C32 -Time-Series Models < C3 -Econometric Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods, O41 -One, Two, and Multisector Growth Models < O4 -Economic Growth and Aggregate Productivity < O -Economic Development, Technological Change, and Growth

Keywords: real covergence, unit root tests, central and eastern europe Real convergence, Unit root tests, Central and Eastern Europe JEL classification: C32, O41

This article examines the real convergence hypothesis in some Central and East European countries (both towards the German and the US economies) by means of using time series techniques during the period 1950-2003. We do not find evidence of real convergence for the whole period. However, when we allow for structural breaks, we find evidence of a catch-up process during the nineties-2003 period for Poland, Czech Republic and Hungary towards Germany and only for Poland towards the US economy.

Introduction

There has been in recent years an emerging body of empirical literature on convergence in per capita output across different economies. The interest on this subject may be explained, at least in part, as a prediction test of the neoclassical growth model [START_REF] Solow | A contribution to the theory of economic growth[END_REF] as opposed to the "new" endogenous growth models [START_REF] Romer | Increasing returns and long-run growth[END_REF][START_REF] Lucas | On the mechanics of economic development[END_REF]. As it is well known, the neoclassical model predicts (under some assumptions) that per capita output will converge to each country's steady-state (conditional convergence) or to a common steady-state (unconditional convergence), regardless of its initial per capita output level. On the contrary, in endogenous growth models there is no tendency for income levels to converge, since divergence can be generated by relaxing some of the neoclassical assumptions (e.g., incorporating non convexities in the production function). Furthermore, the great differences observed in per capita output and in growth rates across countries justify a deeper study on convergence. However, among the great number of empirical paper which studies convergence, little attention has been paid to the Central and East Europe countries' experience. 1 For example, [START_REF] Estrin | Testing for ongoing convergence in transition economies, 1970 to 1998[END_REF] analyze whether there has been convergence within the bloc or between the bloc as a group and the West over the period from 1970 to 1998. The results show little evidence of convergence within the bloc and with respect to the West. In other paper, [START_REF] Kocenda | Macroeconomic convergence in transition economies[END_REF] analizes the real and nominal convergence in Central and Eastern Europe for some macroeconomic variables such as real industrial output, monetary agregate (M1), producer and consumer prices and 1 Although there are several papers which study the economic growth process in Central and Eastern European countries (see for example [START_REF] Estrin | Testing for ongoing convergence in transition economies, 1970 to 1998[END_REF][START_REF] Kocenda | Macroeconomic convergence in transition economies[END_REF][START_REF] Dawson | Exports and economic growth in Central and East European countries during transition[END_REF]Dritsakis, 2004;Janicki et al., 2004or Kominek, 2004), little attention has been paid to the real convergence process in the post 1950 period. In this paper we use data of some Central and East European economies that cover the second half of the twentieth century. The past fifty years can be characterized as having higher disparity in productivity performance in Europe. Whereas both Eastern and Western Europe achieved rapid productivity growth during the period 1950-1973, West European growth rates have mostly been higher than in Eastern Europe. Between 1973 and1989 both Eastern and Western Europe have experienced a productivity slowdown, and not much further convergence has taken place in any of the two regions. However, on the whole, the slowdown was bigger in Eastern Europe than in Western Europe so that divergence between the two regions increased further. The collapse of communism at the end of the 1980s created very diverse effects among East European countries, which explained the rapid rise in divergence within Eastern Europe. The collapse of productivity during the period 1989-1992 raised divergence between Eastern Europe and European Union, but since 1992 the recovery of productivity growth has led to a convergence path between the two regions. Since 1993-94, most Central and Eastern European countries have seen a recovery of growth. However, there has been substantial diversity across countries. Some countries (Czech Republic or Hungary) are now more or less back to the 1989 output level, while Poland has surpassed it. Other countries (including Bulgaria and Romania) also show recovery but at a much slower pace. For example, Czech Republic is now at per capita income levels between 60 and 70 percent of the EU -average, but others (Bulgaria and Romania) are only at 20 to 30 percent of the EU per capita income level. 2 2 See Van [START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF] and [START_REF] Barbone | EU accesion and economic growth. The challenge for Central and Eastern European countries[END_REF]. The differential behavior of the growth rates of these countries, their difficulties to converge to real per capita GDP levels of developed countries and the little research found in the literature regarding this group of countries motivates the analysis on real convergence made in this paper. In this paper we examine the real convergence hypothesis for some Central and East European economies towards leading economies, both within the European Union (such as Germany) or outside Europe (such as the US). 3 Empirical testing of the convergence hypothesis provide several definitions of convergence and thus, different methodologies to test it. In a cross-section approach, a negative (partial) correlation between growth rates and initial income is interpreted as evidence of unconditional (conditional) beta-convergence. In this context, one of the most generally accepted results is that while there is no evidence of unconditional convergence among a broad sample of countries, the conditional convergence hypothesis holds when examining more homogenous groups of countries (or regions) or when conditioning on additional explanatory variables. Examples in this context are [START_REF] Baumol | Productivity growth, convergence, and welfare: what the long-run data show[END_REF]), De Long (1988), [START_REF] Dowrick | OECD comparative economic growth 1950-1985: catch-up and convergence[END_REF], [START_REF] Grier | An empirical analysis of cross-national economic growth, 1951-1980[END_REF], [START_REF] Barro | Economic growth in a cross section of countries[END_REF], [START_REF] Barro | Convergence across states and regions[END_REF][START_REF] Christiano | Searching for breaks in GNP[END_REF], 1995), [START_REF] Mankiw | A contribution to the empirics of economic growth[END_REF], etc. In a time series approach, stochastic convergence asks whether permanent movements in one country's per capita output are associated with permanent movements in another countries' output, that is, it examines, whether common stochastic elements matter, and how much persistent the differences among countries are. Thus, stochastic convergence implies that output differences among economies cannot contain unit roots. Empirical tests on this hypothesis have been carried out by [START_REF] Campbell | International evidence on the persistence of economic fluctuations[END_REF], [START_REF] Cogley | International evidence on the size of the random walk in output[END_REF], Bernard (1991), 3 We use as benchmark economies both Germany (as an economy representing the European Union standards) and the US economy (in a more global context, one of the leader international economies used as F o r P e e r R e v i e w 5 [START_REF] Carlino | Are U.S. regional incomes converging? A time series analysis[END_REF], [START_REF] Bernard | Convergence in international output[END_REF], Cunado et al. (2003), Beliu et al. (2004), and, in general, they do not find evidence of convergence. However, when the convergence tests take into account the possibility of structural breaks, the evidence of convergence is reinforced. Greasley and [START_REF] Greasly | Time-series based tests of the convergence hypothesis: some positive results[END_REF] found evidence of bivariate convergence between Belgium and Netherlands, France and Italy, Australia and the UK, and Sweden and Denmark. [START_REF] St. Aubyn | Convergence across industrialised countries (1890-1989): new results using time series methods[END_REF] finds evidence of convergence between US and each of the UK, Australia and Japan, using the Kalman filter methodology. [START_REF] Cellini | Segmented stochastic convergence across the G-7 countries[END_REF] detect stochastic convergence only for the US and Canada, and the US and the UK when they allow for structural breaks. [START_REF] Strazicich | Are incomes converging among OECD countries? Time series evidence with two structural breaks[END_REF] examine the differences in per capita incomes of fifteen OECD countries with the US economy over the period 1870-1994 allowing for two structural breaks and they reject the unit root null hypothesis in eleven of the fifteen countries, thus supporting the stochastic convergence hypothesis.

In this paper, we apply time series convergence tests allowing for structural breaks to the differences in per capita output for some Central and East European countries to the US and to Germany using data for the period 1950-2003. The outline of the paper is as follows. Section 2 describes the methodology employed in the article to test for convergence. Section 3 covers the empirical analysis and Section 4 offers some conclusions.

benchmark in most of the analysis on real convergence).

Time Series Convergence Tests

In a time series testing framework, countries i and j convergence if their outputs are cointegrated with cointegrating vector [1,-1], that is, the difference

k t j k t i y y + + -, ,
must be a stationary I(0) process with no deterministic components (unconditional convergence), where y i is the log real GDP per capita in country i and likewise y j for country j.

Since most of the procedures for testing the unit root hypothesis include the cases of no regressors, an intercept, and an intercept and a linear trend, we can distinguish between long-run convergence (unconditional or conditional4 depending on the significance of the intercept, α 0 in equation ( 1)) and convergence as a catch-up (if the log of relative output is trend stationary, α 1 >0 in equation ( 1)). Although this last definition5 may be open to criticism because the presence of a time trend allows for permanent per capita output differences, it might be appropiate in a context in which convergence is an on-going process [START_REF] Bernard | Convergence in international output[END_REF]Oxley and Greasly, 1995), as the one observed for less developed countries, such as the Central and East European countries analyzed in this paper. In this context, we will test for convergence analyzing the integration order of the relative incomes using the following equation:

t j t p j j t t e RI c RI t RI + ∆ + + + = ∆ - = - ∑ 1 1 1 0 β α α , (1) where
) ln( ) ln( i t US t t y y RI - = or ) ln( ) ln( i t GERMANY t t y y RI - =
, the p extra regressors, ∆RI t-j are added to eliminate possible serial correlation in the error terms. However, these type of unit root tests may fail to recognise convergence when structural breaks are present. For example, St. Aubyn (1999), [START_REF] Cellini | Segmented stochastic convergence across the G-7 countries[END_REF] show that the introduction of structural breaks makes the existence of convergence across countries more clear.

For the Central and East European case, we could think in the existence of one or more breaks in the convergence process during the period 1950-2003. As [START_REF] Perron | The great crash, the oil price shock and the unit root hypothesis[END_REF] pointed out, these tests perform poorly when there is a break in the constant or deterministic trend function. However, Perron's method has been criticized on the grounds that the break point is chosen exogenously. Several authors, such as [START_REF] Christiano | Searching for breaks in GNP[END_REF], [START_REF] Perron | Nonstationarity and level shifts with an application to Purchasing Power Parity[END_REF] or [START_REF] Zivot | Further evidence on the great crash, the oil price shock and the unit root hypothesis[END_REF] have developed methods to endogenously search for a break point and test for the presence of a unit root when the process has a broken constant or trend and have demonstrated that their test are robust and more powerful than the augmented [START_REF] Dickey | Distribution of the estimators for autoregressive time series with a unit root[END_REF] and [START_REF] Phillips | Testing for a unit root in a time series regression[END_REF]) tests6 . However, these last procedures have also been critized in the literature [START_REF] Nunes | Testing for unit roots with breaks: evidence on the great crash and the unit root hypothesis reconsidered[END_REF]Lee andStrazicich, 2001, 2003), since these type of tests derive their critical values assuming no breaks under the null, so that, in the presence of a unit root with break, these tests will tend to reject the null hypothesis suggesting that the time series is stationary around a break when it is nonstationary with a break. In order to solve this problem, we will use the endogenous two-break 7 LM unit root test proposed by [START_REF] Lee | Minimum LM unit root test with two structural breaks[END_REF] which is unaffected by breaks under the null. Following these authors, a unit root test statistic can be obtained by estimating the following model:

F o r P e e r
∑ = - - + ∆ + + ∆ ′ = ∆ 1 1 γ φ δ , (2)
where Z t reflects the deterministic components, δ ψ t

x t t Z y S - - =
, t=2,3,…,T. δ ~is a vector of coefficients in the regression of ∆y t on ∆Z t and δ ψ 1

1 Z y x - =
, where y 1 and Z 1 denote the first observations of y t and Z t , respectively. e t is the contemporaneous error term and is assumed independent and identically distributed with zero mean and finite variance.

∆S t-i are added to eliminate possible serial correlation. When

{ } t Z t , 1 =
, we have the statistic proposed in [START_REF] Schmidt | LM tests for a unit root in the presence of deterministic trends[END_REF]. If we want to account for some structural breaks, we can extend the models A (which allows for a one-time change in level) and C 8

(which allows for a change in both the level and trend) considered by [START_REF] Perron | The great crash, the oil price shock and the unit root hypothesis[END_REF] and define Z t in the following ways:

{ }' , , , 1 2 1 D D t Z t = for model A and { }' , , , , , 1 2 1 2 1 DT DT D D t Z t =
for model C, where D j =1 for t ≥T Bj +1 and zero otherwise, DT j =t for t ≥T Bj +1 and zero otherwise, and T Bj are the date of the breaks.

The unit root null hypothesis is described by φ=0 and the LM test t-statistic is defined by: τ ~=t-statistic for the null hypothesis φ=0.

(3)

To implement the test, the number of augmentation terms

k i S i t ,..., 1 , ~= ∆ - that
correct for serial correlation in equation ( 2) must be determined. At each combination of break points, k is determined by following the general to specific procedure suggested by [START_REF] Perron | The great crash, the oil price shock and the unit root hypothesis[END_REF]. The procedure begins with a maximum number of lagged first-differenced 7 We use this two-break LM unit root test and not the one-break LM test because an examination of the empirical results reveals that the two structural breaks included in the model were significant in all the five analyzed countries for the period 1950-2003. terms (k=8) and examines the last term to see if it is significantly different from zero at the 10% level. If it is insignificant, the maximum lagged term is dropped and the model is reestimated with k=7 terms and so on, until either the maximum term is found or k=0. After determining the "optimal" number of k, the unit root test statistic is estimated using equation ( 3). The process is repeated for each λ, to determine the LM test statistic with the minimum t-value. 9

Empirical Analysis

The data used in this section are annual log real GDP per capita in 1990 Geary-Khamis PPP-adjusted dollars. The series runs from 1950 to 2003 for five Central and East European countries (Bulgaria, Czech Republic, Hungary, Poland, Romania) plus the US and Germany. All the variables have been obtained from [START_REF] Maddison | The world economy: A millennial perspective[END_REF]. 10 . As convergence measure, we define the differences of each of the log real per capita GDP series with respect to Germany and the US. 11

The results from the augmented Dickey Fuller (ADF) tests are reported in Tables 1 and2. We are unable to reject the unit root hypothesis in favor of unconditional convergence for any of the Central and Eastern European countries neither when relative incomes are measured with respect to the US or Germany. 8 In the empirical analysis, and as in [START_REF] Lee | Minimum LM unit root test with two structural breaks[END_REF], we consider Model C which allows for two changes in level and trend. 9 See [START_REF] Lee | Minimum LM unit root test with two structural breaks[END_REF] for a more detailed description of the test. The computation of the LM unit root test statistic has been carried out using the Gauss codes provided by Junsoo Lee and available on the web site http://www.cba.ua.edu/~jlee/gauss. 10 We have applied the same unit root tests to an alternative dataset obtained from the Penn World Table, version 6.1 [START_REF] Heston | Penn World Table Version 6.1[END_REF]. The analyzed variables are real per capita GDP adjusted for PPP and the sample periods range from 1991 to 2000 for Bulgaria, 1990[START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]for Czech Republic, 1970[START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]for Hungary, 1979[START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]for Poland, 1960[START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]for Romania and 1970[START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF] for Germany. The results, which are consitent with those obtained with the Maddison dataset, are presented in the Appendix. 1 and2 about here)

When we include an intercept and a time trend in the model, we can only reject the unit root hypothesis in favor of conditional convergence towards the German economy for the case of Czech Republic. However, in this case, trend stationarity is a necessary but not sufficient condition for converge or catch-up [START_REF] Carlino | Are U.S. regional incomes converging? A time series analysis[END_REF], since it is also needed that countries with a per capita output level below the average must have grown more than the average. In order to test for this hypothesis, we follow [START_REF] Tomljanovich | Are US regions converging? Using new econometric methods to examine old issues[END_REF] and run the following regression for this case in which we found trend stationarity:

t t u t RI + + = β µ , (4)
where the relative per capita output is regressed on a constant and a linear time trend, and u t follows a stationary process. β represents the average growth of RI t over time and µ represents the initial level of RI t . For convergence, µ and β must be of opposite sign. When convergence is measured with respect to Germany or the US, β must be positive, since the initial per capita output of the Central and Eastern European countries are lower than those of the US and Germany.

The little evidence of convergence or catch-up among this group of countries could be due to the existence of different convergence speeds in the convergence process or the case in which countries pass through convergence to nonconvergence processes (or viceversa), two possibilities which will be studied while allowing for structural breaks 11 We have carried out our empirical analysis for these five economies since [START_REF] Maddison | The world economy: A millennial perspective[END_REF] (2003). In Tables 3 and4 we report the minimum LM statistic and the date of the breaks.12 (Insert Tables 3 and4 about here)

The main results presented in these tables may be summarized as follows: First, a broad examination of the significance of the dummy variables indicate that the convergence processes of the different East European countries have experienced structural changes which should be taken into account when analyzing the order of integration of relative incomes. Second, we can reject the unit root null hypothesis in all the cases. Following [START_REF] Tomljanovich | Are US regions converging? Using new econometric methods to examine old issues[END_REF] and [START_REF] Nieswiadomy | Are political freedoms converging?[END_REF], we must study if there has been a catch-up process in per capita output after the structural break for all these cases, so that we run the following regression:

t t u t t t RI + + + + + + = 3 2 2 1 1 3 2 1 β β β µ µ µ , ( 5
)
where µ 1 and β 1 are the intercept and the slope before the first break, µ 2 and β 2 the intercept and the slope after the first break and µ 3 and β 3 the intercept and the slope after the second break. Testing for converge for the last period is equivalent to testing whether the parameters µ 3 and β 3 are different from zero and negatively related. The last columns in Tables 3 and4 summarize the results found in this analysis. In this case, and following [START_REF] Tomljanovich | Are US regions converging? Using new econometric methods to examine old issues[END_REF] and [START_REF] Nieswiadomy | Are political freedoms converging?[END_REF] β-convergence condition), d denotes divergence (with only one coefficient statistically significant at 10%), and U denotes unit root (we did not find evidence to reject the unit root null hypothesis). We find evidence of a catch-up process after the second break towards Germany for Czech Repubic, Hungary and Poland, but only for Poland towards the US economy. Third, while the break point varies from country to country, most of them occur in the late sixties-early seventies and in late eighties. This means that the relative performance of these Eastern European countries is characterized by a first period of rapid divergence from 1950 to late-sixties-early seventies, a second period of ralentization of this divergence process with the general productivity slowdown since 1973, and a third episode of convergence since late eighties-nineties as a result of the recovery after the transition in 1989. However, even though the direction of the trends is more or less uniform in the five countries, the results suggest that these economies show different behaviors (see [START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]. For example, while Czech Republic, Poland and Hungary have diminished their per capita GDP differences with Germany, this is not the case for Bulgaria and Romania.

Furthermore, Poland is the only country which has also diminished its per capita GDP differences with the US. According to some papers such as Janicki et al. (2003) or [START_REF] Dawson | Exports and economic growth in Central and East European countries during transition[END_REF], a relevant variable which explain the different behaviour of these countries is their trade openness.

Finally, we apply the same methodology to real per capita GDP adjusted for PPP data obtained from the Penn World Table for a more recent period (1991( -2000 for Bulgaria; for Bulgaria;[START_REF] Cogley | International evidence on the size of the random walk in output[END_REF][START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]for Czech Republic, 1970-2000 for Hungary;[START_REF] Dickey | Distribution of the estimators for autoregressive time series with a unit root[END_REF][START_REF] Van Ark | Economic growth and labour productivity in Europe: half a century of East -West comparisons[END_REF]

Concluding Remarks

In this article we have examined the real convergence process of some Central and Easter

European countries by means of using time-series tests over the period 1950-2003. In particular, we have analyzed the convergence process of some East European countries towards the German per capita GDP and the US economy, first based on ADF unit root tests and then allowing for structural breaks.

Using the first tests, we find no evidence of unconditional convergence (stationarity of the differences in per capita GDP levels with no deterministic terms) for any of the Central and East European countries analyzed neither with respect to the German economy or the US. When we include an intercept and a time trend, we can only reject the unit root null hypothesis for the Czech Republic towards Germany. However, the inspection of the coefficients on the intercept and the time trend suggests that there have been an increase in the per capita GDP differences between these two economies, and thus, a divergence process, when the whole period is considered.

However, when we analyze the possibility of structural breaks, we find significant evidence of two structural breaks in the convergence process of these countries, with the breaks occurring in all the cases in early seventies and late eighties. We interpret this result indicating that the relative performance of these [START_REF] Lee | Break point estimation and spurious rejections with endogenous unit root tests[END_REF]. *, ** and *** indicate significant at the 10%, 5% and 1% levels, respectively. C denotes catch-up (with both µ 2 and β 2 are significant) and d denotes divergence (with only one coefficient statistically significant at 10%).

TABLE A4. LM unit root tests (PWT data)

Testing the integration order of the differences of log real per capita GDP series with US [START_REF] Lee | Break point estimation and spurious rejections with endogenous unit root tests[END_REF]. *, ** and *** indicate significant at the 10%, 5% and 1% levels, respectively. C denotes catch-up (with both µ 2 and β 2 are significant), D denotes divergence (stationarity around two time breaks which do not satisfy the above βconvergence condition) and d denotes divergence (with only one coefficient statistically significant at 10%).

Page 23 of 23

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

  interest rates. The results show evidence of convergence in macroeconomic fundamentals over the period 1991:01-1998:12.

  , C denotes catch-up (those cases in which the unit root hypothesis was rejected in favor of stationarity around different time trends and satisfy the β-convergence hypothesis in equation (5), c denotes catch-up (with only one coefficient, µ 3 or β 3 , statistically significant at 10%), D stationarity around different time trends which do not satisfy the above

  Romania) and the results, which are presented in the Appendix, are consistent with those obtained with Maddison data.

	2000 for
	F o
	r
	P e
	e
	r
	R e
	v i
	e
	w
	for Poland and 1970-
	13

TABLE 2 . ADF unit root tests

 2 Testing the integration order of the differences of log real per capita GDP series with the US

		With no regressors	With intercept	With intercept and	Converging?
				time trend
	Bulgaria	-0.30	-1.10	-1.36	U
	Czech Republic	-0.07	-1.24	-2.32	U
	Hungary	-0.20	-1.26	-1.88	U
	Poland	-0.35	-1.54	-1.89	U
	Romania	-0.17	-1.32	-1.87	U
	The 10%, 5% and 1% critical values are: Model with no regressors: -1.61, -1.95, -2.61. Model with an intercept:-2.60, -
	2.92, -3.57. Model with an intercept and a linear time trend: -3.18, -3.50, -4.16.
	*, ** and *** indicate significant at the 10%, 5% and 1% levels respectively. U denotes unit root.

TABLE 3 .

 3 LM unit root testsTesting the integration order of the differences of log real per capita GDP series with Germany 5% and 1% asymptotic critical values have been obtained from[START_REF] Lee | Minimum LM unit root test with two structural breaks[END_REF]. *, ** and *** indicate significant at the 10%, 5% and 1% levels, respectively. C denotes catch-up (with both µ 2 and β 2 are significant) and d denotes divergence (with only one coefficient statistically significant at 10%).

		LM stat (Model C)	T B	Converging?
	Bulgaria	-5.58***	1972, 1988	d
	Czech Republic	-8.29***	1965, 1989	C
	Hungary	-6.64***	1965, 1988	C
	Poland	-4.67**	1966, 1988	C
	Romania	-6.13***	1972, 1988	d
	The 10%,

TABLE 4 .

 4 LM unit root testsTesting the integration order of the differences of log real per capita GDP series with US

		LM stat (Model C)	T B	Converging during last period?
	Bulgaria	-6.30***	1973, 1993	d
	Czech Republic	-7.11***	1972, 1989	d
	Hungary	-6.99***	1973, 1989	d
	Poland	-7.67***	1972, 1988	C
	Romania	-6.90***	1972, 1988	D

The 10%, 5% and 1% asymptotic critical values have been obtained from

[START_REF] Lee | Minimum LM unit root test with two structural breaks[END_REF]

. *, ** and *** indicate significant at the 10%, 5% and 1% levels, respectively. C denotes catch-up (with both µ 2 and β 2 are significant), c denotes catch-up (with only one coefficient statistically significant at 10%), D denotes divergence (stationarity around two time breaks which do not satisfy the above β-convergence condition) and d denotes divergence (with only one coefficient statistically significant at 10%).

TABLE A1 . ADF unit root tests (PWT data)

 A1 Testing the integration order of the differences of log real per capita GDP series with Germany 5% and 1% critical values are: Model with no regressors: -1.61, -1.95, -2.61. Model with an intercept:-2.60, -2.92, -3.57. Model with an intercept and a linear time trend: -3.18, -3.50, -4.16. *, ** and *** indicate significant at the 10%, 5% and 1% levels respectively. U denotes unit root.

		With no	With intercept	With intercept and	Converging?
		regressors		time trend
	Bulgaria, 1991-2000	0.25	-1.59	-3.27	U
	Czech Republic, 1990-2000	0.62	-2.06	-1.43	U
	Hungary, 1970-2000	-0.40	-1.66	-2.51	U
	Poland, 1979-2000	-0.13	-1.12	3.92	U
	Romania, 1970-2000	-0.44	-2.34	-2.55	U
	The 10%,

TABLE A2 . ADF unit root tests (PWT data)

 A2 Testing the integration order of the differences of log real per capita GDP series with the US 5% and 1% critical values are: Model with no regressors: -1.61, -1.95, -2.61. Model with an intercept:-2.60, -2.92, -3.57. Model with an intercept and a linear time trend: -3.18, -3.50, -4.16. *, ** and *** indicate significant at the 10%, 5% and 1% levels respectively. U and D denote unit root and divergence, respectively.Page 22 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	With no regressors 1.07 2.06 0.16 0.01 -0.80 F Czech Republic, 1990-2000 Bulgaria, 1991-2000 Hungary, 1970-2000 Poland, 1979-2000 Romania, 1970-2000 o r P e With intercept -1.69 -2.17 -0.70 -3.34* -2.10 e r The 10%, Submitted Manuscript R e	With intercept and time trend -2.76 -1.85 -2.46 3.19 -1.44	Converging? U U U D U
	v i
	e
		w
			23

TABLE A3 . LM unit root tests (PWT data)

 A3 Testing the integration order of the differences of log real per capita GDP series with Germany

		LM stat (Model	T B	Converging?
		C)
	Bulgaria, 1991-2000	n.a.	n.a.	n.a.
	Czech Republic, 1990-2000	n.a.	n.a.	n.a.
	Hungary, 1970-2000	-6.42***	1989	C
	Poland, 1979-2000	-29.32***	1993	C
	Romania, 1970-2000	-6.30***	1987	d
	The 10%, 5% and 1% asymptotic critical values have been obtained from

  5% and 1% asymptotic critical values have been obtained from

		LM stat (Model C)	T B	Converging during last period?
	Bulgaria	n.a.	n.a.	n.a.
	Czech Republic	n.a.	n.a.	n.a.
	Hungary	-5.46***	1988	d
	Poland	-17.99***	1990	C
	Romania	-6.30***	1987	D
	The 10%,

According to neoclassical models, unconditional or absolute convergence holds when per capita GDP of the different countries convergence to the same steady state. In contrast, conditional convergence applies when per capita GDP of each economy converge to its own steady state. In this last case, the constant α 0 measures the differences in the steady state of each of the economies.

[START_REF] Carlino | Are U.S. regional incomes converging? A time series analysis[END_REF], for example, use this methodology in order to allow initially low income countries to grow faster than higher income countries.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UKSubmitted Manuscript

Recent empirical application of these tests can be found inLeybourne et al. (2003),[START_REF] Atkins | Trend breaks and the Fisher hypothesis in Canada and the United States[END_REF],[START_REF] Sen | Are US macroeconomic series difference stationary or trend-break stationary?[END_REF],Hacker et al. (2005) orNarayan (2005a,b),[START_REF] Sen | Are US macroeconomic series difference stationary or trend-break stationary?[END_REF],[START_REF] Atkins | Trend breaks and the Fisher hypothesis in Canada and the United States[END_REF] orNarayan (2005a, b) among others.

In all the cases, the dummy variables which account for the structural breaks were significant.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Appendix

In the appendix, we show the results obtained when we apply the same methodology to data from the Penn World Table, version 6.1. As in the text, the results from the ADF tests are reported in Tables A1 andA2. Tables A3 andA4 report the one-break minimum LM statistic and the date of the break. 13 As above, the results also suggest the existence of a structural break in the convergence processes of these countries occurred in late eightiesearly nineties. For the period after this structural break, the results also show evidence of a catch-up process for Poland and Hungary towards Germany and for Poland towards the US economy.

(Insert Tables A1, A2, A3 and A4 about here) 13 The one-break LM minimum statistic has not been applied in the cases of Bulgaria and Czech Republic because the sample period in these countries range from 1990/1 to 2000. For the rest of the countries we have only allowed for one-break since the sample period range from 1970/9-2000.


Dr Sonia Bhalotra
email: s.bhalotra@bristol.ac.uk

Near Rationality In Wage Setting

Keywords: efficiency wages, unions, near rationality efficiency wages, unions, near rationality. JEL Classification: J31 J51 L21

This paper argues that it is interesting to study near rational behaviour in the context of an efficiency wage model, where there are positive if decreasing returns to increasing the wage beyond the efficient level. Previous research has found it difficult to distinguish between efficiency wage and bargaining models, which have similar empirical predictions. But unions are a priori more likely to develop in environments in which the technology favours efficiency wage payments. This makes it interesting to investigate what it costs the firm to deviate from the efficiency wage. If it does not cost a lot, firms may give in to union demands. This paper derives expressions for the wage deviation and for the associated profit loss. For illustrative purposes, these are calibrated for UK, US and Indian manufacturing, taking a plausible parametrisation of the effort-wage function and using available estimates of the wage and employment elasticities of output. While there is evidence of positive effort returns to wages in the UK and India, the results are consistent with wage bargaining pushing the wage above the efficient level. The associated profit loss is considerably larger in the UK than in India. In contrast, US firms pay wages that are insignificantly different from the efficiency wage.

Introduction

This paper suggests the relevance of allowing for near rationality in wage setting behaviour and derives the expressions necessary to investigate it. To illustrate the argument, wage deviations and associated profit losses are calibrated for three countries for which estimates of relevant parameters are available.

Consider firms setting wages in an environment in which worker effort is wagedependent. The optimal or efficiency wage is then the wage at which effort returns to increasing the wage exactly offset the costs. An interesting feature of this environment is that increasing the wage beyond the efficient level will yield positive (although diminishing) effort returns. Therefore, other things being equal, a firm operating in circumstances in which productivity is a function of the wage rate is more likely to give in to demands for wage increases. This may be argued to encourage unionisation of its workers.

Previous research has remarked at the difficulty of disentangling union bargaining and efficiency wage effects. While inherently distinct, these two models of wage setting have in common that they can both explain certain stylised features of the labour market that are difficult to reconcile with a competitive model of the labour market. For example, both models are consistent with unemployment and wage differentials that persist after controlling for worker and job characteristics and that show little tendency to dissipate over time (e.g., [START_REF] Dickens | Inter-industry wage differences and industry characteristics[END_REF]Krueger and Summers, 1988;[START_REF] Groshen | Sources of intra-industry wage dispersion: how much do employers matter[END_REF]. A useful way of investigating whether the observed wage is the efficient wage is to directly test the first order condition of the efficiency wage model. According to this, the output elasticities of employment and wages should be equal (see Section 2). If a statistical test rejects equality, we can reject the null of optimality. This paper argues that it is then interesting to investigate near rationality, or to investigate how large a profit loss the firm is incurring in having deviated from the optimal wage. Small deviations that result in small losses are consistent with transactions or information costs. A further possibility is that a small positive wage deviation arises on account of union power. If, in this case, the associated profit loss is small then the economic consequences of the distinction between the efficiency wage and bargaining models are limited. In general, when the profit loss associated with deviating from the optimality condition is small then the decision rule used is near-rational. There is no rigorous definition of "small" just as there is no definitive choice of statistical significance level. The idea of near rationality is discussed in Akerlof andYellen (1985a, 1985b), who argue that the predictions of a hypothesis should be robust to near rational behaviour. In [START_REF] Akerlof | The macroeconomic applications of a dynamic envelope theorem[END_REF] this is cast in terms of inertial behaviour, while [START_REF] Cochrane | The sensitivity of tests of the intertemporal allocation of consumption to nearrational alternatives[END_REF] argues that near rational behaviour may arise on account of stylisations employed by the economist or on account of heuristic decision making. Empirical investigation of near rationality has been limited. In an early paper, [START_REF] Akerlof | Irving Fisher on his head: The consequences of constant threshold-target monitoring of money holdings[END_REF] finds that the utility loss associated with fairly substantial deviations from optimal money holdings is trivial. More recently, [START_REF] Cochrane | The sensitivity of tests of the intertemporal allocation of consumption to nearrational alternatives[END_REF] shows that deviations from the rule for intertemporal allocation of consumption implied by the permanent income hypothesis result in very small losses in utility. Both of these studies use macroeconomic data. There does not appear to have been any attempt to investigate near rational behaviour on the part of firms or, indeed, in an efficiency wage setting1 . [START_REF] Cochrane | The sensitivity of tests of the intertemporal allocation of consumption to nearrational alternatives[END_REF] points out that near rational behaviour is less likely amongst firms than amongst consumers because any slack in firm performance is likely to attract profit-seeking activities like takeover. However, if transactions costs or costs imposed by dissatisfied workers (or unions) rather than "mistakes" underlie small deviations from profit maximisation, then persistence in these costs can support persistence of near rational behaviour. In any case, the question is worth investigating so as to allow the data to speak for themselves. This paper derives the necessary expressions for an efficiency wage model. It shows that the deviation of the wage from its optimal level can be cast in terms of the difference in the point estimates of the wage and employment elasticities of output, for a given parameterisation of the effort function. The associated profit loss can then be calculated as a function of the wage deviation, the employment elasticity of output, and the curvature of the effort function. For illustrative purposes, available production function estimates for UK, US and Indian manufacturing are used to perform these calibrations.

Section 2 sets out the basic theory and the optimality condition, while Section 3 derives conditions that obtain in the neighbourhood of the optimum. In Section 4, the profit

A Direct Test of The Efficiency Wage Hypothesis

The General Case

The basic tenet of an efficiency wage model is that firms may find it profitable to pay wages in excess of the supply price of labour if this brings sufficiently large gains in productivity. Such behaviour is consistent with a range of theoretical models, surveyed by [START_REF] Katz | Efficiency wage theories: A partial evaluation[END_REF], Akerlof and Yellen (1986: 1-21), [START_REF] Layard | Unemployment: Macroeconomic Performance and the Labour Market[END_REF]. In the recruit (e.g. [START_REF] Weiss | Job queues and layoffs in labour markets with flexible wages[END_REF] retain (e.g., [START_REF] Stiglitz | Alternative theories of wage determination and unemployment in LDCs: The labour turnover model[END_REF] and motivate [START_REF] Shapiro | Equilibrium unemployment as a worker discipline device[END_REF] versions of the model, paying a relatively high wage induces higher productivity through self-selection, lower turnover and higher morale respectively. In the original efficiency wage model of [START_REF] Leibenstein | Economic Backwardness and Economic Growth[END_REF], paying an absolute wage that may be higher than the competitive wage enables greater effort. In this paper, we will concentrate upon the Shapiro and Stiglitz model in which a wage premium raises productivity by discouraging shirking.

The unobserved effort of workers, E, is an input in the production function, Y=Y(E(W), N(W), K, A), where Y is value added ouput, N is employment, K is capital stock, A is an index of productivity and W is the relative wage. Maximising profits with respect to the wage and employment in this very simple and general framework yields the first order conditions ∂Y/∂N = W/P and (∂Y/∂E)(∂E/∂W) = N/P. Solving these yields the condition which defines the efficiency wage: e EW = e YN / e YE , where e ij is the elasticity of i with respect to j. Neither e EW nor e YE is observable but rearranging gives e YE e EW = e YN , or e YW = e YN

(1)

The elasticities in (1) are estimable. If the elasticity of output with respect to the wage equals its elasticity with respect to employment, then the firm is paying the efficiency wage. This wage pays for itself. The intuition is straightforward. Since the wage bill is symmetric in W and N, equilibrium must have the property that the marginal increase in N is as productive as the marginal increase in W. If wage bargaining coexists with efficiency wage considerations, we may expect that the agreed wage exceeds the pure efficiency wage. In that case, e YW < e YN , or the wage does not quite pay for itself. Notice that the Solow condition, e EW = 1, is a

A Specific Case

It is useful to impose some structure on the effort and production functions for purposes of the analysis in Section 3. Let the production function incorporating effort, E, be

Y = A K β N α [E(W)] α ν (2)
where ν is an i.i.d. productivity shock that is assumed to be uncorrelated with changes in A, N and K. Notice that effort is specified as a perfect substitute for employment. While this does not affect the optimality condition, it simplifies the ensuing profit loss calculations. Let

E = -θ + W δ ; 0 < δ <1 (3)
E'(W)>0 and E''(W)<0, or there are positive but decreasing returns to increasing the wage. A negative intercept is specified in the effort function so as to rule out the possibility of nonnegative effort at a zero wage. If θ≤0, then a zero wage is the efficiency wage2 . To avoid clutter, A and K are suppressed because they do not depend upon the wage. The function we work with is

Y = N α α α α [-θ θ θ θ + W δ δ δ δ ] α α α α (4)
The first order conditions for profit maximisation are

∂π/∂N = 0 ⇒ αY/N -W/P = 0 (5) ∂π/∂W = 0 ⇒ P∂Y/∂W-N = 0 (6) Define γ ≡ ∂lnY/∂lnW = W/Y (∂Y/∂W) (7) F o r P e e r R e v i e w 6
Together ( 5), ( 6) and ( 7) imply the optimality condition,

γ γ γ γ = WN/PY = α α α α (8)
which is (1). Thus profit maximisation (or rationality) implies that the wage will be set at a level that equates the wage elasticity of output (γ) to the employment elasticity of output (α);

γ and α are the key parameters, estimable from a production function. Using ( 4) and ( 7), we can write γ as

γ = αδW δ [-θ + W δ ] -1 (9)
At the efficiency wage (W * ) where γ = α, (9) implies

(W * ) δ δ δ δ = θ θ θ θ / (1-δ δ δ δ) (10)
Clearly, the optimal wage depends only upon the parameters of the effort function3 .

Near Rationality

The Wage Deviation

Let ω be the actual wage, ω * the efficiency wage and ∆ω the deviation defined by ω = ω * + ∆ω. Then ω δ = (ω * + ∆ω) δ = (ω * ) δ [1 + (∆ω/ω * )] δ , or

ω δ ≈ (ω * ) δ [1 + δ∆ω/ω * ] (11)
It was demonstrated earlier that, at ω * , γ=α. Let us find γ when the wage deviates by ∆ω from its optimal level. Substituting (11) in ( 9) gives

γ ≈ αδ (ω * ) δ [1 + δ∆ω/ω * ] / {(ω * ) δ [1 + δ∆ω/ω * ] -θ θ θ θ } (12)
Substituting for ω * using (10

) gives γ ≈ α [1 + δ∆ω/ω * ] / [1 + ∆ω/ω * ], or ∆ω ∆ω ∆ω ∆ω/ω ω ω ω * ≈ ≈ ≈ ≈ (α α α α -γ γ γ γ) / (γ γ γ γ -αδ αδ αδ αδ) (14) F o r P e e r R e v i e w 7
Though δ is unknown, we can use the fact that δ lies between 0 and 1 to calibrate the wage deviation implied by estimates of α and γ for alternative values of δ in this range (see Section 4).

The Profit Loss

Profit in a neighbourhood of the optimum is given by a second-order Taylor series expansion

π (ω * + ∆ω) ≈ π(ω * ) + π′(ω * )∆ω + (1/2) π″(ω * )(∆ω) 2 (15)
where π′(ω * )= dπ/dω and π′′(ω * )= d 2 π/dω 2 < 0, both evaluated at the efficiency wage, ω * .

Optimality implies that π′(ω * )=0, so the proportional profit loss in deviating from the optimal wage, [π(ω * ) -

π (ω * + ∆ω)] / π(ω * ) is ∆π ∆π ∆π ∆π / π(ω * ) = -(1/2) π″ π″ π″ π″(ω ω ω ω * )(∆ω ∆ω ∆ω ∆ω) 2 /π(ω * ) (16)
It is assumed that value-added prices (P) are exogenously determined. Until it becomes necessary to choose functional forms, the analysis proceeds with the most unrestrictive specifications. Profit is given by π(ω) = PY[N(W), E(ω)]-WN(W). Employment is taken to be set after the wage, by the marginal revenue product (MRP) condition, ∂π/∂N=0, which implies

P(∂Y/∂N) = W (17)
Taking the total derivative of π with respect to the wage and using (17) to simplify gives

d π/dW = P ∂Y/∂W -N (18)
Taking the second derivative, we have

d 2 π/dW 2 = P(∂ 2 Y/∂W 2 ) -(dN/dW) [1 -P(∂ 2 Y/∂N∂W)] (19)
Differentiating both sides of (17) gives d[P(∂Y/∂N)]/dW=1, or

P(∂ 2 Y/∂N 2 ) (dN/dW) + P(∂ 2 Y/∂N∂W)] =1 (20)
Using this to substitute out the term in square brackets in (19) gives

F o r P e e r R e v i e w d 2 π π π π/dW 2 = P∂ ∂ ∂ ∂ 2 Y/∂ ∂ ∂ ∂W 2 -P(∂ ∂ ∂ ∂ 2 Y/∂ ∂ ∂ ∂N 2 ) (dN/dW) 2 (21)
Evaluated at the optimal wage and employment, (21) provides π″(ω * ) in ( 16). So as to obtain an expression for profit loss in terms of estimable parameters, the terms in ( 21) are now computed for the specific production function, (4).

The second derivative of (4) with respect to N is

∂ ∂ ∂ ∂ 2 Y/∂ ∂ ∂ ∂N 2 = α α α α(α α α α -1) (Y/N 2 ) ( 22
)
Taking the second derivative of (4) with respect to W gives

∂ 2 Y/∂W 2 = (αδ N α / Z 2 ) (ω δ -θ) α-2 ω δ-2 [δ(α-1) ω δ + (δ-1) (ω δ -θ) ] ( 23
)
where Z denotes the wage deflator (P c or W a as the case may be). Since the second derivatives are evaluated at the optimum, we can use ( 10) in ( 23), substituting ω * for ω.

Writing N * for N(ω * ) and simplifying, this gives

∂ 2 Y/∂W 2 = [α (α + δ -2) / (W * ) 2 ] [θ δN * /(1-δ)] α (24)
We now derive an expression for N * , the optimal level of employment. Since Y = N α [-θ + Using (25) to substitute for N * in (24), we have

∂ ∂ ∂ ∂ 2 Y/∂ ∂ ∂ ∂W 2 = [α α α α (α α α α + δ δ δ δ -2) Y * / (W * ) 2 ] ( 26
)
We now need an expression for the third term in (21), dN/dW. For a given wage, the optimal employment level is given by the MRP condition. For, Y=N α E(W) α , ∂π/∂N=0 implies αN α- Substituting ( 22), ( 26) and ( 28) in ( 21) gives d 2 π/dW 2 = α (δ -1) PY * / (W * ) 2 ( 29)

Substituting ( 29) into ( 16) gives the proportional profit loss incurred in deviating from the efficiency wage:

∆π ∆π ∆π ∆π / π π π π(ω ω ω ω * ) = -[α α α α (δ δ δ δ -1) / 2(1 -α α α α)] (∆ ∆ ∆ ∆W/W * ) 2 (30)
where we have used the fact (see ( 8)) that π(W * ) = PY * -W * N * = PY * (1-α). With ( 14), the wage-deviation term in (30) can be eliminated if one wants an expression for profit loss in terms of α, γ and δ instead of in terms of α, δ and a wage deviation.

An Illustration: Estimates for the UK, USA and India

In this Section, equations ( 14) and ( 30) are used to estimate the profit loss arising from deviations from the efficiency wage in each of the three countries for which a direct test of the first-order conditions is available. Using data for the UK, the US and India respectively, [START_REF] Wadhwani | A direct test of the efficiency wage model[END_REF], [START_REF] Levine | Can wage increases pay for themselves? Tests with a production function[END_REF] and xxx 5 (1995), estimate versions of the production function:

lnY it = αlnN it + βlnK it + θlnH it + ϕlnS it + γlnW it +τ t + (a i + ε it ) (31)
where subscripts i and t denote the manufacturing unit and year of observation. The τ t are time dummies denoting aggregate productivity growth; Y is a measure of value added, N is employment, K is capital stock, H is an index of utilisation, S represents skill, W is the 4 Recall that a given percentage increase in employment has the same effect on costs (the wagebill) as the same percentage increase in the wage so that, at the efficiency wage, the output produced by marginal changes in employment and the wage is equal (Section 3).

5 Xxx refers to the author of this paper, for anonymity in blind refereeing. 9), γ is a function of the wage level. To allow for this, the India study includes a quadratic in the log wage, though the squared term turns out to be insignificant. The other studies do not allow this. However, we are not primarily concerned here with the correctness of the published studies as our purpose here is only to illustrate the nature of the calculations. For the same reason, we do not discuss the institutional backgrounds in the three countries.

Relevant specifics of the three studies are presented in Table 1. The US study expresses all variables as growth rates and estimates the equation by OLS. The UK and India studies both use the GMM estimator of [START_REF] Arellano | Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations[END_REF]. The India study presents estimates for a range of alternative estimators including 1-step and 2-step GMM. The 2-step GMM estimates for India are reported here for comparability with the UK estimates but the 1-step estimates are also reported as they are likely to be more reliable6 .

Recall that the efficiency wage model predicts α=γ. Estimates of (31) reject this equality for the UK but not for the USA. For India, the preferred estimator (1-step GMM) cannot reject equality but an alternative estimator (2-step GMM) rejects equality at the 1% level. In both Britain and India, the point estimates α>γ, and this is consistent with bargaining resulting in a wage greater than the efficiency wage, though the difference in the point estimates is much larger and more significant in Britain. If indeed union bargaining is overlaid on the efficiency wage environment in Britain and India, how much of a wage premium does unionisation extract over and above what the firm would like to offer? The figures in Table 2 illuminate this question. The point estimates for the US indicate that companies pay less than the efficiency wage, though not significantly less. As they are optimising, the question of near rationality does not strictly arise. Calculations based upon the point estimates are nevertheless presented so as to allow the reader to compare the profit losses in a case where the statistical test cannot reject optimality with a case in which it can. 14) and ( 30) depend upon the curvature of the effort-wage function, We do not know δ but do know that 0<δ<1 7 . In addition, ( 14) implies the range, 0<δ<(γ/α) 8 . The wage and profit deviations can therefore be calibrated for δ in the range 0<δ<min(1, γ/α) While this is not as convenient as knowing δ, theoretical restrictions place it in a fairly narrow range. In his investigation of the utility loss incurred by deviating from an optimal consumption rule, [START_REF] Cochrane | The sensitivity of tests of the intertemporal allocation of consumption to nearrational alternatives[END_REF] similarly needs to assign a value to the relative risk aversion parameter.

He selects the (rather larger) range 1 to 10, and occasionally 30. This is based not on a theoretical restriction on the parameter as in the present study, but on the range of estimates of it obtained by other authors.

We conduct two exercises. First, we use only (30) and compute the profit loss for hypothetical wage deviations of 5 and 10 per cent. We expect that the profit loss will be increasing in α, decreasing in δ and independent of γ. We then use ( 14), which allows us to estimate the wage deviation implied by the data and plug this in to (30). Now the profit loss is increasing in |α-γ| and increasing in δ (via the wage deviation). The results are in Table 2.

Consider the first panel, showing hypothetical wage deviations for given values of δ.

As expected, profit loss is increasing in α. It is therefore larger in the UK than in India. In both cases, the losses are small: the profit function is indeed very flat in the neighbourhood of the optimum. For instance, for δ=0.1, a 5% deviation in the wage from its optimal value results in profit losses that range between 0.2% in the UK and 0.14% in India. Consistent with a statistical test being unable to reject optimality, the corresponding profit loss in the USA is 0.04%. For larger values of δ, the losses are even smaller. Intuitively, the larger is δ the greater is the effort-return to increasing the wage, and this mitigates the profit lost from paying too much.

The estimated wage deviations in the second panel of Table 2 depend upon the estimated divergence between α and γ for a given δ. They are strikingly large in each case, being smaller in India than in the UK 9 . Since the UK has the biggest α (and so big numbers in 7 This is a strict inequality. If δ=0 then effort is not wage dependent. If δ=1 then the effort-wage relation is linear but the more plausible situation is that there are decreasing effort returns to increasing the wage. 8 Suppose 1>δ>(γ/α), which implies that α>γ. Simple rearrangement shows that (α-γ)/(γ-αδ)<(-1) which, by ( 14), implies ∆W/W * <(-1). But this implies W<0, which is absurd. 9 In fact, the divergence |α-γ| is even smaller in India than in the US. As discussed, the fact that the US study does not reject optimality while the preferred estimates of the Indian study do may be put down to the latter using the correct IV estimator. This strengthens the case for complementing a Panel 1) and also the biggest difference between α and γ (and so even bigger numbers in Panel 2), the profit losses implied by the UK data are so large that they are produced only for illustrative purposes: the Taylor series approximations used to derive (30) are not valid for such large changes. However, for our purposes, all that matters is that they are so large that they are not consistent with near rational behaviour. This is an interesting result in itself and it suggests an important modification to the interpretation of the Wadhwani and Wall paper.

While Wadhwani and Wall reject the pure efficiency wage condition and acknowledge that union activity is likely to have pushed wages beyond the efficiency wage, they emphasise that a significant positive coefficient on the relative wage (i.e., a significant γ) supports the efficiency wage model. The analysis presented here emphasises the quantitative importance of union activity or other factors that push wages above the efficient level in the UK.

Consider the other two country cases presented in Panel 2. The wage deviation implied by the US estimates is large but it translates in to profit losses of the order of 3%, which may be deemed tolerable. In the case of India, the 2-step GMM estimates imply profit losses that range between 4.6% and 14% (as δ ranges between 0.1 and 0.5) but the 1-step estimates imply losses of 1.5% to 3.5%, similar to the case of the US. Notice that the estimated wage deviation is increasing in δ and that this effect dominates the effect seen in Panel 1, as a result of which the profit losses in the second panel of Table 2 are increasing in δ.

Although none of the three countries for which estimates of (31) are available quite fits this pattern, it is conceivable that, for some other sample of data, the pure efficiency wage condition, α = γ, is rejected but the associated profit losses are very small. This is likely if, for example, α is relatively small, the divergence between α and γ is large, and their standard errors of estimate are small. In this situation, the analysis suggested in this paper would importantly modify the statistical conclusion by identifying near rational firms in which the offered wage almost pays for itself.

Conclusions

This paper argues that it is interesting to study near rational behaviour in the context of an efficiency wage model because, with effort being a positive function of the wage, the statistical test of the first-order conditions with an estimate of the economic implications of small deviations suggested by the second order calculations. profit-wage function may be expected to be flatter than otherwise. Deviations from the exact optimum may arise because of heuristic decision making, mistakes, transactions costs, and also, possibly, on account of firms finding that it does not cost too much to indulge union wage demands. We derive an expression for the wage deviation and the associated profit loss that permit these quantities to be calculated using estimates of parameters of a wageaugmented production function. The force of the argument is illustrated by performing these calculations using UK, US and Indian data. Using hypothetical wage deviations we find, as expected, that the profit function is remarkably flat in all three countries. A statistical test is unable to reject the hypothesis that employers in the US pay the efficient wage. In Indian and British manufacturing, however, wages are higher than the efficient wage. This is consistent with the coexistence of wage bargaining and efficiency wage considerations. Our calculations suggest a considerable difference in what this costs employers in the two countries. Profits in the UK are substantially lower than would be expected in a pure efficiency wage model-the wages paid in the UK do not pay for themselves. The profit lost in paying a wage above the efficient wage in India is small by contrast. This is useful information with which to complement the standard statistical metric applied to testing the predictions of economic models.

  estimates of wage-augmented production functions for the three countries are calibrated and their implications discussed. Section 5 concludes.

  e EW = e YN / e YE that arises if and only if effort is specified as labouraugmenting (i.e., e YN = e YE ).

  ω δ ] α , Y * = (N * ) α [-θ + (ω * ) δ ] α . Using (10) again to substitute for ω * , this gives Y * = (θδN * /1-δ) α (25)

  α = W/P. Taking the derivative of log N with respect to log W gives (α-1) dlnN / dlnW = 1 -α (dlnE/dlnW) implies that the effort-wage elasticity is unity (the Solow condition), (27) implies the intuitive result that the wage elasticity of employment is minus one at the efficiency wage

  a i are unobserved time-invariant efficiency effects, and ε it denotes i.i.d. productivity shocks. As is clear from (

	Submitted Manuscript
	relative wage,
	F o
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	P e
	e
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Page 10 of 15 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Levine (p. 1103) remarks in passing that near-rational behaviour will result in the optimality condition being approximately verified by the data but does not proceed further.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UKSubmitted Manuscript

It is straightforward to demonstrate this. Without any loss of generality, let ω=(W/P c ). Now if θ=0,then π = [PN α ω αδ -P c ωN] = [PN α(1-δ) (ωN) αδ -P c (ωN)].From this, it is clear that π can be made arbitrarily large by making N large while keeping ωN (costs) constant. In other words, the optimum is at N=∞, W=0. Now let θ>0. Then π = [PN α (θ + ω δ ) α -P c ωN] ≥ [PN α θ α -P c ωN] and, as before, it is clear that profits can be expanded infinitely by raising employment, keeping the wage close to zero. Also see[START_REF] Akerlof | Labor contracts as partial gift exchange[END_REF].

This follows directly from the specification of effort as labour-augmenting in (2). It is nevertheless instructive to write down equations (5)-(9) since they are used in Section

Investigations byArellano and Bond indicate that the 2-step estimates are associated with spuriously small standard errors in finite samples but the UK study reports only the 2-step GMM estimates. In principle, therefore, the statistical rejection of α=γ that the UK study finds may be reversed using the one-step estimates. In practise, the absolute difference for the UK of α-γ = 0.65-0.39 is large enough that this is unlikely. Indeed, our results in Table2indicate that the size of this difference implies very large deviations from optimal wages and profits.


Joachim Wagner
email: wagner@uni-lueneburg.de

Are Nascent Entrepreneurs Jacks-of-all-trades? A Test of Lazear's Theory of Entrepreneurship with German Data*

Keywords: JEL classification: J23, R12 Entrepreneurship, Jack-of-all-trades Theory, Rare Events Logit, Germany

Are Nascent Entrepreneurs Jacks-of-all-trades? A Test of Lazear's Theory of Entrepreneurship with German Data

Introduction

In a recent paper that has the potential of becoming a pivotal element in the field Edward Lazear (2002) proposed the jack-ofall-trades theory of entrepreneurship. He uses a coherent model of the choice between self-employment and paid employment to show that having a background in a large number of different roles increases the probability of becoming an entrepreneur. The intuition behind this proposition is that entrepreneurs must have sufficient knowledge in a variety of areas to put together the many ingredients needed for survival and success in a business, while for paid employees it suffices and pays to be a specialist in the field demanded by the job taken. Lazear used a data set of Stanford alumni to test this prediction of his model and found it to hold -those with more varied experience have much higher probabilities of starting their own business.

Stanford alumni might not be representative for the millions of people facing the choice between self-employment and paid employment. This paper contributes to the entrepreneurship literature by empirically testing Lazear's jack-of-all-trades hypothesis using a large recent representative sample of the German population. It considerably extends and improves my earlier work on this topic reported in Wagner (2003) in three ways:

First, instead of using a ready-made data set that has been collected for different aims and, therefore, contains variables only that can at best be viewed as proxy variables for the concept central to Lazear's model -the number of professional Third, given that entrepreneurs tend to be a rare species (at least in Germany) application of the standard textbook logit or probit model is not appropriate when the decision to become an entrepreneur or not is modeled empirically. Therefore, a version of the logit model is used that takes care of the rare events nature of the decision to start one's own business.

The rest of the paper is organized as follows: Section 2 introduces the data used and presents descriptive statistics, section 3 discusses the results from the econometric investigation, and section 4 concludes.

Data and descriptive statistics

The data used in this paper are taken from a representative survey of the population aged 18 to 64 in 11 (out of 97) socalled planning regions in Germany that was conducted using computer assisted telephone interviewing by TNS EMNID, a leading opinion research institute, between June and August 2003. This survey is part of the research project Regional Entrepreneurship Germany, its determinants, and its consequences for regional development. 1 The questionnaire asked for socio-demographic characteristics (e.g., sex, age, employment status, education, fields of professional experience) and a number of items related to entrepreneurial activities (e. g., whether the interviewee is currently engaged in starting an own business). 2

The data set contains information on 12.000 people. 3 In the survey the interviewee was asked whether she/he is (alone or with others) actively involved in starting a new business that will (as a whole or in part) belong to her/him, and whether this business did not pay full time wages or salaries for more than three months to anybody (including the interviewee). Those who answered in the affirmative are considered to be nascent entrepreneurs. 4 To test Lazear's jack-of-all-trades hypothesis 1 For further information about the REM project see Bergmann et al. (2002). REM is closely related to GEM, the Global Entrepreneurship Monitor, a multi-country study that investigates the same topics at a national level (see Reynolds et al. 2000).

2 An English version of the questionnaire is not yet available; a German version is available from the author on request.

3 The data will be made available for public scientific use after the completion of the REM project. do not opt for a business of their own. 5

The variety of professional experience of an interviewee that is at the heart of Lazear's theory of entrepreneurship is measured by two variables:

-The survey includes a tailor-made question asking in how many different professional fields the interviewee has been active in the past, explaining that this does not mean the number of employers she/he worked for. The answer is included in the empirical investigation as the "number of fields of experience".

-The survey collects information about professional degrees completed after school, i.e. whether or not the interviewee successfully passed apprenticeship, managed to qualify formally as a master craftsperson, or received a degree from a polytech or university. The "number of professional degrees" (ranging from zero to three) is included as a variable in the empirical investigation.

5 As has been argued in the introduction, this approach instead one in ten 5 fields (so that 90 percent of all interviewees reported between 1 and 5 fields of experience), and 99 percent of all respondents mentioned up to 13 fields, the few remaining answered by reporting 15 (N=21), 18 (N=2), 20 (N=21), 30 (N=1), 43 (N=1), and 50 (N=2). Given that most of these numbers seem to be at best guesstimates, and that extreme values can have a large impact on the results from econometric investigation, a restricted sample was constructed limited to observations with 13 or less reported fields, and all computations were performed using this restricted sample, too.

[Table I near here]

From the upper panel of table I it can be seen that nascent entrepreneurs on average have one more field of experience and a 6

Note that contrary to both Lazear (2002) and Wagner (2003) nationality can not be included in the model used here because in the REM survey this information is not collected. From the descriptive evidence reported in table I, therefore, we have some hints in favor of Lazear's jack-of-all-trades hypothesis.

A test of the jack-of-all-trades hypothesis

In To check the robustness of these results the same model was estimated using a restricted sample were all observations are dropped that report a number of fields of experience larger than 13. From the results reported in column 2 of table II it can be seen that the big picture does not change.

Discussion of the results hitherto was limited to the statistical significance of the estimated coefficients and the direction of influence conducted by the variables. Information on the extent of this influence, or on the economic relevance, however, is even more important. Evidently, a variable that has no statistically significant impact can be ignored from an economic point of view, but the opposite is not true: A variable that is highly significant statistically might not matter at all economically -if the estimated probability for being a nascent entrepreneur increases by 0.00001 percentage points when an individual has experience in 5 instead of 2 fields the number of fields of experience can be ignored in the discussion of reasons for becoming a nascent entrepreneur irrespective of any high level of statistical significance indicated by the prob-value.

Unfortunately, the estimated coefficients from the rare events logit model can not easily be used for statements about the size of the ceteris paribus effect of a change on the value of an exogenous variable on the probability of being self-

8

To check for non-linear relationships an augmented model has been estimated that includes squared terms for age and number of fields of experience, too. The squared terms were never statistically significant at any conventional level. we consider a 40 years old male, and then compute the estimated probability for different combinations of the number of fields of experience and the number of professional degrees. 9 Results of this exercise are reported in table III.

[Table III

  has experience in -here a survey is used that includes a tailor-made question on this topic.Second, instead of comparing self-employed and paid who are in the process of starting their own business -and those who decide to continue working as paid employees. This should provide a much sharper test of Lazear's hypothesis because it makes sure that the reported number of fields of experience refers to a period that lies before the start of the own business.

  2003 which focuses on the extent of the difference in entrepreneurial activities between regions in

4

  This definition of a nascent entrepreneur is identical to the definition used in the multi-country GEM project mentioned in footnote 1; see Reynolds et al. 2000, p.9.

  are compared with paid employees who

  the size of this effect depends on both the value of the exogenous variable under consideration and on the values of all other variables in the model. A way to ease interpretation of the results is to compute the estimated probability of being a nascent entrepreneur for (hypothetical) individuals with different combinations of values of those exogenous variables that are at the center of interest. We follow this strategy: Based on the results reported in tableII

  The restricted sample is limited to persons with up to 13 reported fields of experience.Page 14 of 16Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK The estimates are based on the results reported in table II for a 40 years old male.2 The restricted sample is limited to persons with up to 13 fields of experience.

	Table I Descriptive statistics _________________________________________________________________________________________________ Nascent entrepreneurs Paid employees A: Unrestricted sample Mean Std. Dev. Mean Std. Dev. Sex (dummy; 1 = Male) 0.79 0.41 0.61 0.49 Age (years) 37.91 9.31 40.28 10.33 Number of fields of experience 4.26 4.73 3.27 2.61 Number of professional degrees 1.20 0.61 1.08 0.53 Number of cases 174 4808 B: Restricted sample 1 Sex (dummy; 1 = Male) 0.79 0.41 0.61 0.49 Age (years) 37.80 9.19 40.26 10.32 Number of fields of experience 3.58 2.09 3.13 2.06 Number of professional degrees 1.20 0.60 1.08 0.53 Number of cases 168 4766 _________________________________________________________________________________________________ Table III Estimated probability for being a nascent entrepreneur (percent) 1 _________________________________________________________________________________________________ Number of fields of experience A: Unrestricted sample 1 2 3 4 5 6 7 8 9 10 Number of professional degrees 0 2.4 2.6 2.8 3.0 3.2 3.4 3.7 4.0 4.4 4.7 1 3.4 3.7 3.9 4.3 4.6 4.9 5.3 5.6 6.1 6.5 2 4.8 5.2 5.5 6.0 6.4 6.9 7.5 8.0 8.5 9.2 3 6.7 7.3 7.8 8.3 9.1 9.6 10.3 11.1 11.8 12.7 B: Restricted sample 2 Number of professional degrees 0 2.3 2.5 2.8 3.0 3.3 3.6 3.9 4.3 4.6 5.1 1 3.3 3.6 3.9 4.3 4.7 5.1 5.5 6.0 6.5 7.0 2 4.7 5.1 5.6 6.0 6.5 7.1 7.8 8.5 9.0 10.0 1 Submitted Manuscript 3 6.6 7.2 7.9 8.5 9.2 10.0 11.0 11.8 12.6 13.8
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Page 16 of 16 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

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Research for this paper was done as part of the project Regional Entrepreneurship Monitor (REM) Germany financially supported by the German Research Foundation under grants number WA 610/2-1 and WA 610/2-2. This project is conducted jointly with Rolf Sternberg (University of Cologne, Germany) who is supported with grants number STE 628/71 and STE 628/7-2.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

All computations were done using the setx and relogitq ados that come with relogit; see fotnote 7.