast region. The dashed

series in black is the gasoline price for Alaska and the solid line in black is the gasoline

price for Hawaii. Vertical lines are estimated structural break dates, where the former one

is for the state of Alaska and the other is for most of other states in West Coast region.

From both plots, there are some features that should be noticed. First of all, there is co-

movement across states, illustrated by the thick parts in both plots. The common trends in

individual gasoline prices is likely to result in the presence of cross-sectional dependence in

the regression residuals of equation (3.3). Secondly, as Table 3.4 shows, the null hypothesis

of no structural break in state gasoline prices is rejected for most states, which may lead to

the presence of structural breaks in the relationship between gasoline prices, measured by

the coefficients of equation (3.3).10

Given the presence of cross-sectional dependence and structural breaks in state-level

gasoline prices, I begin testing for the LOP by first running regressions of state gasoline

prices on the reference price with a constant as equation (3.3). As mentioned before, state

gasoline prices can differ because of transportation cost, quality and etc, and these (time-

constant) differences are captured by the constant term αi in the regression.

Common shocks in individual prices may cause cross-sectional dependence in the re-

gression residuals of equation (3.3). Meanwhile, the presence of structural breaks in the

price variables may indicate structural changes in the intercept and slope coefficients, and

thus lead to structural breaks in the residuals of equation (3.3). Therefore, to deal with

both cross-sectional dependence and structural breaks in the regression residuals, I use the

hybrid unit root test method discussed in Section 3. Unlike the unit root test used in the

literature which overlooks both issues in the residuals, the hybrid method is able to correct

for adverse effects on the unit root test.

Table 3.5 and 3.6 summarize the residual diagnostic test for the panel of OLS residuals.

Particularly, Table 3.5 illustrates the preliminary test for the presence of structural break

in each residual series, while Table 3.6 summaries the result of testing the presence of

structural breaks in the common component and the result of unit root tests. As shown

in the first part of Table 3.6, the null hypothesis of cross-sectional independence in the

panel of residuals can be rejected according to the Pesaran’s (2004) CD test. Moreover,

the estimated number of common factors is five.11 With regard to structural breaks in

8See Table 3.3 for the information of states.9Details about the estimated dates of break for each state is reported in Table 3.4.

10Specifically, for most states in regions except the West Coast, the break date is at the time whenT = 127, corresponding to July, 1999. While the time of break is T = 183, which is March, 2004, for moststates in the West Coast, and it is T = 110, or February, 1998 for Alaska.

11These common factors may be due to some regional shocks that cannot be controlled by the national

68

−1.

0−

0.5

0.0

0.5

1.0

1.5

Individual Logarithm Price

States in East−Coast, Midwest, Gulf−Coast, Rocky−Mountain RegionsT

dolla

rs p

er g

allo

n in

loga

ritm

1989M1 1991M1 1993M1 1995M1 1997M1 1999M1 2001M1 2003M1 2005M1 2007M1 2009M1 2011M1

−1.

0−

0.5

0.0

0.5

1.0

1.5

Individual Logarithm Price

States in West−Coast RegionsT

dolla

rs p

er g

allo

n in

loga

ritm

1989M1 1991M1 1993M1 1995M1 1997M1 1999M1 2001M1 2003M1 2005M1 2007M1 2009M1 2011M1

Figure 3.2: Individual state-level gasoline prices and Break date (vertical line)

69

Table 3.3: Reference Table for StatesID State ID State

1 Connecticut 26 Nebraska2 Maine 27 North Dakota3 Massachusetts 28 Ohio4 New Hampshire 29 Oklahoma5 RhodeIsland 30 South Dakota6 Vermont 31 Tennessee7 Delaware 32 Wisconsin8 Maryland 33 Alabama9 New Jersey 34 Arkansas10 NewYork 35 Louisiana11 Pennsylvania 36 Mississippi12 Florida 37 New Mexico13 Georgia 38 Texas14 North Carolina 39 Colorado15 South Carolina 40 Idaho16 Virginia 41 Montana17 West Virginia 42 Utah18 Illinois 43 Wyoming19 Indiana 44 Alaska20 Iowa 45 Arizona21 Kansas 46 California22 Kentucky 47 Hawaii23 Michigan 48 Nevada24 Minnesota 49 Oregon25 Missouri 50 WashingtonNote: States 1 -17 belong to PADD-I, East Coast; States 18-32 belong to PADD-II, Mid-west; States 33 - 38 belong to PADD-III, Gulf Coast; States 39 - 43 belong to PADD-IV,Rocky Mountain; States 44 - 50 belong to PADD-V, West Coast.

70

Tab

le3.

4:T

est

for

bre

akin

ind

ivid

ual

log

(pri

ce)

IDB

reak

test

Bre

ak

dat

eB

reak

frac

tion

IDB

reak

test

Bre

akd

ate

Bre

akfr

acti

on1

8.47∗

Ju

l-99

127

2610

.36∗

Ju

l-99

127

25.7

7∗

Ju

l-99

127

277.

85∗

Dec

-97

108

35.

65∗

Ju

l-99

127

2810

.78∗

Ju

n-9

912

64

10.8

7∗

Ju

l-99

127

296.

14∗

Ju

l-99

127

57.6

8∗

Ju

l-99

127

308.

48∗

Ju

l-99

127

610

.63∗

Ju

l-99

127

3113

.17∗

Ju

l-99

127

712

.23∗

Ju

l-99

127

328.

92∗

Ju

l-99

127

812

.07∗

Ju

l-99

127

3313

.74∗

Ju

l-99

127

911.

48∗

Au

g-99

128

3418

.57∗

Ju

l-99

127

107.

96∗

Ju

l-99

127

3512

.97∗

Ju

l-99

127

117.

84∗

Ju

l-99

127

3613

.00∗

Au

g-99

128

1213.

25∗

Ju

l-99

127

378.

40∗

Mar

-04

183

1315.

35∗

Ju

l-99

127

389.

95∗

Ju

l-99

127

1419.

32∗

Ju

l-99

127

3913

.82∗

Mar

-04

183

1514.

46∗

Ju

l-99

127

4016

.05∗

Feb

-04

182

16

15.0

2∗

Ju

l-99

127

4112

.34∗

Mar

-14

183

1712.

08∗

Ju

l-99

127

4216

.99∗

Feb

-04

182

18

9.92∗

Ju

l-99

127

4314

.44∗

Mar

-14

183

1911.

42∗

Ju

l-99

127

448.

09∗

Feb

-98

110

20

7.01∗

Ju

l-99

127

456.

56∗

Feb

-03

170

21

7.32∗

Ju

l-99

127

469.

15∗

Mar

-99

123

2213.

92∗

Ju

l-99

127

4710

.48∗

Ap

r-04

184

239.

87∗

Ju

l-99

127

4810

.72∗

Feb

-04

182

24

8.07∗

Ju

l-99

127

4910

.87∗

Mar

-14

183

258.

92∗

Ju

l-99

127

5011

.56∗

Mar

-14

183

Note

:M

od

el-3

of

Per

ron

and

Yab

u(2

009)

isco

nsi

der

ed,

i.e.

,si

mult

aneo

us

bre

akb

oth

inth

ein

terc

ept

and

inth

esl

ope.∗

ind

icat

esth

enu

llhyp

oth

esis

of

no

stru

ctu

ral

bre

ak

isre

ject

edat

5%si

gnifi

cant

leve

l.

71

the residuals, results from Table 3.5 first indicate that the null of no structural break is

rejected for a majority of residual series. Therefore, during the panel unit root test, I use

the method of Bai and Carrion-i Silvestre (2009) to test for unit roots in the idiosyncratic

component and the univariate unit root test of Carrion-i Silvestre et al. (2009) for unit root

in the common component, respectively. Given Ttotal = 266 in the sample, I allow for an

arbitrary three structural breaks in the unit root test.

As explained in the appendix, the univariate unit root test of Carrion-i Silvestre et al.

(2009) requires a pre-test for the presence of structural breaks. Therefore, before unit root

test for the common component, I test for the null of no structural breaks following Perron

and Yabu (2009). The middle part of Table 3.6 suggests that for most estimated common

factors, I am able to reject the null of no break at the 5% significance level. As a result, I

use the univariate unit root test from Carrion-i Silvestre et al. (2009) to test for unit root in

each estimated common factors except the forth common factor, for which I use the ADF

test. Results from the last column of the middle part and the lower part report that the null

hypothesis of a unit root in the panel of regression residuals is not rejected due to the unit

root in one out of five common factors. In sum, following the hybrid unit root test, residuals

are not stationary because of the presence of both unit root and structural breaks in the

common factors. The unit root test on the residuals implies that there is no time-invariant

cointegrating relationship between state gasoline prices and the reference national average

price, suggesting that the regression model is misspecified and the test for the regression

coefficient is invalid.

One possible explanation for the absence of a time-invariant cointegration relationship

between the state-level price and the national average in the panel may be due to the

inclusion of prices for the state of Hawaii and Alaska. Both states are not geographically

contiguous with any other state on the mainland in the US. Therefore, the response of

gasoline price to common shocks in both states may require a longer period because some

inter-state transmission of gasoline products may not be available for them or because

the determinants of prices in both states may be different from states on the mainland.12

Excluding both states, the conclusion does not change. As Table 3.7 suggests, the null

hypothesis of unit root in the panel of residuals still cannot be rejected due to non-stationary

common factors. Thus, even for the contiguous 48 states on the mainland, individual

prices do not cointegrate with the national average price level with a constant cointegrating

vector.13

price level or may be caused by the structural breaks in the degree of market integration which are commonand left in the residuals.

12For instance, the price of gasoline in Hawaii may be different for many reasons: Hawaii is a very smallmarket that cannot easily import or export refined gasoline. In addition, the refining industry in Hawaii haslow cracking capacity, low desulfurization capacity and is undersized.

13This conclusion is in sharp contrast to the conclusion of Holmes et al. (2013) who could not reject thenull hypothesis of the presence of the LOP for state gasoline markets in the US with the same dataset.

72

Tab

le3.

5:T

est

for

bre

akin

ind

ivid

ual

OL

Sre

sid

ual

s

IDB

reak

test

Bre

ak

dat

eB

reak

frac

tion

IDB

reak

test

Bre

akd

ate

Bre

akfr

acti

on1

4.9

2∗

Au

g-99

128

261.

90S

ep-9

469

210.

56∗

Mar

-92

3927

10.0

7∗

Mar

-99

123

33.

45∗

Sep

-94

6928

11.6∗

Jan

-98

109

49.6

5∗

Mar-

92

3929

23.9

4∗

Dec

-95

845

5.8

5∗

Au

g-99

128

301.

44Ju

l-96

916

18.

10∗

Ju

l-99

127

315.

94∗

Dec

-01

156

71.

43S

ep-9

469

328.

30∗

Mar

-01

147

89.

46∗

Oct

-94

7033

12.2

6∗

Jan

-94

619

0.58

Sep

-06

213

346.

99∗

Sep

-99

129

102.7

9M

ar-

92

3935

19.8

8∗S

ep-0

520

111

2.5

3M

ar-

92

3936

7.42∗

Sep

-94

6912

10.8

7∗

Mar-

0215

937

1.55

Mar

-05

195

13

9.98∗

Sep

-98

117

385.

01∗

Feb

-02

158

14

8.53∗

Au

g-93

5639

8.26∗

Mar

-92

3915

6.2

2∗

Ju

l-99

127

406.

66∗

Nov

-99

131

16

5.54∗

Oct

-94

7041

2.66

Nov

-98

119

17

15.

57∗

Ju

l-97

103

422.

53D

ec-9

913

218

11.

40∗

Nov

-02

167

431.

68A

pr-

9240

19

2.25

Dec

-99

132

447.

37∗

Mar

-99

123

203.3

8∗

Mar-

94

6345

5.92∗

Mar

-92

3921

5.1

5∗

Jan

-00

133

463.

27∗

Oct

-98

118

223.3

5∗

Feb

-99

122

473.

44∗

Mar

-99

123

2313

.23∗

Oct

-99

130

4812

.70∗

Oct

-96

9424

5.2

4∗

Oct

-02

166

491.

08N

ov-9

913

125

5.8

8∗

Nov

-99

131

508.

67∗

Oct

-99

130

Note

:M

od

el-3

of

Per

ron

and

Yab

u(2

009)

isco

nsi

der

ed,

i.e.

,si

mult

aneo

us

bre

akb

oth

inth

ein

terc

ept

and

inth

esl

ope.∗

ind

icat

esth

enu

llhyp

oth

esis

of

no

stru

ctu

ral

bre

ak

isre

ject

edat

5%si

gnifi

cant

leve

l.

73

Table 3.6: Diagnostic tests for OLS residuals

Presence of Common Factors (CF)

Statistics Conclusion

CD 11.16∗ dependentNo. of CF 5

Test for Structural Break and Unit Root in CF

Factors Break Test Break Date (T ) Unit Root Test Unit Root?

CF1 5.49∗ May-00, Feb-06, Oct-08 (137, 206, 238) 8.91 YesCF2 8.98∗ Mar-99. Jun-01, Mar-04 (123, 150, 183) 5.57∗ NoCF3 3.49∗ Aug-94, Oct-98, Nov-01 (68, 118, 155) 4.07∗ NoCF4 2.52 — -4.64∗ NoCF5 5.41∗ Feb-98, Apr-01, Sep-03 (110, 148, 177) 3.42∗ No

Test for Unit Root in Idiosyncratic

Z statistics P statistics Pm statistics Unit root?

-5.25∗ 509.94∗ 28.98∗ No

Note: The null hypothesis of CD test is cross-sectional independent. The 5% critical valuefor break test (Exp −WFS) is 3.12 for model with simultaneous break in both interceptand slope. The number of structural breaks in unit root test is 3. The estimated fractionsof structural breaks are reported in the parenthesis in the third column of the middle part.Unit root test is based on the value of MPGLST (For Factor 4, I report the ADF statistics).For unit root test in idiosyncratic component, the number of structural breaks is 3 andstatistics are illustrated in Appendix equation D.25, D.26, and D.27 specifically.

74

Table 3.7: Diagnostic tests for OLS residuals, excluding Hawaii and Alaska

Presence of Common Factors (CF)

Statistics Conclusion

CD 19.06∗ dependentNo. of CF 4

Test for Structural Break and Unit Root in CF

Factors Break Test Break Date (T ) Unit Root Test Unit Root?

CF1 3.49∗ May-00, Feb-06, Oct-08 (137, 206, 238) 8.84 YesCF2 9.69∗ Dec-91, Aug-94, Mar-99 (36, 68, 123) 4.99∗ NoCF3 1.84 — -6.43∗ NoCF4 8.29∗ Mar-00, Apr-03, Sep-05(135, 172, 201) 3.37∗ No

Test for Unit Root in Idiosyncratic

Z statistics P statistics Pm statistics Unit root?

-5.14∗ 535.21∗ 31.69∗ No

Note: The null hypothesis of CD test is cross-sectional independent. The 5% critical valuefor break test (Exp −WFS) is 3.12 for model with simultaneous break in both interceptand slope. The number of structural breaks in unit root test is 3. The estimated fractionsof structural breaks are reported in the parenthesis in the third column of the middle part.Unit root test is based on the value of MPGLST (For Factor 3, I report the ADF statistics).For unit root test in idiosyncratic component, the number of structural breaks is 3 andstatistics are illustrated in Appendix equation D.25, D.26, and D.27 specifically.

75

3.4.2 Test of the LOP based on Relative Prices

The LOP implies that relative price series, logPi,t/ log Pt, is mean-reverting, or I(0). There-

fore, the LOP can also be examined by testing for unit roots in relative price series. Since

relative price series implicitly assume a fixed value of the coefficients (βi = 1) in equation

(3.3), it ignores the change in the degree of market integration. Moreover, unobserved com-

mon factors in individual price series will also lead to cross-sectionally dependent relative

price series. As a result, the test of the LOP based on relative price series is likely to be

affected by both cross-sectional dependence and structural breaks.

Table 3.8 presents the preliminary test for the structural break in each relative price

series. As suggested, the null hypothesis of no structural break is rejected for most states.

In addition, I construct a panel of relative price series and test for the presence of cross-

sectional dependence and structural breaks in both components of the panel. Results are

reported in Table 3.9. As previously, I allow for three structural breaks in the unit root

test.

Based on results in Table 3.9, I reject the null hypothesis of cross-sectional independence

in the CD test and estimate five common factors for the panel of relative price series. In

addition, I find rejections of the null of no structural break for three common factors.

Finally, based on the unit root test of both components, I find that the panel of relative

price series contains a common unit root. As in the previous section where I examine the

situation when excluding the state of Hawaii and Alaska, I also construct a panel of 48

states on the mainland and repeat the same empirical analysis. I report relevant results in

Table 3.10. The same conclusion for all 50 states that the panel of relative price series is

I(1) also holds when excluding Hawaii and Alaska.

In Table 3.11, I list the dates of structural break that are reported in both tests of the

LOP regression residuals and the relative prices. The dates of structural breaks estimated

from common factors coincide with some vital shocks to the petroleum industry in the US.

For example, March 1999 and May 2000 are indicated as two dates of structural break.

During this period, there were major mergers in the petroleum industry in the US. The

merger of petroleum company is likely to change the production and distribution of gasoline.

Thus, it is possible that it will also change the degree of state market integration. Moreover,

the common break date at February 2006 may be due to the effects hurricane Katrina

and Rita in the the September of 2005. Both disrupted the production of oil in the Gulf

Coast. Finally, the global recession in 2008-2009 seems also affected the structure of gasoline

industry in the US, through the possible channels such as the closure of refineries or the

modifications to the distribution system.

As reviewed in Section 2, many studies on the degree of gasoline market integration

are based on unit root tests of relative prices, ignoring the critical issues of cross-sectional

dependence and structural breaks. According to results in Table 3.8, 3.9 and 3.10, it is

likely that these studies are subject to size distortion and reduced power problems in the

76

Tab

le3.

8:T

est

for

bre

akin

ind

ivid

ual

log

rela

tive

pri

ce(p

rice

)

IDB

reak

test

Bre

ak

dat

eB

reak

frac

tion

IDB

reak

test

Bre

akd

ate

Bre

akfr

acti

on1

6.2

1∗

Au

g-99

128

262.

44D

ec-9

913

22

4.11∗

Mar

-92

3927

2.96

Mar

-99

123

34.

00∗

Au

g-99

128

289.

29∗

Jan

-98

109

45.

73∗

Mar

-92

3929

23.2

9∗

Oct

-93

585

6.80∗

Au

g-99

128

301.

42A

ug-

9692

612

.27∗

Mar

-92

3931

10.2

3∗

Au

g-99

128

72.

16S

ep-9

469

325.

42∗

Mar

-01

147

89.

31∗

Oct

-94

7033

12.8

2∗

Oct

-93

589

0.48

Oct

-99

130

3413

.61∗

Au

g-99

128

104.6

2∗

Mar-

92

3935

20.2

4∗

Dec

-03

180

114.0

0∗

Oct

-97

106

368.

47∗

Sep

-94

6912

19.4

7∗

Mar-

0215

937

1.44

Mar

-92

3913

18.

59∗

Ju

n-9

912

638

5.35∗

Feb

-02

158

14

13.

87∗

Au

g-99

128

3916

.64∗

Mar

-92

3915

15.0

6∗

Ju

l-99

127

4010

.31∗

Nov

-99

131

16

8.92∗

Oct

-94

7041

6.24∗

Nov

-98

119

17

22.

84∗

Ju

l-97

103

422.

94D

ec-9

913

218

6.94∗

Nov

-02

167

4312

.11∗

Nov

-99

131

19

1.51

Dec

-99

132

446.

96∗

Mar

-99

123

204.2

7∗

Mar-

94

6345

7.20∗

Ap

r-92

4021

7.5

6∗

Jan

-00

133

462.

61O

ct-9

811

822

8.3

2∗

Ju

n-9

242

474.

82∗

Mar

-99

123

2314

.25∗

Oct

-99

130

4815

.74∗

Au

g-96

9224

10.8

2∗

Oct

-02

166

491.

95O

ct-9

913

025

5.8

0∗

Nov

-99

131

5010

.14∗

Oct

-99

130

Note

:M

od

el-3

of

Per

ron

and

Yab

u(2

009)

isco

nsi

der

ed,

i.e.

,si

mult

aneo

us

bre

akb

oth

inth

ein

terc

ept

and

inth

esl

ope.∗

ind

icat

esth

enu

llhyp

oth

esis

of

no

bre

akis

reje

cted

at5%

sign

ifica

nt

leve

l.

77

Table 3.9: Diagnostic tests for relative price level

Presence of Common Factors (CF)

Statistics ConclusionCD 10.44∗ dependentNo. of CF 5

Test for Structural Break in CF

Factors Break Test Break Date (T ) Unit Root Test Unit Root?CF1 9.59∗ May-00, Feb-06, Oct-08 (137, 206, 238) 9.11 YesCF2 10.49∗ Mar-99, Jun-01, Mar-04 (123, 150, 183) 5.46∗ NoCF3 3.04 — -3.06∗ NoCF4 0.96 — -7.68∗ NoCF5 7.61∗ Feb-98, Sep-03, Apr-07 (110, 177, 220) 3.47∗ No

Test for Unit Root in Idiosyncratic

Z statistics P statistics Pm statistics Unit root?

-5.08∗ 355.42∗ 18.06∗ No

Note: The null hypothesis of CD test is cross-sectional independent. The 5% critical valuefor break test (Exp −WFS) is 3.12 for model with simultaneous break in both interceptand slope. The number of structural breaks in unit root test is 3. The estimated fractionsof structural breaks are reported in the parenthesis in the third column of the middle part.Unit root test is based on the value of MPGLST (For Factor 3 and 4, I report the ADFstatistics). For unit root test in idiosyncratic component, the number of structural breaksis 3 and statistics are illustrated in Appendix equation D.25, D.26, and D.27 specifically.

78

unit root test. Therefore, their conclusions about the LOP are questionable.

3.5 Conclusion

In this paper, I study the degree of retail gasoline market integration in the US taking into

account two important issues neglected in the literature: cross-sectional dependence and

structural breaks. To deal with adverse effects from both issues, I come up with a hybrid

panel unit root test by combining methods that are recently developed. Using this hybrid

method, I find that previous conclusions about perfect market integration or the LOP in

the US gasoline market may be due to the failure of considering these issues.

More specifically, I show that cross-sectional dependence and structural breaks are

present in the panel regression residuals of an empirical model and in the panel of rela-

tive price series. As a result, the test of the LOP is adversely affected if adhering to the

conventional method in the literature. I use a hybrid unit root test procedure to test for

unit roots in a dependent panel while at the same time accounting for structural breaks.

In contrast to previous literature that found a cointegrating relationship between gasoline

prices, I cannot reject the null of no cointegration.

My results also have implications for energy policy: results here suggest that state

gasoline markets are not spatially integrated. Therefore a nation-wide policy change such

as the Renewable Fuel Standard (RFS) program or the Keystone Pipeline project may not

affect all state gasoline prices with the same magnitude. Moreover, state gasoline prices used

in this paper do not contain tax at any level. Therefore, it is more likely that state-gasoline

prices with tax also diverge as the tax level varies a lot across states.

As mentioned earlier, the regression model used to test for the LOP may be misspecified

when there are changes in the degree of gasoline market integration. In this paper, I focus

on the test of a constant LOP and do not explicitly model these changes. Therefore, they

are left as structural changes in the regression residuals. Given the empirical findings in

this paper and the feature of the gasoline market in the US, a natural extension of this

paper is to model the structural break in the coefficient of regression model explicitly and

examine the LOP with the modified model.

Finally, the performance of the proposed hybrid panel unit root test may be better

evaluated with the help of some Monte Carlo simulations. With small sample size, the

estimated date of structural breaks may be biased, and reduced power and size distortion

may exist in the hybrid test method. Therefore, the results of structural break dates and

the conclusion of the absence of a cointegrating relationship should be used with cautions.

79

Table 3.10: Diagnostic tests for relative price level, excluding Hawaii and Alaska

Presence of Common Factors (CF)

Statistics ConclusionCD 19.44∗ dependentNo. of CF 5

Test for Structural Break in CF

Factors Break Test Break Date (T ) Unit Root Test Unit Root?CF1 8.24∗ May-00, Feb-06, Oct-08 (137, 206, 238) 9.08 YesCF2 13.23∗ Mar-99, Jun-01, Mar-04 (123, 150, 183) 5.60∗ NoCF3 1.54 — -6.04∗ NoCF4 12.06∗ Dec-98, Sep-03, Sep-08 (120, 177, 237 ) 3.39∗ NoCF5 5.48∗ Nov-91, Feb-94, Jun-01(35, 62, 150) 3.11∗ No

Test for Unit Root in Idiosyncratic

Z statistics P statistics Pm statistics Unit root?

-5.08∗ 355.42∗ 18.06∗ No

Note: The null hypothesis of CD test is cross-sectional independent. The 5% critical valuefor break test (Exp −WFS) is 3.12 for model with simultaneous break in both interceptand slope. The number of structural breaks in unit root test is 3. The estimated fractionsof structural breaks are reported in the parenthesis in the third column of the middle part.Unit root test is based on the value of MPGLST (For Factor 3, I report the ADF statistics).For unit root test in idiosyncratic component, the number of structural breaks is 3 andstatistics are illustrated in Appendix equation D.25, D.26, and D.27 specifically.

80

Table 3.11: Estimated Dates of Break in Common FactorsBreak date OLS residuals Relative prices OLS residuals Relative prices

(50) (50) (48) (48)

(Year-Month)1999-03 X X X XPotential Explanation Major mergers in the petroleum industry:

BP and Amoco in 1998; Exxon and Mobil in 1999

2000-05 X X X XPotential Explanation Major mergers in the petroleum industry:

BP/Amoco and Arco in 2000

2004-03 X X XPotential Explanation Nine million acres of Alaska’s National Petroleum Reserve opened

for long-term production

2006-02 X X X XPotential Explanation Hurricane Katrina &Rita in 2005 Aug-Sep

2008-10 X X X XPotential Explanation Worldwide recession

81

Chapter A

Appendix: Tables

A.1 Additional Tables for Essay 1

Table A.1: State Code and Regional CPI

States Regional Consumer Price Index

AK Anchorage, AK (MSA)AL SouthAR SouthAZ WestCA Los Angeles-Riverside-Orange County, CA (CMSA)CO Denver-Boulder-Greeley, CO (CMSA)CT New York-Northern New Jersey-Long Island, NY-NJ-CT-PA (CMSA)FL Miami-Fort Lauderdale, FL (CMSA)GA Atlanta, GA (MSA)IA MidwestID WestIL Chicago-Gary-Kenosha, IL-IN-WI (CMSA)IN Chicago-Gary-Kenosha, IL-IN-WI (CMSA)KS Kansas City, MO-KS (MSA)KY Cincinnati-Hamilton, OH-KY-IN (CMSA)LA SouthMA Boston-Brockton-Nashua, MA-NH-ME-CT (MSA)MD Philadelphia-Wilmington-Atlantic City, PA-NJ-DE-MD (CMSA)ME Boston-Brockton-Nashua, MA-NH-ME-CT (MSA)MI Detroit-Ann Arbor-Flint, MI (CMSA)MN Minneapolis-St. Paul, MN-WI (MSA)MO Kansas City, MO-KS (MSA)MS SouthMT West

82

Table A.2: State Code and Regional CPI, continued

States Regional Consumer Price Index

NC SouthND MidwestNE MidwestNH Boston-Brockton-Nashua, MA-NH-ME-CT (MSA)NJ New York-Northern New Jersey-Long Island, NY-NJ-CT-PA (CMSA)NM WestNV WestNY New York-Northern New Jersey-Long Island, NY-NJ-CT-PA (CMSA)OH Cleveland-Akron, OH (CMSA)OK SouthOR Portland-Salem, OR-WA (CMSA)PA New York-Northern New Jersey-Long Island, NY-NJ-CT-PA (CMSA)RI NortheastSC SouthSD MidwestTN SouthTX Dallas-Fort Worth, TXUT WestVA Washington-Baltimore, DC-MD-VA-WV(CMSA)VT NortheastWA Seattle-Tacoma-Bremerton, WA (CMSA)WI Chicago-Gary-Kenosha, IL-IN-WI (CMSA)WV Washington-Baltimore, DC-MD-VA-WV(CMSA)WY West

83

A.2 Additional Tables for Essay 2

Table A.3: Sub-Sample Country GroupGroup Name Country List

High Income Australia, Austria, Bahamas, Bahrain, Barbados, Belgium, Bermuda, Brunei, Canada,Cyprus, Denmark, Equatorial Guinea, Finland, France, Germany, Greece,Hong Kong, Hungary, Iceland, Ireland, Israel, Italy, Japan, Republic of Korea,Luxembourg, Macao, Malta, Netherlands, New Zealand, Norway, Oman, Poland,Portugal, Puerto Rico, Singapore, Spain, St. Kitts & Nevis, Sweden, Switzerland,Trinidad &Tobago, United Kingdom, United States

UpperMid Income Algeria, Angola, Antigua & Barbuda, Argentina, Botswana, Brazil, Bulgaria,Chile, China, Colombia, Costa Rica, Cuba, Dominica, Dominican Republic,Ecuador, Gabon, Grenada, Iran, Jamaica, Jordan, Lebanon, Malaysia, Maldives,Mauritius, Mexico, Namibia, Palau, Panama, Peru, Romania, Seychelles,South Africa, St. Lucia, St.Vincent & Grenadines, Suriname, Thailand, Tunisia,Turkey, Uruguay, Venezuela

LowerMid Income Albania, Belize, Bhutan, Bolivia, Cameroon, Cape Verde, Republic of Congo,Cote d‘Ivoire, Djibouti, Egypt, El Salvador, Fiji, Ghana, Guatemala, Guyana,Honduras, India, Indonesia, Iraq, Kiribati, Lesotho, Marshall Islands,Fed. Sts. Micronesia, Mongolia, Morocco, Nicaragua, Nigeria, Pakistan,Papua New Guinea, Paraguay, Philippines, Samoa, Sao Tome & Principe,Senegal, Solomon Islands, Sri Lanka, Sudan, Swaziland, Tonga, Vanuatu,Vietnam, Zambia

Low Income Afghanistan, Bangladesh, Benin, Burkina Faso, Burundi, Cambodia,Central African Republic, Chad, Comoros, Dem. Rep. Congo, Ethiopia, Gambia,The, Guinea, Guinea-Bissau, Haiti, Kenya, Liberia, Madagascar, Malawi, Mali,Mauritania, Mozambique, Nepal, Niger, Rwanda, Sierra Leone, Somalia, Tanzania,Togo, Uganda, Zimbabwe

Note: Sub-sample are grouped according to World Bank Country Groups and based on dataavailability of the whole sample.

84

Table A.4: Sub-Sample Country Group, continuedGroup Name List of Countries

OECD-AH Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece,Iceland, Ireland, Italy, Japan, Luxembourg, Netherlands, New Zealand,Norway, Portugal, Spain, Sweden, Switzerland, United Kingdom, United States

OECD Australia, Austria, Belgium, Canada, Chile, Denmark, Finland, France, Germany,Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Republic of Korea, Luxembourg,Mexico, Netherlands, New Zealand, Norway, Poland, Portugal, Spain, Sweden,Switzerland, Turkey, United Kingdom, United States

Non-OECD All rest countries in the sample except OECD countries

Developed Australia, Austria, Belgium, Canada, Cyprus, Denmark, Finland, France, Germany,Greece, Hungary, Israel, Ireland, Italy, Japan, Luxembourg, Malta, Netherlands,New Zealand, Norway, Poland, Portugal, Romania, Spain, Sweden, Switzerland,United Kingdom, United States

Developing Algeria, Angola, Argentina, Bahrain, Bangladesh, Barbados, Benin, Bermuda,Bolivia, Botswana, Brazil, Burkina Faso, Burundi, Cameroon, Cape Verde,Central African Republic, Chad, Chile, China, Colombia, Comoros,Dem. Rep. Congo, Republic of Congo, Costa Rica, Cote d‘Ivoire, Cuba, Djibouti,Dominican Republic, Ecuador, Egypt, El Salvador, Equatorial Guinea, Ethiopia,Gabon, The Gambia, Ghana, Guatemala, Guinea, Guinea-Bissau, Guyana, Haiti,Honduras, Hong Kong, India, Indonesia, Iran, Iraq, Israel, Jamaica, Jordan, Kenya,Republic of Korea, Lebanon, Lesotho, Liberia, Madagascar, Malawi, Malaysia, Mali,Mauritania, Mauritius, Mexico, Morocco, Mozambique, Namibia, Nepal, Nicaragua,Niger, Nigeria, Oman, Pakistan, Panama, Papua New Guinea, Paraguay, Peru,Philippines, Rwanda, Sao Tome and Principe, Senegal, Sierra Leone, Singapore,Somalia, South Africa, Sri Lanka, Sudan, Taiwan, Tanzania, Thailand, Togo,Trinidad & Tobago, Tunisia, Turkey, Uganda, Uruguay, Venezuela, Vietnam,Zambia, Zimbabwe

EU Austria, Belgium, Bulgaria, Cyprus, Denmark, Finland, France, Germany,Greece, Hungary, Ireland, Italy, Luxembourg, Malta, Netherlands, Poland,Portugal, Romania, Spain, Sweden, United Kingdom

Note: Sub-sample are grouped according to World Bank Country Groups and based on dataavailability of the whole sample.

85

Chapter B

Appendix: Figures

B.1 Additional Figures for Essay 1

Histogram for income elasticity

Beta for income

Fre

quen

cy

−2 −1 0 1 2 3 4

05

1015

β1i

Figure B.1: Distribution of individual coefficient estimates.

The regression equation is log V ISit = αi + β1i log(

YitCPIit

∗ 100)

+ β2i log(PAIRitCPIit

∗ 100)

+

β3i log(PRMtCPIit

∗ 100)

+ uit.

86

Histogram for price elasticity of airfare

Beta for airfare

Fre

quen

cy

−1.0 −0.5 0.0 0.5

02

46

810

12

β2i

Figure B.2: Distribution of individual coefficient estimates.

The regression equation is log V ISit = αi + β1i log(

YitCPIit

∗ 100)

+ β2i log(PAIRitCPIit

∗ 100)

+

β3i log(PRMtCPIit

∗ 100)

+ uit.

87

Histogram for price elasticity of room rate

Beta for room_rate

Fre

quen

cy

−5 0 5

05

1015

β3i

Figure B.3: Distribution of individual coefficient estimates.

The regression equation is log V ISit = αi + β1i log(

YitCPIit

∗ 100)

+ β2i log(PAIRitCPIit

∗ 100)

+

β3i log(PRMtCPIit

∗ 100)

+ uit.

88

Chapter C

Appendix for Essay 2

C.1 The Comparison Between the Pooled Estimator and the

Mean Group Estimator

Coakley et al. (2001) explored the small sample properties of a mean group and two pooled

panel estimators of a regression coefficient under homogeneous and heterogenous coefficients

designs. For a static linear regression of a panel,

yit = αi + βixit + uit, (C.1)

three estimators are compared: the pooled OLS (POLS) estimator, the fixed effects (FE)

or ’within’ estimator, and the mean group (MG) estimator.

First, under the design of homogeneous coefficient βi, all three estimators are shown to

be unbiased by Monte Carlo simulations. In contrast, when βi is allowed to vary randomly

across groups, with E(βi) = β, it is shown in the simulations that the two pooled estimators

are likely to be biased when the regressor xit is correlated with βi.

In particular, under the assumption of heterogenous βi, the POLS and FE estimator

actually estimates

yit = αi + βxit + uit, (C.2)

with uit = βixit−βxit+uit. In such regression, the component (βi−β)xit is in the error term

and will introduce dependence between the estimated coefficient and the regressor. This is

because the fixed effect estimator βFE can be written as a weighted average of individual

estimates,

βFE =N∑i=1

(Si∑Ni=1 Si

)βi =N∑i=1

wiβi (C.3)

As a result, when the weight, defined as Si∑Ni=1 Si

, is positively correlated with βi, the βFE

is biased upward and vice visa.

89

With heterogenous βi, the mean group estimator,

βMG = N−1N∑i=1

βi (C.4)

coincides with βFE when Si = S or the weights wi are independent of βi. Otherwise, the

difference between the mean group estimator and the FE estimator exists when both N and

T go to infinity. The attraction of the mean group estimator is that since the individual

estimates tend to show extreme heterogeneity, averaging may produce better estimates.

This would be the case when the heterogeneity is the product of country-specific shocks

which happen to be correlated with the regressors but which cancel out when averaged

across countries.

90

Chapter D

Appendix for Essay 3

In this section, I provide details about three tests used in this paper. They are: the test

for the presence of structural break of Perron and Yabu (2009), the univariate test for a

unit root of Carrion-i Silvestre et al. (2009) and the panel test for unit roots of Bai and

Carrion-i Silvestre (2009).

D.1 Univariate Test for the Presence of Structural Breaks in

the Time Series

Perron and Yabu (2009) propose a Wald test for the null hypothesis of no structural breaks

in a univariate time series without knowing whether the relevant series is I(0) or I(1).

Specifically, the test is based on an assumed DGP of the series as,

yt = x′tΨ + ut, (D.1)

ut = αut−1 + et, with − 1 < α ≤ 1 (D.2)

where xt is a (r × 1) vector of deterministic components and Ψ is a (r × 1) vector of

unknown parameters. The null hypothesis is no structural break: RΨ = γ, with R is a

(q×r) full-rank matrix and γ is a (q×1) vector with q restrictions. Therefore, the rejection

of the null suggests that there is, at least, a structural break. In this paper, three types of

the break are considered (assuming the alternative is a single structure break):

Model-1 (Structural change in the intercept of a series or level shift):

xt = (1, DUt, t)′ and Ψ = (µ0, µ1, β0)′, where DUt = 1 for t > T1.

The hypothesis of interests is µ1 = 0.

Model-2 (Structural change in the slope or in the time trend):

xt = (1, t,DTt)′ and Ψ = (µ0, β0, , β1)′, where DTt = (t− T1) for t > T1.

The hypothesis of interests is β1 = 0.

Model-3 (Simultaneous structural changes both in the intercept and in the slope):

xt = (1, DUt, t,DTt)′ and Ψ = (µ0, µ1, β0, , β1)′.

The hypothesis of interests is µ1 = β1 = 0.

91

To test the null hypothesis of no structural break, the Wald statistics for testing the

restriction of parameters is obtained via feasible GLS estimation. The GLS estimation of

the parameters is obtained by applying OLS to the regression as,

(1− αL)yt = (1− αL)x′tΨ + (1− αL)ut, (D.3)

for t= 2, ....T and together with

y1 = x′1Ψ + u1. (D.4)

for t = 1. Under the case of unknown structural breaks, the estimation of the break date

is obtained by minimizing the sum of squared residuals from a regression of the relevant

series on a constant, a time trend, a level-shift dummy and a slope-shift dummy. The value

of α is obtained by a bias-corrected estimates, denoted as αM . When T12 |αM − 1| > 1,

αM = (

T∑t=2

utut−1/

T∑t=2

u2t−1) + C(τ)σα (D.5)

and otherwise αM = 1. In the above equation, C(τ) is calculated following equation (7) in

Perron and Yabu (2009) and σα is the standard deviation of the OLS estimate of α, which

is (∑T

t=2 utut−1/∑T

t=2 u2t−1). The Wald statistic for testing the null hypothesis is defined

as,

WFS(λ1) = [R(Ψ − Ψ)]′[s2R(X′X)−1R′]−1[R(Ψ − Ψ)] (D.6)

where X = (1− αML)xt for t = 2, ...T , and = x1 for t = 1 and s2 = T−1∑T

t=1 e2t .

The statistics defined in equation (9) assumes the prior knowledge of the date of struc-

tural break. To account for the unknown break date, an exponential functional form of the

Wald statistics is modified as,

Exp−WFS = log

[T−1

∑Λ

exp(1

2WFS(λ′1))

](D.7)

where Λ = ε ≤ λ′1 ≤ 1− ε for some ε > 0 and λ′1 denotes the generic break date. In this

paper, the value of the parameter ε is set to be 0.01.

D.2 Univariate Test for a Unit Root with Structural Breaks

Early unit root tests dealing with structural breaks did not model the breaks in the null

hypothesis. This means that, under the null hypothesis, a level shift in the series is modeled

as it comes from the tail of the distribution of the DGP, and a slope change is taken as

errors with a different mean in sub-samples (Kim and Perron, 2009). As argued by Carrion-i

92

Silvestre et al. (2009), Kim and Perron (2009) and many others, since a structural break will

happen regardless of the unit root in the series, unit root test which assume an unknown

date of structural break occurring only under the alternative hypothesis of stationarity are

undesirable for two reasons. First of all, these tests impose an asymmetric treatment when

allowing for a structural break. As a result, these tests are shown to be not invariant to the

structural break when the DGP of the series has a unit root and a structural break. Secondly,

early unit root tests do not exploit the information from the presence of a structural break

in the series, and are shown to have small power.

To avoid disadvantages of early unit root tests and to improve the power of tests, Kim

and Perron (2009) propose a new procedure for unit root test which allows for a structural

break under both hypothesis. And Carrion-i Silvestre et al. (2009) extend their method

to allow for an arbitrary number of structural breaks and to the use of the quasi-GLS de-

trending method to obtain better local asymptotic power for a variety of tests. In the paper

of Carrion-i Silvestre et al. (2009), the series yt is assumed to be generated by the following

DGP,

yt = dt + ut, (D.8)

ut = αut−1 + vt, (D.9)

and the deterministic component dt is given by

dt = z′tΨ. (D.10)

Under the situation of m structural breaks, zt = [z′t(T00 ), ..., z′t(T

0m)] and Ψ = (Ψ′0, ...,Ψ

′m),

with the first terms as deterministic components and corresponding coefficients: zt(T00 ) =

(1, t)′ and Ψ0 = (µ0, β0)′.

In this paper, three types of breaks are considered:

Model-1, break in the intercept only.

dt = µ0 + β0t+ µjDUt(T0j ), for 1 ≤ j ≤ m.

Model-2, break in the time trend only.

dt = µ0 + β0t+ βjDTt(T0j ), for 1 ≤ j ≤ m.

Model-3, simultaneous break in both the intercept and the time trend.

dt = µ0 + β0t+ µjDUt(T0j ) + βjDTt(T

0j ), for 1 ≤ j ≤ m.

Here, DUt(T0j ) = 1 and DTt(T

0j ) = (t − T 0

j ) for t > T 0j , and 0 otherwise and the T 0

j

denote actual break dates from the DGP. In this paper, the unknown fraction of structural

break, λ = Tj/T , is estimated from a global minimization of the sum of squared residuals

(SSR) of the GLS-detrended model discussed below, over all possible break fractions, i.e.,

λ = argminS(α, λ).

93

The feasible point optimal statistics, PGLST = {S(α, T 0) − αS(1, T 0)}/s2(T 0),1 to test

the null hypothesis of a unit root, α = 1 against the alternative hypothesis α = α < 1, is

constructed from quasi-GLS de-trending variables defined as yα1 = y1, zα1 = z1 and

yαt = (1− αL)yt, (D.11)

zαt (T 0) = (1− αL)zt(T0), (D.12)

α = 1 + c/T (D.13)

and the choice of c follows Elliott et al. (1996), which decides the alternative hypothesis as

α = 1 + c/T .

To overcome the size distortion of PGLST for the case with negative MA coefficients and

to account for the presence of multiple structural breaks, a new test statistics, MPGLST =

[c2T−2∑T

t=1 y2t−1 + (1 − c)T−1y2

T ]/s2(T 0), is considered in this paper. Carrion-i Silvestre

et al. (2009) shows that the limiting distribution of both PGLST and MPGLST under estimated

dates of structural break are the same as in the case of known dates of break. Moreover,

the simulation shows that the size of both tests is close to the normal size and the power

quickly approaches to the limit value suggested.

Yet, results from simulations also indicate that both statistics will exhibit size distortion

when the true DGP of the series tested has no structural break. This is because when

no structural break occurs, the estimate of the break fraction has a non-degenerate limit

distribution on the interval [0, 1] instead of converging to either 0 or 1 under the null

hypothesis and the asymptotic results derived under the case with structural break do not

hold. To deal with this issue, the authors suggests that a pre-test for the presence of

structural breaks following Perron and Yabu (2009) can help. They argue that If there is

no break in the trend function, the proper unit root test procedure is to simply apply a

standard Dickey and Fuller (1979) type test.

D.3 Panel Test for Unit Roots with Structural Breaks and

Common Factors

To test for unit roots in the idiosyncratic disturbance terms of a panel, taking in to ac-

count common trends and structural breaks in individual deterministic components, Bai and

Carrion-i Silvestre (2009) propose a modified Sargan-Bhargava test. In the panel dataset,

1Where S(α, T 0) is the minimum of function: S∗(Ψ, α, T 0) =∑Tt=1(yαt − Ψ′zαt (T 0)). And s2(T 0) is the

estimate of the spectral density at frequency zero of vt.

94

the DGP for each series Yi,t is assumed as:

Yi,t = Di,t + F ′tπi + ei,t, (D.14)

(1− L)Ft = C(L)ut, (D.15)

(1− ρiL)ei,t = Hi(L)εi,t (D.16)

with Di,t = µi +∑li

j=1 θi,jDUi,j,t, and DUi,j,t = 1 for t > T ij for model 1(level shifts),

and Di,t = µi + βit +∑li

j=1 θi,jDUi,j,t +∑mi

k=1 γi,kDTi,k,t, and DUj,t = 1 for t > T ia,k and

DTk,t = (t− Tb,k) for t > T ib,k for model 2 (level and slope changes).

The null hypothesis, ρi = 1, suggests a unit root in the idiosyncratic component of the

individual series with allowance for structural breaks. In the above set-up, common factors,

Ft, capture the co-movement of individual series as well as cross-sectional correlation. To

estimate unobserved factors and idiosyncratic components consistently, procedures from Bai

and Ng (2004) are applied to differenced data. Differencing equation (17), the model for

level shifts becomes,

∆Yi,t = ∆F ′tπi + ∆e∗i,t, (D.17)

∆e∗i,t = ∆ei,t +

li∑j=1

θi,jI(T ij ) (D.18)

With I(T ij ) being impulses, obtained by differencing the mean breaks DUi,j,t. To be more

compact, equation for differenced model can be rewritten as:

yi = fπi + zi (D.19)

Where yi = ∆Yi = (∆Yi,2,∆Yi,3, ...,∆Yi,T )′, and f = ∆F = (∆F2,∆F3, ...,∆FT )′, and

zi = ∆e∗i = (∆e∗i,2,∆e∗i,3, ...,∆e

∗i,T )′.

On the other hand, the model for both level slope changes becomes,

∆Yi,t = ∆F ′tπi + βi +

mi∑k=1

γi,kDUi,k,t + ∆e∗i,t, (D.20)

∆e∗i,t = ∆ei,t +

li∑j=1

θi,jI(T ij ) (D.21)

And in a matrix format, it becomes,

yi = fπi + aiδi + zi (D.22)

Where yi, f and zi are defined earlier, and δi = (βi, γi,1, ..., γ′i,mi

) and ai = (ai,2, ..., ai,T )′

with ai,t = (1, DUi,t, ..., DUi,mi,t)′.

95

Because the principal components method provides consistent estimates for f, πi, zi as

in Bai and Ng (2004), the panel unit root test is based on independent series of idiosyncratic

components computed as,

ei,t =t∑

s=2

zi,s (D.23)

The Modified Sargan-Bhargava (MSB) test statistics for each individual i is constructed as,

MSBi =T−2

∑Tt=1 e

2i,t−1

σ2i

(D.24)

Where σ2i is a consistent estimator of the long-run variance of ei,t − ρiei,t−1.

The authors show that with level shifts, the limiting distribution for individual statistics

is invariant to structural breaks and argue that there is no need to estimate dates of level

shifting.2 With slope changes, the method first estimates the dates of structural breaks

for each individual unit equation-by-equation. Then the vector of common factors and

coefficients in the equation (25) are obtained following an iteration procedure.

Constructed following equation (27), individual MSB statistics are shown to be cross-

sectionally independent. To increase the power of unit root test, the authors provide two

approaches to construct statistics for panel test. The first statistics of panel test calculates

the average of individual statistics

Z =√NMSB − ξ

ζ→ N(0, 1) (D.25)

Where MSB = N−1∑N

i=1MSBi, ξ = N−1∑N

i=1 ξi, ζ = N−1∑N

i=1 ζi, with ξi and ζi denote

the mean and the variance of individual MSB statistics respectively, given by ξi = 12 and

ζ2i = 1

3 . The second approach pools individual p-values from MSBi.

P = −2N∑i=1

lnpi → χ22N (D.26)

or for large panels,

Pm =−2∑N

i=1 lnpi − 2N√4N

→ N(0, 1) (D.27)

Based on Monte Carlo simulation, Bai and Carrion-i Silvestre (2009) shows that all statistics

have non-trivial power when the autoregressive parameter is close to the null hypothesis,

and P and Pm statistics have empirical size close to the nominal level.

2However, the estimation of structural breaks might help to improve finite sample property.

96

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