Regional growth in West Germany: convergence or divergence?

Economic Modelling 16 Ž1999. 489]502

Regional growth in West Germany: convergence or divergence? Michael FunkeU , Holger Strulik Department of Economics, Hamburg Uni¨ ersity, Von-Melle-Park 5, 20146 Hamburg, Germany

Abstract Using data from the 11 West German Lander for the period 1970]1994 we investigate the ¨ issue of regional convergence across Germany allowing for heterogeneity over cross-sections and over time. The paper finds evidence in favour of conditional convergence, but persistent inequality of regional steady states. Q 1999 Elsevier Science B.V. All rights reserved. JEL classifications: B23; C31; O30; O41; O47 Keywords: Growth; Convergence; Time series tests; Cross-section tests; West Germany

1. Introduction The past 10 years have witnessed a resurgence of academic interest in growth. Many of the crucial debates in the theory and empirics of economic growth are encapsulated in the question of economic convergence or divergence. Is there a tendency for the poorer regions to grow more rapidly than the richer regions, and thereby to converge in living standards? Or instead, are there tendencies for the initially richer regions to get richer, and the poor to get poorer, so that the gap across different regions tends to widen over time? The upsurge of empirical work on growth has demonstrated no overall tendency for convergence in the world. Many poor countries failed to grow faster than rich countries; many in fact experienced negative per capita growth, so the gap between the developing and the rich countries has widened. On the contrary, convergence seems to hold among the U

Corresponding author. E-mail address: [email protected] ] hamburg.de

0264-9993r99r$ - see front matter Q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 2 6 4 - 9 9 9 3 Ž 9 9 . 0 0 0 1 1 - 5

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OECD countries alone.1 In the regional context, the question of convergence has also been discussed in great detail.2 However, despite the voluminous empirical efforts in this area it is easy to be sceptical of past results. Most of the literature uses cross-sectional averages or starting values for time-series data. Applying such an approach has two shortcomings. First, the use of cross-section data makes it impossible to control for unobserved region-specific differences, possibly biasing the results. Second, long-run averages ignore important changes which have occurred over time for the same region. In this paper, we therefore use Bayesian panel data techniques which permits the estimation of different convergence rates and steady states for each cross-section unit. Finally, we address convergence and shock persistence from a time series perspective. The remainder of the paper is organized as follows. In Section 2, we present some stylized facts of regional growth in Western Germany. In Section 3, we develop a minimal framework for the empirical analysis of growth, discuss alterative empirical specifications and look at evidence regarding convergence across West German Lander. Along the way, we will briefly discuss some of the econo¨ metric problems which arise in connection with convergence equations. Section 4 gives a summary and conclusions.

2. Stylized facts of regional growth per capita Žstates . from Fig. 1 shows the full array of data for the 11 West German Lander ¨ 1970 to 1994.3 The first visual impression from Fig. 1 is that there seems to be only little evidence of convergence towards a single per capita income level across the 11 West German Lander. On the contrary, these differences remain quite substan¨ tial: in 1994 the ratio of GDP per capita between the richest ŽHamburg. and poorest ŽSaarland. region was approximately 2.0:1 Žcompared to 2.1:1 25 years earlier .. We can gain further descriptive insights into changes in dispersion by looking at the coefficient of variation. Fig. 2 gives descriptive evidence on this measure of dispersion across West Germany. The index of inequality has fallen gradually from the beginning of the 1970s until the end of the 1980s. However, there seems to be an inflexion point at the end of the 1980s. Since then the dispersion of income has increased again.4 The concept of convergence is operationalised in at least three different ways in the literature. Convergence in the standard deviation of per capita income given in 1

Various economists have therefore suggested that there may be a convergence club, meaning a subset of countries for which convergence applies, while countries outside the club would not necessarily experience convergence vis-a-vis those in the club. 2 Ž1997.. An excellent review of the literature is available in Hofer and Worgotter ¨ ¨ 3 More details on the data source and regional coverage are provided in Section 5. The data start in 1970 because GDP data are not available for some Lander prior to 1970. ¨ 4 One explanation is that the West German Lander have benefited in different ways from German ¨ unification.

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Žper capita GDP, constant 1991 prices, Fig. 1. Per capita GDP in the 11 West German Lander ¨ 1970]1994..

Fig. 2 is known as s-convergence. The second concept that has been used in the literature is b-convergence. In its simplest form, b-convergence means that regions that start out the sample period with below average incomes tend to grow faster than do regions that start with above-average incomes. Clearly, the theoretical concept of b-convergence is compatible with constant or even rising coefficients of variation. Any approach which tries to discriminate among alternative theoretical approaches therefore requires more than the descriptive inspection of the time

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Fig. 2. Dispersion of per capita income in West Germany.

path of a measure of income dispersion. The purpose of the paper is therefore to investigate whether a more systematic analysis confirms the stylized facts presented above.

3. Estimation issues and results Barro and Sala-i-Martin Ž1991, 1992, 1995. introduced the notion of conditional b-convergence in which regions tend to grow more rapidly the greater is the gap between its initial per capita income level and its own long-run per capita income level.5 In discrete notation, the path for per capita income, Yt , around the steady state is ln

Yt

ž / Ytyi

s a y Ž 1 y eyb . ln Ž Ytyi .

Ž1.

where a s g q Ž 1 y eyb . ln Ž Y U .

Ž2.

Y U is the steady state of Yt , g is a parameter of technological progress and b is said to signify convergence. With decreasing returns to reproducible factors of 5 Barro et al. Ž1995. have recently suggested an open economy version of the standard Solow growth model which is probably more appropriate for the regional dataset used in the paper. They assume that a country can borrow abroad to finance its physical capital stock while its human capital must be financed by domestic savings because only physical capital can be used as a collateral. The model leads to the same reduced form as in Eq. Ž1. with b being higher than in the closed economy version of the model.

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production, poorer regions will gradually reduce the distance which separates them from their wealthier neighbour regions. The intuition behind economic convergence seems quite clear, its measure, however, is not straightforward and a number of alternative methodologies have been suggested. The simplest way to test the underlying theory is to use a cross-section dataset. Alternatively, there is a growing convergence literature that uses panel and time series techniques.6 All three alternative methods are used here. 3.1. Cross-section estimates The traditional and simplest way of presenting the evidence is to compute average growth rates and initial income levels, and to present scatterplots or regressions of average income growth rates on initial income. In other words, we first explore the hypothesis of absolute or unconditional b-convergence in a cross-section framework. The scatterplot in Fig. 3 constitutes the simplest test of the underlying growth model. As can be seen, the relationship between lnŽY1994rY1970 . and lnŽY1970 . is indeed negative, as suggested by the theory. A more formal test is offered in Table 1, which presents the basic results for cross-sectional regressions. We regress the average annual growth rate, lnŽY1994rY1970 ., on a constant and the initial per capita income level, lnŽY1970 ..7 The OLS regression results indicate that the west German Lander have converged, but the speed of ¨ convergence is only approximately 0.6% per year. In other words, the gap has narrowed, but at a snail’s pace. The result implies a coefficient of capital in the production function much higher than the observed share of this factor in national income. The corresponding ‘half-life’ tU is the solution to expŽybtU . s 0.5. Taking logs on both sides implies that tU f 0.69rb s 114.9 years. Regional convergence in Western Germany between 1970 and 1994 is therefore much slower than in Barro and Sala-i-Martin Ž1995., and Seitz Ž1995.. Additionally, the fit is very poor, suggesting that other factors have played a role as determinants of the growth rate. One difficulty with the OLS estimation results is that outliers may affect inference. In the last column of Table 1 we therefore re-estimated the ‘unconditional

6

These techniques seem reasonable since convergence is, by definition, a dynamic concept which cannot be captured by cross-sectional studies. See, for example, Carlino and Mills Ž1993.; Islam Ž1995.; Bernard and Durlauf Ž1996. and Lee et al. Ž1997.. 7 Eq. Ž1. is non-linear. Of course, for small values of b a linear regression is an excellent approximation. There is nothing in the Solow model that says that the steady states should be the same for all regions. The recent empirical literature has therefore often tested for conditional b-convergence which allows for different steady state levels of per capita income due to differences in human capital, labour force participation, political regimes, fiscal policy, the rate and the variability of inflation, the rate of investment, a well-developed financial system and the degree of openess. We have not included such variables into the equation because they do not differ very much across the 11 Lander. Barro and ¨ Sala-i-Martin Ž1991. and Barro and Sala-i-Martin Ž1995. have also argued that the omission of region-specific characteristics may not be crucial to describe the evolution of steady states and Levine and Renelt Ž1992. have shown that most of these additional conditioning variables do not even survive robustness tests in cross-country datasets.

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Table 1 Cross-sectional regressionswdependent variable: lnŽY1994rY1970 .x OLS

WSDE

Constant

0.09 Ž2.9.

0.08 Ž3.2.

lnŽY1970 .

y0.006 Ž2.1.

y0.006 Ž2.3.

0.07

0.06

R2 Normal w x Ž2.x

1.50

]

Functional w x Ž1.x

0.02

]

2

2

Notes. The OLS t-statistics in parantheses are based upon White’s heteroscedasticity-adjusted standard errors. The diagnostics include White’s functional form misspecification test ŽFUNCTIONAL. and Jarque and Bera’s test for normality ŽNORMAL.. The equation in the last column was estimated using Huber’s Ž1973. weighted squared deviation estimator ŽWSDE..

b-convergence’ equation using Huber’s Ž1973. estimator. The estimator minimizes the sum of squared residuals for the observations corresponding to ‘small’ residuals, but, for the observations corresponding to ‘large’ residuals, the estimator minimizes absolute residuals. In the presence of outliers the estimator is therefore more robust than OLS. Despite this modification, however, the convergence rate still turns out to be only 0.6% per year and the large residuals indicate that differences in initial per capita income levels are far from providing a satisfactory explanation of the observed variation of growth rates. 3.2. Panel data estimates In the above regressions we have averaged the data over time and have estimated a single cross-section across the 11 Lander. Contrary to this pure ¨ cross-section approach which abstracts from the time-varying dimension of the data we are now pooling the data and allow for parameter heterogeneity. By exploiting a pooled time-series and cross-sectional structure, less information is lost than taking an average value for each variable for each region over the period in question. In other words, panel data estimates introduced here provide more transparent and intuitively more reasonable results. The Bayesian approach used below allows to estimate different rates of convergence of each Land to its own steady state, in that sense gives information about divergence by testing for conditional convergence.8 Hence, a high degree of inequality among regions could persist, and we could observe high persistence in the relative positions of the different regions. We first reformulate the growth equation as a dynamic panel data model. Let yi t be 8 Lee et al. Ž1997, pp. 381]385., have recently shown that the traditional cross-section estimates of b-convergence are subject to substantial asymptotic bias.

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Fig. 3. Scatterplot of lnŽy1994ry1970 . against lnŽy1970 ..

the ratio of Ž YitrYtq. where Yit is the i-th Land per capita income in period t and Ytq is aggregate Žaverage. per capita income in West Germany in period t. Allowing for different steady states and different convergence rates across the 11 Lander gives the following expression for yit :9 ¨ ln Ž yit . s ¨ y i ,0 q r i ln Ž yi ,ty1 .

i s 1,2, . . . , N; t s 1,2, . . . ,T

Ž3.

The model allows for initial per capita incomes to influence future growth through the parameter n. The corresponding statistical model can be written as ln Ž yit . s a i q r i ln Ž yi ,ty1 . q « it

Ž4.

Note that b i s ylnŽr i . and e it represent independent drawings from a normal distribution with mean zero and variance se2 . The model allows the initial conditions to influence future growth through a i . The Žrelative. steady state value of yit is a irŽ1 y r i . which is a measure of efficiency and reflects total factor productivity in region i. First, consider the case < r < - 1. If r i is less than 1 and a i s 0, then there is convergence of per capita income across the different regions to the same steady state. On the contrary, for < r < - 1 and a i ) 0 there is conditional b-conver9

Canova and Marcet Ž1995. have shown that Eqs. Ž3. and Ž4. are consistent with the standard neoclassical growth model. 10 The term a irŽ1 y r i . does, however, not have the usual interpretation of steady state any more since ´ logarithm of per capita the logarithm of average per capita income is substracted from individuals income. Thus the ratio a irŽ1 y r i . depict’s the difference of the i y th Land steady state from the global steady state. It can be negative which implies that in steady state this region grows at a lower rate than the average does.

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gence but long-run persistence of inequality. For < r < G 1, there is again persistence of inequality for all a i .10 Using the ratio lnŽ yit . instead of lnŽ Yit . as our basic variable avoids problems of serial and cross-unit correlation.11 For estimation, we have imposed a Bayesian prior on the parameters to be estimated.12 The basic idea is that the cross-section coefficient vectors are assumed to be ‘drawn’ from a distribution with a common mean. More precisely, the prior information is expressed through the normal density functions Ž r i y r j . ; N Ž 0,sr2 . Ž a i y a j . ; N Ž 0,sa2 .

;i, j ;i, j

Ž5. Ž6.

Note that Eqs. Ž5. and Ž6. do not require any a priori belief about the level of any coefficient. If the distributions have small variances, the coefficients will be almost identical; with larger variances, the procedure ‘suggests’ that they have similar values.13 Somewhat similar shrinkage estimators have recently been used by Canova and Marcet Ž1995. and Maddala and Wu Ž1996. using different subsets of data from the Penn World Tables. As is typically the case with Bayesian methods, when the prior and the data evidence provide non-conflicting information, the combination can show a huge improvement in precision over either alone. If the two variances s 2 ’s are set at approximately zero, then equality of coefficients across regions is imposed and therefore the regression results are identical to those obtained in Table 1. For example, imposing sa2 s sr2 s 0.00001 approximately leads to the ‘uniform’ annual convergence rate of b s 0.5%. In other words, the individual least squares estimators shrink towards the pooled estimator and the model reproduces the results in Table 1 under tight prior restrictions.14 This result shows that recasting the underlying growth model in Eq. Ž3. and considering time spans of just 1 year does not affect the results, i.e. the pooled regression produce strikingly similar results as the cross-sectional framework. We next analyse how panel estimates change these results if one assumes that the region-specific effects are Bayesian in nature. The set of results for the case of heterogeneity in parameter estimates across regions can be seen in Table 2 below. The average 11 Canova and Marcet Ž1995, pp. 25]26. have shown that this specification of the growth model is consistent with a business cycle shock and a trend that is common to all states; the business cycle variations within each state are then governed by r i and an i.i.d. shock. 12 If slope homgeneity is assumed the traditional pooled fixed effects estimation procedure can be used. This approach has been followed recently by Islam Ž1995. and Knight et al. Ž1992. who both estimated growth equations using data averaged over 5-yearly time spans. There are a variety of IV and GMM estimators available in the literature which are consistent wfor a review compare Baltagi Ž1995, pp. 125]148.x. However, these estimators are generally not consistent under slope heterogeneity wsee Lee et al. Ž1997, pp. 385]388. and Pesaran and Smith Ž1995.x. 13 Using posterior parameter estimates trading-off the information contained in the cross-section and the time-series dimension is related to the literature on ‘exchangeability prior’ discussed in Leamer Ž1978, pp. 270]277., Lindlay and Smith Ž1972. and Maddala Ž1991.. 14 The results differs slightly from that in Table 1 due to the lagged dependent variable. Eq. Ž4. can only be estimated over the sample period 1971]1994.

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Table 2 Panel data estimates using exchangeability priors State

a

r

Convergence rate

Steady state

Schleswig-Holstein

0.029 Ž2.2.

0.833 Ž11.0.

0.182

0.178

Hamburg

0.026 Ž2.0.

0.870 Ž13.5.

0.138

0.205

Lower Saxony

0.018 Ž1.3.

0.893 Ž10.8.

0.112

0.177

Bremen

0.019 Ž1.8.

0.899 Ž16.2.

0.106

0.193

North Rhine-Westphalia

0.009 Ž1.0.

0.945 Ž16.3.

0.057

0.179

y0.002 Ž0.2.

1.009 Ž21.4.

y0.010

0.156

Rhineland-Palatine

0.013 Ž0.9.

0.928 Ž11.9.

0.076

0.175

Baden-Wurttemberg ¨

0.018 Ž1.2.

0.903 Ž10.8.

0.103

0.184

Bavaria

0.008 Ž1.8.

0.958 Ž17.8.

0.043

0.183

Saarland

0.03 Ž2.1.

0.835 Ž10.9.

0.180

0.178

West-Berlin

0.018 Ž1.9.

0.899 Ž14.9.

0.106

0.188

Hesse

Notes. Estimation was carried out using a variation on Theil’s Ž1971, pp. 347]352. mixed estimation technique. Figures in parantheses are t-ratios. We have used a grid search procedure to determine the s 2 ’s which maximise the likelihood. This procedure is in the spirit of Sims and Uhlig’s Ž1991. helicopter tour. The preferred choices were sa2 s 0.1 and sr2 s 0.08.

conditional b convergence rate increases to 9.94% per year, implying that the ‘half-life’ tU is 6.94 years. The individual convergence rates vary from a low 0% ŽHesse. up to 18% ŽSchleswig Holstein, West Berlin.. Except for Hesse, the ordering of steady states appears quite reasonable: Hamburg, Bremen, BadenWurttemberg and Bavaria occupy the top positions. These findings are in agree¨ ment with the cross-country results of Knight et al. Ž1992.; Canova and Marcet Ž1995.; Islam Ž1995.; Evans Ž1996. and Lee et al. Ž1997. who all found a substantial increase in the convergence rates and different steady state levels when allowing for heterogeneity in panel data sets. Thus their stylized results for convergence across industrial andror developing countries carry over to the question of regional convergence. In conclusion, the estimation results in Table 2 can be summarized as follows: Ž1.

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the extremely low convergence rate given in Table 1 is probably the result of a biased estimation procedure that ignores fixed effects in the data; Ž2. there are significant differences in yU , i.e. there is no common equilibrium across regions determined by shared technologies and tastes; 15 Ž3. a key finding is that the data strongly support the notion of conditional b-convergence; and Ž4. the significant a i-coefficients in six Lander, however, indicate persistence of inequality, i.e. with ¨ the passage of time some rich regions tend to remain rich while other poor regions continue to lag behind. Whether this is a depressing result for poor regions depends on what determines the ‘conditional’ nature of the catch-up process. Are low income regions held back by policies that can be changed easily and quickly? Or are more fundamental forces at work? We approach this question by trying to explain the determinants of the regional yU s a irŽ1 y r i . point estimates. An interesting result is that there appears to be a significant positi¨ e connection between the initial per capita income levels in 1970 and the estimated steady states yU . Spearman’s rank order correlation g and Kendall’s t between lnŽ Yi,1970 . and the estimated steady state values yU in Table 2 turn out to be 0.577 and 0.491, respectively, which are both significant. This implies that on average the Lander ¨ which are initially below the average per capita income level will fail to improve their relative standing in the cross-regional distribution. 3.3. Panel unit root tests Finally, we employ panel-based unit root tests to consider the question of convergence in per capita GDP across the West German Lander from a time-series ¨ perspective.16 They test for persistence of shocks on income for each Land. To carry out these tests, we again use Eq. Ž4. presented above. The augmented Dickey]Fuller version of Eq. Ž4. can be written as Dln Ž yit . s a i y Ž 1 y r i . ln Ž yi ,ty1 . q « i t

i s 1,2, . . . , N;

t s 1,2, ??? ,T

Ž7.

The ad hoc disturbance term e it is often interpreted as technological or productivity shock. The reduced form wEq. Ž7.x allows to test whether there is in fact any convergence at all, by comparing the null hypothesis H0 : r i s 1 with the alternative r i - 1 for all i. Panel-based unit root tests provide a natural way of testing this hypothesis. In other words, if the I Ž1. null hypothesis is accepted, then shocks on output differences persist into the indefinite future. The procedure used in the paper has been suggested by Levin and Lin Ž1993. and may be briefly summarized as consisting of the following stages. Levin and Lin Ž1993. consider the use of pooled cross-section time series data  x it 4 to test the null 15

These results, however, must be interpreted with care since the region-specific dummies reflect a number of factors about which we know very little. 16 Bernard and Durlauf Ž1996. have shown that time series tests are based on a stricter notion of convergence than cross-section tests. This might explain why time series tests have generally accepted the non-convergence hypothesis wsee, for example, Quah Ž1992. and Bernard and Durlauf Ž1995.x.

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hypothesis that each individual time series contains a unit root against the alternative hypothesis that each time series is stationary, i.e. follows a stationary ARMA process. Within the class of stationary ARMA models, Levin and Lin Ž1993. consider three variants ŽModels I]III., each distinguished by the deterministic variables included: In Model I, no deterministic variables are included; in Model II, a constant is included; in Model III, the deterministic list includes both a constant and a time trend.17 The null hypothesis may be tested against the given alternatives by performing the following regression:

˜e i t s d¨˜i ,ty1 q ˜« it

Ž8.

where ˜ e it and ¨˜i ,ty1 are normalised residuals constructed from the following two auxiliary regressions: p

ˆe i t s Dx i t y

Ý pˆ i L Dx i ,tyL y aˆ m i d m t

Ž9.

Ls1 p

¨ˆi ,ty1 s x i ,ty1 y

Ý fˆ i L Dx i ,tyL y aˆ m i d m t

Ž 10 .

Ls1

where D is the first difference operator and d m Ž m s I, II, III. represents the vector of deterministic variables; d1 m s  B4 , d 2 m s  14 , and d 3 m s  1,t 4 . The coefficients on d m t , and a m i Ž m s II, III. are allowed to differ across i. ˜ e it and ¨˜i ,ty1 are the normalised equivalents of ˆ e it and ¨ˆi ,ty1 where the normalisation consists of scaling ˆ e it and ¨ˆi ,ty1 by the standard error from the regression18 Ž 11. ˆe i t s d¨ˆi ,ty1 q ˆ« it A total of NT˜ observations are used in regression Ž8., where T˜ s ŽT y p y 1. is

the average number of observations for each Land in the panel and p s N 1rN Ý is1 x i is the average lag length from an individual augmented Dickey]Fuller regression and N denotes the number of regions. Under the null hypothesis that d s 0 for all i s 1,..., N in Eq. Ž8., Levin and Lin Ž1993. show that the regression t-statistic on d Ž t d . has a standard Normal distribution for Model I, but diverges to negative infinity for Models II and III. However, they provide a corrected value for t d , which we label tUd , which is shown to have a standard normal distribution under the null. Since the null hypothesis imposes a cross-equation restriction on the first-order partial autocorrelation coefficients, this panel test procedure yields a much higher power than performing a separate unit root test for each individual. In other words, pooling yields a dramatic improvement in the power of the unit root tests against stationary alternatives.19 Next we report the test statistics for the underlying dataset. 17

Model II is therefore equivalent to Eq. Ž7. above. Such a normalisation allows for the existence of heterogeneity across regions. 19 Levin and Lin Ž1993. show that the test statistic is super-consistent with respect to the number of time periods. An alternative panel-based unit root test has recently been suggested by Im et al. Ž1995.. 18

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Table 3 Panel unit root tests U

Lag length p 1 2 3

U

U

td Model I

td Model II

td Model III

0.427 0.801 0.807

2.377 3.168 3.174

1.602 1.602 1.612

Notes. tUd is the adjusted t-ratio using formula Ž16. of Levin and Lin Ž1993.. Models I, II and III labels denote the deterministic specification used to calculate tU d . The statistic is distributed asymptotically as a standard normal variable. Pretesting indicated that lag lengths Ž p . of 2 years for Models I and II and 3 years for Model III are appropriate.

The results in Table 3 critically depend upon the chosen deterministic specification. The estimates for model II, however, which correspond to Eq. Ž7. above indicate that all the series considered as a panel are I Ž0., i.e. stationary around a constant. This implies that the hypothesis of complete persistence is rejected by the data.

4. Interpretation Doubts have grown in recent years about the value of the convergence hypothesis. Partly this scepticism concerns the inability of cross-sectional studies to discern convergence because it abstracts from the time-varying dimension of the data and is thus uninformative about the dynamics of the process determining per capita income. We have therefore tackled the question of convergence across the West German Lander via a panel and time-series perspective. In summary, the evidence ¨ suggests that growth in the West German Lander is consistent with the traditional ¨ conditional b-convergence hypothesis. On the other hand, however, the 11 states do not share a common steady state. Thus the results for Western Germany confirm those of Quah Ž1993, 1994. on the immobility over time of individual countries with respect to the ability to converge to the world average level of real per capita GDP. In fact, during the 25 years of our analysis only Hesse moved from the group of lower income regions to the group of higher income regions. The results are also consistent with the empirical evidence in Obstfeld and Peri Ž1998. showing a high persistence of regional unemployment rates in across European countries. Authors such as Azariades and Drazen Ž1990. and Durlauf Ž1993. have shown how production complementarities can interact with market failure to generate multiple steady states. Furthermore, the persistence of the steady states over time implies that productive technology is intrinsically kind to the technological leader: the initially rich Lander tend to have higher steady states as a result of increasing ¨ returns to scale in one form or another. A variety of endogenous growth models have recently been put forward which assume some non-convexity in production, or

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some externality arising from the accumulation of human capital. In these models, regional GDP per capita can actually diverge. Agglomeration economies have also been emphasized which can lead to centripetal forces and uneven growth patterns. On a policy note, it seems that economic integration and identical institutions in West Germany have not produced homogeneity despite various policy measures which have been invented to reduce these differences. For example, the high persistence of regional GDP emerges despite the German inter-state tax revenue . which works as an automatic stabilizer and sharing system Ž Landerfinanzausgleich ¨ provides regional insurance. 20 It seems that the availability of regional transfer schemes facilitates delayed regional adjustment.21 A supplementary explanation is that the transfer schemes are not working properly.22 The overall conclusions of the paper for the future prospects of European integration are bitter-sweet. The good news is that the single market in Germany is working: long-lasting clusters of different steady states in Western Germany are apparent. The bad news is that poor regions outside the successful states will probably stay poorer. It seems that, just like everything else, success tends to cluster.

5. Data appendix All GDP data were taken from ‘Arbeitskreis Volkswirtschaftliche Gesamtrechnung der Lander’, Statistisches Landesamt Baden-Wurttemberg, Stuttgart. The ¨ ¨ population data are published in Statistisches Bundesamt, Fachserie 1, Wiesbaden.

Acknowledgements This research was undertaken with support from the European Commission’s Phare ACE Programme 1996. An earlier version of this paper was presented at the Economics Faculty Seminar, Kiel University, Germany. We would like to thank seminar participants and an anonymous referee for helpful comments on an earlier draft.

References Azariades, C., Drazen, A., 1990. Threshold externalities in economic development. Q. J. Econ. 105, 501]526. 20

For an analysis of the redistribution system see Zimmermann Ž1989.. Obstfeld and Peri Ž1998. have presented similar evidence for governmental fiscal stabilizers to depressed areas in Canada, Italy and the US. In all three countries the ranking of high-unemployment regions is remarkably stable over time and correlates well with ranking by net transfer inflow per capita. 22 Fagerberg and Verspagen Ž1996. have analysed the impact of regional policy measures of the EU. They show that the EU support to R & D and investment only impacts positively on growth in regions for which the rate of unemployment is below a certain threshold value. In regions with high unemployment, i.e. where the problems are most manifest, these policies seem largely ineffective. 21

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