Copyright

by

Christy Spivey

2006

The Dissertation Committee for Christy Spivey

certifies that this is the approved version of the following dissertation:

Marriage, Career, and the City:

Three Essays in Applied Microeconomics

Committee:

________________________________ Daniel Hamermesh, Supervisor

________________________________ Stephen Trejo, Supervisor

________________________________ Paul Wilson

________________________________ Gerald Oettinger

________________________________ Michael Oden

Marriage, Career, and the City:

Three Essays in Applied Microeconomics

by

Christy Spivey, B.S., M.S.

Dissertation

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

The University of Texas at Austin

May 2006

Dedication

To my parents,

who always encouraged me and were always proud of me.

v

Acknowledgements

I would like to thank my co-supervisors, Daniel Hamermesh and Stephen Trejo,

who provided invaluable suggestions and guidance throughout the dissertation process. I

am grateful for the numerous helpful comments offered by Paul Wilson and Gerald

Oettinger on various drafts of these essays. I would also like to thank Michael Oden for

serving on my dissertation committee. Steve McClaskie at the Ohio State Center for

Human Resource Research has been invaluable in guiding me through many data issues.

Daniel Slesnick provided advice and encouragement early in my graduate career, when it

was most needed. Last, but not least, I would like to thank my future husband, Andrew

Habas, for reading many drafts of my essays and actually being interested in Economics.

vi

Marriage, Career, and the City:

Three Essays in Applied Microeconomics

Publication No._____________

Christy Spivey, Ph.D.

The University of Texas at Austin, 2006

Supervisors: Daniel Hamermesh and Stephen Trejo

This dissertation is comprised if three essays in Applied Microeconomics. The

first essay examines the effect of an individual’s risk aversion on time to marriage. The

financial risk aversion measure is based on a series of hypothetical gambles over family

income that were offered to respondents of the National Longitudinal Survey of Youth

1979. The estimates support a theoretic model of search, indicating that more risk averse

respondents marry sooner than their more risk loving counterparts. In addition, the effect

of risk aversion on time to marriage is larger in magnitude and more statistically

significant for men. One possible explanation for the different results between the sexes

is that women value risk aversion as a desirable trait in potential mates.

The second essay explores how nonemployment spells and career expectations

affect wages. Wages are affected by total nonemployment time, by recent work

interruptions, and by some past interruptions. Interruptions affect women’s wages further

vii

into the future compared to men, but the wage loss associated with any given interruption

is less severe for women. One potential reason for the gender differences is that men are

more likely to take time off from working for reasons that are negatively related to their

productivity. Future career interruptions, which workers presumably anticipate in many

cases, affect current investment in human capital to some degree for both sexes. A very

small fraction of the gender wage gap is attributable solely to timing of experience.

The third essay examines the current viability of the basic predictions of the

Mills-Muth monocentric model of city structure. One previous study uses a cross-section

of cities to test the comparative statics predictions, namely that city area is increasing in

population and income but decreasing in agricultural land value and commuting costs.

While it finds support for the predictions, the data used are from 1970, and there has been

a growing consensus that the monocentric model is no longer useful. Despite the

increasing polycentricity of cities, there is evidence that the Mills-Muth comparative

statics predictions hold for modern cities. Also, densely populated cities are more likely

to have subcenters.

viii

Table of Contents

List of Tables ...........................................................................................................x

List of Figures ....................................................................................................... xii

Chapter 1: Introduction ...........................................................................................1

Chapter 2: Desperation or Desire? The Role of Risk Aversion in Marriage ..........4 2.1 Introduction...............................................................................................4 2.2 Literature Review......................................................................................6

Determinants of Risk Aversion..............................................................8 Risk Aversion and Behavior ..................................................................9

2.3 Theoretical Model...................................................................................11 2.4 Data and Empirical Specification ...........................................................16

Risk Measure .......................................................................................17 Empirical Specification........................................................................22

2.5 Results....................................................................................................25 Supply-Side or Demand-Side Behavior? .............................................29

2.6 Conclusion .............................................................................................31

Chapter 3: Time Off at What Price? The Effects of Career Interruptions on Earnings.......................................................................................................................33 3.1 Introduction.............................................................................................33 3.2 Literature Review....................................................................................35

Cross-Sectional Studies .......................................................................36 Panel Data Studies ...............................................................................37

3.3 Data and Empirical Specification ...........................................................40 3.4 Results.....................................................................................................45

An Application of the Work History Model: Wage Gaps and Employment Expectations................................................................................52

The Role of Career Expectations .........................................................55 3.5 Conclusion ..............................................................................................58

ix

Chapter 4: The Mills-Muth Model of Urban Spatial Structure: Surviving the Test of Time? ............................................................................................................60 4.1 Introduction.............................................................................................60 4.2 Implications and a Test of the Mills-Muth Model ..................................62 4.3 Data .........................................................................................................65 4.4 Empirical Model and Results..................................................................67 4.5 Conclusion ..............................................................................................75

Chapter 5: Conclusion...........................................................................................77

Table and Figures...................................................................................................81

Appendix A: Chapter 2 ..........................................................................................99 A.1 Proof That Risk Aversion is Decreasing in Reservation Quality..........99 A.2 Change in Risk Category .....................................................................100 A.3 Survival Analysis to Explore Possible Endogeneity of Risk Aversion and

Timing of Marriage............................................................................101

Appendix B: Chapter 3 ........................................................................................103 B.1 Wage Change Equations for Women..................................................103 B.2 The Earnings Gap Between Mothers and Non-Mothers ......................104

Appendix C: Chapter 4 ........................................................................................105 C.1 Brueckner and Fansler Results............................................................105 C.2 Census Definitions ...............................................................................107 C.3 Additional Maximum Likelihood Results............................................109

Bibliography ........................................................................................................113

Vita . .....................................................................................................................117

x

List of Tables

Table 2.1 Distribution of Risk Aversion in 1993 by Characteristics.....................81

Table 2.2 Distribution of Risk Aversion by Age at First Marriage .......................82

Table 2.3 Survival Analysis of Time to First Marriage for Whole Sample Using 1993

Risk Measure ....................................................................................83

Table 2.4 Survival Analysis of Time to First Marriage for Siblings Using 1993 Risk

Measure.............................................................................................85

Table 2.5 Survival Analysis of Time to First Marriage by Gender Using 1993 Risk

Measure.............................................................................................86

Table 2.6 Spousal Characteristics of Married Respondents by Risk Attitude.......87

Table 3.1 Percentage of Respondents Who Work More Than X% of the Time after

the Start of Their Career, by Gender and Schooling Level in 1994 .88

Table 3.2 Fixed Effects Estimates Using Continuous Experience Measures ........89

Table 3.3 Fixed Effects Estimates Using Alternative Experience Measures.........91

Table 3.4 Ratios of Estimated Wages ....................................................................93

Table 3.5 Decomposition of the Gender Wage Gap..............................................94

Table 3.6 Fixed Effects Estimates Using Expectation Measures ..........................95

Table 4.1 Basic Descriptive Statistics....................................................................96

Table 4.2 Results Using Fraction of Households Owning at Least One Car as

Commuting Cost Proxy ....................................................................97

Table 4.3 Results Using Congestion Cost as Commuting Cost Proxy ..................98

Table A.1 Change in Risk Category ....................................................................100

Table A.2 Survival Analysis of Time to First Marriage for Marriages Occurring After

1993.................................................................................................101

xi

Table A.3 Survival Analysis of Time to First Marriage Using 2002 Risk Measure..

.........................................................................................................102

Table B.1 First and Last Wage Change Equations for Women...........................103

Table B.2 Decomposition of the Wage Gap Between Mothers and Non-Mothers….

.........................................................................................................104

Table C.1 Brueckner and Fansler Maximum Likelihood Estimates....................105

Table C.2 Brueckner and Fansler Linear Estimates.............................................105

Table C.3 Brueckner and Fansler Elasticities From Linear Equations................106

Table C.4 Results Using Fraction of Workers Using Public Transport as Commuting

Cost Proxy.......................................................................................109

Table C.5 Results Using Average Travel Time to Work as Commuting Cost Proxy

.........................................................................................................110

Table C.6 Results Using Travel Time Index as Commuting Cost Proxy ............111

Table C.7 Results Using Daily Vehicle Miles of Travel Per Freeway Lane Mile as

Commuting Cost Proxy ..................................................................112

xii

List of Figures

Figure 2.1 Cox Proportional Hazard Functions .....................................................84

Figure 3.1 Predicted Wage-Experience Profiles....................................................92

1

Chapter 1: Introduction

This dissertation is composed of three essays that essentially examine the causes

and outcomes of individuals' decisions, whether they are family formation decisions,

career decisions, or location decisions. Two essays examine the gender differences in the

causes and outcomes of these decisions, and the last one examines how these decisions

collectively amount to market forces that result in an organized urban structure.

The first chapter considers one potential cause of marriage. It uses a panel data

set that follows individuals for over twenty years to determine if an individual’s attitudes

about risk can affect the timing of entry into first marriage. Risk averse individuals may

be likely to marry sooner because they are unwilling to wait and see if a better potential

mate will come along. Using a financial risk aversion measure that is based on a series of

hypothetical gambles over family income, this chapter demonstrates, in accordance with

a theory of marital search, that individuals who are more risk averse marry sooner. It also

demonstrates that the impact of risk attitudes on marriage is larger for men, which brings

up some interesting gender differences. A potential explanation, supported by the data, is

that women view risk aversion as a desirable trait in men. Marriage offers the risk averse

another benefit: risk pooling. Perhaps women value this aspect of marriage more than

men.

The second chapter examines the wage outcomes of deciding to take a substantial

amount of time off from working. Using the same panel data set as the previous chapter,

it illustrates that, in agreement with previous studies, current wages are affected by the

2

total time an individual has spent away from work. It also shows that, when total time

spent away from work is segmented into recent and past spells, wages are impacted by

recent work interruptions as well as by some past interruptions. In terms of gender

differences, the effect of a career interruption impacts wages further into the future for

women, but men are penalized more for taking time off from work at a given point in

time. A large portion of the gender differences can likely be traced to the reason for

taking time off from work. Women are more likely to do so for family reasons, whereas

men’s time off is more likely due to reasons that are negatively related to their

productivity. Women may also face more discrimination by employers. Future career

interruptions, which workers presumably anticipate in many cases, affect current

investment in human capital to some degree for both sexes. A very small fraction of the

gender wage gap is attributable solely to timing of experience.

The third chapter investigates how individuals’ decisions about where to live and

work accumulate to support the predictions of a simple model of urban spatial structure.

More specifically, it questions whether the classic Mills-Muth model of a monocentric

city is still viable given the changing nature of cities. Household and firm location

decisions depend upon one another, and many workers do not commute to the center of

the city as the polycentric nature of urban areas increases. Despite these changes, this

chapter finds fairly good support for the model’s basic comparative statics predictions,

namely that city area is increasing in population and income but decreasing in

agricultural land value and commuting costs. Another finding is that densely populated

cities are more likely to have subcenters.

3

What follows is a detailed investigation of the aforementioned topics. Each

chapter will empirically test the predictions of the relevant theoretical model and provide

interpretations of the results in the context of the existing literature.

4

Chapter 2: Desperation or Desire? The Role of Risk Aversion in Marriage

2.1 INTRODUCTION

Attitudes toward risk are an important determinant of a vast array of decisions,

including marriage and divorce, choice of education, and choice of career. However,

most empirical studies implicitly assume identical risk preferences across households.

Such a strategy undoubtedly results in appreciably different predicted behavior than does

one that permits risk preferences to vary. Unfortunately, few datasets allow for

construction of a measure of interpersonal variation in risk that is based on economic

theory. As a result, few empirical studies explicitly investigate the impact of risk

preference on behavior, and none employ an empirical measure of risk aversion to

investigate the relationship between risk preferences and marriage.

This paper uses information on risk preferences from the 1979 National

Longitudinal Survey of Youth (NLSY79) and survival analysis to predict how

interpersonal variation in these preferences affects the time to marriage in the context of a

search model. Thus, one main contribution of this paper is to add to the literature on how

risk attitudes affect behavior. While other studies do employ a similar measure of risk

aversion, most of these studies ask what demographic variables affect risk aversion. A

few ask how these measures affect behaviors like the propensity to smoke or invest in

5

risky assets. These studies are, however, cross-sectional, and do not employ survival

analysis as does this paper.

Another contribution of this paper is to expand our understanding of what

motivates individuals to marry. Many of the usual suspects (e.g., love, desires for

emotional support and to have children, as well as financial incentives and economies of

scale that marriage provides) are difficult to measure. In empirical studies, researchers

can control for observable characteristics, such as age and education, some of which

probably serve as proxies for unobservable characteristics. Risk aversion directly affects

the timing of marriage decision due to the uncertainty that is inherent in the process of

searching for a mate, yet no previous studies use an empirical measure of risk aversion to

study marital history.

I borrow a search model from the employment literature and show that, due to the

uncertainty of the process, the more risk averse marry sooner. Risk preference variables

are constructed from a series of hypothetical gambles over lifetime income that were

offered to respondents in the NLSY79. I examine how the risk preference variables

affect the hazard rate into marriage and present estimates that support the theoretical

predictions. I also exploit sibling data from the NLSY79 to examine the robustness of the

empirical results by controlling for unobserved family effects that might be correlated

with risk attitudes and find qualitatively similar results. In addition, I find that risk

preferences affect the timing of marriage differentially for the sexes, with a larger and

more statistically significant effect of risk preferences on the hazard rate into marriage for

men. One possible explanation for this finding is that women value risk aversion as a

desirable characteristic in a spouse. This explanation is supported by other empirical

6

evidence. Specifically, spouse quality, in terms of education and other measurable traits,

is lower for more risk averse men than for more risk loving men. This finding is in

accordance with a prediction of the search model: the reservation “price” is decreasing in

risk aversion. On the other hand, spouse quality of more risk averse women is not

consistently lower than for more risk loving women, suggesting that more than a

woman’s own risk aversion affects her decision to marry. Overall, the results suggest

that risk preferences have some causal influence on the timing of marriage, whether it is

from a supply-side standpoint in the case of the basic search model or from a demand-

side standpoint, where risk aversion is a desirable trait.

The remainder of the paper is organized as follows. The next section discusses

the related literature and the types of risk measures typically used by economists. Section

3 presents the theoretical model, while Section 4 discusses the data and descriptive

statistics. Section 5 presents and discusses the empirical findings. Finally, the last

section contains concluding remarks.

2.2 LITERATURE REVIEW

Various approaches have been taken in the literature to construct empirical

measures of risk aversion that vary across individuals. The two main methods used to

calculate measures based on economic theory (an Arrow-Pratt measure) are (i) evaluating

the actual behavior of individuals; and (ii) asking them hypothetical questions with

specific scenarios. For both methods, the argument of the utility function has varied

(consumption and asset allocation, for example). Depending on the argument used, a

single set of preferences can be represented by different measures of risk aversion.

7

Not all datasets contain consumption information, and asset information is often

incomplete and inaccurate. Since this is the case with the NLSY79, this review focuses

on studies that construct an empirical measure of risk aversion through hypothetical

questions asked of respondents. Unlike many studies that evaluate actual behavior, these

studies allow construction of a risk aversion measure for a representative sample of the

population and do not focus on just one segment of the population, such as stock market

investors or agricultural producers.

When respondents are asked for a reservation price for a gamble over their

lifetime family income, the Arrow-Pratt measure of relative risk aversion can be

constructed. Often, the questionnaire asks whether respondents would be willing to

accept a gamble over their income. Depending on the answer, respondents are then asked

whether they would be willing to accept a more risky or less risky gamble. The

respondents can then be put into one of four categories of risk aversion, and the bounds

on the Arrow-Pratt measure can be calculated. However, only a handful of surveys

contain the type of questions required to do this. Several studies utilize these data to

explore how demographic variables affect risk aversion, and fewer use these measures to

investigate how risk aversion affects behavior. Since many decisions over the course of

an individual’s life are influenced by attitudes toward risk, whether consciously or

subconsciously, the few studies employing data that investigate the effect of risk attitudes

on behavior are of particular interest. Apparently, however, no existing studies focus

directly on the relationship between interpersonal variation in risk aversion and marriage

outcomes.

8

Determinants of Risk Aversion

Studies that focus on how demographic variables affect risk aversion, as opposed

to the effects of risk aversion on a specified outcome, include Miyata (2003), Hartog et

al., (2002), and Donkers et al. (2001). A common finding is that observable

characteristics tend to explain a small amount of the variation in risk aversion among

people. This finding supports the idea that each person has some innate risk preference,

though it may evolve over time due to age, having children, etc. Nevertheless, there are

some relationships between risk aversion and demographic characteristics that are

noteworthy.

Donkers et al. and Hartog et al., using several cross-sectional Dutch datasets, find

that females are more risk averse than men, older individuals exhibit more risk aversion,

and income is negatively correlated with risk aversion. Hartog et al. also find that civil

servants are more risk averse than private sector employees, and the self-employed are

less risk averse. The relationships found between risk preferences and demographic

variables in the two studies are for the most part expected, which is encouraging for the

usefulness of their risk measures. However, one disadvantage is that both studies use

surveys that ask individuals about lottery tickets, not their income.

In one dataset used by Hartog et al., marriage is significantly related to risk

aversion; single and cohabiting individuals are less risk averse than married couples.

Since marriage can be viewed as a contract that increases the cost of separation, the

authors argue that risk averse individuals will want to make it more difficult for their

partner to leave. Miyata, using the results of investment games played by 400 households

in rural Indonesia to identify attitudes toward risk, finds that one’s living situation is

9

significant; an individual living with parents is less risk averse than one living in a

nuclear household.

Risk Aversion and Behavior

In studies that explore how risk aversion affects behavior, risk attitudes are found

to be correlated in an expected way with behavior almost without exception. Barsky et

al. (1997) explore the impact of risk aversion on a variety of behaviors for about 11,000

individuals aged 51-61 using the Health and Retirement Study, which uses the same

format of risk questions as the NLSY79.1 They find, as expected, that those who smoke,

drink heavily, have no health or life insurance, hold stocks or risky assets, and immigrate

are more risk tolerant. In each instance, the coefficient on the measure of risk tolerance is

significant, but there is so much variability in these behaviors that risk tolerance explains

little of it (though the latter is true for all covariates).

Guiso and Paiella (2001) use the 1995 Bank of Italy’s Survey of Household

Income and Wealth, which asks 8,135 households what they would pay for a security that

provides equal probability of gaining 10 million lire or losing all capital invested. Their

findings are similar to that of Barsky et al. in that the effects of risk attitudes are as

expected. More specifically, risk averse individuals are more likely to work in the public

sector and less likely to be self-employed, have a much lower probability of holding risky

assets, and are less likely to move and be job changers. The degree of risk aversion has a

1 Barsky et al. ask respondents about lotteries over income rather than spending or consumption because pretesting of the survey instruments revealed that respondents better understood income lotteries. They argue that, given the low levels of financial wealth of most respondents, permanent income and permanent labor income are similar. They argue that the lottery questions can be interpreted as asking respondents about “permanent consumption.”

10

negative effect on the probability of moving from place of birth, changing jobs, and

incurring chronic disease. It is encouraging that similar survey questions in different

countries yield a similar distribution of risk attitudes and correlations with observed

behavior.

Of course, there are valid criticisms and potential sources of noise in attempting to

measure risk attitudes through experiments and hypothetical questions. For example,

some respondents may not understand the questions but nonetheless answer them. Those

who are risk averse may be less likely to answer if the questions are not properly

understood. Moreover, perhaps their responses do not match what their decisions would

be in reality.2 Experimental attempts to measure risk preferences have brought forth

concerns about preference reversal violations of expected utility theory.3 In addition,

respondents may value their job for more than pecuniary reasons and so be hesitant to

leave it for a large expected increase in income.

Furthermore, in previous studies it has been common to assume that a single,

intrinsic risk preference, measured by taking chances over money, dictates risk taking in

all spheres of life. However, there are different kinds of risk aversion, and it is quite

plausible that an individual might be willing to take chances with their money but not

their health. A recent preliminary study by Dohmen et al. (2005) sheds some light on this

issue using the 2004 wave of the German Socioeconomic Panel (SOEP). The survey asks

approximately 22,000 individuals several different types of risk questions. Respondents

are asked the same type of questions about gambles over lifetime income used in the

2 However, Binswanger (1981), Camerer and Hogarth (1999), and Dohmen at al. (2005) find that hypothetical experiments are not at a serious disadvantage to games with real financial rewards.

11

NLSY79, but they are also asked about their willingness to take chances in five different

domains: financial matters, career, health, car driving, and sports and leisure. The study

finds that, while average willingness to take risks is different across domains, there is a

strong correlation across domains. Overall, there is evidence that a single risk parameter

is relevant for all domains to some extent. The authors argue that their findings may

indicate some “malleability” of risk preferences but more probably are indicative of

differences in how individuals perceive risk across domains.

Despite their imperfection, risk measures constructed from hypothetical questions

may still be informative. The questions are designed so that bounds on the Arrow-Pratt

measure of risk aversion can be calculated, so economic theory is not ignored. Using

these measures should be viewed as steps along the way to better understanding what

determines and what is affected by interpersonal variation in risk.

2.3 THEORETICAL MODEL

The question remains: Does marriage attract the risk averse sooner than risk

lovers, all else equal? Marriage may or may not increase “emotional risk.” Certainly

entering into marriage opens up the possibility of divorce, which is more costly than

ending a cohabiting union. However, since a marriage contract raises the cost of

separating, the conditional probability of a union ending may be lower once marriage has

occurred. Sahib and Gu (2002) show that the “risk premium,” which compensates an

individual for the potential failure of a marriage, is smaller for the more risk averse.

Thus, more risk averse individuals need fewer incentives to enter into marriage.

3 See Harless and Camerer (1994).

12

Marrying sooner than the average person should be attractive to the risk averse

because it mitigates the uncertainty of the future. Finding an “acceptable” mate is easier

than finding the “perfect” mate, and the risk averse searcher may be willing to accept one

of the first options that come along because hope is low that an even better option will

come along in the future. As Pissarides (1974) and Lippman and McCall (1976) argue in

the job search literature, more risk averse individuals attach less value to further search

because any searcher must compare an offer that is known with the uncertainty of another

draw from the wage distribution.

First consider a simple one-sided partial equilibrium model of marital search, in

the spirit of the familiar one-sided job search model. Here, however, it is necessary to

relax the standard assumption of risk neutrality and allow for concavity of the utility

function. Searchers are infinitely-lived and identical in all respects except for their

degree of risk aversion, with discount factor β and concave monotonically increasing

utility functions Ui(qi), where qi denotes the quality of the offer received by searcher i in

the marriage market. Quality is an index of traits of the individual making the offer,

which captures their worth as a marriage partner. It may include measurable traits such

as income as well as intangible characteristics. For now, I will assume that the risk

aversion of the offerer is not included in their quality, so that the searcher does not care

about a potential mate’s level of risk aversion. Also assume that all singles are part of the

marriage market, women are searchers, with men making the offers. A two-sided search

framework will be discussed later.

Women receive a single offer per period from the distribution F(q) with support

[0,∞), taken as given for now, so that the probability of receiving an offer does not

depend upon the man’s level of risk aversion. The offer at hand can be accepted and the

marriage lasts forever,4 or the offer can be rejected and the woman can continue

searching without the possibility of recalling previous offers of marriage. Denote the

expected present discounted value of an offer of quality level qi as Qi and the expected

present discounted utility from searching as Si. Then the payoff to accepting a current

offer of can be expressed as follows: 0iq

β−

=1

)( 00 iii

qUQ (2.1)

Assuming no costs to search and that the flow of utility equals 0 while searching, the

value of searching for one more period is

{ }),max( iiqi SQES β= (2.2)

The offer is accepted if , implying a reservation quality ii SQ ≥0iq such that

iii S

qU=

− β1)(

, or ⎭⎬⎫

⎩⎨⎧

−−=

−)

1)(

,1

)(max(

1)(

βββ

βiiii

qii qUqU

EqU

. (2.3)

Then, ∫∫∞

∂−

+∂−

=−

iq

iiq

iiii qFqU

qFqUqU

)(1

)()(

1)(

1)(

0 ββ

ββ

β. (2.4)

This is equivalent to ∫∞

∂−−

+−

=− q

iiiiiiii qFqUqUqU

qU)()]()([

1)(

11)(

ββ

ββ

β, (2.5)

which simplifies to ∫∞

∂−−

=q

iiiiii qFqUqUqU )()]()([1

)(β

β . (2.6)

13

4 When this assumption is relaxed and an exogenous probability of divorce is allowed, the relevant predictions of the search model still follow.

Equation (2.6) implicitly defines the searcher’s reservation quality iq , equating

the opportunity cost of searching one more period with the expected lifetime benefit of

one more search, given the current offer . In other words, Equation (2.6) holds when

equals

0iq

0iq iq .

To determine how an individual’s risk aversion affects the reservation wage,

Pratt’s (1964) Theorem is useful. Pratt defines the risk premium as the amount of

money that makes an individual indifferent between a certain amount and a gamble with

an expected value equal to the certain amount; i.e.,

ir

).()( iii rEIUIEU −= (2.7)

If ri >0, then the individual is risk averse. Pratt also shows that the risk premium varies

directly with the Arrow-Pratt coefficient of absolute risk aversion. Given this definition

of the risk premium, it is not difficult to see how affects the search problem in the

current context. A positive risk premium increases the opportunity cost of searching one

more period, or, equivalently, decreases the expected lifetime benefit of another search.

The higher the risk premium, the more quality that is required to induce the individual to

give up the certain offer in the current period for the uncertain outcome of further search.

ir

To show this more rigorously, assume that there are two levels of risk aversion

among searchers. Type A searchers are globally more risk averse than type B searchers,

so )]([)( qUGqU BA = (2.8)

for some strictly concave and monotonically increasing function G. Pratt’s Theorem

implies that for all q. If the two searchers are faced with the same quality BA rr >

14

distribution, then the more risk averse searcher has the lower reservation quality level. In

other words, given F(q), if )]([)( qUGqU BA = for all q, then BA qq < . In the context of

job search, this result has been established by Nachman (1975), Hall et al. (1979), and

Vesterlund (1997).5 It is well known that a lower reservation level leads to an earlier

optimal stopping time, so the expected duration of singledom is shorter for the more risk

averse. This results simply because the per period probability of accepting an offer is

))(1( iqF− , which is decreasing in iq .

The one-sided search problem can be extended to a two-sided one, for now

maintaining the assumption that a potential partner’s risk aversion does not enter an

individual’s utility function through the quality index. Both sexes are searching, and for

simplicity assume each searcher is matched with another once per period. One sex

initiates an offer, and does so if the other’s quality exceeds their reservation level. The

offeree accepts if their reservation quality level is exceeded, so the more risk averse the

offeree, the more likely the acceptance occurs. Thus, in the basic two-sided model, the

prediction that the more risk averse marry sooner still holds.

If searchers value risk aversion as a desirable trait in potential mates, so that one’s

quality is a function of one’s risk aversion, the model becomes slightly more complex.

Suppose, for simplicity, that only a female’s utility is increasing in the male’s risk

aversion through his quality index. If men initiate offers, more risk averse men do so

because their reservation quality is more likely to be exceeded. Own risk aversion may

still affect women’s probability of accepting an offer, and so the risk averse women may

155 See Appendix A.1 for proof of this proposition.

16

require lower levels of quality to exceed their reservation level. Nevertheless, because

women value risk aversion, they are more likely to accept, the more risk averse the man,

all else equal. If women initiate offers, they are more likely to do so to men with higher

levels risk aversion, holding their own risk aversion constant. The man accepts if his

reservation quality level is exceeded, and the more risk averse the man, the more likely

an acceptance occurs. If women demand risk aversion but their own risk aversion does

not affect the likelihood of ending the search process, then own risk aversion should

matter more for men in the timing of marriage. However, if risk aversion is demanded by

women and affects their reservation quality, then the extent to which the effect of own

risk aversion on time to marriage will differ between the sexes is ambiguous.

2.4 DATA AND EMPIRICAL SPECIFICATION

The NLSY79, which began annual interviews in 1979 with over 12,000

individuals aged 14–22, continued interviewing that sample annually through 1993, and

since 1994 has followed the group with interviews every two years. The NLSY79

contains three subsamples: a cross-sectional sample of 6,111 respondents designed to be

representative of the civilian U.S. youth population; a supplemental sample of 5,295

respondents designed to oversample civilian Hispanic, black, and economically

disadvantaged non-black/non-Hispanic U.S. youth; and a sample of 1,280 respondents

designed to represent the population ages 17–21 who were enlisted in the military.

Following the 1984 interview, 1,079 members of the military subsample were no

longer eligible for interview, but 201 respondents randomly selected from the entire

military subsample remained in the survey. Following the 1990 interview, none of the

17

1,643 members of the economically disadvantaged, non-black/non-Hispanic subsample

were eligible for interview. In 1993, a key year for this study, 9,011 individuals were

available for interview, and they are followed in this study from 1979 until 2002.

Because the household was the primary sampling unit in the initial surveys, several

thousand pairs of siblings are included in the data, and this will prove useful in the

empirical estimation.

One advantage of using the NLSY79 for this analysis is the detail of respondents’

marital histories. Information on marriages and divorces is not limited to marital status at

the time of interview. At each interview, respondents are also asked for the month and

year each of their marriages began and ended. This serves to fill in missing information

if a respondent has not been interviewed each year of the survey and also serves to clarify

and correct inconsistent marital history data.

Risk Measure

An underutilized series of questions from the 1993 wave of interviews allows

construction of a variable indicating an individual’s attitude toward income risk.

Respondents, then aged 28-36, were asked two questions relevant to constructing this

variable. All respondents were asked the following question (Gamble 1):

“Suppose that you are the only income earner in the family, and you have

a good job guaranteed to give you your current (family) income every year

for life. You are given the opportunity to take a new and equally good

job, with a 50-50 chance that it will double your (family) income and a 50-

18

50 chance that it will cut your (family) income by a third. Would you take

the new job?”

If the answer was “No,” respondents were then asked the following (Gamble 2):

“Suppose the chances were 50-50 that it would double your family income

and 50-50 that it would cut it by 20 percent. Would you take the new

job?”

If the answer to the first question was “Yes,” respondents were asked the following

(Gamble 3):

“Suppose the chances were 50-50 that it would double your family income

and 50-50 that it would cut it in half. Would you still take the new job?”

These three questions allow categorization of respondents into four groups. Respondents

who answered “No” to both questions will from now on be referred to as “Very Strongly

Risk Averse”; 46% of respondents fall into this category. Respondents who answered

“Yes” to both questions will be called “Weakly Risk Averse,” and 25% fall into this

category. Respondents who answered “No” to the first question but “Yes” to the second

will be called “Strongly Risk Averse,” and this applies to 12% of respondents. Those

who answered “Yes” to the first question and “No” to the second will be referred to as

“Moderately Risk Averse,” which applies to the remaining 17% of the respondents. This

distribution of risk preferences is consistent with that found in previous studies, in which

slightly more than a third to slightly more than one half of individuals fall into the most

risk averse category.

The responses of individuals are viewed as resulting from an expected utility

calculation. If U is the individual’s utility function and I the lifetime income, or

“permanent consumption” in Barsky et al.’s terminology, then an expected utility

maximizer will accept the 50-50 gamble of doubling lifetime income rather than cutting it

by the fraction 1-α if the following holds:

)()(21)2(

21 IUIUIU ≥+ α (2.9)

In other words, the expected utility of the gamble is at least as great as the utility from

having current income for certain. Note that the labels assigned to the categories

correspond to varying degrees of risk aversion, since the NLSY79 gambles are more than

actuarially fair (the expected values are always greater than I):

EI Gamble 1 = III34)

32(

21)2(

21

=+ (2.10)

EI Gamble 2 = III57)

54(

21)2(

21

=+ (2.11)

EI Gamble 3 = III45)

21(

21)2(

21

=+ (2.12)

Therefore, a risk neutral agent would accept any of the three gambles. As I have labeled

the categories, only a Weakly Risk Averse individual would accept all of the lotteries.

An advantage to using this risk measure is that respondents are asked to gamble

over family income, and respondents are asked to consider that family income is own

income. Therefore, if the respondent is not the main breadwinner in the family, the

survey design attempts to eliminate the potential problem that the respondent would be

more or less likely to gamble with the spouse’s income. In addition, measuring risk

aversion in this way requires no assumption on the form of the respondent’s utility

function. It only requires that relative risk aversion is constant over the relevant region.

19

20

One disadvantage, however, is that respondents are not asked these questions in an earlier

year. When the risk questions are first asked, over 50% of respondents have been or are

married, which presents possible endogeneity problems. Marital decisions could

certainly have an impact on risk attitudes.

Respondents are not asked these risk questions on a regular basis over time.

However, the NLSY79 did repeat these questions in 2002. In 2002, 54% of respondents

are considered Very Strongly Risk Averse, 18% are Weakly Risk Averse, 12% are

Strongly Risk Averse, and 16% are Moderately Risk Averse. While a similar percentage

of respondents fall into the middle two categories in 2002 as in 1993, there has been an

overall shift towards risk aversion. Appendix A.2 illustrates the change in risk category

between 1993 and 2002. Of those who were Weakly Risk Averse in 1993, about 24%

remained in the same category in 2002, 35% became Very Strongly Risk Averse, and

17% were not interviewed in 2002. It is not surprising that fewer respondents are willing

to take big risks in 2002, since respondents are almost ten years older, have more

children, and face more responsibility in general. While this pattern cannot help resolve

endogeneity issues, it does support the argument that individuals have an inherent risk

parameter that is shifted over time by changes in personal characteristics and

circumstances.

The remainder of the descriptive statistics will focus on the 1993 risk measures

since they avoid more endogeneity problems than do the 2002 risk measures. In addition,

only 7,224 respondents were available to answer the risk questions in 2002, compared to

over 9,000 in 1993. Table 2.1 presents the distribution of risk aversion by demographic

characteristics. Women are relatively more risk averse than men, with 49% being Very

21

Strongly Risk Averse to the men’s 43%. As expected, a higher percentage of men are

Weakly Risk Averse, with 29% compared to women’s 21%. In addition, even within the

age group of 28-36, the young tend to be more risk tolerant. It is encouraging that these

data reveal the above two patterns with respect to sex and age, as they corroborate the

findings of past studies.

Table 2.1 also reveals that respondents with children in the house are more risk

averse in general, although those with children ages 6 to 13 are the most risk averse

among parents. The distribution of risk aversion is similar for all races, with whites

slightly less Weakly Risk Averse. Respondents with less than a high school education

are more polarized than the general population, with a comparatively large percentage

falling into the Very Strongly Risk Averse and Weakly Risk Averse categories. High

school graduates are more risk averse than the general population, while college

graduates and those who have attended graduate school are less risk averse, with a higher

percentage falling into the middle two categories of risk aversion.

Table 2.2, which is critical to exploring the relationship between marriage and

risk aversion, presents the distribution of risk aversion by age at first marriage. There is a

clear trend between age at first marriage and risk category. For the total population, the

percentage of Very Strongly Risk Averse respondents never increases and almost always

decreases with age at first marriage, and the percentage of Weakly Risk Averse

respondents never decreases and almost always increases with age at first marriage.

When the same analysis is carried out by sex, the trends remain almost as strong for both

sexes. For women, the only exception is the 21-25 year age group, at which point the

percentage of Weakly Risk Averse individuals falls before increasing for the subsequent

age group. For men, the same age group is the exception, where the percentage of

Weakly Risk Averse individuals falls temporarily and the percentage of Very Strongly

Risk Averse increases temporarily.

Empirical Specification

I estimate a hazard model to investigate the determinants of time to first marriage.

Survival analysis is appropriate for the questions at hand for at least two reasons. First, it

is necessary to substitute for the normality assumption that Ordinary Least Squares

requires, since assuming normality of time to an event is problematic. Second, right-

censored spells (those individuals who never get married during the timeframe of the

data) should be included in the analysis in order to fully utilize the information contained

in the data. Hazard models handle both right-censored spells and time-varying covariates

fairly easily. I use the semiparametric Cox proportional hazards model because no

assumption is made about the underlying shape of the baseline hazard. Under

proportional hazards, the hazard rate into marriage for person j at time t is

β)(0 )()( tX

jjethth = (2.13)

where h0(t) is the baseline hazard faced by everyone at time t. The estimated coefficients

(β’s) on the explanatory variables (X’s) shift the hazard rate up or down, depending on

their signs. To expound, if T is denoted as the random variable representing time to

failure, or exit from a given state, f(t) is T’s probability density function, and F(t) is the

cumulative distribution function, then the survivor function S(t) = 1-F(t) = Pr(T>t) reports

the probability of surviving beyond time t. Following from this, the hazard function h(t)

= f(t)/S(t) is the instantaneous rate of failure. Cox regression results are based on 22

23

forming, at each failure time, the risk pool and then maximizing the partial log likelihood

of observed failure outcomes, accounting for right censoring.

In the jargon of survival analysis, “failure” in this analysis means a first marriage

occurs. I assume individuals become “at risk” to fail at age 16.6 While respondents are

not legally adults at this age, they gain a certain measure of independence since, at the

time, 16 was the youngest age at which individuals could marry without parental consent

in most states. On a more practical note, several hundred respondents get married before

the age of 18, but only about 60 are married prior to age 16. Analysis time t is thus

measured in months from turning age 16, and the failure time is marked by the number of

months that elapse until first marriage.

The empirical specification includes dummy variables for the risk categories,

excluding the Weakly Risk Averse category. Since the risk questions asked of

respondents require dichotomous answers (yes/no), not reservation prices, I cannot

employ expected utility theory to calculate exact Arrow-Pratt measures of risk aversion.

It is possible, however, to use expected utility theory to calculate bounds on the Arrow-

Pratt measures,7 but these are not included in the regressions. They contain no more

information than the dummy variables, as each individual in the same risk category

would have the same bounds on the Arrow-Pratt measure. I am concerned about the

ordinal properties of the risk measure, and the indicator variables capture this ordinality.

Other explanatory variables include education, the log of the respondent’s weekly

real income, dummy variables for sex, race (white, black, other), the age of children in

6 Results are not substantively different when I assume individuals first become “at risk” at age 18.

the household (no children, children less than 6, and children over 6), region (south, west

northeast, north central), whether the current residence is urban or rural, whether

respondents are currently living with their parents, and whether they lived with their

parents until age 18. Explanatory variables are collected annually for respondents, and

every two years starting in 1994. Estimation of a hazard model with time-varying

covariates requires the assumption that the explanatory variables remain constant

between respondent interviews. This is clearly an oversimplification, but, as Wooldridge

(2001) points out, researchers cannot get very far empirically without this assumption.

The hazard model specified in Equation (2.13) assumes there is no unobserved

heterogeneity in the probability of transition to first marriage. It is likely, however, that

unobserved family-specific traits, such as attitudes about marriage and age at marriage,

affect time to first marriage. Moreover, it is possible that the unobserved heterogeneity is

correlated with one or more of the covariates. If this is the case, parameters estimated via

the typical proportional hazards model will be biased, as the hazard framework usually

assumes that any unobserved heterogeneity is uncorrelated with the covariates. Family-

specific unobserved heterogeneity may be correlated with our covariates of interest, the

risk attitude variables. Depending on when risk attitudes form, parental attitudes about

risk may be transferred to children to a certain extent. For this reason, I also estimate a

model with family fixed effects by exploiting the availability of sibling data in the

NLSY79. The hazard rate becomes

kjk tXjk ethth δβ+= )(

0 )()( (2.14)

24

7 The bounds of the Arrow-Pratt measure of relative risk aversion are [0,1) for the Weakly Risk Averse,

25

for sibling j in family k, where δk represents the unobserved family heterogeneity.

2.5 RESULTS

Table 2.3 presents the results of two Cox proportional hazards estimations. First,

I present estimates of the proportional hazards model in Equation (2.13) for the full

sample interviewed in 1993, assuming no unobserved heterogeneity (Specification 1).

Second, I present estimates of the same proportional hazards model for the full sample

with standard errors adjusted to allow for possible correlation within families

(Specification 2). This specification also stratifies on variables that fail the proportional

hazards test at the 0.01 level of significance. This means that a separate baseline hazard

is estimated for the stratified variables, which are sex, race, region of residence, whether

or not the respondent is enrolled in school, and whether or not they live in an urban

location. In other words, for example, I do not constrain the hazard function for males to

be a proportional replica of the hazard function for females.

The results indicate risk preferences do matter. A Wald test shows that all of the

coefficients on the risk preference variables are significant at the 1% level. Relative to

the Weakly Risk Averse, being in any other risk category shifts the hazard up and

increases the conditional probability of marriage. The hazard ratios are presented for

ease of interpretation. The hazard ratios for Specification 1 tell us that someone who is

Very Strongly Risk Averse faces a hazard rate that is 1.31 times the hazard faced by

someone who is Weakly Risk Averse, while someone who is Moderately Risk Averse

faces a hazard rate that is 1.19 the hazard faced by the Weakly Risk Averse. The hazard

[1,2) for the Moderately Risk Averse, [2,3.76) for the Strongly Risk Averse, and [3.76,∞) for the Very

26

ratios for Specification 2 are very similar. Figure 2.1 compares the estimated hazards for

the Weakly Risk Averse and Very Strongly Risk Averse groups. The shape of the hazard

is not surprising; it increases sharply at first and almost monotonically decreases

thereafter. After about 75 month of analysis time (months since age 16), the hazard

exhibits consistent duration dependence in the sense that the longer a respondent remains

single, the lower the conditional probability of marriage. Moreover, the hazard for the

Very Strongly Risk Averse lies above that for the Weakly Risk Averse at all analysis

times.

Most of the other explanatory variables in Specification 1 shift the hazard in the

expected direction. For example, being male shifts the hazard down since, in any given

interval, the conditional probability of marriage is lower for men. In the NLSY79, men

marry an average of two years later than women. Living in an urban area or in the

Northeast decreases the conditional probability of marriage. While there may be a larger

selection of mates in urban areas, there are also a larger variety of activities than in rural

areas and perhaps less traditional views about marriage and family. Conversely, living in

the South increases the probability of marriage. Being enrolled in school and currently

living with parents also decreases the hazard rate. Having lived with both parents until

age 18 increases the hazard rate, but this coefficient is not statistically significant.

Income increases the hazard rate, and educational attainment decreases it at first.

Surprisingly, after about the high school level of educational attainment, education begins

to increase the hazard. This unexpected result could be due in part to reverse causality,

where marriage decisions cause educational outcomes. The hazard ratios for the

variables remain very similar under Specification 2, with the one exception that having

27

no children in the household now reduces the hazard rate. This seems to capture demand-

side behavior more than in Specification 1, since single women with no children have no

need for a father figure.

Although the ideal situation would involve the risk questions being asked before

any marriages occur, it could also be helpful to perform the survival analysis only for

marriages that occur after the 1993 questions are asked. Unfortunately, this is

problematic because the respondents are already aged 28-36 in 1993 and only a few

hundred respondents are married after 1993. In fact, the frequency of first marriages

peaks almost a decade before 1993. Nevertheless, the hazard analysis performed on the

sample limited to those who marry after 1993 yields the expected sign for all risk

categories. Results are presented in Table A.2 of Appendix A.3. While the estimated

coefficients are not statistically significant, the fact that being Very Strongly Risk Averse

increases the hazard rate the most relative to the Weakly Risk Averse category is

encouraging.

To support the idea that at least some element of risk attitudes is intrinsic, I have

repeated the Cox hazards estimation using the risk preference variables for 2002. The

results are presented in Table A.3 of Appendix A.3. The signs of the risk variable

coefficients and the pattern of the hazard ratios are the same as in Specification 1 in

Table 2.3, which uses the 1993 risk variables. The estimated coefficients are statistically

significant at the 5% level, which is less significant that in Specification 1. It is

encouraging that the results hold up fairly well when using a risk measure that is

collected almost ten years after the first measure. Also, the hazard ratios are smaller in

magnitude and have a smaller variance when the 2002 risk measures are used than when

28

the 1993 measures are used. If reverse causality was a problem in that the longer an

individual is married, the more risk averse he or she becomes, then we would expect to

see a larger magnitude and variance in the hazard ratios when the 2002 variables are

used. .

The above results support the theory presented; nevertheless, causality cannot be

assumed. It may be that unobserved heterogeneity in families explains the results, but the

NLSY79 can be used to shed some of this doubt. A useful feature of the NLSY79 is its

inclusion of multiple-respondent households. In 1979, over 46% of the total sample

consisted of siblings in 2,448 households. Table 2.4 presents the estimation of the basic

hazard rate in Equation (2.13) for the sample of siblings interviewed in 1993

(Specification 3). The hazard ratios for the risk preference variables are extremely

similar as in the full sample. Table 2.4 also presents estimates of the model in Equation

(2.14) for the sample of siblings interviewed in 1993, allowing for fixed unobserved

heterogeneity at the family level (Specification 4). The results indicate that unobserved

heterogeneity at the family level cannot explain the results found in the cross-section

regarding the effect of risk attitudes on time to marriage. The statistical significance of

the risk variables remains comparable to previous results. In addition, the effect of risk

preference on time to marriage is actually magnified once fixed effects are included. For

example, once fixed heterogeneity is taken into account, the Very Strongly Risk Averse

face a hazard 75% greater than the Weakly Risk Averse compared to a hazard 34%

greater when fixed effects are excluded. Finding that the basic results are upheld when

family fixed effects are included makes a causal interpretation of the effect of risk

attitudes on marriage more plausible.

29

Supply-Side or Demand-Side Behavior?

Table 2.5 presents the basic hazard estimation separately for the two sexes and

reveals an interesting difference. While the signs on the coefficients of the risk variables

remain the same as for estimation on the whole sample, the hazard ratios suggest that the

effect of risk preference on time to marriage is magnified for men for the Very Strongly

Risk Averse and the Weakly Risk Averse. Moreover, the statistical significance of these

two risk categories is much greater for men.8 Overall, the results suggest that risk

preferences matter more for men than women when it comes to the timing of marriage.

A possible explanation of the differential results between the sexes, one hinted at in the

theory section, is that both supply-side and demand-side behavior are reflected in the

estimates. On the supply side, the more risk averse marry sooner because of the

uncertainty of future prospects. On the demand side, women view risk aversion as a

desirable trait in a mate because risk averse men may exhibit more responsible behavior,

financially and otherwise, than their more risk loving counterparts. Risk aversion signals

that a potential husband will not take unnecessary risks and will therefore be a good

provider or partner. This finding points to another reason that the more risk averse may

marry sooner; namely, marriage is a form of risk pooling that provides insurance against

unexpected shocks to income or health. Perhaps women value this aspect of marriage

more so than men.

Risk aversion should also have some bearing on who an individual marries, not

only when they marry. If the basic job search model holds, then the risk averse

8 The same pattern is observed when the Cox proportional hazards estimation is performed separately for the sexes using the 2002 risk preference variables. Results are available upon request.

30

respondents will not only marry sooner than their more risk loving counterparts but will

also settle for a lower reservation quality level. Thus, their spouses should have less

desirable characteristics than the spouses of more risk loving respondents. On the other

hand, on the demand side, if risk aversion is a trait that women find desirable in men,

then risk averse men may have other desirable traits as well. Spousal characteristics are

limited in the NLSY79, but Table 2.6 presents the majority of spousal characteristics of

married respondents by risk category. The spouses of married, Very Strongly Risk

Averse men have less desirable characteristics (education, income, hours worked,

fraction that work) than the spouses of married, Weakly Risk Averse men. The education

variable may be the most relevant in this situation, since the labor supply variables for

wives are partly determined by household preferences over the wife’s allocation of time.

However, this may also be evidence that risk aversion is a signal of being a good

provider, since the more risk averse men match up with women who work less. Overall,

these basic descriptive statistics support the predictions of a basic marriage search model

in which the risk averse individual accepts a lower reservation quality and therefore

marries earlier. In contrast, the spouses of married, Very Strongly Risk Averse women

are not consistently less desirable. While incomes and years of education are lower for

spouses of risk averse women, the differences in the means of these variables between the

Weakly Risk Averse and Very Strongly Risk Averse wives are not statistically

significant. However, husbands fare better in other categories. These basic statistics do

corroborate the result that risk attitudes affect time to marriage more strongly for men.

Risk averse men may be willing to accept a lower reservation quality (less desirable

spousal characteristics in general) in order to marry sooner and avoid future uncertainty

31

about the likelihood of meeting a marriageable partner again. While some risk averse

women marry sooner as well, they also value risk aversion in their mates, which

magnifies the effect of risk preference on men’s time to marriage.

2.6 CONCLUSION

Understanding the role that risk preferences play in influencing behavior is

important, since risk attitudes likely play a central role in all kinds of decision-making.

While this need to understand the relationship between individual variation in risk

attitudes and behavior is widely acknowledged, limited empirical studies exist that

undertake the task. This is largely due to a lack of the type of data required to construct

empirical measures of risk aversion. Nevertheless, some appropriate data do exist, but no

studies have analyzed the relationship between risk preferences and the timing of marital

decisions. The current study attempts to do just this.

The initial theoretical motivation is a basic search model inspired by job search.

The model predicts that the more risk averse searcher’s penchant for a certain outcome

results in a lower reservation quality compared to their more risk loving counterparts, and

thus they enter into marriage sooner. The initial empirical results, including within-

family analyses, support this basic prediction. Further inspection of the data suggests that

risk preferences affect marital decisions differentially between the sexes. Risk attitudes

seem to have a larger and more statistically significant effect on time to marriage for men

than for women. This leads to the hypothesis that demand-side behavior, not only

supply-side behavior, may be reflected in the empirical results. Women may view high

levels of risk aversion as a desirable characteristic, so that a potential mate’s quality

32

increases with risk aversion. Since the basic search model predicts that the risk averse

have a lower reservation quality level than other searchers, one might expect the

characteristics of their spouses to be less desirable than the spousal characteristics of the

more risk loving. Some basic descriptive statistics support this prediction for spouses of

men, but not spouses of women. This outcome further supports the hypothesis that

women’s demand for risk aversion is on display, since the spouses of risk averse women

actually have more desirable characteristics than other spouses.

Several extensions specific to the study at hand come to mind. First, the

theoretical model could be made more realistic. At present, the model implicitly assumes

that remaining single is strictly dominated by searching for a spouse. In addition,

marriage may be attractive to the risk averse for additional reasons not modeled here. In

particular, marriage may act as a form of insurance in which access to pooled resources

insures against unexpected shocks. Next, richer data would allow analysis of other

intriguing questions, such as how risk preferences influence the transition from

cohabitation to marriage and whether population trends in age at first marriage over time

can be partially attributed to changes in risk preferences.

33

Chapter 3: Time Off at What Price? The Effects of Career Interruptions on Earnings

3.1 INTRODUCTION

The possible earnings effects of career interruptions have long been a concern to

labor economists when estimating traditional Mincerian wage equations. Early

investigations of such effects focused on women, who are more likely than men to spend

time out of the work force. More recent work has also investigated career discontinuity

among men, partly in order to determine whether there are gender differences in how

time out of the labor force affects wages. This paper focuses on how career interruptions

and career expectations affect the wages of women and men.

Many of the previous studies, as well as casual observation, suggest that

individuals who interrupt their employment can generally expect a reduction in their

earning power upon their return to work, whether or not they return to the same

occupation. Speculation suggests several factors that could contribute to the loss of

earning power: skeptical employers, lost contacts, decreased confidence, and eroded

skills. In addition, theory suggests that individuals who expect to interrupt their career in

the future will accept a higher wage early in the career in trade for slower subsequent

wage growth as a result of reduced human capital investment. Thus, taking expectations

into account allows for a clearer picture of a person's lifetime wage profile.

34

This paper fits in well with and extends the more recent research on career

interruptions. It uses similar, non-traditional wage equations to answer several questions.

Do workers who interrupt their career pay a penalty? Is the penalty different for men and

women? Does the timing of the interruption matter, and are these effects different for

men and women? Is there a rebound effect when workers return to the labor force, and

how do such effects compare for men and women? However, this study uses more

complete data over a longer time span than have previous studies. It also extends recent

research by attempting to answer two questions about career expectations. First, does the

expectation of an interruption affect current and future wages? Second, does that effect

(if it exists) differ between the sexes?

The answers to these questions could help labor economists in at least two

important ways. First, they obviously could have a bearing on how best to specify a

wage equation. Second, they are also essential if researchers want to know what factors

contribute to the gender earnings gap, as well as earnings gaps between other groups.

The fact that women are more likely than men to have career interruptions, with

repercussions for their human capital accumulation, must be taken into account along

with the many other factors that could affect the gender earnings gap—among them,

women's job choice and career expectations, the effect on productivity of unpaid work

associated with motherhood and housework, unobservable differences between mothers

and non-mothers in such factors as "career motivation," and of course discrimination in

the labor market—before that gap can be satisfactorily understood and before policy

decisions regarding it are made. In this paper, a non-traditional wage equation is used in

an effort to determine how much of the gender wage gap is due to the timing of work

35

experience. This study also departs from previous work on career interruptions by trying

to answer how career expectations affect current wages in a true panel data setting and by

addressing the implications of career expectations for the gender gap.

3.2 LITERATURE REVIEW

Most researchers acknowledge that wages rise more quickly with time spent in

paid employment than with time spent in other non-educational activities. Hence, the

wages of a worker upon reentry into the labor force are expected to be below those of

similar workers who have remained continuously employed. In addition, it may be the

case that the reentry wage is below the pre-interruption wage for the given worker,

depending on the length of the interruption and assuming the worker did not interrupt his

or her career for educational purposes. Once workers return to work, wages are expected

to rebound. Human capital theory explains this rebound as resulting from the restoration

of skills. Others argue that another factor contributing to the rebound is the time it takes

for firms to learn about a worker's productivity.

All of the papers in this literature draw from the theoretical model presented by

Mincer and Polachek (1974), which is an extension of the basic formulation of the human

capital earnings function to account for discontinuities in the labor market experience of

individuals. A wide variety of studies since the early 1970s have investigated the

existence of a wage depreciation effect for workers with career interruptions. In general,

most studies have focused on women and have indeed found a statistically significant

depreciation effect, one that ranges from around 0.6% to over 5% annually. Past studies

fit into two general categories: those estimating cross-sectional equations using wages at

36

one point in time, and those that have been able to use wages from at least two points in

time.

Cross-Sectional Studies

Much of the early empirical work exploring the effects of career interruptions on

wages was limited to cross-sectional analysis using retrospective data on labor force

experience. Some studies simply regressed the logarithm of wages at one point in time

on total work experience, total time spent out of the labor force, and a vector of

individual characteristics. Rekko et al. (1993), for example, found that a year spent not

working reduced the wage rate by approximately 1.4%. Other studies were more

ambitious and segmented time spent working and not working in a chronological manner.

The earliest study of this type, by Mincer and Polachek, examined married women aged

30–44 who were surveyed as part of the 1966 National Longitudinal Survey (NLS) of

Mature Women. Using a vector of work experience segments and a vector of home-time

segments as explanatory variables, they found that a career interruption was associated

with not only a penalty of foregone experience or tenure, but also a statistically

significant negative annual return of approximately 1.5%.

Mincer and Ofek (1982) estimated a similar segmented empirical specification

using the same data set, focusing on short-run depreciation, the loss associated with the

most recent interruption, and long-run depreciation, the loss associated with the sum of

previous interruptions. They found that the long-run depreciation effect ranged from

0.6% to 1.1%, while the short-run effect ranged from 3.3% to 7.6%. They concluded that

the cost of work interruption is substantially higher in the short run than in the long run.

37

Corcoran (1977) conducted a study similar to that of Mincer and Ofek using a cross-

section from the Panel Study of Income Dynamics (PSID). Her results differed

somewhat from those of previous studies: labor force withdrawals, she found, had either

statistically insignificant or very small significant negative effects on wages. Overall,

labor force withdrawals were associated with statistically significant depreciation only

when the interruption occurred soon after the completion of school and the start of one's

first job; withdrawals that occurred well into one's career had little impact.

Panel Data Studies

Mincer and Ofek extended their cross-sectional model by using the wage at the

time of the most recent interruption and the wage at the time of reentry into the work

force to estimate wage change equations. They estimated that real wages at reentry were

from 5.9% to 8.9% lower per year than at the point of labor market withdrawal. They

also found that a rapid restoration of wages occurred throughout the first five years after

reentry and that only a relatively small part of this growth was tenure-related. In a sense,

then, their findings implied that it costs less to restore human capital than to accumulate

it. Corcoran, Duncan, and Ponza (1983) estimated wage change equations similar to

those of Mincer and Ofek for the years 1967–79, using a national sample of white women

from the PSID. However, they estimated wage change equations over the whole time

span, which is 13 years, rather than using only wages just prior to the last labor force

withdrawal and immediately following, as Mincer and Ofek did. This enabled the

estimation to take advantage of more of the information that was available in the panel

data set. They also found that wages dropped significantly following a career

38

interruption (from 3.3% to 4.1% per year) and that rapid wage growth followed reentry

(5.1% in the first year), so that the net loss in wages from dropping out of the labor force

was small.

Several more recent panel studies have considered career interruptions of both

men and women. Using a Swedish company-level data set, Stafford and Sundstrom

(1996) attempted to explore the role of signaling by comparing the effects of career

interruptions on wages for men versus women. They estimated earnings equations with

cumulative measures of work experience and interruption time and found that time out

had a much larger negative wage effect for men than for women. Light and Ureta (1995)

departed from the trend of employing cumulative measures. Considering young, white

workers from the NLS young men and women samples, they estimated a wage model that

included an array of experience variables measuring the fraction of time spent working in

the last year, 2 years ago, 3 years ago, and so on, back to the beginning of an individual's

career. An array of indicator variables was created that equaled one when the career was

in progress but the individual did not work in the last year, 2 years ago, and so on.

Light and Ureta's model yielded markedly higher estimated returns to experience

and lower returns to tenure for both men and women than have models that measure work

experience cumulatively and use the quadratic functional form. The data rejected the

standard model but not their model. This result suggests that conventionally specified

wage equations provide a misleading picture of early career wage growth not only for

women but also for men. Light and Ureta's finding that men are penalized more severely

than women for career interruptions accords with results reported by Stafford and

Sundstrom. For men, the drop in earnings upon returning to work after a year-long

39

interruption was about 25%. Four years after the interruption, wages were still 10%

lower than they would have been if no interruption had occurred. Women experienced an

initial drop of about 23%, and they caught up to their continuously employed

counterparts after 4 years. Unfortunately, missing data are a particular problem with the

NLS's samples of young men and women because interviews sometimes occur every two

years, not annually. As a result, the number of weeks worked is not known for every year

of a respondent's career. The number of weeks worked may also be missing when a

given individual is not interviewed in a given year.

In a provisional study, Kunze (2002) used a model similar to that of Light and

Ureta and a West German panel data set spanning the years 1975 to 1997 for 17,000

individuals. She was able to distinguish several different reasons for career interruptions:

unemployment, parental leave for female workers, national service for male workers, and

other non-work spells. As expected, she found that human capital depreciation was less

severe in the long run than in the short run; in addition, it differed across reasons for the

interruption. Comparing this model to the more traditional Mincerian quadratic model,

Kunze found little difference in predicted wages for men between the two models. For

women, however, the more flexible model predicted much higher wages than the

Mincerian model, and the gap widens as experience accumulates; in fact, after 10 years of

accumulated work experience the difference is about 20%. The drawbacks to this study

include the fact that only full-time, skilled workers who were observed in apprenticeship

training after high school and who had no further education were included. Individuals

were thus mainly followed over their early careers, but workers who were not working

40

continuously from age 26 to age 30 were dropped in an attempt to analyze more highly

attached workers.

3.3 DATA AND EMPIRICAL SPECIFICATION

The panel data analysis for this paper uses the National Longitudinal Survey of

Youth 1979 (NLSY79), which began annual interviews in 1979 with over 12,000

individuals aged 14–22, continued interviewing that sample annually through 1993, and

since 1994 has followed the group with interviews every two years. This study focuses

on the men and women from the representative sample of the NLSY79, comprising 6,111

individuals, over the time period 1979–2000.

The NLSY79 contains the longest and most complete record of work history

information compared to the other NLS samples. A weekly labor force status is available

for each respondent up to the date of the very last interview, regardless of how often the

respondent has been interviewed in the past. For example, even though the survey has

been conducted every two years since 1994, respondents are now asked to report their

labor force activity in the previous two years. Moreover, a respondent who misses an

interview in a given year in the NLSY79 is asked to fill in his or her labor force activity

since the date of the last interview. This information is updated in the weekly labor status

array. The other NLS samples that have followed respondents’ careers for a substantial

amount of time have not been consistently updated in this way. Because of the great

detail, missing data for number of weeks worked in a given year are not as great a

problem for the NLSY79 as for the young male and female cohorts used by Light and

41

Ureta. On the other hand, recall may be a more serious problem, although the design of

the survey attempts to minimize this.

The key variables created from these data include an array of experience variables

that measure the fraction of time worked in the last year, 2 years ago, and so on, back to

the beginning of the career. These are called FRCWKSWRKD1, FRCWKSWRKD2, . . . ,

FRCWKSWRKD22 (some individuals are observed as many as 22 years into their career),

where FRCWKSWRKDn denotes the fraction of weeks worked n years ago, by calendar

year. This fraction equals zero either because an individual's career has not begun or

because that person experiences a true career interruption. To distinguish between those

two conditions, an interruption dummy variable array is created, INTRP1, INTRP2, . . . ,

INTRP20. When FRCWKSWRKDn is zero but the career is in progress, INTRPn equals

one. INTRPn therefore capture the effect of not working for an extended period of time.

While there is certainly nothing magical about a calendar year, there are three

reasons for these particular formulations of the FRCWKSWRKDn and INTRPn variables:

the NLSY79 data facilitate using a calendar year; career interruptions of less than 6

months are less likely to have an impact on wages, especially for women who take

maternity leave, as current state laws require that women be allowed to return to work at

the same pay rate within a certain time range (6 months is most common, but for some

states it is as much as a year); and this formulation is a good first step because it allows

direct comparison with the results of the most recent studies (Light and Ureta 1995;

Kunze 2002), which also used the calendar year.

42

Defining the start of an individual's career, which also determines when work

experience begins accruing, is somewhat arbitrary. Here the start year is defined as the

first year that an individual is at least 18 years of age and either not enrolled in school or

employed full-time (greater than 30 hours per week) for at least 45 weeks out of the year.

The start year ranges from 1979 to 1993. Approximately 30% of individuals started their

career in 1979, and about 90% began their career before 1985.

Approximately 2,994 individuals, some 60% of whom were male, had worked

some amount in every year following the start of the career. While men may have had

more active and continuous work histories than women overall, they experienced career

interruptions as well. Total time spent out of the labor force for men was 2.9 years on

average, with a standard deviation of 3.7. Women spent on average 5.3 years out of the

labor force, with a standard deviation of 5.1. The total number of times INTRPn took on

the value of one was, on average, 2.53 for women and 0.93 for men. For women with

more than a high school education, this value was 1.75 compared to 3.12 for those with a

high school education or less. For men, the corresponding numbers were 0.69 and 1.09,

respectively. Although the INTRPn dummy variables only capture interruptions of a

sizeable duration and may not capture the whole duration, these cursory summary

statistics indicate that more educated workers interrupted their careers less frequently or

for shorter periods of time than did the less educated.

Table 3.1 presents the percentage of respondents who worked more than a given

amount of time after their career began, by gender and educational level, taking into

account any missing data. Educational attainment in 1994 is used as the benchmark,

43

since there are fewer missing values for that year than for later years and less than 5% of

the sample was enrolled in 1994. Moreover, the percentage enrolled did not decrease

much in subsequent years.

It is clear from the table that the more educated tended to work for a larger

fraction of potential career time than did the less educated. The only anomaly is that men

who attended graduate school were slightly less attached to the labor force than were

male college graduates, but this anomaly occurs because some men were still attending

graduate school as of 1994. The numbers also reveal that, not surprisingly, women were

less attached to the labor force than were men. Overall, about 75% of women had

worked more than half of their potential career, as compared to 89% of men. But men

were not as attached to the labor force as might be expected: less than 80% of them

worked more than 70% of the time. These numbers suggest that women took more time

to accumulate a given amount of experience than men, yet men seem to have experienced

appreciable nonemployment spells.

These percentages are slightly lower than similar calculations made by Light and

Ureta. For their comparable analysis, however, Light and Ureta only analyzed men and

women from ages 24 to 30, and they confronted important gaps in the data. Nevertheless,

in both cases, substantial variation in accumulated experience remains after accounting

for gender and education. As Light and Ureta pointed out, this suggests that wage

equations that employ the sum of experience and many individual-level controls may not

be the best way to measure differences in work experience.

Several variations on the following general wage model are explored in this

paper:

itiitit uZXWage +++= 21)ln( ββα (3.1)

The dependent variable is the natural logarithm of the average hourly wage, deflated by

the CPI, for person i at time t. The Xit represent regressors that vary over time for each

person, while the Zi include the time-invariant regressors. The Xit include experience

measures, such as the previously discussed FRCWKSWRKD1, FRCWKSWRKD2, . . . ,

FRCWKSWRKD22 and INTRP1, INTRP2, . . . , INTRP20, as well as dummy variables

indicating whether an individual was married, whether the individual had children present

in the household, how much education had been attained (less than high school, high

school graduate, some college, college graduate, or graduate school), whether the person

was currently enrolled in school, region of residence (Northeast, North Central, South,

West), and whether the individual was working part-time (less than 30 hours per week).

The unemployment rate for the labor market of current residence is also included. The

impact of the educational attainment variables is allowed to vary over the two decades, as

are the experience variables where possible, in accordance with previous findings that the

returns to education and experience were changing over this time period (see, for

example, Katz and Murphy 1992; Bound and Johnson 1992). Here the Zi include only a

dummy variable indicating if the person was white. Separate equations are estimated for

men and women.

The error term uit can be expressed as the sum of an individual component vi and

a random component εit, both random variables with zero mean and constant variance.

The random component is assumed to be uncorrelated with the explanatory variables, but

it is likely that the individual-specific component is correlated with a number of the 44

45

regressors. In fact, a Hausman test following random effects estimation of all

specifications presented below allows rejection of the null hypothesis of no correlation at

the 1% significance level. Thus fixed effects estimates are presented, which exploit the

within-person variation across time and yield consistent estimates.9

Although weeks worked are available for years in which individuals were not

interviewed, wages are not. Thus, observations for the years 1995, 1997, and 1999

cannot be included. Individuals potentially reported wages for up to 19 years, but not all

wages are used. Observations that precede the starting date of one's career are excluded.

Obviously, years in which an individual did not work have no positive wage observations

either. Individuals who never worked are thus excluded. Only 114 respondents, over

56% of them female, reported never working throughout 1979–99 once their career

began. The few individuals (11) with full years of missing labor force status are also

excluded. These criteria yield a sample of 5,935 individuals, 49% of whom are male, and

69,909 observations. Individuals appear in the unbalanced panel a minimum of once and

a maximum of 19 times, with an average of approximately 11.6 times.

3.4 RESULTS

Specification 2 (Basic Segmented Model) in Table 3.2, which includes total years

of actual experience and total years of nonemployment and their respective squares,

verifies that total time out of the labor force mattered. In both cases, wages fell at a

9 Hausman-Taylor (1981) instrumental variables estimation could potentially increase efficiency by exploiting both within-person and cross-person variation, but these estimates are not presented here because the gain from doing so is minimal. The only advantage is to allow estimation of the coefficient on the race variable, the only time-invariant variable in the model. Since this model includes no endogenous

46

decreasing rate with cumulative nonemployment time. The finding that total time out of

the labor force mattered, and not just whether an interruption occurred, suggests that not

all human capital accumulation was job-specific. For men, the loss incurred from the

first year of nonemployment in each decade was very similar, and virtually identical in

the 1990s, to the return to the first year of experience in that decade. Women faced a

similar scenario, with a slightly larger difference between the absolute values of the

return to experience and the return to nonemployment in the 1980s. The penalty from the

first year of nonemployment was approximately 74% of the gain from the first year of

employment for women in the 1980s, compared to over 82% for men. Thus, the absolute

loss associated with nonemployment was larger for men in both decades, and women

were not penalized as much as men for nonemployment in the 1980s relative to the return

to experience, though they were penalized at a similar rate in the 1990s. In addition,

although overall returns to experience were lower in the 1990s than in the 1980s, there

was a slight convergence in the returns to experience between the sexes over time.

These results are consistent with Light and Ureta's finding that interruptions are

less damaging for women than for men in the sense that the initial wage loss is smaller

and the rebound is quicker. It is possible that, in general, women select into careers that

are compatible with nonemployment, so that human capital is more easily restored. Light

and Ureta also suggested that men may be more likely than women to stop working for

reasons that are negatively correlated with their productivity. These results are also

consistent with women's increasing commitment to the labor force, since women's

time-invariant variables, Hausman-Taylor instrumental variables will yield the same coefficients as fixed effects on all the time-varying variables.

47

relative penalty from nonemployment increased by the 1990s, while their return to

experience crept closer to that of men. While discrimination against women may have

been declining, women may have been expecting fewer interruptions in the 1990s onward

and may have been transitioning to jobs less conducive to human capital restoration.

Specification 3 (Segmented Model with Interruption Dummies) is meant to

investigate how the timing of interruptions affected wages. Experience is still measured

cumulatively, but the INTRP1, INTRP2, . . . , INTRP20 dummy variables are included. This

specification is motivated by the disparate results of previous studies that estimated wage

change equations, in which the difference between an individual's first and last observed

wage over the course of the career was estimated as a function of the duration of the most

recent interruption, the duration of the sum of other nonemployment time, the sum of

experience prior to the most recent interruption, and the sum of experience after the most

recent interruption. Some researchers, such as Mincer and Ofek, have found that the loss

associated with the most recent interruption is statistically significant and greater than the

loss associated with the sum of previous nonemployment time; however, others have

found that the most recent interruption has no statistically significant effect on wage

growth. Corcoran, for example, found that only interruptions occurring near the start of

one's career have any statistically significant impact.

My replication of a basic wage change equation for women, presented in

Appendix B.1, suggests that the most recent career interruption alone did not have a

statistically significant impact on wage growth, though total time spent out of the labor

force did. This result seems counterintuitive, as one would expect interruptions that

48

occur relatively recently to have more impact on wage growth than those that occur

farther in the past. On the other hand, this result may simply be a function of the data

used. My data span a much longer time period than those used in previous studies that

have estimated wage change equations, and the likelihood that any given interruption

over such a long period will be statistically significant may be low. Because of the

inconsistent results and the fact that wage change equations do not make use of all

available data, considering the timing of nonemployment in a true panel study is relevant.

For both men and women, the null hypothesis that the coefficients on the

interruption dummies are jointly equal to zero is rejected at the 1% significance level.

The estimates indicate that more recent interruptions mattered as far back as 4 years ago

in a consistent manner for men. Prior to that, only interruptions 8 years ago and 20 years

ago are statistically significant at all. Why an interruption occurring 8 years ago mattered

and one occurring 7 years ago did not is unclear, but the large negative effect of an

interruption 20 years ago is difficult to ignore. This statistically significant result could

be owing to a combination of two factors.

First, as Corcoran found, interruptions early in the career matter. Second, the

construction of the data only allows interruptions as far back as 20 years. For some

individuals, an interruption 20 years ago may not have been the first career interruption,

so this variable may be picking up earlier interruptions. For women, with one or two

exceptions, interruptions mattered as far back as 9 years, so statistically significant

interruptions were more numerous for women than for men. However, in general, the

absolute and relative losses associated with interruptions were not as steep for women as

for men, which is consistent with the estimates of Specification 2, the Basic Segmented

49

Model. For example, men experienced a loss of almost 4.8% if they did not work three

years ago, which is 68% of the return to the third year of experience in the 1980s,

whereas women faced a loss of 2.9%, only 47% of the return to the third year of

experience in the 1980s. What Specification 3 adds beyond Specification 2 is that the

effect of past interruptions was more persistent for women, since they continued to be

influential as far back as 9 years. A possible explanation that is also consistent with a

lesser penalty for women than for men for a given interruption is that employers viewed

women's work interruptions as a signal that these workers were more likely to leave in

the future, and hence hired them for jobs that were compatible with nonemployment,

such as ones that required less training.10

The most detailed specification, Specification 4 (Work History Model with

Interruption Dummies) in Table 3.3, is very similar to that of Light and Ureta. It

accounts both for differences in total work experience accumulated and for the timing of

the experience by including the fraction of weeks worked array as well as the interruption

dummy variables. While some individuals are observed as far as 22 years into their

career, so that the experience array could contain as many as 22 elements, estimation

results for only 10 years are included separately, as the statistical significance of the

fraction of weeks worked falls off approximately 10 years ago for both men and women.

10 Specification 1 (Basic Mincer Model) is presented for the sake of comparison. The returns to experience in Specification 3 are similar to those in Specification 1. Comparing the estimates from Specification 2 to Specification 1, the returns to experience when interruption time is included are very similar for both sexes during the 1990s, but they increase slightly for the 1980s. The reason for this is not readily apparent, but it should be kept in mind that these are different models. It may also have something to do with the fact that not all experience is observed for individuals who began working prior to 1979, so the observed experience has inflated returns. Why the inclusion of nonemployment exacerbates this possible inflation remains unclear.

50

For years prior to 10 years in the past, summary measures are calculated. The fraction of

an individual's career that was spent working prior to 10 years ago is calculated, along

with the number of year-long interruptions experienced. The results indicate that, for

both sexes, once the timing of work experience has been taken into account with the

fraction of weeks worked variables, interruptions have no statistically significant

additional loss associated with them. The null hypothesis that the interruption variables

are jointly equal to zero cannot be rejected at the 20% level of significance for either men

or women.

Specification 5 (Basic Work History Model) presents the estimation with just the

fraction of weeks worked variables included. These estimates imply that specifications

including the sum of experience underestimate the return to experience in more recent

years and overestimate the return in past years. Light and Ureta's finding that their more

flexible work history model yielded higher returns to experience once a person's career

had been under way for about 6 years is not corroborated here. This is not immediately

apparent by looking at the estimates, but it can be seen by examining Figure 3.1, which

shows the general trend of the predicted natural logarithm of wages against years of

experience for Specifications 2, 3, and 5 for men and women. Specification 1, the Basic

Mincer Model, is not graphed because it is almost indistinguishable from the graph of

Specification 3, the Segmented Model with Interruption Dummies. The overall trends

look remarkably similar for men and women, which Light and Ureta also found. Prior to

about 12 years of experience, the various specifications yield only small differences in

predicted wages. After that, Specification 2 yields slightly higher returns to experience

than Specification 3, while Specification 5 yields lower returns. These trends also differ

51

from Kunze's findings. She showed that the difference between her work history model

and the simple Mincerian model was very small for men, but the work history model

consistently yielded higher returns for women.

The possible reasons for the differences between the studies are numerous. Each

study uses a slightly different sample and spans a different time period, with Kunze's

sample coming from a different country. Both Light and Ureta and Kunze used a young

sample; Kunze's sample was especially attached to the labor force. My sample spans a

wider range of ages and uses more complete data. Confining the analysis to the younger

workers in my sample produces results similar to those reported for my whole sample:

the Basic Work History Model continues to yield lower returns to experience than the

other specifications after about 12 years of experience has been accumulated. In

addition, the three studies use three different models. Notably, Kunze's model took the

reason for the interruption into account, which may be why she found differences

between the sexes, whereas Light and Ureta and I do not. One important common

finding of all three studies is that measuring an individual's experience in a more detailed

fashion than simply with a cumulative measure appears to be important at higher

experience levels. At low levels of experience, a cumulative measure provides just as

much information.

To further investigate the effect of interruptions, in Table 3.4 I present some

calculations based on the various estimates presented above. More specifically, Table 3.4

presents the wages of workers who experienced an interruption last year, 2 years ago, 3

years ago, and 4 years ago relative to the wages of workers who worked continuously.

The calculations assume that workers were five years into their working lives during the

52

1980s. Specification 1, the Basic Mincer Model, allows for an interruption only in the

sense that a year of experience is foregone. Specification 2 takes cumulative

nonemployment time into account, but the return to an interruption is the same no matter

when the interruption occurs. Intuitively, however, the penalty associated with a given

interruption should decline over time, and Specification 3, the Segmented Model with

Interruption Dummies, and Specification 5, the Basic Work History Model, allow for that

possibility.

For men, the loss in earnings upon returning to work ranged from about 13% to

almost 16% depending on whether Specification 3 or Specification 5 is considered, but

wages had rebounded to a great extent after just one year. For women, the penalty upon

returning to work ranged from almost 12% to almost 15%. In addition, the relative wage

rebound over four years was the same for both sexes under Specification 3,11 but it was

slightly quicker for men under Specification 5. This is consistent with the point made in

the previous discussion that although women are not penalized as much as men for a

given interruption, the effect of their interruptions persists longer.

An Application of the Work History Model: Wage Gaps and Employment

Expectations

Estimating alternatives to traditional Mincerian wage equations is certainly useful

for analyzing career interruptions, which unquestionably affect wages. However, when

career interruptions are not the explicit topic of study, are their wage effects large enough

11 The rebound is slower for women than for men when workers with more years of experience have interruptions further in the past than four years, which is consistent with the previously reported finding of this analysis that more past interruptions mattered for women than for men.

53

to justify supplementing traditional Mincerian wage equations? Light and Ureta applied

their work history specification to an analysis of the earnings gender gap. They

decomposed the gender wage gap into the portion due to differences in returns to

experience and the portion due to timing of experience by comparing the wages of men

and women with equal amounts of experience, using a procedure similar to that proposed

by Blinder (1973) and Oaxaca (1973).

First, Light and Ureta calculated the wage gap due to differences in the returns to

and timing of experience by multiplying each person's values for the fraction of weeks

worked by the coefficients for his or her gender and then subtracting the women's

average log wage for a particular experience category from the men's average for the

same experience category. This was decomposable into a portion due solely to timing

and a portion due solely to returns. The wage gap due solely to timing was calculated by

multiplying the fraction of weeks worked for all individuals by the coefficients from the

male regression and then subtracting the women's average from the men's average. Light

and Ureta found that the observed wage gap between men and women averaged about

40% across experience categories. The gap due to timing and returns between men and

women ranged from about 10% to 28%, depending on the experience level. The gap due

solely to timing ranged from less than 1% to about 6%; while these percentages are small,

they accounted for 20% to 30% of the total experience gap (due to both timing and

returns) for most experience groups.

My replication of this procedure yields slightly different results, as can be seen in

Table 3.5. Workers had up to 22 years of experience in the sample, and the wage gap

estimated by Specification 5, the Basic Work History Model, ranges from 13% to 20%,

54

depending on the amount of experience acquired. It is not surprising that the total gender

wage gap is smaller than Light and Ureta found, as their sample spanned an earlier time

period, 1968–81. The wage gap due to both timing of and returns to experience ranges

from a negligible amount to over 5%. This suggests that the vast majority of the gender

wage gap in my sample was accounted for by differences in mean endowments of the

other explanatory variables and the returns to these endowments. For almost all

experience groups, about 20% to 25% of the total estimated wage gap is accounted for by

the timing of and returns to experience. Light and Ureta, in contrast, found that for most

experience groups, almost 50% of the total gap was due to the timing of and returns to

experience.12 The wage gap due solely to the timing of experience in my sample is very

small, ranging from 0.6% to over 2%. However, between 18% and 50% of the gap due to

timing and returns is explained by timing, which is comparable to the range found by

Light and Ureta.

Light and Ureta's findings lead one to question the automatic use of the Mincerian

wage equation that pervades labor economics, and my findings corroborate this concern

to a lesser degree. While the estimated portion of the total gap explained by both the

timing of and the returns to experience is larger in Light and Ureta's study than in the

12 As with any wage gap decomposition, caution must be taken when interpreting the results. The effect of changes in individual coefficients used in the decomposition on the gender gap depends not only on how the variables are measured but also on the assumption that all of the other coefficients remain unchanged. Another possible reason for the difference, one might surmise, is that Light and Ureta's sample was slightly younger than mine. However, when I repeat this procedure for a sample similar to theirs, I find that for most experience groups less than 20% of the total wage gap is explained by timing and returns.

55

present one, the two studies show that a similar portion of the timing and returns gap is

accountable to the timing of experience alone.13

The Role of Career Expectations

Another potential problem with comparing wage equations between the sexes and

calculating wage gaps is the lack of consideration for career expectations, and exploring

this topic seems a natural extension of this study. Perhaps women's returns to experience

are lower than men's because their career interruptions are expected to a greater degree

than men's, and hence women invest less in human capital. If the currently estimated

returns to the fraction of weeks worked are underestimated for women because of a

failure to take career expectations into account, then the portion of the gap due to timing

will be understated, while the portion due to returns alone will be overstated. Human

capital theory predicts that individuals who expect interruptions will have slower wage

growth than those who are employed continuously or who experience unanticipated

interruptions. They are willing to accept this slower wage growth in return for a higher

initial wage. Thus, if expectations about future interruptions affect current decisions

about human capital investment, the interaction of a variable indicating the extent of

future career interruptions with current experience will have a negative coefficient, while

including the variable by itself will result in a positive coefficient.

13 An analysis of the earnings gap between women without children and women with children, presented in Appendix B.2, yields slightly different results. The timing effect again explains a very small portion of the overall gap, and for most experience groups it explains a smaller portion of the gap due to timing and returns than it does for the gender gap decomposition. Holding the amount of experience constant, the returns to experience explain most of the total gap between mothers and non-mothers. Again, however, caution must be exercised in interpreting detailed wage decompositions.

56

The question of whether a future planned interruption will have an impact on

current earnings growth has been discussed at length (see, for example, Polachek 1975;

Weiss and Gronau 1981), but few attempts have been made to determine the impact

empirically. No study has been able to make full use of panel data, and none has looked

at both men and women. Sandell and Shapiro (1979) used a variable from the National

Longitudinal Surveys of Young Women (NLSYW) indicating what an individual

expected to be doing at 35 years of age as of the start of the survey in 1968. They

estimated a cross-sectional wage equation that included a dummy variable equal to one if

a woman planned to work at age 35 and interaction terms for work experience and plans

to work, and their results supported the human capital hypothesis. However, their wage

equations did not incorporate time spent out of the labor force, just work experience;

thus, it may be that these interaction terms were capturing the effects of time spent out of

the labor force.

Cox (1984) used data from the 1973 Current Population Survey and the 1937–73

Social Security Longitudinal Earnings Public Use File to estimate segmented earnings

functions for women, interacting a future interruption with current experience. He

restricted his study to women who experienced either no interruptions or one interruption

at most, which neglected a large number of individuals and resulted in a small sample

size. Nevertheless, his results partially supported the human capital hypothesis. Earnings

growth in general was lower if a future work interruption existed, but relatively longer

future career interruptions were associated with a slightly higher rate of earnings growth

early in the life cycle.

57

My analysis, presented in Table 3.6, includes both men and women. For each

year, I calculate the fraction of future years spent not working, FUTINTRP, and interact

this variable with current work experience. Specification 2 with Expectations is an

extension of the Basic Segmented Model. As human capital theory predicts, the

coefficient on FUTINTRP is positive and statistically significant for both sexes, but the

magnitude is larger for men. This suggests that women did not require as high an initial

wage to compensate them for slower wage growth prior to an interruption. Moreover, the

interaction between FUTINTRP and experience has negative coefficients in both decades.

The absolute magnitudes of the coefficients are similar across the sexes, but relative to

the return to experience, women faced slower wage growth prior to interruptions. In

addition, the interaction terms are more statistically significant for women; in fact, the

interaction term for men in the 1980s is insignificant. This is consistent with women

being more likely than men to expect future interruptions. Controlling for expectations

does not significantly affect the returns to experience for either sex, suggesting that there

are other explanations for the return to experience for women being lower than that for

men. Again, one possibility is employer discrimination.

Specification 5 with Expectations is an extension of the Basic Work History

Model. The fraction of weeks worked n years ago, for example, is interacted with the

value of FUTINTRP n years ago in order to measure what an individual's career

expectations were n years ago. Now the coefficient on FUTINTRP is not statistically

significant for women, but it is still positive and statistically significant for men. This is

more extreme than the result from Specification 2, suggesting that women did not require

any compensation for slower wage growth due to future interruptions. The coefficients

58

on the interaction terms, while mostly negative for both sexes, are statistically significant

only about half of the time. Because of the unwieldy nature of this specification, I am

hesitant to place much emphasis on these results. It is interesting to note, however, that

the returns to past experience again do not increase once an attempt is made to control for

career expectations. This suggests that the portion of the gender gap due to timing is not

understated because of a failure to take career expectations into account.

Of course, it is important to remember that this analysis uses an ex post measure

of expectations, which assumes that individuals correctly anticipate future interruptions.

An ex post measure of expectations is certainly not perfect, but it is the most practical

approach given data limitations. More specifically, the measure used here assumes that

individuals correctly anticipated how much interruption time they would experience in

the future, not just whether an interruption would occur. It seems reasonable to suppose

that a worker is able to correctly predict more than just the existence of any future

interruptions. Nevertheless, it is encouraging that other specifications with simpler

measures of expectations (not presented here), such as whether an interruption of at least

a year occurs in the future, yield similar general conclusions. Taken together, the results

suggest that future career interruptions do affect current wages and are expected to some

degree for both sexes, probably more so for women than for men.

3.5 CONCLUSION

This study finds that total nonemployment time has a statistically significant

depreciation effect on wages, which corroborates past findings. Previous literature,

however, has been divided as to whether any given interruption, especially the most

59

recent interruption, matters. Researchers estimating wage change equations in the 1970s

and 1980s failed to come to a consensus. More recent studies have found that only

interruptions occurring in the past few years matter. This paper, using data that are more

complete and span a longer time period than the data used in previous studies, finds that,

while more recent interruptions mattered, past interruptions and ones that occurred at the

very beginning of an individual's career also mattered. It also finds that wage losses

associated with nonemployment were less severe for women than for men, although more

past interruptions seemed to matter for women than men. In addition, once the timing of

an individual's work experience has been taken into account, I find that little further

penalty is associated with long periods of nonemployment. In these data, the timing of

experience explains a very small percentage of the gender wage gap, and controlling for

career expectations does not change this result. However, career expectations did affect

current wages for both men and women to some extent, though there is limited evidence

suggesting that women's interruptions were more anticipated.

When career interruptions are not the focus of study, it is not clear whether

estimating traditional Mincerian wage equations is justified. However, this study

indicates that such estimations are less problematic than previous ones, like Light and

Ureta's. It is beyond the scope of this paper to investigate whether depreciation effects

vary with type of interruption, but such a study might provide insight into why the wage

losses of interruptions vary by sex. It might also be useful in exploring the respective

roles of human capital, signaling, and job mismatch theories in individuals' work

histories.

60

Chapter 4: The Mills-Muth Model of Urban Spatial Structure:

Surviving the Test of Time?

In fact, I believe that the remarkable fact is not that the chimp types so badly, but that it types at all; the broad predictions from the simple models remain more accurate than I would have expected, given the massive dispersion of employment in U.S. metropolitan areas and the pervasiveness in the U.S. of fragmented local government jurisdictions.

- Edwin S. Mills (2000), p. 18

4.1 INTRODUCTION

Does the chimp still really type? To what extent do the very broadest predictions

of the original Mills-Muth model of urban spatial structure apply today? The statement

above by Mills coupled with an empirical study by Brueckner and Fansler (1983), which

finds that the most general implications do hold for a sample of 1970 urbanized areas,

provoke these questions. Since urban spatial structure analysis grows extremely

complicated with efforts to add increased realism to the models, and many researchers in

urban economics and related areas still evoke implications of the Mills-Muth model in

their work, it seems useful to know if the basic model still applies at the city level. Given

the changing nature of cities over the past decades, especially the increased polycentricity

of cities and the less predictable commuting patterns, one might be skeptical that the

model does in fact still hold substantial predictive power.

61

McMillen (2004) provides a thorough review of the various ways that the Mills-

Muth model has been empirically tested and an argument that, despite the changing

nature of cities and a general consensus that the basic model is no longer accurate, the

monocentric city model is still the dominant model of urban structure. Attempts to

directly estimate the predictions of the Mills-Muth model fall into two categories: (i)

studies that look at one city at a time and try to determine whether the price of a housing

unit, the capital-land ratio, land values, and population density all fall with increasing

distance from the central city; and (ii) studies that test the model’s comparative statics

predictions, that city area is increasing in population and income but decreasing in

agricultural land value and commuting costs, with a cross-section of cities or by looking

at one city over time. The comparative statics approach using a cross-section of cities is

uncommon; in fact, the Brueckner and Fansler study is the only one that analyzes more

than a handful of cities. They compare 40 urbanized areas using 1970 data, and despite

using measures of commuting cost that certainly aren’t perfect, they find strong support

for the model’s predictions.

What follows is in part an update to the Brueckner and Fansler study. I estimate a

slightly modified version of their empirical model in order to test comparative statics

results of the Mills-Muth model. However, while they test these implications with 1970

data for a relatively small sample of urbanized areas due to data limitations, I attempt to

overcome these limitations and test the predictions for all urbanized areas using 2000

data. I also use different measures of commuting costs, where available, and address the

changing nature of cities with data on commuting patters and the polycentricity of cities.

The results suggest that the monocentric model of the city still has predictive power in

the year 2000. The next section of the paper discusses the implications of the model

tested by Brueckner and Fansler as well as their findings. Section 3 discusses the data

used in the empirical analysis, Section 4 presents the empirical model and the results, and

Section 5 contains discussion and concluding remarks.

4.2 IMPLICATIONS AND A TEST OF THE MILLS-MUTH MODEL

The simple Mills-Muth model, as outlined by Brueckner and Fansler, assumes

that consumers have the same income I at the CBD and have identical preferences over

housing (residential lot size), q, and a composite numeraire good, z. Housing rents for

price p(x) per unit, where p depends on distance x from the CBD. Consumers also face a

commuting cost t per round-trip mile and maximize utility subject to a budget constraint:

Max U(z,q) s.t. I = z + p(x)q + tx (4.1) z,q,x Because consumers are free to move around and p varies with x, an implication of the

model is that, in equilibrium, all consumers reach the same utility level u. To keep a

consumer indifferent between any two given locations, the price of housing must be

lower at the location that is farthest from the CBD. Inputs to housing are assumed to be

capital and land, with a constant returns to scale housing production function. Producers

maximize profit per unit of land, ph(K) – iK – r, where r is land rent, i is the rental price

of capital, K is capital per unit of land, and h is amount of housing per unit of land.

If population density is defined as D(x,t,I,u) ≡ h(K)/q, then the equilibrium for the

city can be written as:

aruItxr =),,,( (4.2)

62

∫ =x

NdxuItxxD0

),,,(2π (4.3)

where x is the distance to the urban edge, ra is the agricultural land rent, and N is the

urban population. Equation 4.2 is an arbitrage condition, which indicates that urban land

rents must equal agricultural land rents at the urban edge. Equation 4.3 simply states that

the urban population must be accommodated inside the city boundary. The following

comparative statics results, first derived by Wheaton (1976) and requiring a utility

function such that both goods are normal and have positive income effects, are the ones

tested in the empirical estimation:

0,0,0,0 <∂∂

<∂∂

>∂∂

>∂∂

tx

rx

Ix

Nx

a

(4.4)

As population increases, so does the radius of the city. A higher level of income

increases city size as demand for housing increases. A city becomes smaller with an

increase in the value of agricultural land, which increases the opportunity cost of urban

land. On the other hand, an increase in the commuting cost decreases city size because of

the income effect and hence less housing demand. It should be noted that the model

presented here, in its simplest form, does not account for time costs of commuting. As

McMillen points out, expanding the model to account for time costs leads to an

ambiguous comparative statics prediction for income. While an increase in income leads

residents to prefer living farther from the central city due to an increase in demand, it also

increases the opportunity cost of time spent commuting, making housing closer to the

central city more desirable. Thus, the net effect is ambiguous, though typically empirical

63

64

studies find what the basic model predicts, that an increase in income leads to a larger

city size.14

Brueckner and Fansler use a Box-Cox specification, with a single transformation

parameter applied to both dependent and independent variables, and show that an

urbanized area’s total land area (and hence distance from the city center to the urban-rural

boundary) increases with population and income but decreases with agricultural land

values. They use data from the 1970 Census, and their data set consists of only forty

urbanized areas with 1970 populations that range from 52,000 to 257,000. Because data

on agricultural land values are available only by county, their sample includes only

urbanized areas contained within a single county in an effort to accurately measure land

values adjacent to the developed portion of the city. However, this clearly neglects a

large number of urbanized areas. In addition, their proxies for commuting cost have no

significant effect upon land area, though the coefficients are negative as expected. The

two proxies are the percentage of commuters using public transportation and the

percentage of households owning at least one automobile. The intuition behind these

proxies is that high levels of automobile usage and low levels of public transportation

usage indicate a low cost of commuting per mile. The former hopefully indicate low

congestion levels, holding income constant, while the latter are associated with a high

time cost per mile. Overall, their results, reproduced in Appendix C.1, support the

simplest predictions of the basic Mills-Muth model. They argue this is evidence that city

size is determined by an organized, market-driven allocation of land use, not uncontrolled

14 See Mankin (1972) who finds that when leisure and commuting distance are complements, it is possible that a rise in wage income will reduce commuting distance.

65

sprawl.

4.3 DATA

The data employed are from the 2000 Census of Population and Housing, the

Texas Transportation Institute, and both the 1997 and 2002 Censuses of Agriculture. I

also use McMillen and Smith’s (2003) estimated number of subcenters in an urbanized

area. The unit of observation is the United States urbanized area (UA).15 The urbanized

area is used as opposed to the Metropolitan Statistical Area (MSA) because the

boundaries are less artificial. While the physical shape of an MSA is defined by county

boundaries, the shape of an urbanized area is driven to a larger extent by market forces

and where people choose to work and live. Moreover, while the model assumes that

agricultural land is adjacent to but outside of the circular city's boundary, an MSA is

much more likely to contain agricultural land than is an urbanized area. The sample used

here consists of all 452 urbanized areas in the United States as of 2000, which have

populations ranging from just under 50,000 to over 17 million. Data are also available

for smaller cities and towns, which the Census calls urban clusters (UC).

The measure used for agricultural land values is calculated using the 2000 Census

and the 1997 and 2002 Censuses of Agriculture. Two measures of agricultural land

values are available, the market value of agricultural products sold per acre and the

estimated market value of agricultural land and buildings per acre. It is unclear which

variable Brueckner and Fansler used, as they call their measure simply the agricultural

15 See Appendix C.2 for relevant Census definitions.

66

land value per acre. Nevertheless, the measure that excluded buildings would seem to

better coincide with the requirements of the theoretical model. Land values are available

by county, but many urbanized areas have land area in more than one county. Thus, it is

necessary to find a way to compute one land value per urbanized area in order to be

consistent with an assumption of the model, namely that agricultural land rent is constant

beyond the urban-rural boundary. The Census of Population and Housing contains

information on the percentage of an urbanized area’s total land area that is comprised by

any given county. The Census of Agriculture provides the value of agricultural land, and

a value for 2000 is imputed from the two different years available for the Census based

on the annual growth rate. Then, the land value for each county that makes up part of an

urbanized area is weighted by the percentage of the urbanized area that falls in that

county. The result is a weighted average land value for each urbanized area in dollars per

acre. While it would be ideal to have the length of the urbanized area's boundary that

falls in each county, such data are not readily available.

Measuring commuting cost is most problematic. There are perhaps no measures

better than the one used by Brueckner and Fansler available for all urbanized areas. The

only other possibility that the Census offers is the average commute time or the

percentage of workers whose commute lasts more than a certain amount of time.

Although it is not a monetary cost, longer commutes will be positively correlated with

monetary costs and opportunity costs. In addition, the Texas Transportation Institute

provides several possible measures of commuting cost, but only for 85 large urbanized

areas. One is a travel time index, which is a measure of congestion during peak periods.

More specifically, it is the ratio of the travel time during the peak period to the time

67

required to make the same trip at free-flow speeds. Another possibility is the thousands

of miles traveled per day by vehicles per mile of freeway lane. This captures commuting

cost at all times of day, whereas the travel time index does so for peak periods of

congestion. Last, the institute also calculates a monetary cost of congestion, measured as

the value of travel delay and extra fuel consumed in traffic congestion. Delay is the extra

travel time compared to some standard, in this case 65 mph on freeways and 30 mph on

city streets.

The income measure, available from the 2000 Census, is simply the median

family income in the urbanized area. Other useful measures are available to address the

increasing polycentricity of urbanized areas and investigate how this might affect the

empirical results. The Census does have information on the percentage of workers living

in an MSA who work in the central city of the same MSA. In addition, McMillen and

Smith have estimated the number of subcenters in over 60 areas using commuting costs

from the Texas Transportation Institute. They identify subcenters as local peaks in the

predictions from nonparametric regressions of employment density on distance from the

city center. Table 4.1 presents some basic descriptive statistics of the key variables.

4.4 EMPIRICAL MODEL AND RESULTS

Since data requirements are not sufficient to allow non-parametric estimation, a

Box-Cox equation is estimated, where area of the urbanized area in square miles is

related to population, average agricultural land value, median family income, and a

measure of commuting costs. Allowing for some form of non-linearity seems

reasonable. For example, the land area of an urbanized area might increase with

population at a decreasing rate. Similar suppositions can be made for the other

covariates. Thus, given a vector x of positive covariates, the model to be estimated,

which incorporates transformations on the dependent as well as the independent

variables,16 takes the following form:

∑=

++=4

1

)()(

kkk xy εβα λθ (4.5)

where =)(θyθ

θ 1−y when θ ≠ 0

68

log(y) when θ = 0

and =)(λxλ

λ 1−x when λ ≠ 0

log(x) when λ = 0

Estimation via maximum likelihood is fairly straightforward, partly since the log-

likelihood function incorporates a Jacobian term that prevents θ from becoming too

small. Assuming that ε ~ N[0,σ2], maximization of the following log-likelihood function

with respect to β, θ, and λ yields consistent estimates and is asymptotically efficient:

16 Davidson and MacKinnon (1993) point out that using more than one transformation parameter can help deal with the presence of heteroskedasticity. In a simpler Box-Cox model, the single transformation parameter is forced to play two roles; more specifically, it affects both the properties of the residuals and the functional form of the regression function. When the transformation parameter on the dependent variable is allowed to differ from those on the independent variables, then the former primarily affects the properties of the error terms, while the latter primarily affect the functional form.

2)(

1

)(2

1

2 )(2

1ln)1()log(2

)2log(2

ln βσ

θσπ λθi

n

ii

n

ii xyynnL −−−+−−= ∑∑

==

(4.6)

Table 4.2 presents the maximum likelihood estimates using the complete sample

of 452 urbanized areas and one of the proxies for commuting costs used by Brueckner

and Fansler, the percentage of households owning at least one vehicle. A dummy

variable, not transformed, equal to one if the urbanized area borders a Great Lake,

Mexico, or any coast is included, since such geographical constraints can limit growth

that might occur in their absence. The results of the estimation of Specification 1 are

consistent with the comparative statics predictions of the Mills-Muth model. However,

only the coefficients on population and income are significant at above the 10% level.

The coefficient on income is negative, however, which indicates that, on average, the

effect of the increasing opportunity cost of time as income rises may outweigh that of

increased demand for more affordable housing farther from the central city. The

coefficient on the percentage of households owning at least one car, while positive, is not

quite significant at the 10% level. Moreover, the percentage of households owning at

least one car is certainly not an optimal measure of commuting costs, although it may

have been a better measure in the 1970s than it is today. The results may simply be

reflecting that, in larger cities, people are more likely to need a car to get to their

destination. Bordering a large body of water or Mexico does not have a significant effect

on land area, although the coefficient is positive, so that these cities are larger than

average. Specification 2 includes as a covariate the number of subcenters in the

urbanized area, as estimated by McMillen and Smith. The rationale for including the

number of subcenters is to account for the increasing polycentricity of urbanized areas,

69

70

since the predictions of the Mills-Muth model are based on a monocentric model.

However, once the number of subcenters is included, there are few differences in the

results. The coefficient on population is reduced, but this is not surprising since

population and the number of subcenters are positively correlated. Part of the reason that

few differences between Specification 1 and Specification 2 are seen may be because the

number of subcenters could only be estimated for just over 60 urbanized areas. Although

these 60-plus urbanized areas are for the most part the largest urbanized areas and the

most likely to have subcenters, the assumption was made that the number of subcenters

for the other urbanized areas was zero. Interestingly, however, the coefficient on the

number of subcenters is negative and statistically significant at the 10% level.

Conditional on population, having more subcenters is associated with a smaller land area,

suggesting that subcenters are more likely to develop in densely populated areas.

Because the transformation parameters on the covariates are not significantly different

from zero, and the transformation parameter, theta, on the independent variable is

marginally significant in both Specifications 1 and 2, it seems reasonable to test the Box-

Cox specification against a double-log specification. Using a likelihood ratio test, the

hypothesis that both transformation parameters are equal to zero cannot be rejected at the

1% level of significance for Specification 2. Even though the null hypothesis is rejected

for Specification 1 and is very close to being rejected for Specification 2, having a

transformation parameter on the right-hand side variables that is always insignificantly

different from zero and a left-hand side transformation parameter that is positive and

moderately significant is expected if the correct specification were log-linear with some

heteroskedasticity of the error terms. Thus, a double-log estimation with

71

heteroskedasticity-consistent standard error is presented as Specification 3. The results

are similar, though the estimates are less precise than with the Box-Cox specification.

The estimation reveals that that elasticity of land area with respect to population is 0.91,

with respect to income is -0.39, and with respect to land values is -.03.

Table C.4 in Appendix C.3 presents the same estimations using the other proxy

for commuting costs used by Brueckner and Fansler, the percentage of workers using

public transport. Again, the signs of the coefficients are all consistent with the theory,

but now the coefficients on income and land value are not statistically significant. This

proxy is just as problematic as the previous one. A large fraction of workers using public

transport may not reflect a high commuting cost, especially in the year 2000. Instead, it

may simply reflect that public transportation is better and more heavily used in densely

populated cities. Unfortunately, a very convincing measure of commuting cost is not

available for all urbanized areas. The only other option is using travel time to work. One

might expect this to be positively correlated with a monetary measure of commuting cost,

but it will also be positively correlated with the physical size of the city. Since the theory

would predict that the coefficient on commuting cost would be negative, the positive

correlation may cause us to observe the opposite. A better measure might be travel time

per mile, but the distance to work is not readily available. Nevertheless, Table C.5 in

Appendix C.3 presents the estimations with the average travel time to work as a measure

of commuting costs. The coefficient on average travel time is indeed positive for the

whole sample of urbanized areas, but when the sample is restricted to cities in which over

eighty-five percent of the population works in the central city of their MSA of residence,

the coefficient becomes negative. The non-transformed variables for the number of

72

subcenters and for being on a large body of water are left out because there is hardly any

variation in them when the sample is restricted to cities that have a large fraction of

workers commuting to the central city. This result provides evidence that the predictions

of the Mills-Muth model may in fact hold up better for monocentric cities. Overall, the

predictions of the model hold up fairly well despite which problematic measure of

commuting cost is used.

In order to use the better measures of commuting cost that are available, it is

necessary to restrict the sample to 85 urbanized areas, the cities for which the Texas

Transportation Institute calculates these measures. Table 4.3 presents estimates with the

institute’s measure of annual congestion cost, in millions of dollars. It is the value of

travel delay and extra fuel consumed in traffic congestion annually, where delay is the

extra travel time compared to some standard, in this case 65 mph on freeways and 30

mph on city streets. One benefit of this measure is that it is an actual monetary cost of

congestion. All covariates, including the commuting cost, have significant coefficients

with the expected sign. Bordering a large body of water or the coast now is negatively

correlated with the physical size of the city, although it is still not statistically significant.

This is a reasonable outcome for larger cities that might be constrained by geography,

whereas across all cities, such geographical locations afford cities opportunity for

economic growth to a certain point. Although both transformation parameters are

statistically different from zero when the number of subcenters is included, I have also

presented the double-log specification. Similar results are found when the congestion

cost is converted to a per person or per peak traveler measure. Moreover, similar results

are found when using the other two measures provided by the institute, the travel time

73

index and the daily vehicle miles of travel per mile of freeway lanes. These results are

presented in Tables C.6 and C.7 in Appendix C.3.

In all of the estimations using the Texas Transportation Institute measures of

commuting cost, the coefficient on income is now positive and significant, where it was

negative and usually significant when the estimation was performed on the whole sample

of urbanized areas. The cities for which the Texas Transportation Institute provides data

are for the most part the largest cities in the country, so this indicates that in larger

urbanized areas the tradeoff between housing demand and commuting cost elasticities is

different than in smaller cities. In larger ones, the price effect of increased demand for

housing when income rises outweighs the effect of the increase in aversion to time spent

commuting. The tradeoff between these two elasticities would be an interesting topic for

further study.

Compared to the Brueckner and Fansler results, these results are quite similar,

which is fairly impressive given the amount of time that passed and the changes in cities

that occurred in the interim. They obtain estimates with the expected sign for all

covariates. Moreover, all are significant at the 5% level with the exception of the proxies

for commuting cost. Most of the variables I use are measured in a comparable way, save

for perhaps the value of agricultural land and the commuting cost variables for estimation

on the smaller sample of urbanized areas. My estimates using the alternative land value

measure, the estimated value of land and buildings per acre, do not yield significant

results. Brueckner and Fansler find the coefficient on land value to be significant, so if

this is the measure they use, then perhaps this is evidence that it is more difficult to find

the expected signs and significance using modern data due to the increasing complexity

74

of cities. It is not that the Mills-Muth model does not hold to a large extent for modern

cities, but perhaps it requires better measurement of the variables of interest to get the

results predicted by the theory. Their estimation involves only one transformation

parameter on both dependent and independent variables, and it converges to a much

higher value of 0.53. Since the value of 1 lies at the edge of the confidence interval for

the transformation parameter, they also present a linear specification and the

corresponding elasticities evaluated at the sample means. The elasticities indicate that a

1% increase in population results in an increase in land area of approximately 1.1%, a 1%

increase in land values results in a decrease in land area of approximately 0.25%, and a

1% increase in income increases area by about 1.5%. The elasticity with respect to

population is quite similar in the current study, though the elasticity with respect to land

value is smaller, and the elasticity with respect to income is of the opposite sign for the

whole sample of urbanized areas. Brueckner and Fansler only include urbanized areas

contained within a single county in their study. This reduces the sample to only 40

urbanized areas, the populations of which range from 52,000 to 257,000, out of a total of

248 urbanized areas in 1970. In this study, when the sample is restricted to urbanized

areas associated with one county, 234 urbanized areas remain, with populations ranging

from 50,000 to 2.7 million. Estimation of the model when only one-county urbanized

areas are included does not reveal stronger support for the model using 2000 data.

However, urbanized areas contained in one county are not much more likely to have a

larger percentage of workers commuting to the central city.

75

4.5 CONCLUSION

The Mills-Muth model and its assumptions are no doubt highly stylized.

However, quite a bit of research subsequent to its inception supports many of its

generalizations. For example, making the assumption that an urbanized area is

monocentric is a large one, one that seems especially sensitive to the passage of time.

The development of secondary employment centers in many urban areas has become

quite a widespread phenomenon, and the literature indicates that the degree of

polycentricity has been increasing over time. Mills supports his argument that the biggest

failure of the model is the predicted location of all businesses in adjoining space in the

CBD by pointing out that only about 10% of metro-area employment in the 1990s was

located in the CBD in some U.S. cities. Certainly casual observation suggests that, at

least in some cities, commuters pass one another in opposite directions on their way to

work. A comprehensive model should then allow for heterogeneity of preferences as

well as subcenters, otherwise people would move to reduce commuting costs. However,

by treating each subcenter as a miniature urbanized area, Muth (1969) shows that patterns

of land use around the subcenters follow the predictions of the model.

Assuming that all urban residents earn the same income is of course unrealistic.

This issue has been addressed by a number of studies, including Wheaton (1976) and

Hartwick et al. (1976), who analyze comparative statics results of an equilibrium in

which the city has several income classes. The results show that most of the crucial

predictions of the model still hold under these circumstances. Moreover, the model treats

housing as a single commodity, floor space. Clearly houses are characterized by a vector

of amenities and attributes, and the literature on hedonic pricing makes it clear that these

76

different attributes matter when it comes to the value of a house. However, several

studies have included a vector of housing attributes in an analysis of urban spatial

structure, and it turns out that once again many of the important predictions of the model

remain intact.17

While many studies have attempted to add needed realism to the simple

monocentric model, they often simultaneously highlight the simple model’s artfulness

and success in capturing some essential features of cities. It is likely that refinements and

caveats are necessary to allow more flexibility in the model’s predictions if the

predictions are to hold empirically in the future. Yet, despite the fact that city structure,

while still governed by market forces, has grown increasingly complex, it seems that the

chimp still types, if at an increasingly slower rate.

17 See, for example, Büttler (1981) and Brueckner (1983).

77

Chapter 5: Conclusion

The three chapters comprising this dissertation have examined potential causes

and outcomes of some of the most important decisions an individual can make: when to

marry, whether or not take time off from work, and in what location to live and work.

They have tested the theoretical predictions underlying these decisions with recent data

and have provided some answers, which undoubtedly have created more questions and

further avenues for exploration.

The first chapter provides insight into the nature of human behavior. More

specifically, it adds to knowledge of what compels people to marry when they do. Many

factors come into play to affect the timing of an individual’s marriage, some out of one’s

control. Yet personal feelings and attitudes are a major factor, and this essay shows that

attitudes about risk are relevant. Intuitively, there are at least two ways in which risk

attitudes affect timing of marriage, through the search process itself and because of risk

pooling. This chapter finds that the risk averse marry sooner, and the effect is larger for

men. There is evidence that women value risk aversion and the behavior that comes

along with it in their potential mates. This idea is certainly consistent with gender

research in other fields, such as Psychology, where there is a general consensus that

women value men with significant financial resources while men value other

characteristics such as physical attractiveness. Perhaps men are less willing to take a

chance on an intelligent woman for fear she will find a better option down the road.

78

While a few previous studies in Economics empirically test how risk attitudes affect

behavior, none ask how these attitudes affect family formation and dissolution. This

chapter opens up several avenues of potential research. Can changes in risk attitudes

explain a portion of the decline in marriage rates? Do more risk averse people marry

more risk averse people, as the search model predicts? New surveys that contain a richer

set of questions about risk attitudes make some of these questions answerable.

The second chapter investigates the wage implications of an individual’s actual

decision to stop working for an extended period of time as well as the implications of

how much they expect to work in the future. It is no surprise that taking an extended

break from work has a negative impact on wages, as there is plenty of anecdotal evidence

from, for example, mothers who go back to work once their children start school. This

essay finds that a given career interruption affects wages for a longer period of time for

women even though the initial penalty is larger for men. The investigation also suggests

that the timing of work experience does not explain a large portion of the gender wage

gap. Moreover, the empirical work supports the theory that women’s career interruptions

are more anticipated than men’s. This essay contributes to the literature because it spans

a longer period of time than previous studies and incorporates the effect of expectations

about career interruptions on future wages. Future research that is able to carefully

distinguish between the various reasons for career interruptions would be useful because

perhaps then the causes of the gender differences observed here could be better

understood. On a more practical level, such research would be useful for those who are

considering a career interruption so that they can better predict its effect on their career.

79

The third chapter finds that a simple, stylized model of monocentric city structure

developed decades ago holds up fairly well using modern data at the city level. This

might be surprising to some researchers, as there seems to be a general consensus of late

that the basic model can no longer be applied to urban structure because of increasing

polycentricity. Commuters pass one another in opposite directions on their way to work

now more than ever, and the number of employment subcenters in various cities is on the

rise. This essay empirically tests the comparative statics predictions of the simple model

for all urbanized areas, something that has not been done previously. The last study to

include more than a handful of cities was conducted over thirty years ago. This chapter

also begins to account for the level of polycentricity in cities by using recent estimates of

the number of subcenters for many cities. A richer study would look at many urbanized

areas over time at a finer level than the city as a whole, but the data collection for such a

project would be daunting. Nevertheless, this essay does provide other ideas for future

study. For example, what is the net effect of an increase in income on housing location

choice? Do residents choose to live farther away from the center of the city to take

advantage of lower prices, or do they choose to live closer to the center to avoid the

increased opportunity cost of time?

Each chapter asks important questions about how and why people make important

decisions and the outcomes of these decisions. The answers either give us insight into an

aspect of individuals’ decision-making processes or provide information to both

individuals making the decisions and policymakers who must deal with the implications

of these decisions. For example, if the timing of work experience does not account for a

majority of the gender earnings gap, it is necessary to discover what does in order to

80

effectively narrow the gap. Each chapter also provokes additional questions, an

important function of research, whose answers will further knowledge of the fundamental

nature of human behavior.

Table and Figures

Table 2.1 Distribution of Risk Aversion in 1993 by Characteristics

Very Strongly Risk Averse

Strongly Risk Averse

Moderately Risk Averse

Weakly Risk Averse Observations

Total Population 46 12 17 25 9,008

Sex:Men 43 11 17 29 4,46Women 49 13 17 21 4,54

Age:28-30 44 12 18 27 3,27431-33 47 12 17 24 3,56634-36 48 12 16 24 2,168

Education:Less than high school 46 8 16 30 1,303High school 49 11 16 24 3,915Some college 45 13 18 24 2,08College graduate 41 15 19 25 1,059Graduate School 41 18 18 23 644

Race:White 46 13 18 23 4,52Black 47 10 15 28 2,72Hispanic 46 11 16 27 1,760

Kids:No kids in HH 41 11 17 30 3,510Kids less than 6 in HH 48 13 17 22 3,479Kids 6 to 13 in HH 51 11 16 21 1,802Kids 14 and older in HH 50 10 16 25 214

Distribution of Risk Aversion in 1993 by Characteristics (%)Table 2.1

26

6

80

81

Table 2.2 Distribution of Risk Aversion by Age at First Marriage

Age at First Marriage

Very Strongly Risk Averse

Strongly Risk Averse

Moderately Risk Averse

Weakly Risk Averse Observations

Less than 21 52 11 16 21 2,09221-25 49 13 17 21 2,34025-30 43 14 18 25 1,61930+ 41 13 18 29 1,055

Never Married 41 10 16 34 1,723

Less than 21 53 11 16 20 1,43521-25 50 16 18 17 1,14525-30 46 17 16 21 69530+ 45 13 17 26 443

Never Married 45 11 17 27 729

Less than 21 47 11 16 25 65721-25 49 10 16 24 1,19525-30 42 12 19 27 92430+ 38 12 19 31 612

Never Married 38 9 15 38 994

Men

Distribution of Risk Aversion by Age at First Marriage (%)Table 2.2

All

Women

82

Table 2.3 Survival Analysis of Time to First Marriage for Whole Sample Using 1993 Risk Measure

83

Varia

ble

Coe

ffici

ent

Haz

ard

Rat

ioz-

stat

istic

P>|z

|C

oeffi

cien

tH

azar

d R

atio

z-st

atis

ticP>

|z|

Very

Stro

ngly

Ris

k Av

erse

0.26

91.

317.

460.

000

0.27

01.

317.

460.

00St

rong

ly R

isk

Aver

se0.

233

1.26

4.82

0.00

00.

236

1.27

4.98

0.00

Mod

erat

ely

Ris

k Av

erse

0.17

11.

193.

820.

000

0.18

21.

204.

030.

00W

hite

0.09

51.

102.

280.

023

Blac

k-0

.525

0.59

-11.

060.

000

Mal

e-0

.239

0.79

-8.0

20.

000

Educ

atio

n-0

.126

0.88

-3.1

70.

002

-0.0

670.

94-1

.57

0.12

Educ

atio

n Sq

uare

d0.

006

1.01

4.05

0.00

00.

004

1.00

2.23

0.03

No

Kids

in H

H0.

041

1.04

0.48

0.63

0-0

.127

0.88

-1.3

80.

17Ki

ds L

ess

than

6 in

HH

0.19

61.

222.

160.

031

0.05

61.

060.

580.

56U

rban

-0.1

590.

85-4

.20

0.00

0Lo

g W

eekl

y R

eal I

ncom

e0.

150

1.16

16.7

00.

000

0.15

11.

1615

.55

0.00

Enro

lled

in S

choo

l-0

.488

0.61

-11.

490.

000

Live

d w

ith P

aren

ts u

ntil

180.

046

1.05

1.50

0.13

50.

058

1.06

1.82

0.07

Nor

thea

st-0

.174

0.84

-3.9

80.

000

Sout

h0.

126

1.13

3.32

0.00

1W

est

0.00

01.

00-0

.01

0.99

2Li

ve w

ith P

aren

ts N

ow-0

.166

0.85

-5.3

10.

000

-0.1

920.

83-5

.94

0.00

Basi

c M

odel

(Spe

cific

atio

n 1)

Stra

tifie

d M

odel

with

Clu

ster

ed S

tand

ard

Err

ors

(Spe

cific

atio

n 2)

Surv

ival

Ana

lysi

s of

Tim

e to

Firs

t Mar

riage

Tabl

e 2.

3

Cox

Pro

porti

onal

Haz

ards

Mod

el U

sing

199

3 R

isk

Mea

sure

Figure 2.1 Cox Proportional Hazard Functions

84

0.002.004.006.008.01Smoothed hazard function

010

020

030

040

0an

alys

is ti

me

love

risk9

3=1

Cox

pro

porti

onal

haz

ards

regr

essi

on

noris

k93=

1V

ery

Str

ong

ly

Ris

k A

vers

e W

eakl

y R

isk

Ave

rse

Table 2.4 Survival Analysis of Time to First Marriage for Siblings Using 1993 Risk Measure

85

Varia

ble

Coe

ffici

ent

Haz

ard

Rat

ioz-

stat

istic

P>|z

|C

oeffi

cien

tH

azar

d R

atio

z-st

atis

ticP>

|z|

Very

Stro

ngly

Ris

k Av

erse

0.29

31.

346.

110.

000

0.56

11.

756.

690.

000

Stro

ngly

Ris

k Av

erse

0.20

71.

233.

180.

001

0.40

01.

493.

590.

000

Mod

erat

ely

Ris

k Av

erse

0.18

11.

202.

980.

003

0.39

91.

493.

880.

000

Whi

te0.

057

1.06

1.03

0.30

1B

lack

-0.5

490.

58-8

.58

0.00

0M

ale

-0.2

790.

76-7

.00

0.00

0-0

.641

0.53

-9.0

60.

000

Educ

atio

n-0

.024

0.98

-0.4

10.

682

-0.1

480.

86-1

.26

0.20

7Ed

ucat

ion

Squa

red

0.00

21.

001.

050.

296

0.00

91.

012.

080.

037

No

Kids

in H

H0.

219

1.25

1.84

0.06

70.

537

1.71

3.55

0.00

0Ki

ds L

ess

than

6 in

HH

0.35

31.

422.

770.

006

0.59

81.

824.

200.

000

Urb

an-0

.141

0.87

-2.7

30.

006

0.12

51.

131.

370.

172

Log

Wee

kly

Rea

l Inc

ome

0.15

01.

1612

.26

0.00

00.

163

1.18

10.2

90.

000

Enr

olle

d in

Sch

ool

-0.4

810.

62-8

.44

0.00

0-0

.495

0.61

-7.3

40.

000

Live

d w

ith P

aren

ts u

ntil

180.

061

1.06

1.41

0.15

7-0

.004

1.00

-0.0

30.

974

Nor

thea

st-0

.108

0.90

-1.8

60.

063

-0.0

380.

96-0

.17

0.86

1So

uth

0.14

71.

162.

880.

004

0.51

81.

683.

070.

002

Wes

t0.

040

1.04

0.67

0.50

40.

271

1.31

1.54

0.12

4Li

ve w

ith P

aren

ts N

ow-0

.149

0.86

-3.5

60.

000

-0.1

940.

82-3

.73

0.00

0

Tabl

e 2.

4Su

rviv

al A

naly

sis

of T

ime

to F

irst M

arria

ge fo

r Sib

lings

Cox

Pro

porti

onal

Haz

ards

Mod

el U

sing

199

3 R

isk

Mea

sure

Bas

ic M

odel

(Spe

cific

atio

n 3)

Bas

ic M

odel

with

Sib

ling

Fixe

d E

ffect

s

(S

peci

ficat

ion

4)

Table 2.5 Survival Analysis of Time to First Marriage by Gender Using 1993 Risk Measure

86

Varia

ble

Coe

ffici

ent

Haz

ard

Rat

ioz-

stat

istic

P>|z

|C

oeffi

cien

tH

azar

d R

atio

z-st

atis

ticP>

|z|

Ver

y S

trong

ly R

isk

Aver

se0.

382

1.47

7.80

0.00

00.

169

1.18

3.17

0.00

2S

trong

ly R

isk

Aver

se0.

278

1.32

4.00

0.00

00.

173

1.19

2.53

0.01

1M

oder

atel

y R

isk

Ave

rse

0.24

71.

284.

060.

000

0.09

61.

101.

450.

148

Whi

te0.

079

1.08

1.35

0.17

80.

118

1.13

1.99

0.04

7B

lack

-0.5

300.

59-7

.95

0.00

0-0

.517

0.60

-7.5

80.

000

Edu

catio

n-0

.205

0.81

-3.7

30.

000

-0.0

450.

96-0

.73

0.46

4E

duca

tion

Squ

ared

0.00

91.

014.

390.

000

0.00

31.

001.

420.

155

No

Kid

s in

HH

-0.1

510.

86-0

.83

0.40

8-0

.023

0.98

-0.2

20.

822

Kid

s Le

ss th

an 6

in H

H0.

191

1.21

0.96

0.33

80.

040

1.04

0.38

0.70

2U

rban

-0.2

260.

80-4

.33

0.00

0-0

.101

0.90

-1.8

20.

069

Log

Wee

kly

Rea

l Inc

ome

0.20

11.

2213

.91

0.00

00.

110

1.12

9.14

0.00

0E

nrol

led

in S

choo

l-0

.484

0.62

-7.3

70.

000

-0.4

970.

61-8

.86

0.00

0Li

ved

with

Par

ents

unt

il 18

0.01

31.

010.

300.

768

0.07

11.

071.

590.

111

Nor

thea

st-0

.187

0.83

-3.0

00.

003

-0.1

720.

84-2

.79

0.00

5S

outh

0.22

21.

254.

190.

000

0.04

81.

050.

880.

380

Wes

t-0

.033

0.97

-0.5

20.

603

0.03

31.

030.

530.

596

Live

with

Par

ents

Now

-0.2

440.

78-5

.46

0.00

0-0

.069

0.93

-1.5

70.

117

Tabl

e 2.

5

Men

(Spe

cific

atio

n 5)

Wom

en (S

peci

ficat

ion

6)

Surv

ival

Ana

lysi

s of

Tim

e to

Firs

t Mar

riage

by

Gen

der

Cox

Pro

porti

onal

Haz

ards

Mod

el U

sing

199

3 R

isk

Mea

sure

Table 2.6 Spousal Characteristics of Married Respondents by Risk Attitude

Weakly Risk Averse

Very Strongly Risk Averse

Weakly Risk Averse

Very Strongly Risk Averse

Fraction that Work 0.75 0.73 0.93* 0.95*

Hours Worked 32.80* 31.73* 43.00 43.56

Income 16,247* 13,833* 30,676 29,974

Education 12.88 12.75 12.79 12.68

Fraction Weeks Worked in Year 0.68 0.67 0.88* 0.91*

*Indicates differences in the means are significant at the 5% level.

Table 2.6Spousal Characteristics of Married Respondents by Risk Attitude

Married Men Married Women

87

Table 3.1 Percentage of Respondents Who Work More Than X% of the Time after the Start of Their Career, by Gender and Schooling Level in 1994

Group 10% 30% 50% 70% 90%

Women 95 87 75 57 29Less than High School 82 62 39 22 5High School 97 88 72 52 24Some College 99 93 83 65 35College Graduates 99 96 88 73 49Grad School 100 97 91 81 49

Men 97 94 89 79 49Less than High School 97 91 82 64 31High School 98 96 91 81 48Some College 99 97 92 81 50College Graduates 99 99 97 94 72Grad School 99 98 97 92 61

Table 3.1Percentage of Respondents Who Work More Than X% of the Time

after the Start of Their Careerby Gender and Schooling Level in 1994

88

Table 3.2 Fixed Effects Estimates Using Continuous Experience Measures

89

Independent Variable t-stat t-stat t-stat

Experience 80s 0.085 *** 28.2 0.102 *** 31.8 0.086 *** 28.4Experience2 80s -0.004 *** -13.4 -0.005 *** -16.6 -0.004 *** -13.7Experience 90s 0.051 *** 17.8 0.053 *** 18.1 0.048 *** 16.3Experience2 90s -0.001 *** -9.2 -0.001 *** -9.6 -0.001 *** -8.2Nonemployment 80s -0.093 *** -13.0Nonemployment2 80s 0.009 *** 7.2Nonemployment 90s -0.055 *** -12.1Nonemployment2 90s 0.002 *** 5.9Int1 -0.094 *** -5.1Int2 -0.032 ** -2.0Int3 -0.048 *** -3.3Int4 -0.038 *** -2.6Int5 -0.010 -0.7Int6 -0.019 -1.3Int7 0.003 0.2Int8 -0.035 ** -2.1Int9 0.000 0.0Int10 0.022 1.1Int11 -0.012 -0.6Int12 0.002 0.1Int13 -0.015 -0.6Int14 -0.001 -0.1Int15 -0.028 -0.9Int16 -0.036 -1.1Int17 0.053 1.4Int18 -0.009 -0.2Int19 -0.035 -0.5Int20 -0.162 ** -2.0Part Time 0.049 *** 5.8 0.051 *** 6.0 0.051 *** 6.1Enrolled -0.132 *** -14.9 -0.126 *** -14.3 -0.131 *** -14.9High School Grad 80s -0.064 *** -4.1 -0.032 ** -2.1 -0.054 *** -3.4Some College 80s -0.080 *** -3.9 -0.026 -1.3 -0.063 *** -3.1College Grad 80s 0.060 ** 2.4 0.143 *** 5.5 0.079 *** 3.0Graduate School 80s 0.033 1.0 0.126 *** 3.9 0.053 * 1.6Less High School 90s -0.062 *** -3.2 -0.001 -0.1 -0.035 -1.8High School Grad 90s -0.082 *** -3.7 -0.003 -0.2 -0.050 ** -2.2Some College 90s 0.010 0.4 0.108 *** 4.0 0.048 * 1.8College Grad 90s 0.189 *** 6.3 0.298 *** 9.7 0.226 *** 7.4Graduate School 90s 0.205 *** 6.2 0.330 *** 9.6 0.244 *** 7.3Married 0.055 *** 9.2 0.050 *** 8.5 0.055 *** 9.3Children Present 0.011 * 1.9 0.012 * 1.9 0.011 * 1.9Urban 0.017 ** 2.5 0.013 * 1.8 0.015 ** 2.3Northeast 0.081 *** 4.6 0.078 *** 4.4 0.079 *** 4.5North Central -0.043 *** -2.7 -0.045 *** -2.9 -0.042 *** -2.7West 0.080 *** 4.7 0.079 *** 4.6 0.080 *** 4.7Unemployment Rate -0.028 *** -11.7 -0.032 *** -13.1 -0.029 *** -12.1White

R 2 Within 0.266 0.273 0.268# of Observations 36,429 36,429 36,429

*Statistically significant at the .10 level; **at the .05 level; ***at the .01 level

Specification 2: Basic Segmented Model

Specification 3: Segmented Model with Interruption Dummies

Coefficient Coefficient Coefficient

(dropped) (dropped) (dropped)

Table 3.2Fixed Effects Estimates of Wage Equations Using Continuous Experience

Measures, 1979-2000Men

Specification 1: Basic Mincer Model

90

Independent Variable t-stat t-stat t-stat

Experience 80s 0.069 *** 23.1 0.081 *** 26.2 0.070 *** 23.5Experience2 80s -0.002 *** -7.6 -0.003 *** -10.1 -0.003 *** -8.2Experience 90s 0.046 *** 17.5 0.045 *** 17.1 0.039 *** 13.9Experience2 90s -0.001 *** -7.7 -0.001 *** -7.9 -0.001 *** -5.4Nonemployment 80s -0.065 *** -11.8Nonemployment2 80s 0.005 *** 6.6Nonemployment 90s -0.049 *** -16.0Nonemployment2 90s 0.002 *** 10.5Int1 -0.076 *** -6.1Int2 -0.046 *** -4.4Int3 -0.029 *** -2.9Int4 -0.020 ** -2.0Int5 -0.015 -1.5Int6 -0.023 ** -2.2Int7 -0.030 *** -2.8Int8 0.010 0.9Int9 -0.028 ** -2.4Int10 0.010 0.8Int11 -0.009 -0.7Int12 -0.026 * -1.8Int13 0.003 0.2Int14 -0.001 -0.1Int15 0.005 0.2Int16 -0.036 * -1.7Int17 -0.031 -1.2Int18 -0.029 -1.0Int19 0.036 0.9Int20 -0.086 * -1.7Part Time -0.017 *** -3.3 -0.009 * -1.8 -0.012 ** -2.3Enrolled -0.069 *** -9.8 -0.067 *** -9.6 -0.068 *** -9.7High School Grad 80s -0.016 -1.0 0.007 0.4 -0.003 -0.2Some College 80s -0.013 -0.7 0.033 1.6 0.006 0.3College Grad 80s 0.112 *** 4.7 0.182 *** 7.5 0.137 *** 5.7Graduate School 80s 0.127 *** 4.3 0.205 *** 6.9 0.158 *** 5.4Less High School 90s -0.038 ** -2.1 0.044 ** 2.1 0.021 1.1High School Grad 90s -0.012 -0.6 0.087 *** 3.7 0.056 ** 2.5Some College 90s 0.053 ** 2.2 0.161 *** 6.4 0.124 *** 5.0College Grad 90s 0.188 *** 7.0 0.306 *** 10.8 0.260 *** 9.3Graduate School 90s 0.270 *** 9.2 0.397 *** 12.9 0.347 *** 11.5Married 0.014 *** 2.8 0.010 ** 2.1 0.014 *** 2.8Children Present -0.033 *** -5.7 -0.007 -1.2 -0.022 *** -3.8Urban 0.013 * 2.0 0.009 1.3 0.010 1.5Northeast 0.096 *** 5.8 0.089 *** 5.4 0.092 *** 5.6North Central 0.043 *** 2.9 0.037 ** 2.5 0.040 *** 2.8West 0.111 *** 6.8 0.109 *** 6.8 0.110 *** 6.8Unemployment Rate -0.010 *** -4.5 -0.014 *** -6.4 -0.013 *** -5.6White (dropped) (dropped) (dropped)

R 2 Within 0.229 0.238 0.233# of Observations 33,480 33,480 33,480

*Statistically significant at the .10 level; **at the .05 level; ***at the .01 level

Coefficient Coefficient Coefficient

Table 3.2 contd.Fixed Effects Estimates of Wage Equations Using Continuous Experience

Measures, 1979-2000Women

Specification 1: Basic Mincer Model

Specification 2: Basic Segmented Model

Specification 3: Segmented Model with Interruption Dummies

Table 3.3 Fixed Effects Estimates Using Alternative Experience Measures

Independent Variable t-stat t-stat t-stat t-statFWW1 0.173 *** 20.6 0.169 *** 21.2 0.160 *** 21.9 0.157 *** 23.3FWW2 0.072 *** 11.6 0.069 *** 11.3 0.051 *** 8.8 0.051 *** 9.1FWW3 0.068 *** 8.6 0.069 *** 9.1 0.065 *** 9.1 0.064 *** 9.4FWW4 0.050 *** 5.8 0.052 *** 6.3 0.046 *** 5.9 0.046 *** 6.2FWW5 0.039 *** 4.5 0.038 *** 4.6 0.031 *** 3.9 0.032 *** 4.2FWW6 0.041 *** 4.7 0.042 *** 4.9 0.027 *** 3.4 0.032 *** 4.2FWW7 0.019 ** 2.2 0.019 ** 2.3 0.036 *** 4.4 0.039 *** 5.0FWW8 0.029 *** 3.2 0.034 *** 3.8 0.032 *** 3.7 0.027 *** 3.4FWW9 0.023 ** 2.5 0.023 ** 2.5 0.026 *** 3.0 0.029 *** 3.5FWW10 0.019 ** 2.0 0.017 * 1.9 0.026 *** 2.9 0.023 *** 2.8FWW11+ 0.083 *** 9.6 0.083 *** 9.8 0.078 *** 9.3 0.079 *** 9.7Int1 0.020 1.0 0.013 1.0Int2 0.027 1.6 0.000 0.0Int3 -0.004 -0.3 0.003 0.3Int4 -0.015 -1.0 0.000 0.0Int5 0.001 0.1 -0.004 -0.4Int6 -0.008 -0.5 -0.017 -1.6Int7 0.000 0.0 -0.017 -1.5Int8 -0.035 ** -2.0 0.018 1.6Int9 -0.004 -0.2 -0.018 -1.4Int10 0.015 0.8 0.014 1.1 # Int11+ 0.006 1.0 0.000 -0.1Part Time 0.063 *** 7.5 0.063 *** 7.5 -0.001 -0.1 -0.001 -0.2Enrolled -0.129 *** -14.7 -0.129 *** -14.7 -0.068 *** -9.7 -0.068 *** -9.7High School Grad 80s -0.049 *** -3.2 -0.048 *** -3.2 -0.004 -0.3 -0.004 -0.3Some College 80s -0.054 *** -2.7 -0.053 *** -2.7 0.018 0.9 0.017 0.9College Grad 80s 0.100 *** 3.9 0.101 *** 4.0 0.162 *** 6.8 0.161 *** 6.9Graduate School 80s 0.077 ** 2.4 0.079 ** 2.5 0.176 *** 6.1 0.175 *** 6.1Less High School 90s -0.096 *** -8.7 -0.097 *** -8.9 -0.071 *** -4.9 -0.075 *** -5.3High School Grad 90s -0.103 *** -6.3 -0.103 *** -6.4 -0.033 * -1.9 -0.035 ** -2.1Some College 90s -0.005 -0.3 -0.006 -0.3 0.042 ** 2.1 0.039 ** 2.0College Grad 90s 0.164 *** 6.2 0.164 *** 6.3 0.181 *** 7.5 0.178 *** 7.5Graduate School 90s 0.184 *** 6.2 0.185 *** 6.3 0.265 *** 9.9 0.261 *** 9.9Married 0.047 *** 7.9 0.046 *** 7.8 0.012 *** 2.6 0.012 ** 2.6Children Present 0.015 ** 2.4 0.015 ** 2.4 -0.014 ** -2.3 -0.015 *** -2.6Urban 0.003 0.4 0.003 0.4 -0.001 -0.1 0.000 -0.1Northeast 0.073 *** 4.2 0.073 *** 4.2 0.085 *** 5.2 0.085 *** 5.2North Central -0.045 *** -2.9 -0.045 *** -2.9 0.037 ** 2.5 0.037 ** 2.6West 0.075 *** 4.4 0.075 *** 4.4 0.108 *** 6.7 0.108 *** 6.7Unemployment Rate -0.034 *** -14.6 -0.034 *** -14.8 -0.019 *** -8.6 -0.019 *** -8.6White (dropped) (dropped) (dropped) (dropped)

R 2 Within 0.273 0.272 0.241 0.241# of Observations 36,429 36,429 33,480 33,480

*Statistically significant at the .10 level; **at the .05 level; ***at the .01 level

Specification 4: Work History Model with

Interruption Dummies

Specification 5: Basic Work History Model

Specification 4: Work History Model with

Interruption Dummies

Specification 5: Basic Work History Model

WomenMen

Table 3.3Fixed Effects Estimates of Wage Equations Using Alternative Experience Measures, 1979-2000

Coefficient Coefficient Coefficient Coefficient

91

Figure 3.1 Predicted Wage-Experience Profiles

92

Table 3.4 Ratios of Estimated Wages

93

Spec

ifica

tion

1Sp

ecifi

catio

n 2

Spec

ifica

tion

3Sp

ecifi

catio

n 5

Spec

ifica

tion

1Sp

ecifi

catio

n 2

Spec

ifica

tion

3Sp

ecifi

catio

n 5

10.

953

0.87

00.

868

0.84

50.

954

0.89

50.

885

0.85

42

0.95

30.

870

0.92

20.

933

0.95

40.

895

0.91

20.

950

30.

953

0.87

00.

908

0.93

30.

954

0.89

50.

927

0.93

84

0.95

30.

870

0.91

70.

949

0.95

40.

895

0.93

50.

955

Wor

kers

with

an

inte

rrup

tion

X ye

ars

ago

vers

us w

orke

rs

with

no

inte

rrup

tions

Men

Wom

en

Tabl

e 3.

4

Rat

ios

of E

stim

ated

(Mea

n) W

ages

Table 3.5 Decomposition of the Gender Wage Gap

Years Experience

Total Estimated Gap

Gap Due to Timing and

ReturnsGap Due to

Timing

Column (3) as a Percentage of Column (2)

(1) (2) (3) (4) Men Women0 0.127 0.000 - - 1,867 1,9681 0.144 0.016 0.006 0.348 2,824 2,9452 0.157 0.028 0.007 0.253 2,782 2,8683 0.171 0.037 0.010 0.279 2,713 2,7974 0.186 0.046 0.014 0.313 2,636 2,6635 0.189 0.048 0.011 0.239 2,546 2,5226 0.195 0.050 0.013 0.253 2,455 2,3747 0.190 0.043 0.010 0.243 2,363 2,2198 0.197 0.049 0.014 0.283 2,244 2,0619 0.194 0.045 0.013 0.278 2,116 1,877

10 0.193 0.044 0.013 0.301 1,945 1,67611 0.202 0.054 0.022 0.408 1,787 1,45312 0.188 0.046 0.014 0.295 1,565 1,29013 0.195 0.050 0.018 0.356 1,413 1,11214 0.184 0.044 0.011 0.244 1,191 91215 0.196 0.046 0.012 0.274 1,009 73416 0.187 0.043 0.010 0.224 827 60417 0.198 0.041 0.007 0.180 599 43818 0.197 0.046 0.012 0.270 572 39119 0.199 0.038 0.004 0.115 364 23020 0.203 0.041 0.007 0.172 313 19821 0.202 0.035 0.001 0.037 144 7822 0.170 0.035 0.001 0.027 154 70

0-22 0.200 0.058 0.030 0.516 36,429 33,480

# of Observations

Table 3.5Decomposition of the Gender Wage Gap

Note: Observations are grouped based on years of work experience accumulated, rounded to the nearest whole number.

94

Table 3.6 Fixed Effects Estimates Using Expectation Measures

Independent Variable t-stat t-stat t-stat t-statFutureInt 0.468 *** 4.5 0.166 *** 4.2 0.243 *** 4.2 -0.019 -0.8FutureInt*Experience 80s -0.024 -1.1 -0.026 ** -2.0FutureInt*Experience2 80s -0.001 -0.2 0.000 0.2FutureInt*Experience 90s -0.040 *** -2.8 -0.036 *** -4.2FutureInt*Experience2 90s 0.000 0.4 0.001 ** 2.3Experience 80s 0.102 *** 28.7 0.083 *** 22.3Experience2 80s -0.005 *** -14.7 -0.003 *** -8.7Experience 90s 0.055 *** 18.5 0.047 *** 17.6Experience2 90s -0.001 *** -10.2 -0.001 *** -8.6Nonemployment 80s -0.073 *** -8.7 -0.057 *** -9.6Nonemployment2 80s 0.009 *** 7.3 0.005 *** 6.8Nonemployment 90s -0.034 *** -5.3 -0.042 *** -11.1Nonemployment2 90s 0.003 *** 6.2 0.003 *** 11.1FutureInt1*FWW1 -0.148 *** -3.6 0.054 ** 2.1FutureInt2*FWW2 0.006 0.2 -0.010 -0.4FutureInt3*FWW3 -0.119 *** -2.8 -0.055 * -1.9FutureInt4*FWW4 -0.102 ** -2.2 -0.055 * -1.7FutureInt5*FWW5 -0.071 -1.5 -0.068 ** -2.0FutureInt6*FWW6 -0.008 -0.2 -0.032 -0.9FutureInt7*FWW7 -0.122 ** -2.3 0.001 0.0FutureInt8*FWW8 0.041 0.8 -0.057 -1.5FutureInt9*FWW9 -0.024 -0.4 -0.070 * -1.8FutureInt10*FWW10 -0.166 *** -2.9 -0.094 ** -2.4FutureInt11*FWW11+ -0.072 -1.2 -0.035 -0.9FWW1 0.170 *** 17.4 0.132 *** 14.4FWW2 0.063 *** 8.9 0.046 *** 6.5FWW3 0.075 *** 8.1 0.068 *** 7.8FWW4 0.060 *** 6.1 0.051 *** 5.5FWW5 0.044 *** 4.4 0.040 *** 4.1FWW6 0.038 *** 3.7 0.034 *** 3.5FWW7 0.028 *** 2.8 0.033 *** 3.3FWW8 0.028 *** 2.6 0.032 *** 3.1FWW9 0.019 * 1.8 0.037 *** 3.5FWW10 0.030 *** 2.8 0.037 *** 3.5FWW11+ 0.079 *** 8.2 0.070 *** 7.2

R 2 Within 0.273 0.276 0.239 0.245# of Observations 36,429 36,429 33,480 33,480

Note: The remainder of the explanatory variables are the same as in previous regressions. Full results are available upon request.*Statistically significant at the .10 level; **at the .05 level; ***at the .01 level

Table 3.6Selected Fixed Effects Estimates of Wage Equations Using Expectations Measures, 1979-2000

Men Women

Specification 2 with Expectations

Specification 5 with Expectations

Specification 2 with Expectations

Specification 5 with Expectations

Coefficient Coefficient CoefficientCoefficient

95

Table 4.1 Basic Descriptive Statistics

Mean Minimum MaximumStandard Deviation

Area (Square Miles) 159 12 3,353 302Population 425,527 49,776 17,800,000 1,245,656Income 49,359 25,967 91,741 10,234Land Value per Acre 650 2 7,685 836Fraction HH owning at least 1 Car 0.91 0.68 0.97 0.03Fraction Using Public Transport 0.02 0.00 0.30 0.03Average Travel Time 22.89 14.70 42.49 4.89Number Subcenters 0 0 33 2On Coast, Great Lake, Mexican Border 0.18 0.00 1.00 0.38Percent Working in Central City 0.48 0.00 0.97 0.26

Number of Observations 452

Area (Square Miles) 536 33 3,353 547Population 1,686,604 112,331 17,800,000 2,511,807Income 52,597 25,967 81,226 9,235Land Value per Acre 999 12 7,685 1,310Fraction HH owning at least 1 Car 0.90 0.68 0.95 0.04Fraction Using Public Transport 0.04 0.01 0.30 0.04Average Travel Time 25.27 19.15 37.05 3.58Congestion Cost ($mil) 618 7 10,358 1,354Travel Time Index 1.21 1.04 1.76 0.13Vehicle Miles of Travel per Freeway Mile 13,780 5,533 22,999 3,110Number Subcenters 2 0 33 5On Coast, Great Lake, Mexican Border 0.32 0.00 1.00 0.47Percent Working in Central City 0.53 0.23 0.97 0.20

Number of Observations 85

Table 4.1Basic Descriptive Statistics

Largest Urbanized Areas (with Data from Texas Transportation Institute)

All Urbanized Areas

96

Table 4.2 Results Using Fraction of Households Owning at Least One Car as Commuting Cost Proxy

2

X-s

tatis

tic2

97

X-s

tatis

tict-s

tatis

ticC

onst

ant

-3.3

6-1

.56

-2.0

9**

-2.0

2Po

pula

tion

1.06

***

925.

760.

65**

*90

0.20

0.91

***

54.4

6In

com

e-0

.43

***

15.7

1-0

.27

***

15.2

6-0

.39

***

-3.8

9La

nd V

alue

per

Acr

e-0

.04

*3.

64-0

.03

**4.

33-0

.03

*-1

.63

Frac

tion

HH

ow

ning

at l

east

1 C

ar0.

911.

720.

821.

210.

631.

22N

umbe

r Sub

cent

ers

-0.0

3*

3.56

-0.0

2**

*-2

.79

On

Coa

st, G

reat

Lak

e, M

exic

an B

orde

r0.

050.

700.

061.

100.

040.

97

Tran

sfor

mat

ion

Para

met

ers

z-st

atis

ticz-

stat

istic

θ0.

07**

2.17

0.08

***

2.49

λ0.

010.

440.

061.

50

Num

ber o

f Obs

erva

tions

452

452

452

Log-

Like

lihoo

d/R

2-2

104.

9-2

103.

10.

90

***

indi

cate

s si

gnifi

canc

e at

the

1% le

vel,

** a

t the

5%

leve

l, an

d * a

t the

10%

leve

l.

Estim

ate

Estim

ate

Estim

ate

Tabl

e 4.

2M

axim

um L

ikel

ihoo

d Es

timat

es

Spec

ifica

tion

3:

D

oubl

e-Lo

g M

odel

Spec

ifica

tion

2Sp

ecifi

catio

n 1

Dep

ende

nt V

aria

ble:

Are

a in

Squ

are

Mile

s

Table 4.3 Results Using Congestion Cost as Commuting Cost Proxy

98

X

2-s

tatis

ticX

2-s

tatis

tict-s

tatis

ticC

onst

ant

-33.

76-1

9.18

-13.

04**

*-4

.28

Popu

latio

n1.

20**

*69

.46

0.35

***

72.3

51.

13**

*8.

69In

com

e0.

69**

5.88

0.24

**5.

400.

401.

40La

nd V

alue

per

Acr

e-0

.12

*2.

57-0

.08

*3.

17-0

.04

*-1

.29

Con

gest

ion

Cos

t ($m

il)-0

.54

***

6.90

-0.3

6**

*8.

72-0

.14

-1.7

6N

umbe

r Sub

cent

ers

-0.1

2**

4.21

-0.0

2**

*-3

.67

On

Coa

st, G

reat

Lak

e, M

exic

an B

orde

r-0

.22

0.41

-0.1

30.

11-0

.02

-0.2

6

Tran

sfor

mat

ion

Para

met

ers

z-st

atis

ticz-

stat

istic

0.26

***

2.80

0.29

***

3.50

λθ0.

111.

060.

21**

2.37

Num

ber o

f Obs

erva

tions

8585

85Lo

g-Li

kelih

ood/

R2

-512

.2-5

10.1

0.90

***

indi

cate

s si

gnifi

canc

e at

the

1% le

vel,

** a

t the

5%

leve

l, an

d *

at th

e 10

% le

vel.

Estim

ate

Estim

ate

Estim

ate

Spec

ifica

tion

3:

D

oubl

e-Lo

g M

odel

Spec

ifica

tion

2Sp

ecifi

catio

n 1

Tabl

e 4.

3M

axim

um L

ikel

ihoo

d Es

timat

esD

epen

dent

Var

iabl

e: A

rea

in S

quar

e M

iles

Appendix A: Chapter 2

A.1 PROOF THAT RISK AVERSION IS DECREASING IN RESERVATION QUALITY

Proposition: Given F(q), if )]([)( qUGqU BA = for all q, then BA qq < .

Proof: Let B’s optimal strategy be to reject all offers Bqq < and accept otherwise. Let

WB denote the random payoff that is generated from following this strategy. Similarly, let

A’s optimal strategy be to reject all offers Aqq < and accept otherwise, and let WA denote

the random payoff generated by this strategy. Now it must be determined if qB is an

acceptable offer to a type A searcher. Per the above notation, the following holds:

B

)]([)]([)( BBBBBA WEUGqUGqU == (A.1)

Since WB is associated with B’s optimal strategy, searcher B is worse off when following

A’s strategy, so

)])(([)]([)]([ , AWBABABBB rWEUGWEUGWEUG −≡> , (A.2)

where is the risk premium B would pay to avoid the random payoff WAWBr , A.. Since A’s

risk premium is larger than B’s,

)()])(([)])(([ , AAAABWBAB qUrWEUGrWEUGA

≡−>− . (A.3)

Thus, )()( AABA qUqU > , so AB qq > . (A.4)

In other words, any quality level that type B is willing to accept is also acceptable to the

type A searcher, so A’s reservation quality is less than B’s.

99

A.2 CHANGE IN RISK CATEGORY

Table A.1 Change in Risk Category

1993 Risk CategoryVery Strongly Risk Averse

Strongly Risk Averse

Moderately Risk Averse

Weakly Risk Averse Missing

Very Strongly Risk Averse 53.5 8.7 10.6 11.4 15.8

Strongly Risk Averse 42.0 15.7 13.5 14.2 14.6

Moderately Risk Averse 40.1 11.8 18.5 14.5 15.2

Weakly Risk Averse 35.2 9.5 14.5 23.8 17.0

Table A.1

2002 Risk Category

Change in Risk CategoryBy Percent of 1993 Risk Category

100

A.3 SURVIVAL ANALYSIS TO EXPLORE POSSIBLE ENDOGENEITY OF RISK AVERSION

AND TIMING OF MARRIAGE

Table A.2 Survival Analysis of Time to First Marriage for Marriages Occurring After 1993

Variable Coefficient Hazard Ratio z-statistic P>|z|Very Strongly Risk Averse 0.113 1.12 1.22 0.224Strongly Risk Averse 0.042 1.04 0.32 0.752Moderately Risk Averse 0.070 1.07 0.62 0.534White -0.055 0.95 -0.44 0.658Black -0.274 0.76 -2.11 0.035Male 0.183 1.20 2.09 0.037Education -0.077 0.93 -0.68 0.498Education Squared 0.004 1.00 1.01 0.312No Kids in HH -0.337 0.71 -2.48 0.013Kids Less than 6 in HH 0.043 1.04 0.29 0.773Urban -0.133 0.88 -1.20 0.228Log Weekly Real Income 0.043 1.04 2.09 0.037Enrolled in School 0.033 1.03 0.21 0.831Lived with Parents until 18 -0.058 0.94 -0.71 0.475Northeast -0.047 0.95 -0.40 0.691South 0.152 1.16 1.51 0.131West 0.137 1.15 1.12 0.262Live with Parents Now -0.228 0.80 -2.04 0.042

Table A.2Survival Analysis of Time to First Marriage

Cox Proportional Hazards Model Using 1993 Risk Measurefor Marriages Occurring After 1993

101

Table A.3 Survival Analysis of Time to First Marriage Using 2002 Risk Measure….

Variable CoefficientHazard Ratio z-statistic P>|z|

Very Strongly Risk Averse 0.166 1.18 3.90 0.000Strongly Risk Averse 0.126 1.13 2.25 0.024Moderately Risk Averse 0.105 1.11 2.00 0.045White 0.062 1.06 1.37 0.170Black -0.547 0.58 -10.69 0.000Male -0.227 0.80 -7.11 0.000Education -0.087 0.92 -1.97 0.048Education Squared 0.005 1.00 2.81 0.005No Kids in HH 0.029 1.03 0.33 0.744Kids Less than 6 in HH 0.183 1.20 1.90 0.057Urban -0.130 0.88 -3.22 0.001Log Weekly Real Income 0.152 1.16 15.72 0.000Enrolled in School -0.479 0.62 -10.58 0.000Lived with Parents until 18 0.034 1.03 1.02 0.306Northeast -0.174 0.84 -3.71 0.000South 0.141 1.15 3.50 0.000West -0.012 0.99 -0.25 0.805Live with Parents Now -0.189 0.83 -5.61 0.000

Survival Analysis of Time to First MarriageCox Proportional Hazards Model Using 2002 Risk Measure

Table A.3

102

Appendix B: Chapter 3

B.1 WAGE CHANGE EQUATIONS FOR WOMEN

Table B.1 First and Last Wage Change Equations for Women

Change in Independent Variable t-statTotal Experience 0.031 ** 2.2Change in Total Experience2 -0.001 -0.8Total Nonemployment -0.038 *** -2.7Total Nonemployment2 0.002 * 1.7Years Schooling 0.104 *** 13.4Years Tenure 0.014 *** 4.5Constant -0.022 -0.3

Adjusted R 2 0.231# of Observations 2,012

Change in Independent Variable t-statNoInt 0.087 0.7Previous Experience 0.010 ** 2.0Previous Nonemployment -0.008 -1.0Most Recent Nonemployment 0.021 0.8Most Recent Nonemployment2 -0.002 -1.0Post Experience 0.054 *** 3.9Post Experience2 -0.001 -1.6Total Experience*NoInt 0.041 ** 2.2Total Experience2*NoInt -0.001 -1.2Years Schooling 0.102 *** 13.2Years Tenure 0.010 *** 3.1Constant -0.117 -1.4

Adjusted R 2 0.243# of Observations 2,012

Coefficient

Table B.1First and Last Wage Change Equations for Women, 1979-1998

Cumulative Experience Measures

Coefficient

Segmented Experience Measures

Note: NoInt = 1 if worker never experienced a career interruption.*Statistically significant at the .10 level; **at the .05 level; ***at the .01 level

103

B.2 THE EARNINGS GAP BETWEEN MOTHERS AND NON-MOTHERS

Table B.2 Decomposition of the Wage Gap Between Mothers and Non-Mothers….

Years Experience

Total Estimated Gap

Gap Due to Timing and

ReturnsGap Due to

Timing

Column (3) as a Percentage of Column (2)

(1) (2) (3) (4) Non-Mothers Mothers0 0.058 - - - 1,522 4461 0.111 0.040 0.032 0.822 2,087 8582 0.107 0.040 0.020 0.509 1,892 9763 0.123 0.066 0.032 0.481 1,707 1,0904 0.133 0.081 0.031 0.387 1,489 1,1745 0.132 0.091 0.027 0.295 1,311 1,2116 0.132 0.100 0.022 0.219 1,159 1,2157 0.142 0.111 0.018 0.161 971 1,2488 0.158 0.136 0.026 0.187 851 1,2109 0.178 0.153 0.027 0.175 717 1,16010 0.186 0.171 0.028 0.166 603 1,07311 0.193 0.185 0.037 0.198 494 95912 0.189 0.182 0.028 0.156 412 87813 0.192 0.182 0.027 0.150 351 76114 0.175 0.176 0.018 0.100 258 65415 0.173 0.183 0.024 0.129 217 51716 0.156 0.171 0.008 0.045 176 42817 0.151 0.164 0.000 - 132 30618 0.165 0.173 0.007 0.040 116 27519 0.145 0.162 - - 72 15820 0.161 0.173 0.003 0.016 61 13721 0.146 0.166 - - 28 5022 0.158 0.174 - - 22 48

0-22 0.038 0.014 - - 16,648 16,832

# of Observations

Table B.2Decomposition of the Wage Gap Between Mothers and Non-Mothers

Note: Observations are grouped based on years of work experience accumulated, rounded to the nearest whole number.

104

Appendix C: Chapter 4

C.1 BRUECKNER AND FANSLER RESULTS

Table C.1 Brueckner and Fansler Maximum Likelihood Estimates

Coefficient t-statistic Coefficient t-statisticConstant -16.71 -3.05 -18.72 -1.31N 0.0155 9.04 0.0154 9.16r a -0.0715 -2.86 -0.0705 -2.74y 0.0791 3.23 0.0791 3.23PUBLiC -0.0467 -0.20CARS 0.1117 0.16λ 0.5300 0.5300

Table C.1Maximum Likelihood Estimates

Specification 1 Specification 2

Table C.2 Brueckner and Fansler Linear Estimates

Coefficient t-statistic Coefficient t-statisticConstant -41.07 -2.28 -63.47 -1.24N 0.0004 10.03 0.0004 9.88r a -0.0303 -3.09 -0.0289 -2.89y 0.0062 3.03 0.0062 3.05PUBLiC -0.2444 -0.41CARS 0.2475 0.46R 2 0.7982 0.7985

Table C.2Linear Estimates

Specification 1 Specification 2

105

Table C.3 Brueckner and Fansler Elasticities From Linear Equations

Specification 1 Specification 2N 1.097 1.086r a -0.234 -0.231y 1.497 1.496

Table C.3Elasticities From Linear Equations

106

107

C.2 CENSUS DEFINITIONS

Central City

The largest city of a Metropolitan area (MA). Central cities are a basis for establishment

of an MA. Additional cities that meet specific criteria also are identified as central cities.

In a number of instances, only part of a city qualifies as central, because another part of

the city extends beyond the MA boundary.

Metropolitan statistical area (MSA)

A geographic entity defined by the federal Office of Management and Budget for use by

federal statistical agencies, based on the concept of a core area with a large population

nucleus, plus adjacent communities having a high degree of economic and social

integration with that core. Qualification of an MSA requires the presence of a city with

50,000 or more inhabitants, or the presence of an Urbanized Area (UA) and a total

population of at least 100,000 (75,000 in New England). The county or counties

containing the largest city and surrounding densely settled territory are central counties of

the MSA. Additional outlying counties qualify to be included in the MSA by meeting

certain other criteria of metropolitan character, such as a specified minimum population

density or percentage of the population that is urban. MSAs in New England are defined

in terms of minor civil divisions, following rules concerning commuting and population

density.

Urbanized area (UA)

An area consisting of a central place(s) and adjacent territory with a general population

density of at least 1,000 people per square mile of land area that together have a

minimum residential population of at least 50,000 people. The Census Bureau uses

published criteria to determine the qualification and boundaries of UAs.

108

Urban Cluster

A densely settled territory that has at least 2,500 people but fewer than 50,000. New for

Census 2000.

C.3 ADDITIONAL MAXIMUM LIKELIHOOD RESULTS

Table C.4 Results Using Fraction of Workers Using Public Transport as Commuting Cost Proxy

109

X2

-sta

tistic

X2-s

tatis

tict-s

tatis

ticC

onst

ant

-8.2

0-5

.96

-5.8

2**

*-5

.25

Popu

latio

n1.

18**

*96

0.73

0.76

***

935.

060.

94**

*56

.04

Inco

me

-0.1

62.

34-0

.11

2.34

-0.1

5-1

.49

Land

Val

ue p

er A

cre

-0.0

20.

95-0

.02

1.29

-0.0

1-0

.83

Frac

tion

Wor

kers

Usi

ng P

ublic

Tra

nspo

rt-0

.16

***

44.3

0-0

.20

***

43.3

8-0

.13

***

-6.7

2N

umbe

r Sub

cent

ers

-0.0

2*

3.16

-0.0

2**

*-2

.85

On

Coa

st, G

reat

Lak

e, M

exic

an B

orde

r0.

051.

120.

071.

630.

041.

21

Tran

sfor

mat

ion

Para

met

ers

z-st

atis

ticz-

stat

istic

0.05

*1.

670.

06**

1.95

λθ0.

002

0.06

0.04

1.10

Num

ber o

f Obs

erva

tions

452

452

452

Log-

Like

lihoo

d/R

2-2

,083

.6-2

,082

.00.

91

***

indi

cate

s si

gnifi

canc

e at

the

1% le

vel,

** a

t the

5%

leve

l, an

d *

at th

e 10

% le

vel.

Estim

ate

Estim

ate

Estim

ate

Spec

ifica

tion

3:

D

oubl

e-Lo

g M

odel

Spec

ifica

tion

1Sp

ecifi

catio

n 2

Tabl

e C

.4M

axim

um L

ikel

ihoo

d Es

timat

esD

epen

dent

Var

iabl

e: A

rea

in S

quar

e M

iles

Table C.5 Results Using Average Travel Time to Work as Commuting Cost Proxy

2

-sta

tistic

X2

-sta

tistic

X2

110

X-s

tatis

ticC

onst

ant

-4.3

9-2

.17

-111

.20

Popu

latio

n1.

16**

*88

0.30

0.67

***

846.

0211

1.73

***

50.9

9In

com

e-0

.48

***

17.9

7-0

.30

***

18.5

1-8

.57

0.68

Land

Val

ue p

er A

cre

-0.0

5**

*6.

37-0

.04

***

7.31

0.00

1.14

Aver

age

Trav

el T

ime

to W

ork

0.25

**4.

100.

23**

4.38

-0.0

2**

*2.

67N

umbe

r Sub

cent

ers

-0.0

3**

4.35

On

Coa

st, G

reat

Lak

e, M

exic

an B

orde

r0.

040.

520.

060.

95

Tran

sfor

mat

ion

Para

met

ers

z-st

atis

ticz-

stat

istic

z-st

atis

tic

θ0.

07**

2.26

0.09

***

2.59

-1.5

0**

*-3

.61

λ0.

010.

210.

061.

44-0

.92

***

-3.4

6

Num

ber o

f Obs

erva

tions

452

452

27Lo

g-Li

kelih

ood

-2,1

03.7

-2,1

01.5

-92.

7

***

indi

cate

s si

gnifi

canc

e at

the

1% le

vel,

** a

t the

5%

leve

l, an

d *

at th

e 10

% le

vel.

Estim

ate

Estim

ate

Estim

ate

Spec

ifica

tion

3:

U

As

with

mor

e th

an 8

5% w

orki

ng in

ce

ntra

l city

Tabl

e C

.5M

axim

um L

ikel

ihoo

d Es

timat

esD

epen

dent

Var

iabl

e: A

rea

in S

quar

e M

iles

Spec

ifica

tion

2S

peci

ficat

ion

1

Table C.6 Results Using Travel Time Index as Commuting Cost Proxy

111

X2-s

tatis

ticX

2-s

tatis

tict-s

tatis

ticC

onst

ant

-30.

01-2

3.18

-13.

10**

*-5

.64

Popu

latio

n1.

52**

*15

5.06

0.82

***

146.

121.

08**

*16

.63

Inco

me

0.78

***

6.60

0.48

***

6.30

0.44

*1.

81La

nd V

alue

per

Acr

e-0

.08

1.41

-0.0

71.

63-0

.03

-1.0

0Tr

avel

Tim

e In

dex

-7.4

8**

*23

.64

-8.5

5**

*22

.14

-2.3

5**

*-4

.47

Num

ber S

ubce

nter

s-0

.04

0.89

-0.0

1-1

.59

On

Coa

st, G

reat

Lak

e, M

exic

an B

orde

r-0

.13

0.40

-0.1

20.

24-0

.04

-0.4

6

Tran

sfor

mat

ion

Para

met

ers

z-st

atis

ticz-

stat

istic

0.19

**2.

350.

22**

*2.

55

λθ0.

060.

790.

111.

26

Num

ber o

f Obs

erva

tions

8585

85Lo

g-Li

kelih

ood/

R2

-503

.8-5

03.4

0.92

***

indi

cate

s si

gnifi

canc

e at

the

1% le

vel,

** a

t the

5%

leve

l, an

d *

at th

e 10

% le

vel.

Estim

ate

Estim

ate

Estim

ate

Spec

ifica

tion

3:

D

oubl

e-Lo

g M

odel

Spec

ifica

tion

2Sp

ecifi

catio

n 1

Tabl

e C

.6M

axim

um L

ikel

ihoo

d Es

timat

esD

epen

dent

Var

iabl

e: A

rea

in S

quar

e M

iles

Table C.7 Results Using Daily Vehicle Miles of Travel Per Freeway Lane Mile as Commuting Cost Proxy

112

X

2-s

tatis

ticX

2-s

tatis

tict-s

tatis

ticC

onst

ant

-24.

18-9

.40

-7.2

2*

-1.9

3Po

pula

tion

2.80

***

157.

030.

70**

*14

0.47

1.00

***

16.4

9In

com

e1.

21**

4.61

0.41

**4.

450.

381.

39La

nd V

alue

per

Acr

e-0

.07

0.50

-0.0

61.

04-0

.02

-0.7

2Ve

hicl

e M

iles

of T

rave

l per

Fre

eway

Mile

-1.6

3**

*8.

20-0

.67

***

8.21

-0.4

9**

-1.9

9N

umbe

r Sub

cent

ers

-0.0

82.

41-0

.02

***

-3.7

7O

n C

oast

, Gre

at L

ake,

Mex

ican

Bor

der

-0.1

00.

25-0

.06

0.04

-0.0

2-0

.29

Tran

sfor

mat

ion

Para

met

ers

z-st

atis

ticz-

stat

istic

0.17

**1.

990.

23**

*2.

51λθ

0.00

-0.0

60.

121.

12

Num

ber o

f Obs

erva

tions

8585

85Lo

g-Li

kelih

ood/

R2

-511

.6-5

10.3

0.90

***

indi

cate

s si

gnifi

canc

e at

the

1% le

vel,

** a

t the

5%

leve

l, an

d *

at th

e 10

% le

vel.

Estim

ate

Estim

ate

Estim

ate

Spec

ifica

tion

3:

D

oubl

e-Lo

g M

odel

Spec

ifica

tion

2Sp

ecifi

catio

n 1

Tabl

e C

.7M

axim

um L

ikel

ihoo

d Es

timat

esD

epen

dent

Var

iabl

e: A

rea

in S

quar

e M

iles

113

Bibliography

Barsky, Robert B., F. Thomas Juster, Miles S. Kimball, and Matthew D. Shapiro, 1997. “Preference Parameters and Behavioral Heterogeneity: An Experimental Approach in the Health and Retirement Study,” Quarterly Journal of Economics 112: 537-79.

Binswager, Hans, 1981. “Attitudes Toward Risk: Theoretical Implications of an

Experiment in Rural India,” Economic Journal 91(364):867-90. Blinder, Alan S., 1973. "Wage Discrimination: Reduced Form and Structural Estimates,"

Journal of Human Resources 8(4): 436-55. Bound, John, and George Johnson, 1992. "Changes in the Structure of Wages in the

1980s: An Evaluation of Alternative Explanations," American Economic Review 82(3): 371-92.

Brueckner, Jan K., 1983. “The Economics of Urban Yard Space: An “Implicit-Market”

Model for Housing Attributes,” Journal of Urban Economics 13: 216-34. Brueckner, Jan K., and David A. Fansler, 1983. “The Economics of Urban Sprawl:

Theory and Evidence on the Spatial Sizes of Cities,” Review of Economics and Statistics 65(3): 479-82.

Büttler, H., 1981. “Equilibrium of a Residential City, Attributes of Housing, and Land-

Use Zoning,” Urban Studies 18: 23-39. Camerer, Colin F., and Robin M. Hogarth, 1999. "The Effects of Financial Incentives in

Experiments: A Review and Capital-labor-production Framework,” Journal of Risk and Uncertainty 19: 7-42.

Corcoran, Mary, 1977. "Work Experience, Labor Force Withdrawals, and Women's

Wages: Empirical Results Using the 1976 Panel Study of Income Dynamics," in Women in the Labor Market (eds. Cynthia B. Lloyd, Emily S. Andrews, and Curtis L. Gilroy), New York: Columbia University Press: 216-45.

Corcoran, Mary, Greg J. Duncan, and Michael Ponza, 1983. "A Longitudinal Analysis of

White Women's Wages," Journal of Human Resources 18(4): 497-520.

114

Cox, Donald, 1984. "Panel Estimates of the Effects of Career Interruptions on the Earnings of Women," Economic Inquiry 22(3): 386-403.

Davidson, Russell, and James G. MacKinnon, 1993. Estimation and Inference in

Econometrics, New York: Oxford University Press. Dohmen, Thomas, Armin Falk, David Huffman, Uwe Sunde, Jurgen Schupp, and Gert G.

Wagner, 2005. “Individual Risk Attitudes: New Evidence from a Large, Representative, Experimentally-Validated Survey,” IZA Discussion Paper No. 1730.

Donkers, Bas, Bertrand Melenberg, and Arthur van Soest, 2001. “Estimating Risk

Attitudes Using Lotteries: A Large Sample Approach,” Journal of Risk and Uncertainty 22(2): 165-95.

Guiso, Luigi, and Monica Paiella, 2001. “Risk Aversion, Wealth, and Background Risk,”

CEPR Discussion Paper 2728. Hall, Jeffrey R., Steven A. Lippman, and John J. McCall, 1979. “Expected Utility

Maximizing Job Search,” in Studies in the Economics of Job Search (eds. Steven A. Lippman and John J. McCall), North-Holland Publishing: 133-55.

Harless, David W., and Colin F. Camerer, 1994. “The Predictive Utility of Generalized

Expected Utility Theories,” Econometrica 62(6): 1251-89. Hartog, Joop, Ada Ferrer-i-Carbonell, and Nicole Jonker, 2002. “Linking Measured Risk

Aversion to Individual Characteristics,” Kyklos 55: 3-26. Hartwick, J., U. Schweizer, and P. Varaiya, 1976. “Comparative Static Analysis of a

Residential Economy with Several Classes,” Journal of Economic Theory 13: 396-413.

Hausman, Jerry A., and William E. Taylor, 1981. "Panel Data and Unobservable

Individual Effects," Econometrica 49(6): 1377-98. Katz, Lawrence, and Kevin Murphy, 1992. "Changes in Relative Wages, 1963–1987:

Supply and Demand Factors," Quarterly Journal of Economics 107(1): 35-78. Kunze, Astrid, 2002. "The Timing of Careers and Human Capital Depreciation," IZA

Discussion Paper No. 509. Light, Audrey, and Manuelita Ureta, 1995. "Early Career Work Experience and Gender

Wage Differentials," Journal of Labor Economics 13(1): 121-54.

115

Lippman, Steven A., and John J. McCall, 1976. “The Economics of Job Search: A Survey,” Economic Inquiry 14(2): 155-89.

Mankin, Wyatt, 1972. “A New Look at the Muth Model,” American Economic Review

62(5): 980-81. McMillen, Daniel P., forthcoming. “Testing for Monocentricity,” in A Companion to

Urban Economics (eds. Richard Arnott and Daniel McMillen), Blackwell Publishing.

McMillen, Daniel P., and Stefani C. Smith, 2003. “The Number of Subcenters in Large

Urban Areas,” Journal of Urban Economics 53: 321-38. Mills, Edwin S., 2000. “A Thematic History of Urban Economic Analysis,” Brookings-

Wharton Papers on Urban Affairs 1: 1-52. Mincer, Jacob, and Haim Ofek, 1982. "Interrupted Work Careers: Depreciation and

Restoration of Human Capital," Journal of Human Resources 17(1): 3-24. Mincer, Jacob, and Solomon Polachek, 1974. "Family Investments in Human Capital:

Earnings of Women," Journal of Political Economy 82(2): S76-S110. Miyata, Sachiko, 2003. “Household’s Risk Attitudes in Indonesian Villages,” Applied

Economics 35: 573-83. Muth, Richard F., 1969. Cities and Housing, Chicago: University of Chicago Press. Nachman, David C., 1975. “Risk Aversion, Impatience, and Optimal Timing Decisions,”

Journal of Economic Theory 11 (October): 196-246. Oaxaca, Ronald, 1973. "Male-Female Differentials in Urban Labor Markets,"

International Economic Review 14(3): 693-709. Pissarides, Christopher A., 1974. “Risk, Job Search, and Income Distribution,” Journal of

Political Economy 82(6): 1255-67. Polachek, Solomon William, 1975. "Differences in Expected Post-School Investment as a

Determinant of Market Wage Differentials," International Economic Review 16(2): 451-70.

Pratt, J., 1964. “Risk Aversion in the Small and in the Large,” Econometrica 32: 122-36. Rekko, Ange, Hans Doodeman, Peter de Gijsel, Joop Schippers, and Jacques Siegers,

1993. "The Effects of Temporary Withdrawals on Women's Gross Wage Rates," Jahrbucher fur Nationalokonomie und Statistik 212(1–2): 105-19.

116

Sahib, Padma Rao, and Xinhua Gu, 2002. “To Tie the Knot or Not: Cohabitation,

Marriage, and Individuals’ Attitudes to Risk,” Demographic Research 6(13): 355-81.

Sandell, Steven H., and David Shapiro, 1979. "Work Expectations, Human Capital

Accumulation, and the Wages of Young Women," Journal of Human Resources 15(3): 335-53.

Stafford, Frank P., and Marianne Sundstrom, 1996. "Time Out for Childcare: Signalling

and Earnings Rebound Effects for Men and Women," Labour 10(3): 609-29. Vesterlund, Lise, 1997. “The Effects of Risk Aversion on Job Matching: Can Differences

in Risk Aversion Explain the Wage Gap?” Working Paper, Iowa State University. Wooldridge, Jeffrey M., 2002. Econometric Analysis of Cross Section and Panel Data,

MIT Press. Weiss, Yoram, and Reuben Gronau, 1981. "Expected Interruptions in Labor Force

Participation and Sex-Related Differences in Earnings Growth," Review of Economic Studies 68(4): 607-19.

Wheaton, William C., 1974. “A Comparative Static Analysis of Urban Spatial Structure,”

Journal of Economic Theory 9: 223-37. Wheaton, William C., 1976. “On the Optimal Distribution of Income Among Cities,”

Journal of Urban Economics 3: 31-44.

117

Vita

Christy Spivey was born in Dubai, United Arab Emirates on March 1, 1976, the

daughter of Freida Zelda Spivey and John Colton Spivey. After completing her work at

John Foster Dulles High School in Sugar Land, Texas in May 1994, she entered Tulane

University in New Orleans, Louisiana as a Dean’s Honor Scholar. She spent her junior

year studying abroad at the London School of Economics in London, England. She

received the degree of Bachelor of Science from Tulane University in May 1998,

graduating summa cum laude in Economics. During the following years she was

employed as an Economic Analyst at Lukens Consulting Group, formerly the Economics

Resource Group, in Houston, Texas. In August 2000 she entered the Graduate School of

The University of Texas at Austin, where she earned a Master of Science in 2002. While

at The University of Texas at Austin, she worked as a teaching assistant and as an

instructor and published her first article in a peer-reviewed journal, Industrial and Labor

Relations Review. She was also a Visiting Assistant Professor at Texas A&M University

in College Station, Texas during her last year as a graduate student.

Permanent address: 12910 Council Bluff Drive, Austin, TX 78727

This dissertation was typed by the author.