Unit Roots in Macroeconomic Time Series

7/28/2019 Unit Roots in Macroeconomic Time Series

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nova Economia_Belo Horizonte_15 (3)_145-176_setembro-dezembro de 2005

Unit roots in macroeconomic time series:

theory, implications, and evidence

Gilberto A. LibanioAssistant Professor at Feder al Univer sity of Minas Ge rais (Braz il) and

Doctoral Candidate in Economics at the University of Notre Dame (USA)

Abstract

The theme of unit roots inmacroeconomic time series has receiveda great amount of theoretical and appliedresearch in the last two decades. Thispaper presents some of the main issues

regarding unit root tests, explores someof the implications for macroeconomictheory and policy, and reviews the recentevidence on the presence of unit roots inGDP series for Latin Americancountries. We conclude that a consensual

view on many of the aspects involved hasnot emerged from this literature.

Resumo

A existncia de razes unitrias em series temporais

macroeconmicas tem sido objeto de extensa pesquisa

terica e emprica nas ltimas duas dcadas. O pre-

sente artigo discute algumas das principais questes

relacionadas a testes de razes unitrias, explora al-

gumas implicaes para teoria e poltica macroecon-mica, e apresenta a evidencia recente sobre a existn-

cia de razes unitrias em sries de PIB em pases da

Amrica Latina. O artigo conclui que no se formou

um consenso a respeito de vrias das questes envol-

vidas nesse debate.

Key words

time-series models, unitroots, business fluctuations.

JEL Classification C22, E32.

Palavras-chave

modelos de sries temporais, razes

unitrias. flutuaes econmicas.

Classificao JEL C22, E32.


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1_ IntroductionIt has been two decades since the

influential work by Nelson and Plosser(1982) on the existence of unit roots inmacroeconomic time series waspublished. Their 1982 paper is usuallyrecognized as an important contribution

with repercussions for theory andpolicy, and as the starting point of alarge literature in macroeconomics

and econometrics.Nelson and Plossers main

achievement is to present statisticalevidence that supports the hypothesisof a unit root in the autoregressiverepresentations of a dozenmacroeconomic time series for the US,including GNP, employment, wages,

prices, interest rates, and stock prices.As I will discuss in the followingsections, these results have significantimplications for econometric modeling,for business cycle theorizing, and foreconomic policy prescriptions.

The presence or absence of unitroots, to put it simply, helps to identify

some features of the underlyingdata-generating process of a series. If aseries has no unit roots, it ischaracterized as stationary, andtherefore exhibits mean reversion inthat it fluctuates around a constant long

run mean. Also, the absence of unitroots implies that the series has a finite

variance which does not depend ontime (this point is crucial for economicforecasting), and that the effects ofshocks dissipate over time.

Alternatively, if the series featurea unit root, they are better characterizedas non-stationary processes that haveno tendency to return to a long-run

deterministic path. Besides, the varianceof the series is time-dependent and goesto infinity as time approaches infinity,

which results in serious problems forforecasting. Finally, non-stationaryseries suffer permanent effects fromrandom shocks. As usuallydenominated in the literature, series

with unit roots follow a random walk.In sum, the existence (or lack

thereof) of unit roots in macroeconomictime series brings about importantimplications, and this helps to explain

why this topic has received a greatamount of theoretical and appliedresearch in the last two decades. There

are many different issues in the unitroots literature that are somehow relatedbut can be explored separately. To thequestion why do we care about unitroots in GNP? Cribari-Neto (1996,p. 38) provides the following answer:


Unit roots in macroeconomic time series146


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To a policymaker the answer could be:

Because the policy implications are

different. To a macroeconomist, it couldbe answered that there are theoretical

implications on several theories and

models. Finally, an econometrician

would be satisfied with the answer:

Because the asymptotics are different.

This paper presents some of themain issues regarding unit root tests,

explores some of the implications formacroeconomic theory and policy, andreviews the recent evidence on thepresence of unit roots in GDP seriesfor Latin American countries. Theremainder of the paper is organized asfollows. The next section considers themajor contributions in the literature on

unit root testing (with a focus onaggregate output series), since the workof Nelson and Plosser (1982). Section 3discusses implications for business cycletheorizing, including the initial supportfor real business cycle theories, and thereactions to that perspective. Section 4presents recent empirical results

regarding the existence of unit roots inLatin American GDP series. Finally, thelast section summarizes the arguments,explores some economic policyimplications, and presents possibledirections for future research.

2_ Testing for unitroots in GNP series

Consider two alternative models usedto represent GNP time series:

y a b et t t= + + (1)

y a y et t t= + +- 1 (2)

where: yt represents the naturallogarithm of GNP at time t;trepresents a time trend;bis a constant that gives thegrowth rate of the variable;eis an error term with zeromean and finite variance.

The first specification impliesthat GNP equals the constant aat timezero (y a0 = ) and grows over time at a

constant rate b, with the error termexplaining deviations from the trend ineach year. In other words, the variableyt presents a stationary fluctuationaround the time trend a bt+ . Therefore,the variable is described as trendstationary (TS), and stationarity isachieved by removing the time trend

(detrending), i. e. regressing yt on t.Another feature of model (1) is that thevariance of yt is bounded by thevariance ofet , and the linear forecast ofGNP converges to the time trend a bt+as the forecast horizon increases.

Gilberto A. Libanio 147



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Finally, for the first specification, theeffects of a shock at time ttend to zero

over time, since the error term affectsthe outcome in the current period, buthas no persistent influence insucceeding time periods.

Model (2), on the other hand,specifies that GNP grows at rate afromits previous value, with an error termplaying a role every year. Despite the

apparent similitude between the twomodels, they are indeed very different,and lead to different implications inmany respects.

First, model (2) is non-stationaryand cannot be made stationary throughdetrending. But note that the firstdifference of the series is given by

a et+ , a stationary process. So,stationarity can be achieved bydifferencing, and the model is calleddifference stationary(DS). Model (2) is oneof the simplest AR(1) processes, andcan be described as a random walk withdrift. The dependent variable displays arandom fluctuation given by the error

term et , in addition to the growth givenby the drift term a. Contrarily to model(1), however, there is no tendency foryt to return to a predetermined meanvalue, and its trajectory is given by anaccumulation of disturbances. In other

words, the error term affects notonly what happens in the current

period, but also what happens in allsucceeding periods. In order to better

visualize this point, we can substituterepeatedly for the lagged yt value inequation (2) to get:

y y a et t ii

t

= + +=

01

(3)

It is straightforward to see thatthe variance of yt grows withoutbound over time, and that shocks tothe system (captured by the error term)have a permanent effect on the series.

Also, the mean square error of theforecast of the DS model grows linearly

with the forecast horizon.

Model (2) represents the unit roothypothesis, a terminology arising from thefact that the coefficient on yt- 1 isunity. If this coefficient were less thanunity, the series would be stationary(mean reverting) and random shocks

would dissipate over time.1

In sum, the two models are

indeed different and have differentimplications. Therefore, it is importantto check whether a GNP series can bebetter described as a TS or a DSprocess. This is usually done by testingfor the presence of a unit root in the



1 The macroeconomicimplications of unit rootwill be addressed in moredetail in section 3.


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autoregressive representation of theseries. If a unit root is found, traditional

estimation techniques cannot be usedsince, as is well known, spurious resultsare obtained when two variables withunit roots are regressed on each other:misleadingly high R squares and tstatistics, and very low DW statistics.

There are different tests for unitroots described in the literature.

According to Elder and Kennedy (2001,p. 138), the augmented Dickey-Fuller(ADF) test has become the mostpopular of many competing tests in theliterature. It consists in estimating byOLS a model such as

y a bt uy et t t= + + +- 1 in the form (4)

Dy u y a bt et t t= - + + +-( )1 1 (5)and then testing for u = 1 (null hypothesisof unit root) using a ttest.2 Failing toreject the null is equivalent to failing toreject the existence of a unit root orstochastic trend in the data series.

Two major issues in performingADF tests are the inclusion (or not) of

an intercept term, a trend term, or both,and the selection of the truncation lag.

ADF test results are very responsive tothe presence of intercept and trendterms, and to the number of lagsincluded. In general, including too manydeterministic regressors results in lost

power, whereas not including enoughof them increases the probability of not

rejecting the unit-root null.3

It is important to note that theway in which classical hypothesis testingis carried out ensures that the nullhypothesis is not rejected unless there isstrong evidence against it. Since the vastmajority of unit root tests havenon-stationarity, i. e. a unit root, as the

null hypothesis, it is not surprising thatunit root tests usually conclude thatthere is a unit root in the series. Thisproblem is exacerbated by the fact thatin general unit root tests have lowpower. However, it is also possible todesign tests for the null hypothesis ofstationarity against the alternative of a

unit root. Kwiatkowski, Phillips,Schmidt, and Shin (1992) introducesuch a test, and do it by choosing acomponents representation in whichthe time series under study is written asthe sum of a deterministic trend, arandom walk, and a stationary error.

The null hypothesis of trend stationaritycorresponds to the hypothesis that the

variance of the random walk equalszero. As one could expect, their resultsare frequently supportive of the trendstationarity hypothesis, contrary tothose of the traditional unit root tests.



2 Note that under the null

hypothesis this t statistic isnot asymptotically normallydistributed, and thereforespecial critical values arerequired. Actually, criticalvalues depend on theregression specification andon the sample size. Dickeyand Fuller (1979), amongothers, provide tables with

appropriate critical valuesfor some cases.3 A complete description ofunit root tests is beyond thescope of this article. For anextensive presentation anddiscussion of unit root tests,see Maddala and Kim (1998).


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2.1_ The seminal contributionof Nelson and Plosser (1982)

The work by Nelson and Plosser (1982)is usually considered the starting pointof a vast amount of research on unitroots in macroeconomic time series.

Their paper uses long historical timeseries of annual data for 14 variables forthe US economy, including measures ofoutput, employment, prices, wages,

money stock, and interest rates.Starting dates range from 1860 to 1909,and all series end in 1970. Nelson andPlossers goal is to examine whetherthese time series are better characterizedas TS or as DS processes.

In particular, they intend toquestion the traditional practice of

decomposing output series into asecular component (long rundeterministic trend) and a cyclicalcomponent (stationary short runfluctuations around trend). Nelson andPlosser argue that, if the series isnon-stationary (i. e. features a unit rootin its autoregressive representation),

then the secular component should bemodeled as a stochastic process,responsible for any long runnon-stationarity observed in the series,since the cyclical component is assumedto be transitory. In other words,

Since cyclical fluctuations are

assumed to dissipate over time, any

long-run or permanent movement(non-stationarity) is necessarily

attributed to the secular component

(Nelson and Plosser, 1982, p. 139-140).

In this case, aggregate output isthought of as consisting of anon-stationary growth component plusa stationary cyclical component, being

the total variation in output changesattributed to both components.

Nelson and Plosser (1982) thenanalyze sample autocorrelations and testfor the existence of unit roots in thefourteen long run time series, and findthat the null hypothesis of a unit rootcannot be rejected at 5% for most of

the series. The only exception is theunemployment rate, which, as Nelsonand Plosser recognize it, was on a priorigrounds expected to be stationaryaround a trend with zero slope.

Nelson and Plosser acknowledgethat non-rejection of the null hypothesisdoes not necessarily imply that the null

is true. This is particularly important inthe case of unit root tests, since suchtests usually have low power, i. e.cannot differentiate between unit rootsand a TS alternative with an AR rootarbitrarily close to unity. However, they




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argue, if the deviations from a lineartrend in the series are stationary,

then the tendency to return to the trend

line must be so weak as to avoid

detection even in samples as long as

sixty years to over a century (Nelson and

Plosser, 1982, p. 152).

To sum up, Nelson and Plosserconclude that the evidence presentedsupport the DS representation ofnon-stationarity in economic timeseries, and that in this case economicfluctuations are better explained bymovements in the secular component(caused mainly by real factors, such aschanges in tastes and technology) thanby the cyclical component. As we

will discuss in section 3, this argumentleads to the idea that real businesscycle models are likely to provide abetter explanation for fluctuations inaggregate output than models that seemonetary shocks as the main sourceof the business cycle.

2.2_ Measuring the persistenceof innovations

One of the most important findings ofNelson and Plosser was that GNPseries can be characterized asnon-stationary, and therefore sufferlong-term effects from random shocks.

A question that follows naturally is:how persistent are the impacts of

shocks? In general terms, the answer tothis question relates to the relativeimportance of the random walk secularcomponent vis--vis the stationarycyclical component in the series.

Two different measures ofpersistency were established in theliterature. The first one, proposed by

Campbell and Mankiw (1987), is knownas the cumulative impulse responsefunction. Campbell and Mankiwsstarting point is the assumption that ifoutput series are stationary, andtherefore mean-reverting, then a currentshock should not change ones forecastof output in the long run (say, five to

ten years). They model the change inlog GNP as a stationary ARMAprocess, and calculate the impliedimpulse response functions for the levelof the series, using quarterly real GNPdata for the US from 1947 to 1985.Sixteen different ARMA specificationsare considered, varying both AR (p )

and MA (q) parameters from zero tothree. In most of the specifications(13 out of 16), the model impulseresponses show an impact between 1.2and 1.8 percent over the long runforecast of GNP after a 1 percentshock in the variable.




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Campbell and Mankiws mainconclusion from this evidence is that

innovations in real GNP have persistenteffects. Their results, therefore, extendthe evidence provided by Nelson andPlosser (1982) in favor of unit roots inoutput series. However, Campbell andMankiw (1987) do not completelyaccept Nelson and Plossersinterpretation of such evidence in terms

of the determinants of the businesscycle. In particular, they argue thatdemand shocks may still play animportant role in output fluctuations,and that the finding of persistency inthe series is consistent with a substantialcyclical component. We will return tothis point in section 3.

The second measure ofpersistency found in the literature wasproposed by Cochrane (1988). He showsthat any series with a unit root can beseen as a combination of a stationarycomponent and a random walk. Hismeasure of persistency is then related tothe relative importance of both

components. In other words, Cochrane(1988) aims at addressing the questionhow big is random walk in GNP?

Cochranes measure ofpersistency, known as variance ratio, isbased on the variance of GNPs longdifferences, and is given by:

Vk

y y

y yk

t t k

t t

=-

-

-

-

1

1

var

var

( )

( )(6)

This measure of persistenceranges from zero to one. It can beshown that Vk approaches zero if theseries is stationary, and tends to one incase of a random walk. The intuitionbehind this measure is that if GNPfollows a random walk, then the

variance of its k-differences grows withk, whereas this same varianceapproaches a constant in case of astationary series. So, in case ofstationarity, the value between squarebrackets tends to a constant, andgrowingk causes Vk to converge tozero; in case of a pure random walk, the

ratio of variances grows with k, andtherefore Vk tends to one.

Cochrane (1988) uses annual databetween 1869 and 1986 for the log ofper capita GNP in the US and findsthat the random walk componentresponds for about one-third of totaloutput variance. It means that annual

GNP growth rates contain an importanttemporary component, and the level ofthe series always tends to return to adeterministic trend line. In sum,

These results mean that an AR (2)

about a deterministic trend or a




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difference-stationary ARMA process

with a very small random walk

component is a good in-samplecharacterization of the behavior

of GNP (Cochrane, 1988, p. 916).

2.3_ Testing for unit rootsin series with structural breaks

Another important developmentin the literature about unit roots inmacroeconomic time series isprovided by Perron (1989), whopresented a model to test for unitroots in the presence of an exogenousbreak in the series. In this case, thebasic assumption is that outlyingevents can be separated from thenoise function and be modeled asone-time changes in the deterministicpart of the time series model.

The importance of Perrons worklies in the fact that unit root tests arebiased toward non-rejection of the unitroot null when there are structuralbreaks in the series. To see why this isthe case, consider a time series with two

distinct subperiods, and an abruptone-time change in the mean value ofthe variable between the two intervals.Even if each subperiod is stationaryaround a zero-sloped trend, a trend linefitted through the entire sample will

have a negative slope (assuming that theone-time change is negative, like in the

1929 crash), causing unit root testsnot to reject the null hypothesis.Indeed, Perron (1989) shows with aMonte Carlo experiment that thecoefficient on yt- 1 in equation (4)becomes concentrated around 1 as themagnitude of the break increases, andconcludes that there is a bias toward the

non-rejection of the null in the presenceof structural breaks.Perron (1989) develops a formal

procedure to test for unit roots allowingfor a structural break. Threepossibilities are considered by Perron

when modeling this break:

i. a change in the level of the series

(intercept);ii. a change in the rate of growth

(slope);iii. a change in both intercept and

slope.

In this case, the null hypothesis is that aseries is characterized by the presence

of a unit root, with a one-time changeat time Tb Tb T ( )1 < < . The alternativeis that the series is stationaryaround a broken trend line. Moreformally, these hypotheses can beexpressed as (Enders, 1995):




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H y a y D D e t t p L t 0 0 1 1 2: = + + + +- m m (7)

H y a a t D D e t L T t 1 0 2 2 3: = + + + +m m (8)

where:i. Dp represents a pulse dummy

variable that allows for aone-time jump in the level of aunit root process, and is suchthat Dp = 1 ift Tb= + 1 andzero otherwise;

ii. DL is a level dummy variable thatgives a one-time change in theintercept of a TS process, or aone-time change in the driftterm of a DS process, and issuch that DL= 1 ift Tb> andzero otherwise;

iii. DT represents a dummy variablethat changes the slope of thedeterministic trend line underH1, and is such that D t Tb T = -for t Tb> and zero otherwise.

Perrons testing strategy consistsin estimating the regression equationH1 and use the residuals to estimate:

y a y et t t= +-1 1 (9)

The t-statistic for the nullhypothesis a1 1= is then comparedto the critical values provided byPerron (1989).

Perron (1989) applies thismethodology to test for the presence of

unit roots using the same data asNelson and Plosser (1982). He chooses

the stock market crash of 1929 as abreak point that permanently changedthe level of the series. Also, Perron(1989) applies the same test usingquarterly postwar real GNP series forthe US economy (1947:1 to 1986: III),and includes a one-time change in theslope of the deterministic trend in 1973

due to the oil price shock. Perronsresults challenge most of Nelson andPlossers conclusions. In short, he isable to reject the unit root null in elevenof the series Nelson and Plosser foundto be non-stationary, and proposes thatsuch series are better described asstationary around a trend with a

structural break in 1929. The quarterlyGNP series is also found to bestationary, with a change in the slope ofthe trend in 1973.

Summing up: Perrons analysissuggests that a deterministic trend witha few discontinuities caused by largeand occasional shocks along with

stationary cycles is the bestcharacterization of output fluctuations.In this case, it is argued that persistencearises only from large and infrequentshocks, and that the economy returns toa deterministic trend after small and




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frequent shocks. According to Perron(1989, p. 1361),

Most macroeconomic time seri es are notcharacterized by the presence of a unit

root. Fluctuations are indeed stationary

around a deterministic trend function.

The only shocks which have had

pers istent eff ects are the 1929 crash and

the 1973 oil price shock.

Perrons work has received some

criticism in the literature, based on thefact that the breaking point isexogenously selected. Papers such asZivot and Andrews (1992) andBanerjee, Lumsdaine, and Stock (1992)argue that this exogenous determinationof the breaking points based onobservation of the data can be seen as

data mining, and introduces a pre-testbias towards the rejection of the nullhypothesis.4The intuition behind thisargument is that the choice of breakingpoints based on the observation of datais not consistent with a testing strategybased on a distribution that is supposedto be data independent.

Several attempts have been madeto develop a unit root testing procedureunder the assumption that the breakpoints are not known a priori, but are,instead, endogenously determined. Inthis case, events such as the 1929 crashand the first oil shock are not removed

from the noise function of the series.The adequate procedure usually

involves the specification of a datadependent algorithm to find outwhether or not a breaking point ispresent in the data, and in which periodof the sample it is located. Suchprocedure transforms Perronsunit-root test, which is conditional on aknown breakpoint, into an

unconditional unit-root test.The null hypothesis here is aunit-root process with drift thatexcludes any structural change, and therelevant alternative hypothesis is atrend-stationary process with a possiblestructural change occurring at anunknown point in time. The selection

of the breakpoint is seen as theoutcome of an estimation proceduredesigned to fit the series to a TSrepresentation. The estimation schemechooses the breakpoint that gives most

weight to the TS alternative hypothesis,i. e. the one associated with the lowestt-statistic of the coefficient of the

lagged variable under consideration.To consider the possibility of a

break in the series, three classes ofstatistics are considered:

i. recursive statistics, which arecomputed using subsamples



4 See the Jul 1992 issue ofthe Journal of Business andEconomic Statistics.


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t k= 1, .. . , for k k T= 0 , ... , ,where k 0 is a start-up value and

Tis the full size of the sample;ii. rolling statistics, which arecomputed using a subsample offixed size, rolling through thesample;

iii. sequential statistics, which arecomputed using the full sample,but sequentially allowing for a

hypothetical break or shift atevery point in the sample.

The empirical results using suchstrategies are not conclusive. Zivot and

Andrews (1992) find less evidenceagainst the unit root hypothesis thanPerron (1989) does: they revert Perronsconclusions for five of the eleven

Nelson and Plosser series for which theunit root hypothesis was rejected.Besides, Zivot and Andrews are notable to reject the null of unit root forthe postwar US GNP series. However,their results for some of the series(industrial production, nominal GNP,and real GNP) reinforce Perrons

conclusions against the unit roothypothesis, which is rejected even afterendogenizing the breakpoint selection.

Banerjee, Lumsdaine, and Stock(1992) also find mixed results. Using

postwar data for seven OECDcountries, they are not able to

reject the unit root hypothesis forfive countries (France, Germany,Italy, United Kingdom, and US).For two other countries, however, theunit root is rejected against thealternative of a stationary brokentrend (Canada and Japan).

Another subsequent

development in this literature considersthe possibility of two endogenous breakpoints in the series. Lumsdaine andPapell (1997) argue that unit-root testsare sensitive to the number of breaksunder the alternative hypothesis, andsuggest that the long series analyzed byNelson and Plosser (1982) and others

seem to exhibit two breaks. Theyreexamine the Nelson-Plosser dataallowing for two endogenous breakpoints, and find more evidence againstthe unit-root hypothesis than Zivot and

Andrews (1992), but less than Perron(1989). More specifically, they reject at5% the null of unit roots for seven of

the 13 series analyzed by Nelson andPlosser. Moreover, they reject the unitroots for three of the seven series for

which Perron (1989) rejects, but Zivotand Andrews (1992) fail to reject.5



5 Other papers that examinemacroeconomic time seriesusing the two-breakmethodology includeBen-David, Lumsdaine andPapell (2003), and Lee andStrazicich (2003). Ultimately,this literature brings about aproblem of model selection,in determining the adequatenumber of breaks in theseries. See also Maddalaand Kim (1998).


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2.4_ Tests for unit roots using panel data

All tests presented in the previous

section are based on single-countrydata. Recently, attempts have beenmade in the literature to use panel datain unit root tests (Levin, Lin, and Chu,2002; Im, Pesaran, and Shin, 2003). Ingeneral, the use of panel data is seen asa means of generating more powerfulunit root tests. Levin, Lin, and Chu

(2002, hereafter LLC) assume that allindividuals in the panel have identicalfirst-order partial autocorrelationcoefficients, but other parameters suchas the degree of persistence inindividual regression error, the interceptand trend coefficients are allowed to

vary freely across individuals. Their test

procedures are designed to assess thenull hypothesis, that each individual inthe panel has non-stationary timeseries, versus the alternative hypothesis,that all individuals time series arestationary. Im, Pesaran, and Shin(2003, hereafter IPS), on the otherhand, allow the first order AR

coefficient to differ across countriesunder the alternative hypothesis.6

Panel data unit root tests havebeen used in recent empirical literatureon purchasing power parity, and alsoapplied in testing for unit roots in

inflation rates, unemployment, andnominal interest rates. Despite the

arguments that the use of panel dataincreases the power of unit root tests,this methodology also has someproblems and limitations. First, mostpanel data tests depend on theassumption that there is no cross-sectional correlation among the errorterms; an assumption often violated in

practice. Second, the results of a panelunit root test are sensitive to the time-series variables included in the panel.

Culver and Papell (1997) addresssome of these limitations by performingunit root tests for inflation rate seriesusing sequential break and panel datamodels. Their findings show that the

evidence against the unit-roothypothesis is stronger in panel data teststhan in single-country ADF tests.Finally, Culver and Papell (1997) varythe number of countries in the paneland suggest that the unit-roothypothesis for inflation is very fragile tocross-section variation.

Since the present paper focuseson unit roots tests in GDP series, I willconclude this section by mentioningRapach (2002), who presents many testsfor unit roots in GDP series using paneldata for OECD countries. He conducts



6 A detailed descript ionof the test proceduresdeveloped by LLC and IPS isbeyond the scope of thisarticle. See the originalreferences for more details.


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the tests proposed by LLC and IPS, andalso uses the seemingly unrelated

regressions (SUR) estimator (to handlecross-sectional dependence) and theMADF test (to allow for different first-order partial autocorrelations under thealternative hypothesis and control forcross-sectional dependence). Rapach(2002) tests for unit roots using the fourdifferent methodologies (LLC, IPS,

SUR, MADF) in four distinct series:i. Annual real GDP data, 13

countries, for the period1956-1996, from the IMF;

ii. Quarterly real GDP data, sevencountries, 1965:1 to 1996:4, alsofrom the IMF;

iii. Annual real GDP per capita data,

21 countries, for the period1950-1992, from the Penn

World Tables;iv. Annual real GDP per capita

data, 15 countries, 1900 to1987, using data derived fromMaddison (1989).

For each data set, single-countryADF tests are also conducted. In thiscase, the unit root null hypothesis is notrejected for most of the series. The fourpanel data unit root tests applied byRapach (2002) seem to confirm theinferences drawn from single-country

tests: the null of unit roots is rarelyrejected in these tests. Rapachs main

conclusion is thatthe panel unit root test results reported

in the present paper strongly reinforce

the view that real output levels are

non-stationary(Rapach, 2002, p. 485).

Finally, Rapach suggests that theresults presented should be expandedby allowing for structural breaks in theseries along the lines of Perron (1989)and others, since there is evidence thatthe null of unit roots is more frequentlyrejected when structural breaks areallowed in the deterministic trend.

3_ Implications for macroeconomictheory and policy

The traditional procedure ofdecomposing output fluctuations into along-run trend and short-run cycles isbuilt upon the assumption that thetrend component is a deterministicfunction of time, and the cyclicalcomponent represents a stationarymovement around this trend. As is

well known, this kind of reasoningcannot be maintained if the trendcomponent is non-stationary, i. e. if thetime series features a unit root. Inaddition, unit roots in GNP series pose




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another challenge for traditionaltheories of macroeconomic fluctuations,

which assume output to be mean-reverting and shocks to have onlytemporary real effects.

In view of these considerations,one of the most important issues in theunit root literature since the work ofNelson and Plosser (1982) is theimplications of the presence of unit roots

for macroeconomic theory and policy.3.1_ Unit roots as a support

to real business cycle theory

At first, evidence of unit roots in GDPtime series was used to provide supportfor theories of fluctuations based onreal (as opposed to monetary) factors.

This argument is present in the work of

Nelson and Plosser (1982), and hasstrongly influenced the direction ofmacroeconomic research since the1980s.7 Some authors argue that theadvance of RBC models fullequilibrium models with emphasis ontechnology shocks as the source offluctuations is mainly due to the

empirical findings of Nelson and Plosser(1982). According to McCallum (2000, p.119), the logical basis for the upsurge ofthe RBC movement can be viewed asprincipally empirical. Or, as stated byBackhouse and Salanti (2000, p. 12),

Altho ugh deci sive tests are rarely

possible , some paper s cite one example

where such a test occurred: the rejection

of the hypothesis that monetary shocks

were the cause of the business cycle. This

led directly to the emergence of real

business cycle theory.

The argument used by Nelsonand Plosser (1982) is that most of thefluctuations in output should be

attributable to changes in the trendcomponent, in a trend versus cyclicaldecomposition, which wouldpresumably be unaffected by monetaryfactors. In other words, the existence ofunit roots leads to the inference thatmovements in output are persistent.Since the cyclical component is

assumed to be stationary, it follows thatoutput fluctuations are mostlyassociated with the secular component.

The argument is completed by theidea that monetary shocks arenecessarily temporary and so can onlyaffect the cyclical component, and thatthe long run path of the economy is

mainly guided by real factors such astastes and technology.

Nelson and Plossers mainconclusion in terms of macroeconomictheorizing follows directly from suchreasoning, and can be summarized as:



7 The main effect can beseen as the advance of realbusiness cycle models and thedecline of new classicalmodels developed by Lucas,Sargent, and Barro, amongothers, during the 1970s inwhich monetarymisperceptions wereconsidered the major sourceof output fluctuations.


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We conclude that macroeconomic models

that focus on monetary disturbances as a

source of purely transitory (stationary)

fluc tuations may never be succ essf ul in

explaining a very large fraction of output

fluc tuat ions and that stoc hasti c variation

due to real factors is an essential element

of any model of economic fluctuations.

(Nelson and Plosser, 1982, p. 141)

It is worthwhile to note that theargument rests on a number of implicitor explicit building blocks, all of whichare necessary for the final conclusions.First, Nelson and Plosser use theevidence of unit roots in GNP timeseries, although they recognize thatnone of the tests used can distinguishconclusively between a differencestationary process and a trend stationaryprocess with an autoregressive rootarbitrarily close to unity.

Second, it is inferred thatinnovations in the stochastic trendcomponent have a larger variance thanthe innovations in the transitorycomponent, and this leads to the

conclusion that variations in the cyclicalcomponent of fluctuations are small incomparison with fluctuations in thetrend component. Note that thisinference is dependent upon the abilityof the empirical analysis to differentiatebetween a DS and a TS process.

Third, the classical dichotomybetween real and monetary variables is

assumed. In particular, it is assumedthat the cyclical component isstationary, and mainly affected bymonetary factors, which are neutral inthe long run.8 In this respect, Nelsonand Plosser acknowledge in a footnotethat the theoretical possibility of aTobin effect of sustained inflation on

the steady-state capital stock is ignoredin their analysis. It is clear that oncemoney is allowed to play any significantrole in the long run path of theeconomy, unit roots do not necessarilysupport RBC theories (I will return tothis point later). In addition, concerningthe stationarity of the cyclical

component, Nelson and Plosser admitit is a proposition that cannot beinferred from empirical analysis.However, they justify its use bysaying that it is an assumption webelieve most economists would accept(Nelson and Plosser, 1982, p. 160).

The macroeconomic implications

of the work of Nelson and Plosser(1982) are controversial, and have notgone uncontested. Many arguments indifferent directions have been developedin opposition to Nelson and Plossersfindings.9 In very general terms, twointerrelated lines of criticism can be



8 Indeed, Nelson and Plosserseem to consider a direct and

unequivocal associationbetween aggregate demand,monetary factors, andstationary cycles, on one hand,and aggregate supply, realfactors, and stochastic trendcomponents, on the other.9 In this section I willconcentrate on themacroeconomic implications

of Nelson and Plosserswork. There are alsodevelopments concerningother aspects of their analysis,such as the differentprocedures for testing unitroots discussed in theprevious section of this paper.


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identified. The first one relates to aneffort to reconcile the presence of unit

roots in GNP time series with theoriesof output fluctuations other than RBCmodels; the other one contests the veryexistence of unit roots in the series or,more precisely, stresses the inability ofunit root tests to differentiate between

TS and DS processes in data coveringlimited time spans.

3.2_ Unit roots andNew Keynesian economics

The first reactions to the conclusions ofNelson and Plosser can be seen as anattempt to promote new Keynesianmodels of aggregate fluctuations, in

which GNP is expected to revert to a

long run trend, but in which theadjustment process can be very slowdue to imperfections in goods and labormarkets. A number of papers werepublished during the 1980s withdifferent arguments in this direction.

McCallum (1986) claims that thestatistical evidence provided by Nelson

and Plosser cannot be interpreted asproviding support for RBC theory,since this evidence is equally consistent

with other theories of the businesscycle. His criticism is primarily devotedto the second building block

mentioned before, i. e. that thecyclical component of fluctuations

has little importance relative to thesecular component.According to McCallum (1986),

this point cannot be inferred from thedata presented by Nelson and Plosser(1982), because it depends on thehypothesis that GNP series follows aDS process, which in turn is not

guaranteed. McCallum points out andevaluates three types of evidencepresented by Nelson and Plosser infavor of the hypothesis of nonstationarity. The first piece of evidenceis that the sample autocorrelations forannual GNP data are large and decayslowly. The second one is that the

autocorrelations of annual GNPdifferences are positive and significantat lag one, but often not significant atlonger lags. McCallum shows that bothpieces of evidence are also compatible

with the behavior of a trend stationaryseries with a root close to one, andconcludes that it is not possible to

determine with any degree of certaintyif a series is difference stationary ortrend stationary simply by inspection ofthe autocorrelation functions for levelsand differences. The third piece ofevidence provided by Nelson and




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Plosser (1982) is formal tests of unitroots. Also in this case, McCallum

argues, the evidence is far fromconclusive, since unit root tests havelow power to distinguish between a DSprocess and a TS process with an ARroot close to unity.

In addition, McCallum (1986)shows that if the decomposition of theseries into cyclical and secular

components assumes that the latter isgiven by a DS process, when theprocess under study is actually one ofthe TS class with an AR root close toone, then it follows that the variabilityof the cyclical component will beunderestimated. He concludes that

The time series evidence provided by

Nelson and Plosser (1982) is

inadequate to determine whether the

relevant series are of the DS or TS

class. This evidence itself, then, sheds

little or no light on the issue of the

relative variability of cyclical and secular

components of typical macroeconomic

time series and consequently provides

little or no support for the RBChypothesis(McCallum, 1986, p. 407).

The work of Campbell andMankiw (1987) is also motivated by thefindings of Nelson and Plosser (1982).Campbell and Mankiw assert that their

goal is to question the view that economicfluctuations can be seen as temporary

deviations from a deterministic trend. Inview of that, they provide evidence ofunit roots in postwar GNP time series,and suggest that persistence of shocksis an important aspect of the data,

which should be used more widely forevaluating theories of economicfluctuations (Campbell and Mankiw,

1987, p. 858). However, Campbell andMankiw do not agree with the idea thatthe existence of unit roots is clearevidence that real, supply-side shocksare the main cause of the business cycle,or that fluctuations based on aggregatedemand disturbances should beabandoned.

According to Campbell andMankiw (1987), traditional theoriesof economic fluctuations accept twobasic premises:

i. fluctuations are mainly caused byaggregate demand shocks;

ii. demand shocks have onlyshort-term effects, and the

economy reverts to the naturalrate of output in the long run.

They argue that Nelson and Plossersextreme (p. 876) conclusions followfrom the abandonment of the firstpremise. Alternatively, they suggest that




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another way to cope with persistence ofshocks is to abandon the second

premise, the natural rate hypothesis.This would open the possibility ofaggregate demand shocks havingpersistent effects on output, and thisresult could be explored in models ofmultiple equilibria. Campbell andMankiw conclude:

Perhaps models of temporary nominal

rigidities (e. g., Fischer [1977]) ormisperceptions (e. g., Lucas [1973])could be reconciled with findings of

pers istence by abandonin g the natu ral

rate hypothesis in favor of some highly

potent propagation mecha nism (Campbell

and Mankiw, 1987, p. 877).

In sum, Campbell and Mankiw

seem to provide a response to the workof Nelson and Plosser (1982). In other

words, they point to the validity ofsome of the main aspects of traditionaltheories of the business cycle despitethe findings of Nelson and Plosser.However, it is not clear how modelssuch as Lucas (1973) and Fischer (1977)

could stand without the natural ratehypothesis, and Campbell and Mankiwdo not present any other suggestions inthis direction. Possibly, some sort ofequilibrium rate of output would needto be assumed in the long run, even if

the process of return to trend isassumed to be very slow due to

rigidities and other forms ofimperfections (like in many models inthe new Keynesian literature).

West (1988) offers an answer tothis issue, contesting the evidence ofunit roots in GNP time series, as well asthe need to abandon the idea of anatural rate of output. Wests argument

has two parts. The first part is the wellknown fact that unit root tests cannotdiscriminate between random walk andnear random walk behavior in finitesamples. This implies, according to

West (1988) that simple analysis of asingle-country GNP data series is notsufficient to distinguish between

stationarity and non stationarity, and toevaluate the relative importance ofnominal and real shocks; therefore, thistype of empirical evidence is notsufficient to assert the usefulness ofdifferent theories of the business cycle.

The second part of Westsargument consists in showing that

simple natural rate models in whichnominal shocks are the main cause offluctuations can generate results similarto a near random walk in GDP. Inshort, West (1988) builds a simplemodel with overlapping wage contracts




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in which monetary policy is the onlysource of disturbances. Intuitively, the

wage contracts provide an endogenoussource of persistence, since prices donot move instantaneously, and GNPfluctuations mimic a near random walkbehavior after a monetary policy shock.

This is valid even if there is a long runnatural rate of output to which theeconomy eventually converges; all that is

needed for near random walk behavioris a very slow process of adjustment.In sum, Wests main point is that

Neither stat ionarity of the natural rate

nor nominal shocks playing an

important role in the business cycle are

inconsistent with a root very near tounitybeing present in the GNP process

(West, 1988, p. 207, emphasis added).

It is clear that West minimizesthe importance of unit roots in GNPseries, based on the fact that random

walk and near random walk behaviorcannot be distinguished. However, ifthe actualprocess behind GNP series isdifference stationary (although one

cannot be sure of it), the concept of thenatural rate of unemployment is calledinto question. Moreover, if the idea ofnear random walk is a valid descriptionof the behavior of GNP or, in other

words, if GNP is trend reverting but

with a high degree of persistence, itseems that the concept of a unique and

stable natural rate is not very usefulanyway.10The target is still there, butthe economy never reaches it, andsuccessive shocks may drive economicfluctuations independently of whatthe natural rate is, since its attractionpower is very low.

3.3_ We dont know, and we dont care,and other arguments

Another line of argumentation in theunit roots debate claims that it is notreally important for macroeconomictheorizing whether or not unit roots aredetected in GNP time series. Thisbranch of the literature has a lot incommon with some arguments presented

in the previous section, especially thoseby McCallum (1986) and West (1988),about the inability of unit root tests todistinguish between TS and DSprocesses in finite samples. In this case,however, the criticism seems to be evenmore profound; moreover, there is nota defense of any specific theories of

economic fluctuations.The original contribution to the

we dont know literature is the workof Christiano and Eichenbaum (1990).

Their basic proposition is that it is notpossible to provide a compelling case



10 For a broad discussionof the concept of the naturalrate of unemployment, seeCross (1995).


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that real GNP is either trend ordifference stationary based on theanalysis of postwar data.

According to Christiano andEichenbaum (1990), the main differencebetween the two models can be analyzedby looking at how much an innovation toreal GNP affects the forecast of this

variable into the infinite future. They tryto answer this question by using the

two measures of persistence discussedbefore: the ones by Campbell andMankiw (1987) and Cochrane (1988).

Christiano and Eichenbaum(1990) estimate different ARMAspecifications for real GNP, in order toanalyze the impulse response functionsproposed by Campbell and Mankiw.

They show that for the postwar USdata, the relative plausibility of thetrend and the difference stationaryrepresentations depends critically on theprecise order of the ARMAspecification chosen: under an ARMA(2,2) representation, for instance,GNP can be seen as difference

stationary; under an ARMA (3,3)specification, however, GNP can beseen as trend stationary. According toChristiano and Eichenbaum, neithereconomic theory nor the data canconclusively distinguish between thetwo competing representations.

The nonparametric measure ofpersistence proposed by Cochrane(1988) is also applied to the US data. Inthis case, Christiano and Eichenbaum(1990) argue that the variance ratiostatistic is also not able to provideconclusive information about whetherGNP is a TS or DS process. They showthat the estimations based on postwardata are consistent with the view that

GNP is more persistent than a randomwalk, but are also consistent with theview that GNP is less persistent than arandom walk. Once more, one is notable to tell which is true.

Finally, Christiano and Eichenbaum(1990) explore the implications of unitroots in two different contexts: the

permanent income hypothesis, and realbusiness cycle models. They argue thatthe implications of the presence of unitroots for these models are minimal.

Their conclusion is quite skeptical:

We think macroeconomists should care

very much about the relative importance

of permanent and temporary shocks to

agents environments. But conventionalatheoretical measures of persistence

convey little information about this

question, and structural inferences

based on such measures ought to be

viewed with extreme skepticism

(Christiano and Eichenbaum, 1990, p. 54).




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Other examples of the we dontknow, and we dont care literature areRudebusch (1992), Diebold andRudebusch (1999), and Smith (2000).Rudebusch (1992) calls for a newconsensus that would emphasize thedifficulties of knowing anythingabout the existence of unit roots inmacroeconomic time series. Besides, hepoints out that the tests performed by

Nelson and Plosser (1982) have lowpower not against TS models with anAR root close to unity but, moreimportantly, against plausible TSmodels estimated from the data.

Diebold and Rudebusch (1999)emphasize that there is a great deal ofuncertainty regarding the nature of the

trend in macroeconomic time series, theestimation of persistence to shocks, andthe decomposition of trend and cycle.

Finally, Smith (2000) makes amore general criticism of the attemptsto draw conclusions about the behaviorof macroeconomic variables from theexistence or not of unit roots in theseries.11 He stresses that unit root testsare very sensitive to a number of

variables, such as the sample used, thenumber of lags, the inclusion ofintercept and trend parameters, and theexistence of structural breaks; he arguesthat such sensitivity helps to explain

why there is no consensus aboutwhether macroeconomic variables arestationary or not, even for widelystudied series, such as the US GNP.Moreover, Smith (2000) argues thatstatistical techniques cannot generallygive precise answers to questions ofeconomic interest, and that theseanswers involve interpretation. Hecriticizes the unit root literature bysaying that

much of the problem with the unit

root literature arises from the belief

that estimates or test statistics would

pro vide the answer in themse lve s

(Smith, 2000, p. 200-201).

3.4_ Unit roots and non-mainstreamperspectives in macroeconomics

The existence of unit roots in GDPtime series and the consequentpersistence of shocks can also be usedto support different non-mainstream

views of economic fluctuations andeconomic growth, which emphasize theexistence of multiple equilibria with thepossibility of persistent involuntaryunemployment, due to pathdependence, hysteresis in labor markets,and non-neutrality of money in the longrun, among other considerations.

Dutt and Ros (2003) present abroad review of models in which



11 Strictly speaking, Smith(2000) needs not necessarily tobe included in the we dontknow literature, since hisarguments do not fit exactly inthat category, although thereare some elements in common.


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aggregate demand contractions havelong term effects on output. Their main

goal is to criticize the so-called springtheory of stabilization and growth,which is implicit in the recommendationsof the IMF and other internationalfinancial institutions for economiesdealing with financial and currencycrises, and can be summarized as:

Following an initial contraction, the

economy will be able to spring back to anormal full employment path that is

independent of the size of the contraction

itself. Even more, the economy may

well be able to spring back faster, the

greater the magni tude of the cont ract ion

(Dutt and Ros, 2003, p. 2).

Dutt and Ros (2003) explore a

variety of mechanisms in whichautomatic tendencies of adjustment to anormal path are absent or weak, leadingto persistent effects of shocks in output.

There are, generally speaking, twosubgroups of models. First, Dutt andRos (2003) analyze models in which thetrend-reverting tendencies of the

economy are weakened by some sort ofpath dependence, which change thelong run position of the economy itself.

This includes the effects of hysteresis inlabor markets, the existence ofmultiple equilibria associated with

increasing returns to scale, and theeffects of currency overvaluation inopen economies with balance ofpayment constraints.

The second group of modelspresented by Dutt and Ros (2003)explore situations in which automaticadjustment tendencies are absent oroffset, even if frictions or rigiditiesare removed from the economy. The

reasons for non-convergence relate to:i. regressive income redistribution

due to changes in money andprices, and consequent effectson the propensity to consume;

ii. negative effects of deflation oninvestment, due to increase inthe real value of firms debts;

iii. changes in expectations due tofalling prices and wages, whichcan paralyze consumption orinvestment decisions in case ofpervasive uncertainty;

iv. liquidity trap, which preventsfurther reduction in the interestrate, and therefore prevents

recovery of investments;v. endogeneity of money.

It is clear that in all thesesituations, when subject to a negativeshock, the economy is unable to returnpromptly to its previous trajectory. In




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some cases, the very concept of aunique long-term trend of output isabandoned. All these results arecompatible with the existence of unitroots in output series, or with the ideathat output follows a random walk, withno tendency to return to anypredetermined mean.

In general terms, it can be arguedthat many theories in which aggregatedemand influences the long runequilibrium of the economy, or in

which the concept of a natural rate ofunemployment (unique and stable) isdiscarded, are compatible with thepresence of unit roots in GNP.Examples include the type of modelsdeveloped by Hahn and Solow (1995),12

structuralist models a laTaylor (1991),and the fundamentalist branch ofpost Keynesianism (Davidson, Minsky,among others). The existence or not ofunit roots, however, has not beendiscussed in this literature, and a moredetailed evaluation of these possiblelinks is beyond the scope of this paper.

4_ Empirical evidence of unit rootsfor Latin American countries

The previous section has shown thatthe implications of unit roots formacroeconomic theory and policy are

controversial, and have been subject toconflicting interpretations. Empiricalevidence, on the other hand, has notbeen able to resolve the dispute over

whether or not unit roots are importantto explain output fluctuations.

The empirical literature on theexistence of unit roots in GNP timeseries is enormous but concentratesmainly on developed countries, with the

US coming at the top of the rank.More recently, however, a growingnumber of studies is addressing theissue of unit roots in developingeconomies. In this section, I will reviewthe results of unit root tests applied toLatin American economies, withemphasis on four countries: Argentina,

Brazil, Chile, and Mexico. In general,the results of these studies show thesame difficulties and dilemmasdiscussed in the previous sections.

Thornton (2001) studies therelation between population growth andreal GDP per capita growth in the longrun for seven Latin American countries.

He uses three different techniques,namely, ADF tests, the Johansenmaximal likelihood procedure, andGranger causality tests, to evaluate therelation between population and percapita income in Argentina, Brazil,



12 Note, however, that thework of Hahn and Solow(1995) cannot be classified asnon-mainstreammacroeconomics. Even so,they consider models in whichaggregate demand influences

the long-run path of thesystem, and in which there isno unique and stable naturalrate of unemployment. Iwould like to thank ananonymous referee for hissuggestion about this point.


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Chile, Colombia, Mexico, Peru, andVenezuela over the 1900-1994 period.

Concerning unit root tests,Thornton (2001) performs ADF testsfor levels and first differences of GDPper capita, with intercept and no trend,and also with both intercept and trend.He is unable to reject the null of unitroots in per capita GDP levels for anyof the countries and specifications,

whereas the null is always rejected incase of first differences. Thornton(2001) concludes that per capitaincome in these countries is a I(1)

variable, i. e., non-stationary.The presence of unit roots in

Argentinean GDP series is analyzed bySosa-Escudero (1997), Carrera, Feliz andPanigo (1999) and Utrera (undated).

Sosa-Escudero (1997) presentsthe first attempt to test for unit roots inthe case of Argentina. He uses annualreal GDP data for the 1900-1993period, and quarterly real GDP datafrom 1970:1 to 1994:2. Sosa-Escudero(1997) applies ADF and Phillips-Perrontests allowing for structural breaks. Inparticular, he uses the methodologyproposed by Banerjee et al. (1992) recursive tests, rolling tests andsequential tests in which the date ofthe break is endogenously determined.

The results provided in all tests for

both annual and quarterly data showthat the null of unit root cannot berejected at a 10% level of significance.Sosa-Escudero (1997) concludes bysuggesting that real GDP in Argentinaappears to be non-stationary and,as a consequence, suffers persistenteffects from shocks.

Carrera, Feliz and Panigo (1999)expand this study in two directions.First, they analyze a large number ofmacroeconomic variables (fourteenseries), including GDP, wages, interestrates, unemployment rates, exchangerates, and inflation. Second, theyperform various tests to evaluate thepersistence of shocks in the economy.

Their analysis use quarterly data for theperiod 1980:1 to 1998:4, and comprises:

i. the examination of first orderautocorrelation coefficients;

ii. ADF and PP unit root testswith no breaks;

iii. Cochranes (1988) variance ratiostatistic;

iv. unit root tests with exogenous

breaks (Perron, 1989); andrecursive and rolling ADF testsfor unit roots (Banerjee et al, 1992).

Considering the order of integration ofGDP, Carrera, Feliz, and Panigo (1999)show that they consider it as robustly




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I(1), confirming the unit roothypothesis. This is because GDP seriesappear to be non-stationary in all thetests applied, even when allowance ismade for structural breaks. This resultis compatible with the inferencesprovided by Sosa-Escudero (1997).

Finally, Utrera (undated)provides the third study for the case of

Argentina. In his paper, however, theevidence suggests the opposite result ofthe previous two studies. Utrera usesresampling techniques proposed byRudebusch (1992), in order to obtainthe small sample distributions of the tstatistic used to test the null of unit rootconditional on both the DS null and the

TS alternative hypothesis. This

technique permits the analysis of thesize of the unit root test, as well as itspower to reject false nulls, and allowsfor multiple endogenous structuralbreaks. The tests are applied to annualGDP and GDP per capita data for the1913-1999 period and to quarterly GDPdata for the 1970:1-2000.3period. The

results, in general, support the idea thatArgentinean GDP is stationary arounda broken trend:

i. with no breaks, neither theDS nor the TS hypothesescan be rejected;

ii. with one, two, or threeendogenous structural breaksthe DS null tends to be rejected,

whereas the alternative TShypothesis is not rejected.

Utrera (undated) concludes that GDPin Argentina is better described as astationary variable.13

In the case of Brazil, pioneeringstudies were done by Cribari Neto

(1990, 1992). In the first paper, CribariNeto (1990) analyzes the persistence ofinnovations in Brazilian GDP usingannual data for the 1950-1985 period.

Three different methodologies are used:ADF tests, impulse response functions(Campbell and Mankiw, 1987), andCochranes (1988) variance ratio.

The results suggest that the unit rootshypothesis cannot be rejected, and thatBrazilian GNP is more persistentthan a random walk (a 1% shock willhave an effect greater than 1% in thelong run). In the second paper, CribariNeto (1992) expands the sample forthe 1900-1985 period and, using the

same methodology, confirms theresults of his 1990 study.

Tombini and Newbold (1992)analyze the behavior of Brazilian GDPfor the years 1947-1987. They develop amodel with three structural breaks



13 It is interesting to note thatthe case for stationaritybecomes stronger when alarger number of breaks isincluded. This result isexpected, given the analysis ofPerron (1989), and it is alsointuitive, since any series canbe decomposed intostationary segments if oneallows for a sufficiently largenumber of breaks.


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(interventions) during this period,by incorporating dummy variablesinto the time series a laPerron (1989).

The breaks are:

i. the political turbulences andeconomic reforms in 1962;

ii. the first oil shock in 1973;iii. the second oil shock in 1979.

Tombini and Newbold (1992) intend toestimate the impact of these shocks in

the behavior of GDP over time. Althoughthe paper does not provide formal testsof unit roots, the results provide supportto the hypothesis of a stationary variationaround a broken trend.

Aguirre and Ferreira (2001)provide the most recent study of unitroots in Brazilian GDP. They useannual data for the 1950-1997 periodand perform three different tests: ADFtest with no breaks, KPSS tests (in

which TS is the null hypothesis), andADF tests with endogenous breaks. Inthe first case, the ADF test suggests theexistence of a unit root in the series.

This result is confirmed by the KPSStest, since the null of stationarity isrejected at 5%. However, when allowanceis made for an endogenous break(change in slope in 1979), the oppositeresult is obtained, and the null of unitroots is rejected. Aguirre and Ferreira

(2001) conclude that Brazilian GDP isstationary around a broken trend.

Chumacero (2000) presentsvarious unit-root tests for Chile. Heuses annual and quarterly data14 toperform ADF tests, PP tests, KPSStests, tests with endogenous breaksbased on Zivot and Andrews (1992),and ADF tests with non linear trends.

The evidence based on these tests is notconclusive; in some cases the unit roothypothesis is rejected, and in othercases it is not. Chumacero (2000) alsoproposes an indirect test of unit rootsbased on economic theory, in whichhe uses a representative-agent modelthat maximizes utility over time. In thiscase, the results suggest that the null ofunit root is rejected. Chumacero (2000)concludes that GDP for the Chileaneconomy appears to be stationary.

The presence of unit roots inMexican GDP is discussed by Carstensand Reynoso (1997), Moreno-Brid(1999), Noriega and Ramirez-Zamora(1999), and Castillo Ponce and DiazBautista (2002). Carstens and Reynoso(1997) analyze the effects of monetarypolicy on the Mexican economy.

Among other goals, they try to assessthe relation between money stock andGDP using cointegration techniques.In order to check for the order of



14 The period of analysis isnot specified in the paper.


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integration of the variables, ADF andPP unit root tests are performed, withdifferent specifications for trends andintercepts. In the case of real GDP, theresults suggest the existence of unitroots in the series, and Carstens andReynoso (1997) conclude that MexicanGDP is integrated of order one.

Moreno-Brid (1999) uses unitroot tests and cointegration analysis toestimate the long-run relation betweenexport growth and GDP growth inMexico (1950-1996). His analysis isbased on the balance-of-paymentsconstraints model developed by

Thirlwall. Moreno-Brid (1999) performsADF tests and finds results that suggestthat real GDP is a I(1), or difference

stationary, variable.The paper by Noriega andRamirez-Zamora (1999) presents manysimilarities with the work of Utrera(undated) mentioned before. Noriegaand Ramirez-Zamora (1999) useresampling techniques (Rudebusch,1992) to check for the existence of unit

roots in Mexican GDP (1921-1995) andGDP per capita (1921-1994). Thistechnique allows for multiple structuralbreaks determined endogenously, andcompares the plausibility of DS and TSalternatives. The results shown by

Noriega and Ramirez-Zamora (1999) aresimilar for both variables analyzed, andcan be summarized as the following:

i. in case of no breaks, it is notpossible to discriminate betweenthe DS and the TS specifications;

ii. in case of one, two, or threebreaks, the unit root hypothesisis rejected in favor of a TSspecification.

Noriega and Ramirez-Zamora(1999, p. 182) conclude that

Mexicos real output has fluc tuat ed

stationarily around a 75 year long-run

trend perturbed by three major events in

or around 1931, 1950, and 1980.

Castillo Ponce and Diaz Bautista

(2002) analyze the stochastic behaviorof Mexican GDP using annual data forthe 1900-2001 period. They usedifferent methodologies, that includethe examination of autocorrelationcoefficients, ADF and PP tests with nobreaks, tests with exogenous breaks(Perron, 1989), and tests with

endogenous breaks (Zivot andAndrews, 1992). In accordance withmost of the literature on unit roots,Castillo Ponce and Diaz Bautista (2002)find that GNP is non stationary whentests with no breaks are performed.




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An interesting feature of their results,however, is that the hypothesis of nonstationarity is robust to the inclusion ofbreaks. That is, when exogenous breaks(in 1932, 1983, and 1995) orendogenous breaks (in 1907) areallowed, the null of unit roots is notrejected in the tests. Castillo Ponce andDiaz Bautista (2002) conclude thatMexican GDP is non stationary.

In sum, a quick review of theliterature of unit roots in Latin

American countries shows noconclusive result, which is alsoconsistent with the literature ondeveloped countries. Given the lowpower of unit root tests, and thesensibility of its results to a number ofinfluences, the fact that the evidencepresented is not decisive does not comeas a surprise. There seem to be,however, a general tendency not toreject the null hypothesis of unitroots, and to consider GNP to beintegrated of order one. On the otherhand, when allowance is made for

structural breaks, there is evidencethat the null of unit roots is rejectedmore often, although not in all cases.

This is also not a surprise, given thework of Perron (1989).

5_ Final remarksAs discussed in the previous sections,the issue of unit roots in macroeconomictime series has motivated a vast amountof theoretical and empirical research inthe past two decades. It is interesting topoint out, however, that a consensual

view on many of the aspects involvedhas not emerged from this literature.

There seem to be no consensus aboutthe most appropriate methodologies toperform unit root tests; no consensusabout the theoretical importance of theconcept of unit roots and its implicationsfor macroeconomic analysis; and noconsensus about empirical results ofunit root tests for many countries.

This paper intended to exploresome of these controversies, assessingsome aspects of the unit root literaturein econometrics and macroeconomics.Finally, the article presented the recentempirical evidence on unit roots forLatin American economies.

I conclude by mentioning twopoints. The first one concerns the

implications of the existence of unitroots for macroeconomic policies. Sincethe existence and importance of unitroots in macroeconomic series is a verycontroversial issue, and the literature



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seems to have reached no consensus onmany crucial aspects of the debate, itshould be clear from the beginning thatno strong and conclusive policyrecommendations can be derived here.However, if there is a unit root in GNP,it suggests that automatic return to anormal trend may not occur, andtherefore full employment policies mayhave a role to perform. On the otherhand, it is also possible to make a caseagainst sharp contractions as a responseto financial or currency crises (Dutt andRos, 2003), since the negative effectsof such policies do not tend to dissipatein the short run.

The second point concernsissues not addressed in this paper, orsuggestions for future directions ofresearch. In short, at least four issuescould be mentioned:

i. more detailed analysis of theimplications for macroeconomicpolicies (fiscal, monetary,exchange rate policies) in thepresence of unit roots;

ii. an investigation of the possiblerelation between the unit rootsliterature and non mainstreamperspectives in macroeconomics(post Keynesian, structuralist, etc.);

iii. methodologies to perform paneldata tests of unit roots allowingfor structural breaks, assuggested by Rappach (2002);

iv. extensi on of the analysis of unitroots for developing countriesin general, and Latin Americancountries in particular.



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AGUIRRE, A.; FERREIRA, A.The (in)existence of a unit root inbrazilian gross domestic product.

Applied Economic Letters, v. 8,p. 645-647, 2001.

BACKHOUSE, R.; SALANTI, A.Macroeconom ics and the real wo rld.

New York: Oxford UniversityPress, 2000. (v. 1: Econometrictechniques and macroeconomics).

BANERJEE, A.; LUMSDAINE,R.; STOCK, J. Recursive andsequential tests of the unit-rootand trend-break hypotheses:theory and internationalevidence. Journal of Business

and Economic Statistics, v. 10, n. 3,p. 271-287, July, 1992.

BEN-DAVID, D.;LUMSDAINE, R.; PAPELL, D.Unit roots, postwar slowdownsand long-run growth: evidencefrom two structural breaks.

Empirical Economics, v. 28, n. 2,p. 303-319, 2003.

BLANCHARD, O.; QUAH, D.The dynamic effects of aggregate

demand and supply disturbances.American Economic Review, v. 79,n. 4, p. 655-673, September 1989.

CAMPBELL, J.; MANKIW, G.International evidence of thepersistence of economicfluctuations, Journal of Monetary

Economics, v. 23, p. 319-333, 1989.

CAMPBELL, J.; MANKIW, G.Are output fluctuationstransitory? Quarterly Journal of

Economics, v. 102, p. 857-880, 1987.

CARRERA, J.; FELIZ, M.;

PANIGO, D. Unit roots andcycles in the mainmacroeconomic variables for

Argentina. XXXIV Reunin Anualde la Asociacin Argentina de

Economa Poltica, 1999.

CARSTENS, A.; REYNOSO, A.Alcances de la politica monetari a:

marco teorico y regularidades empiricas

en la experiencia mexicana. Banco deMexico, 1997. (Documento de

Investigacin 9705). 45p.CASTILLO PONCE, R.;DAZ-BAUTISTA, A. Testingfor unit roots: Mexicos GDP.

Momento Econmico, v. 124,n. 2-10, 2002.

CHRISTIANO, L.;EICHENBAUM, M. Unit rootsin real GDP: do we know, and do

we care? Carnegie Rochester

Conference Series on Public Policy,v. 32, p. 7-62, 1990.

CHUMACERO, R. Se busca unaraiz unitaria: evidencia para Chile.

Estudios de Eco noma, v. 27, n. 1,p. 55-68, 2000.

COCHRANE, J. How bigis random walk in GDP?. Journalof Political Economy, v. 96, n. 5,p. 893-92, 1988.

CRIBARI NETO, F. On time

series econometrics. QuarterlyReview of Economics and Finance,v. 36, special i ssue: p. 37-60, 1996.

CRIBARI NETO, F. Persistnciade inovaes e polticaeconmica: a experincia do IIPND. Revista Brasileira de Economia,

v. 46, n. 3, p. 413-428, 1992.

CRIBARI NETO, F. Ocomportamento estocstico doproduto no Brasil. Pesquisa ePlanejamento Econmico, v. 20,n. 2, p. 381-402, 1990.

CROSS, R. The natural rate ofunemployment: reflections on 25years of the hypothesis. Cambridge:Cambridge University Press, 1995.

CULVER, S.; PAPELL, D. Isthere a unit root in the inflationrate? Evidence from sequentialbreak and panel data models.

Journal of A pplied Eco nometrics,v. 12, p. 435-444, 1997.

DICKEY, D.; FULLER, W.Distribution of the estimators forautoregressive time series with aunit root. Journal of the AmericanStatistical Association, v. 74,p. 427-431, 1979.

DIEBOLD, F.; RUDEBUSCH,G. Business cycles. Princeton:Princeton University Press, 1999.

DUTT, A.; ROS, J.Contractionary effects ofstabilization and long run growth.University of Notre Dame, 2003.Unpublished manuscript.

ELDER, J.; KENNEDY, P.Testing for unit roots: whatshould students be taught? Journalof Economic Education, p. 137-146,Spring 2001.

ENDERS, W. Applied econometrictime series. New York: Wiley, 1995.

FISCHER, S. Long-termcontracts, rational expectations,and the optimal money supplyrule. Journal of Political Economy,

v. 85, n. 1, p. 191-205, 1977.

HAHN, F.; SOLOW, R. A criticalessay on modern macroeconomic theory.Cambridge, MA: MIT Press, 1995.



References



32/32

IM, KYUNG SO; PESARAN, M.HASHEM; SHIN,

YONGCHEOL. Testing for unitroots in heterogeneous panels.

Journal of Eco nometric s, v. 115,n. 1, p. 53-74, 2003.

KWIATKOWSKI, D.;PHILLIPS, P.; SCHMIDT, P.;SHIN, Y. Testing the nullhypothesis of stationarity againstthe alternative of a unit root:how sure are we that economictime series have a unit root?

Journal of Eco nometric s, v. 54,p. 159-178, 1992.

LEE, J.; STRAZICICH, M.Minimum lagrange multiplier unitroot test with two structural breaks.Review of Economics and Statistics,

v. 85, n. 4, p. 1082-1089, 2003.

LEVIN, A.; LIN, C.; CHU, C.Unit root tests in panel data:asymptotic and finite-sampleproperties. Journal of Econometrics,

v. 108, n. 1, p. 1-24, 2002.

LUCAS, R. Some internationalevidence on output-inflationtrade-offs. American

Economic Review, v. 63, n. 3,p. 326-334, 1973.

LUMSDAINE, R.; PAPELL, D.Multiple trend breaks and theunit-root hypothesis. Review of

Economics and Stat istics, v. 79,p. 212-218, 1997.

MADDALA, G. S.; KIM, I. Unitroots, cointegration, and structural

change. Cambridge: CambridgeUniversity Press, 1998.

MADDISON, A. The WorldEconomy in t he 20 th C entury.Paris: OECD, 1989.

MCCALLUM, B. Recentdevelopments in monetary policyanalysis: the roles of theory andevidence. In: BACKHOUSE, R.;

SALANTI, A. Macroeconomics andthe Real World. New York: OxfordUniversity Press, 2000. p. 115-139.

MCCALLUM, B. On real andsticky-price theories of thebusiness cycle. Journal of Money,Credit, and Banking, v. 18, n. 4,p. 397-414, November 1986.

MORENO-BRID, J. Mexicoseconomic growth and the balance

of payments constraint: acointegration analysis. InternationalReview of Applied Economics, v. 13,n. 2, p. 149-159, 1999.

NELSON, C.; PLOSSER, C.Trends and random walks inmacroeconomic time series: someevidence and implications. Journalof Monetary Economics, v. 10,p. 139-169, 1982.

NORIEGA, A.,RAMIREZ-ZAMORA, A. Unitroots and multiple structuralbreaks in real output: how longdoes an economy remainstationary? Estudios Econmicos,

v. 14, n. 2, p. 163-188, 1999.

PERRON, P. The great crash, theoil price shock, and the unit roothypothesis. Econometrica, v. 57,p. 1361-1401, 1989.

RAPACH, D. Are real GDPlevels nonstationary? Evidencefrom panel data tests. Southern

Economic Journal, v. 68, n. 3,p. 473-495, 2002.

RUDEBUSCH, G. Trends andrandom walks in macroeconomictime series: a reexamination.International Economic Review,

v. 33, p. 661-680, 1992.SMITH, R. Unit roots and allthat: the impact of time-seriesmethods on macroeconomics. In:BACKHOUSE, R.; SALANTI, A.

Macroeconom ics and the Real W orld.New York: Oxford UniversityPress, 2000. p. 199-218.

SOSA-ESCUDERO, W. Testingfor unit-roots and trend-breaks in

Argentine real GDP. Econmica, v.43, p. 123-142, 1997.

TAYLOR, L. Income distribution,inflation and growth:lectures onstructuralist macroeconomictheory. Cambridge, Mass.: MITPress, 1991.

TOMBINI, A.; NEWBOLD, P .The time-series behavior ofbrazilian real gross domestic

product, 1947-87: an analysis ofinterventions. World Development,v. 20, n. 2, p. 283-288, 1992.

THORNTON, J. Populationgrowth and economic growth:long-run evidence from Latin

America. Southern Economic Journal,v. 68, n. 2, p. 464-468, 2001.

UTRERA, G. Is the ArgentineGDP stationary around a broken

trend? [s. d.]. unpublished manuscript.WEST, K. On the interpretationof near random-walk behavior inGDP. American Economic Review,

v. 78, n. 1, p. 202-209, March 1988.

ZIVOT, E.; ANDREWS, D.Further evidence on the greatcrash, the oil-price shock, and theunit-root hypothesis. Journal of

Business & Economic Statistics,v. 10, n. 3, p. 251-270, 1992.



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Unit Roots in Macroeconomic Time Series