13
This article was downloaded by: [Johann Christian Senckenberg] On: 22 August 2014, At: 07:00 Publisher: Routledge Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK Applied Economics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/raec20 Testing convergence in economic growth for OECD countries S. Nahar & B. Inder Published online: 05 Oct 2010. To cite this article: S. Nahar & B. Inder (2002) Testing convergence in economic growth for OECD countries, Applied Economics, 34:16, 2011-2022, DOI: 10.1080/00036840110117837 To link to this article: http://dx.doi.org/10.1080/00036840110117837 PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http:// www.tandfonline.com/page/terms-and-conditions

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Page 1: Testing convergence in economic growth for OECD countries

This article was downloaded by: [Johann Christian Senckenberg]On: 22 August 2014, At: 07:00Publisher: RoutledgeInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: MortimerHouse, 37-41 Mortimer Street, London W1T 3JH, UK

Applied EconomicsPublication details, including instructions for authors and subscription information:http://www.tandfonline.com/loi/raec20

Testing convergence in economic growth for OECDcountriesS. Nahar & B. InderPublished online: 05 Oct 2010.

To cite this article: S. Nahar & B. Inder (2002) Testing convergence in economic growth for OECD countries, AppliedEconomics, 34:16, 2011-2022, DOI: 10.1080/00036840110117837

To link to this article: http://dx.doi.org/10.1080/00036840110117837

PLEASE SCROLL DOWN FOR ARTICLE

Taylor & Francis makes every effort to ensure the accuracy of all the information (the “Content”)contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensorsmake no representations or warranties whatsoever as to the accuracy, completeness, or suitabilityfor any purpose of the Content. Any opinions and views expressed in this publication are the opinionsand views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy ofthe Content should not be relied upon and should be independently verified with primary sources ofinformation. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands,costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly orindirectly in connection with, in relation to or arising out of the use of the Content.

This article may be used for research, teaching, and private study purposes. Any substantial orsystematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution inany form to anyone is expressly forbidden. Terms & Conditions of access and use can be found at http://www.tandfonline.com/page/terms-and-conditions

Page 2: Testing convergence in economic growth for OECD countries

Testing convergence in economic growth

for OECD countries

S. NAHAR and B. INDER*

Department of Econometrics and Business Statistics, Monash University, Clayton,Victoria 3168, Australia

This article explores tests for absolute convergence in economic activity among a setof countries. It proposes a new test procedure that allows the researcher to identifyparticular countries within the group, which might not be converging. It alsoproposes that convergence among a set of similar countries is better thought of asmovement toward a group leader, rather than movement towards a group mean.Applying the new procedure to 22 OECD countries it ®nds strong evidencefor absolute convergence for the vast majority of countries towards their commonsteady state level. This article also points out why using standard unit root orcointegration tests with Bernard and Durlauf’s de®nition of convergence isinappropriate.

I . INTRODUCTION

The phenomenon of convergence of economic growth isone of the most important issues in modern economics.In neoclassical growth models a country’s per capitagrowth rate tends to be inversely related to its startinglevel of per capita income. In particular, if countries aresimilar with respect to structural parameters for prefer-ences and technology, then poor countries tend to growfaster than rich countries. That is, it is a prediction of

neoclassical economic growth theory that di� erences inper capita income across di� erent economies will tend todecrease or disappear over time. This is broadly referred toas the convergence hypothesis.

It has become common in the literature to test for con-vergence, as a means of validating or refuting this predic-tion of economic theory. Virtually all existing proceduresfor testing for convergence focus on testing whether agroup of countries converge overall. They do not allowthe researcher to investigate how a particular economy isperforming against the wider group. It is also not unusualfor di� erent approaches to testing for convergence to yielddi� erent conclusions.

This article has two objectives. First, it highlights a prob-lem with how some studies have implemented tests for

convergence, and show that this can explain some of theinconsistencies in results between di� erent studies. Second,it develops new tests for convergence that allow one toidentify particular countries within a group that are dis-playing divergent behaviour. These tests are then appliedto data for the OECD countries.

In terms of this second objective, the empirical tests forconvergence reported in this article reveal some interestingobservations. It works with two concepts of convergence,one based on whether a country’s output gap from thegroup `leader’, the USA, is declining. The other looks atwhether there is a decline in the di� erence between percapita GDP of a country and the average per capitaGDP of all countries in the group. Most countries areshown to converge under either measure. However, somenotable exceptions show convergence under one measure,and non-convergence under the other. For example, resultssuggest that New Zealand’s per capita GDP is convergingto the overall average, but there is evidence for signi®cantdivergence from the USA. At the beginning of the sampleperiod, New Zealand had one of the highest per capitaGDP’s, 76% of the US per capita GDP and around 56%higher than the average of OECD countries. However, by1998, New Zealand’s position against the USA had dete-riorated to being only 61% of the USA, while its advantage

Applied Economics ISSN 0003±6846 print/ISSN 1466±4283 online # 2002 Taylor & Francis Ltd

http://www.tandf.co.uk/journalsDOI: 10.1080/0003684011011783 7

Applied Economics, 2002, 34, 2011±2022

2011

* Corresponding author: E-mail: [email protected]

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over the average had disappeared (15% below average!). Incontrast, Norway’s per capita GDP is showing convergencetowards the USA, but divergence from the overall mean.These and other results suggest some interesting patterns incomparative economic performance that might warrantfurther investigation.

Regarding the ®rst objective, results of previous studiesof convergence for OECD countries indicate some poten-tial puzzles with the implementation of existing tests. Earlystudies, including Baumol (1986), Barro (1991), Mankiwet al. (1992) and Sala-i-Martin (1996) interpreted the ®nd-ings of a negative correlation between initial income andgrowth rates of a group of countries as evidence in favourof convergence, and ®nd in favour of convergence ofOECD countries. More recently, Evans and Karras(1996) criticized the above approach and suggested analternative test procedure for a group of economies whichaccounts for time series variation in output. Their resultsstill ®nd in favour of convergence. On the other hand,Bernard and Durlauf (1991, 1995) generally rejected theconvergence hypothesis of OECD countries using standardunivariate and multivariate time series techniques. Theyinterpret the convergence hypothesis as implying that out-put di� erences are transitory/stationary.

From the above discussion it is clear that for similar datasets the results of di� erent approaches are contradictory.Some work is needed to try and reconcile these di� erences.The methodology introduced in this article provides someinsight into the apparent inconsistency in these results. Itemploys econometric techniques that are arguably moreappropriate for the analysis of long-run growth behaviourof per capita output.

The rest of the article is organized as follows. Section IIbrie¯y discusses the convergence hypothesis and highlightsproblems with existing approaches. Section III outlines theproposed new test procedures. Section IV discusses theempirical results, and conclusions are drawn in Section V.

II . THE CONVERGENCE HYPOTHESIS

The neoclassical growth model pioneered by Solow (1956)has generated a large theoretical and empirical literature onthe convergence of economic growth. In the literatureresearchers de®ne the convergence hypothesis in severalways. Sala-i-Martin (1996) de®nes ­ -convergence and ¼-convergence: `there is absolute ­ -convergence if pooreconomies tend to grow faster than rich ones, and agroup of economies are converging in the sense of ¼ ifdispersion of their real per capita GDP levels tends todecrease over time (Sala-i-Martin, 1996: 1020).

Let yit be the logarithm of per capita output for economyi…i ˆ 1; 2; . . . ; N† during period t, and git;T

ˆ …yiT¡ yit

†=…T ¡ t† be economy i’s annual growth rate of GDPbetween t and T and ¼t be the standard deviation of yit

across i at time t. Early empirical work is based on estima-tion of the following model:

gi0;Tˆ ¬ ‡ yi0­ ‡ "iT i ˆ 1; 2; . . . ; N …1†

A negative value for ­ provides evidence in favour ofabsolute ­ -convergence, whereas ­ 5 0 supports non-convergence. It is also common to modify Equation 1 byincluding a set of control variables xi and consider theregression model as follows:

gi0;Tˆ ¬ ‡ yi0­ ‡ x

0i ® ‡ "iT

…2†

A negative ­ implies convergence holds conditionally onsome set of exogenous factors when ® 6ˆ 0, and absoluteconvergence occurs when ® ˆ 0 and ­ < 0. Several studiesconclude in favour of both absolute and conditional con-vergence for OECD countries using this approach.

However, some researchers have pointed out that short-run transitional dynamics and long-run steady-state behav-iour are mixed up in such cross-section regressions.Bernard and Durlauf (1995) proposed a new de®nition ofconvergence which relies on the notions of unit roots andcointegration in time series.

Countries i and j converge if the long-term forecasts ofoutput for both countries are equal, that is:

limn!1 E…yit‡n

¡ yjt‡njIt

† ˆ 0 …3†

where It denotes all information available at time t.Countries m ˆ 1; 2; . . . ; N converge if the long-term fore-

casts of output for all countries are equal, that is:

limn!1 E…y1t‡n

¡ ymt‡njIt

† ˆ 0 8m 6ˆ 1 …4†

The de®nition of convergence asks whether the long-runforecasts of output di� erences tend to zero as the forecast-ing horizon approaches in®nity. Bernard and Durlauf(1995) state that the above de®nition of convergence willbe satis®ed if y1t

¡ ymt is a mean zero stationary process.In order to test for convergence, Bernard and Durlauf

(1995) employ multivariate techniques developed byPhillips and Ouliaris (1988) and Johansen (1988, 1991).The Phillips and Ouliaris (1988) procedure tests for thenumber of linearly independent stochastic trends by ana-lysing the spectral density matrix at zero frequency. If allcountries are converging in per capita output, then the rankof the zero-frequency spectral density matrix of ®rst di� er-ences of output deviations from a benchmark country mustbe zero. Using the Phillips and Ouliaris bounds test, theycould not reject the null of no convergence for the group of15 OECD countries.

The Johansen (1988, 1991) test for cointegration is basedon the estimated rank of the cointegrating matrix.According to Bernard and Durlauf (1995), convergencewould imply the existence of p ¡ 1 cointegrating vectorsand one common stochastic trend for a p dimensional out-put series. Further, the p £ p ¡ 1 cointegration matrix

2012 Nahar and Inder

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would need to share the same space as the following

matrix:

1 0 ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ 0

¡1 1 ...

0 ¡1 . .. ..

.

..

. ... . .

. . .. ..

.

..

. ... . .

. . .. ..

.

..

. ... . .

.1

0 0 ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¡1

2

666666666666666666664

3

777777777777777777775

Again, the Johansen tests reject convergence in the group

of 15 OECD countries.

It is important to point out an inconsistency in Bernard

and Durlauf’s (1995) link between their de®nition of con-

vergence and the stationarity of output di� erences, which

one would suggest explains why they failed to ®nd conver-

gence using either of the above tests. The key point is thatcertain non-stationary y1t

¡ ymt processes can meet their

de®nition of convergence. For example, suppose y1t¡ ymt

is a non-stationary process represented by the following

model:

y1t¡ ymt

ˆ ³=t ‡ ut

where E…ut† ˆ 0, and u1 is a stationary process. As t ! 1,

then ³=t ! 0, so y1t¡ ymt is also converging, since:

limn!1 E…y1t‡n

¡ ymt‡njIt

† ˆ 0

However, a test for the stationarity of y1t¡ ymt may well

®nd in favour of the unit root hypothesis and thus wrongly

conclude that there is non convergence.On a similar vein, Evans and Karras (1996) de®ne

convergence as follows: Economies 1; 2; . . . ; N are said to

converge if and only if, every yit is non-stationary but every

yit¡ ·yyt is stationary, that is:

limn!1 Et

…yit‡n¡ ·yyt‡n

† ˆ ·i…5†

where ·yyt²

PNiˆ1 yit=N, and convergence is absolute or con-

ditional depending on whether ·iˆ 0 for all i or ·i

6ˆ 0 forsome i. The economies are said to diverge if, and only if,

yit¡ ·yyt is non-stationary for all i.

With this de®nition Evans and Karras used a panel data

approach to test whether convergence is conditional or

absolute for a group of countries. The estimated model is

of the form:

¢…yit¡ ·yyt

† ˆ @i‡ »i

…yit¡1¡ ·yyt¡1

‡Xp

n¡1

’in¢…yit¡n¡ ·yyt¡n

† ‡ uit…6†

where »i is negative if the economies converge and zero orpositive if they do not converge, ¯i is a parameter and ’’sare parameters such that all roots of

Pn ’inL

ilie outside

the unit circle, and Li represent the ith lag operator. Evansand Karras found strong evidence in favour of conditionalconvergence for the 48 contiguous US states and a group of54 countries.

As with Bernard and Durlauf ’s de®nition, this articlepoints out that Equation 5 is not equivalent to a de®nitionof stationarity. It can be easily shown that a non-stationary yit

¡ ·yyt process can also meet the above de®ni-tion of convergence. For example, let yit

¡ ·yyt be repre-sented by the following model:

yit¡ ·yyt

ˆ ³

t‡ uit

where E…uitˆ 0†, and uit is stationary. Then the non-

stationary process yit¡ ·yyt is also converging as

limn!1 Et…yit‡n

¡ ·yyt‡n† ˆ 0. Therefore, stationarity is not

a necessary condition for the existence of convergence asde®ned in Equation 5.

The next section develops time series-based tests for con-vergence that allow for non-stationary but converging out-put di� erences, so that the econometric testing procedure isconsistent with the formal de®nition of convergence. Thetests will also allow us to test for convergence of an indi-vidual economy from within a group of countries.

III . A NEW TEST PROCEDURE FORCONVERGENCE

Let yit be the logarithm of per capita output for economyi…i ˆ 1; 2; . . . ; N† during period t. Assume that these econo-mies have eventual access to a common body of technicalknowledge. Let at be the common trend followed by theseeconomies and ·i be a country-speci®c parameter, then thestandard neoclassical growth model would imply for econ-omy i:

limn!1 Et

…yit‡n¡ at‡n

† ˆ ·i…7†

The parameter ·i determines the level of economy i’sparallel balanced growth path, where for all economies ·i

would be non-zero, unless the economies have similarstructures. One would argue that there are two possiblecontenders for how at should be de®ned: the averageGDP per capita of all countries in the group, or theGDP per capita of the group leader, the country with thebest per capita economic performance. The ®rst of thesemeasures is what is most commonly used in the literature ±

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see, for example, the de®nition in Evans and Karras (1996).It is not clear, however, that this is the most appropriatemeasure. The neoclassical theory on which the empiricalconvergence hypothesis is built is that each country has asteady state capital±labour ratio, which in turn drives asteady state level of per capita output. It seems somewhatimplausible to suppose that the sequence of cross-countryaverage per capita incomes would represent the steady statepath to which all countries are converging. For this to bethe case, those countries which are above the averagewould have capital±labour ratios which exceed their steadystate level. A more realistic story to tell is that there is somegroup leader that has the best per capita output ± the clo-sest to the optimal or steady state output that can beobserved. Under the theory, all other countries are growingat a faster rate than this country, and hence converging tothis steady state level.

Thus two sets of results for convergence are expounded,one where deviations from the average per capita incomeare considered (are these deviations declining?), and theother where the per capita output gap between each coun-try and the USA ± the group leader ± is examined (is theoutput gap approaching zero?).

From Equation 7 the de®nition of absolute convergenceis:

limn!1 Et

…yit‡n¡ ·yyt‡n

† ˆ 0 …8†

that is, the long-run average of yit¡ ·yyt must converge to

zero, as the forecast horizon grows. Let us de®nezit

ˆ yit¡ ·yyt as the demeaned per capita output, where ·yyt

may be considered as the steady state information for allcountries at time t. Since zit represents the per capita out-put distance from their steady state value, zit approachingzero as time progresses should be considered as evidence ofconvergence. If zit is heading towards zero with time thenfor every positive and negative zit, the rate of change in zit

with respect to time t is negative and positive respectively.Or, if zit is converging towards zero then for every zit, therate of change in jzit

j with respect to time t is negative, i.e.…@=@t†jzit

j < 0:For simplicity let us consider wit

ˆ z2it. For convergence

to hold wit should always be getting closer to zero; the rateof change in wit with respect to time would be negative, i.e.…@=@t†wit < 0. The de®nition of absolute convergence inEquation 8 thus implies that:

limn!1 Et

…wit‡n† ˆ 0 …9†

since wit > 0, (@=@t†wit < 0 is consistent with wit‡n! 0 as

n ! 1.Therefore, whether an economy is converging can be

evaluated from the sign of …@=@t†wit. To ®nd …@=@t†wit,let one represent wit as a function of time trend t, sayf …t†, and consider:

witˆ f …t† ‡ uit

ˆ ³0‡ ³1t ‡ ³2t

2 ‡ ¢ ¢ ¢ ‡ ³k¡1tk¡1

‡ ³ktk ‡ uit

…10†

where the ³i’s are parameters, and uit is assumed to be anerror term with mean zero both unconditionally and con-ditionally on time. From Equation 10 one can easily ®ndthe slope function:

@

@twit

ˆ f0…t† …11†

One can use estimates of this slope function to check theconvergence of an economy.

In reality the wit series may not have a tendency todecrease uniformly with time. But if the economy tendsto converge then wit should be generally decreasing. Oneconsiders whether the average of these slopes is negative. Itis believed that for convergence to hold, the average slopefunction of wit will be negative. That is:

1

T

XT

tˆ1

@

@twit < 0

This can be obtained from Equation 11 as follows:

1

T

XT

tˆ1

@

@twit

ˆ ³1‡ ³2r2

‡ ¢ ¢ ¢ ‡ ³k¡1rk¡1‡ ³krk

ˆ r0³

where

r2ˆ 2

T

XT

tˆ1

t; . . . ; rk¡1ˆ …k ¡ 1†

T

XT

tˆ1

tk¡2;

rkˆ k

T

XT

tˆ1

tk¡1

r ˆ ‰ 0 1 r2 . . . rk¡1 rkŠ ; and

³ ˆ ‰ ³0 ³1 . . . ³k¡1 ³kŠ

To test the convergence hypothesis let us de®ne the fol-lowing null hypothesis H0 : r

0³ 5 0, against the alternative

hypothesis H1 : r0³ < 0. Thus the null hypothesis was set as

no convergence. To test this, Equation 10 was estimated byordinary least squares (OLS), and then perform a t-test ofthis restriction on the ³ vector.

The same methodology can be applied to check whetherthis data set shows any evidence in favour of absolute con-vergence towards the USA. Let us de®ne dit

ˆ yit¡ yut as

the per capita output gap, where yut is the per capita outputof USA, which may be considered as a targeted economyor a common steady state value of the OECD sample. Sincedit, the per capita output gap, measures the shortfall ordistance from potential per capita output or steady statelevel for each country, dit approaching zero as time pro-gresses should be considered as evidence for convergence.

For the data set the per capita output of all countries arelower than their steady state level (US GDP), therefore,

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Page 6: Testing convergence in economic growth for OECD countries

one only has negative dit. For convergence to hold, the rateof change in dit with respect to time t needs to be positive;i.e. …@=@t†dit > 0. The convergence hypothesis was set asthat the average slope function is positive.

To test the convergence hypothesis we consider a similarmodel as Equation 10:

ditˆ f …t† ‡ uit

ˆ ³0‡ ³1t ‡ ³2t2 ‡ ¢ ¢ ¢ ‡ ³k¡1tk¡1 ‡ ³ktk ‡ uit

…12†

where uit is assumed to be an i.i.d. …0; ¼2† error term. The

following null hypothesis was de®ned: H0 : r0³ 4 0, against

the alternative hypothesis H1 : r0³ > 0, where r is de®ned

above.Recall that according to Bernard and Durlauf (1995), if

one tests the stationarity properties of the demeaned out-put variables or the output gap dit, evidence for stationaritysupports the convergence hypothesis, and the presence of aunit root provides evidence against convergence. Thusresults for the Augmented Dickey±Fuller unit root teston zit, wit and dit were also produced.

IV. RESULTS AND DISCUSSION

Data for annual real per capita GDP for 22 OECD coun-tries from 1950 to 1998 was used. This data set was down-

loaded from the World Bank website, and is based on the

Penn World Tables 5.6 of Summers and Heston (1991) asupdated in 1993, with further updates in the 1990s. The

series for Germany stops in 1992; data from the World

Bank World Tables on Germany’s growth rate in real per

capita GDP for each year of the 1990s was used to continue

this series up to 1998. Interest lies in this sample becausethe convergence hypothesis was rejected by Bernard and

Durlauf (1995), using 15 of these 22 OECD countries.

The natural logs of the 22 OECD countries real per capita

GDP series are plotted in Fig. 1; a cursory examination of

the data suggests that convergence of most series towards acommon mean looks likely. The plot of the cross-sectional

standard deviation of real per capita GDP against time for

these 22 OECD countries is given in Fig. 2; this also indi-

cates evidence in favour of ¼-convergence as de®ned by

Sala-i-Martin (1996). Figure 3 represents the demeaned

per capita GDP, and most of these per capita GDP devi-ations seem to be heading towards zero.

Table 1 represents the results of the convergence tests

based on average slope estimates of the squared demeaned

output and the output gap values1. Tests based on the

squared demeaned output level indicate strong evidence infavour of the convergence hypothesis for each country

except Germany, Iceland and Norway. In fact, Norway

and Germany have positive average slopes, which is evidence

Testing convergence in economic growth for OECD countries 2015

Fig. 1. Log of Real Per Capita GDP

1The AIC was used to select the appropriate value of k for each country in estimating Equations 10 and 12; the selected polynomial order

for each country is reported in Table 1.

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Page 7: Testing convergence in economic growth for OECD countries

for divergence from the mean per capita level of GDP,although the slope for Germany is very small and not sta-

tistically signi®cant. Figures 4, 5 and 6 graph the real percapita GDP of each of these countries, along with the meanat each point in time. These graphs help in interpreting thetest outcomes. For Iceland (Fig. 4), it is clear that the `fail-

ure’ of convergence as suggested by the test is somewhatmisleading. Iceland has for most of the sample period ¯uc-

tuated around the mean output level. It has not needed toconverge, because convergence has already occurred prior tothe sample period. For Germany, Figure 5 con®rms non-convergent behaviour ± in the early 1950s Germany’s per

2016 Nahar and Inder

Fig. 2. Standard deviation of log real per capita GDP

Fig. 3. Demeaned real per capita GDP

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Page 8: Testing convergence in economic growth for OECD countries

capita GDP moved ahead of the average, and has main-

tained that gap ever since. While there is some hint of con-vergence in the 1990s, this is not su� cient to be convincing.

Norway’s performance is slightly di� erent (Fig. 6). At the

start of the sample it was well above average. Convergence

seemed to occur up to the early 1970s, with per capita GDP

of Norway being very close to the average. Since then,Norway has outperformed the average, and has been con-

sistently moving ahead of the average. Regardless of the

speci®c pattern, it seems clear that absolute convergence is

Testing convergence in economic growth for OECD countries 2017

Table 1. Estimates of average slopes and t-ratios for testing convergence of 22 OECD countries

Country

Squared demeaned output Output gap from USA

Polynomial order Average slope Test statistic Polynomial order Average slope Test statistic

Australia 3 70.0055 716.31* 2 0.0027 9.19*Austria 6 70.0015 711.81* 4 0.0165 24.13*Belgium 6 70.0006 720.95* 6 0.0076 9.22*Canada 5 70.0051 710.70* 5 0.0042 7.91*Denmark 6 70.0020 78.95* 6 0.0063 8.61*Finland 6 70.0001 72.35* 6 0.0118 9.48*France 4 70.001 72.13* 2 0.0099 40.24*Germany 6 0.0002 1.20 4 0.148 26.87*Greece 6 70.0114 712.64* 6 0.0179 21.51*Iceland 2 70.0000 70.14 6 0.0133 11.08*Ireland 6 70.0024 74.08* 6 0.0193 20.33*Italy 4 70.0019 722.25* 4 0.0163 29.24*Japan 5 70.0176 724.52* 6 0.0300 33.04*Netherlands 4 70.0004 74.80* 6 0.0088 10.66*New Zealand 6 70.0058 712.73* 3 70.0016 71.79Norway 6 0.0014 5.86 6 0.0145 20.58*Portugal 6 70.0207 713.17* 6 0.0237 16.08*Spain 6 70.0063 78.45* 6 0.0173 15.95*Sweden 6 70.0040 719.82* 6 0.0022 3.22*Switzerland 6 70.0078 716.21* 6 70.0008 70.85UK 5 70.0026 735.49** 4 0.0039 9.81*USA 3 70.0133 731.92*

Note: * indicates signi®cant at the 5% level ± evidence in favour of convergence.

Fig. 4. Comparing log real per capita GDP for Germany with overall mean

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rejected for only these two countries ± Germany and

Norway. Both have outperformed the average.

Tests based on average slopes of per capita output gapsfrom the USA indicate strong evidence in favour of the

convergence hypothesis for each country except

Switzerland and New Zealand. These two countries have

negative average slopes, indicating a move away from theUSA over time.

The estimates of average slopes can be interpreted as the

average rate of convergence for each country towards theUSA. For example, the result for Australia suggests this

country is converging to the USA at a rate of 0.27% per

year. Estimates suggest that Japan is closing the gap with

the USA the fastest ± at a rate of more than 3.0% per

annum, while several countries have quite slow (but stillsigni®cant) rates of convergence ± Australia, Canada,

Sweden and the UK all converge at a rate of less than

0.5% per annum.

In contrast, evidence suggests that New Zealand isdiverging from the USA at the rate of 0.16% per

annum. With a t-statistic of 1.79, this value is marginally

signi®cant ± there is moderate evidence that New Zealandis falling further and further behind the USA over time.

This ®nding is con®rmed by Fig. 7. New Zealand’s

2018 Nahar and Inder

Fig. 5. Comparing log real per capita GDP for Iceland with overall mean

Fig. 6. Comparing real per capita GDP for Norway with overall mean

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Page 10: Testing convergence in economic growth for OECD countries

per capita GDP is consistently lower than that of theUSA, and in the past 25 years, the gap has been slowly

widening. The estimate of average slope for Switzerland is

also negative …¡0:08%† but this is not signi®cantlydi� erent from zero, so there is no evidence that

Switzerland is diverging from or converging towards theUSA. Figure 8 presents clear evidence that Switzerland

has been diverging from the USA since the mid-1970s.

After starting well behind the USA in 1950, Swiss realper capita GDP converged and then surpassed the US

value by the mid-1970s. However, the Swiss performance

has been deteriorating relative to the USA ever since. Thetest result appropriately suggests neither convergence nor

divergence over the whole sample, but the graph showsclearly two separate episodes of ®rst convergence, then

divergence.

Testing convergence in economic growth for OECD countries 2019

Fig. 7. Log real per capita GDP of New Zealand and USA

Fig. 8. Log real per capita GDP of Switzerland and USA

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Page 11: Testing convergence in economic growth for OECD countries

Table 2 reports the results of Augmented Dickey±Fuller

unit root tests for the squared demeaned output, the

demeaned output, and the output gap from the USA.2

Recall Bernard and Durlauf (1995) argue that rejectionof the hypothesis of a unit root in output deviation implies

convergence. Using the demeaned output results, it was

found that convergence to the mean can only be established

for three countries: Australia, Belgium and Italy. This con-

trasts markedly with the conclusions based on the method-

ology that introduced in this article, where one ®nds

convergence to the mean for at least 19 of the 22 countries.Likewise, evidence for convergence to the USA is also

much weaker using the ADF tests: the null of non-

convergence can be rejected for only 10 of the 21 countries.

One could infer from these univariate unit root testing

results that if we follow Bernard and Durlauf (1995) and

test for convergence of this group of OECD countries byusing a multivariate cointegration analysis, the conver-

gence hypothesis, de®ned as stationary output deviations,

is likely to be rejected. But according to our results, the vast

majority of these OECD countries are converging towards

USA and also towards an average level.

It is not surprising that the unit root tests have thus given

a misleading impression. The very slow convergence of

most countries to the USA (Fig. 4) is going to give an

AR (1) coe� cient in a Dickey±Fuller test very close toone, making it almost impossible to reject a null hypothesis

of unity. Consider Fig. 9 for example. This ®gure shows the

output gap between Norway and the USA. Table 1 pro-

vides clear evidence in favour of convergence of Norway’s

real per capita GDP to that of the USA ± a t-statistic of

20.58. This conclusion seems supported by Fig. 9 ± the

di� erence is clearly declining towards zero. In contrast,the ADF test suggests that there is no evidence for conver-

gence ± the test statistic of 70.94 is well short of the rejec-

tion region. The relatively slow rate of convergence of the

output gap has caused the unit root tests to give a mislead-

ing impression.

Including a time trend in the unit root tests would poss-ibly alleviate this problem with unit root tests or cointegra-

tion analysis as a test for convergence, but then rejecting a

unit root does not necessarily imply convergence. A signif-

icant trend in output gap would need to be positive. Even

then, such a model with positive linear trend and stationary

2020 Nahar and Inder

Table 2. Augmented Dickey±Fuller unit root t-tests

Country

Squared demeaned output Demeaned output Output gap from USA

Lag length Test statistic Lag length Test statistic Lag length Test statistic

Australia 3 75.97* 3 73.17* 5 72.87Austria 5 72.68 5 72.48 4 73.03*Belgium 2 74.94* 2 73.16* 0 71.51Canada 5 72.59 5 72.24 4 71.78Denmark 5 70.89 5 70.91 5 73.54*Finland 2 71.95 5 72.56 4 71.79France 3 70.63 3 70.14 5 74.37*Germany 1 72.60 5 71.95 3 74.36*Greece 2 72.76 0 71.88 2 73.55*Iceland 3 73.06* 3 71.53 2 72.20Ireland 1 70.50 1 71.44 1 1.37Italy 5 74.65* 0 73.36* 0 73.70*Japan 5 74.80* 4 72.92 0 74.76*Netherlands 5 71.27 4 71.06 5 73.14*New Zealand 5 72.33 5 70.867 5 70.53Norway 4 70.46 2 70.963 5 70.94Portugal 1 70.60 1 70.317 1 71.15Spain 5 72.67 4 71.80 5 73.10*Sweden 5 70.94 4 70.24 5 73.24*Switzerland 2 70.50 1 0.19 0 71.56UK 4 73.52* 1 72.27 5 71.53USA 5 74.67* 0 72.67

Note: Lag length was chosen by AIC. Models include constant but not time trend. 5% critical value for the ADF tests is 72.93.A * indicates signi®cant at the 5% level ± evidence in favour of convergence.

2In each case, the lag length was chosen by AIC, and models include a constant but no time trend. Results for the squared demeaned

output were not discussed, as tests for convergence based on unit root analysis are usually based on the demeaned output rather thantheir squares. These results were included simply so the reader can compare the ®ndings about convergence using the ADF test with thosefrom Table 1.

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Page 12: Testing convergence in economic growth for OECD countries

error is actually inconsistent with the de®nition of conver-gence, as long term forecasts of the output gap would notconverge to zero. One could consider unit root tests withdeterministic functions of time that do yield converginglong term forecasts (e.g. 1=t). Such models would be di� -cult to use, as standard asymptotics on the unit root testswould not apply.

V. CONCLUSION

This article makes several contributions to the debateabout convergence. First, one contends that for a groupof countries that might share a common steady state out-put level, it may be more appropriate to consider the out-put level of the group leader as the better choice as a proxyfor this level, rather than the mean output level. In thiscase, one deals with the OECD countries, and hence regardreal per capita GDP of the USA as the closest measurableproxy for this steady state level of output. A test for con-vergence then becomes a test for whether a country’s out-put gap from the USA is approaching zero.

The second contribution is to highlight the inappropri-ateness of tests for unit roots and cointegration as an indi-cator of the presence of convergence. It is inappropriate toequate the presence of convergence with stationarity in theoutput di� erence between two countries. Consequently,unit root tests provide misleading signals about the exist-ence of convergence. They are likely to reject convergencein many cases where it clearly exists.

Finally, a methodology for testing for absolute conver-gence was introduced that overcomes the problems with

time series tests based on unit roots. This methodologyallows us to treat di� erent countries in a group di� erently,and to conclude whether each particular country in a groupis converging to a common steady state level. The broad®nding is that the evidence for convergence among thisgroup of OECD countries between 1950 and 1998 isquite strong. There is clear evidence for only one country(Norway) diverging from the mean per capita GDP level.Likewise, only New Zealand has been consistently diver-ging from the US per capita GDP level, with some sugges-tion that Singapore has been diverging in recent years.These empirical tests thus provide much more supportfor the predictions of the neoclassical growth theory thanmost previous literature, even though we have tested forthe much tougher requirement of absolute convergence.One would argue that this more favourable ®nding hascome about through a more appropriate application oftime series techniques than in many previous studies.

ACKNOWLEDGEMENTS

The authors are grateful to Max King for helpful sugges-tions.

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Testing convergence in economic growth for OECD countries 2021

Fig. 9. Di� erence in log real per capita GDP between Norway and USA

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