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Ledesma and Mr. Alan Park for precious help. Correspondence Address: Faculdade de Economia Universidade de Coimbra, Av.Dias da Silva,165, 3004-512.
Are Living Standards converging in the EU? Empirical Evidence from Time Series Analysis. Elias Soukiazis*

Abstract

The propose of this paper is to test the convergence hypothesis using an alternative approach by examining directly the time series properties of the per capita income variable among the EU countries. This approach has been developed recently in the attempt to understand regional differentials in the living standards among different economies. This issue is extremely important for the EU after establishing the criteria of nominal convergence and going ahead with monetary union and the single currency. The important question to address here is whether the integration process in Europe has had a strong impact in reducing the differences in living standards (measured by real GDP per head) among the 15 member States of the EU, over the period 1960-1997. To answer this crucial question a different approach to convergence is applied using a time series analysis based on the concept of co-integration. The paper is organised as follows: the introduction briefly discusses the different approaches which are used to test the convergence hypothesis. Section 2 explains the alternative time series approach in the light of the stationarity and co-integration definitions which can be used to test for convergence. Section 3 describes the data and outlines the empirical evidence on the convergence of living standards among the EU countries over the period 1960-1997. The last section concludes, summarising the main findings.

Keywords: σ and β convergence, living standards, unit root and cointegration tests Acknowledgements: The author would like to thank Professor Tony Thirlwall for helpful discussions and encouragement during the preparation of this paper. The author is also very grateful to Dr. Miguel LeonLedesma and Mr. Alan Park for precious help. Correspondence Address: Faculdade de Economia Universidade de Coimbra, Av.Dias da Silva,165, 3004-512 Coimbra, Portugal. Email: [email protected]

* Assistant Professor at the University of Coimbra, Faculty of Economics, Portugal and visitor at the Department of Economics , Keynes College, University of Kent at Canterbury, U.K.

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1. Introduction

The explanation of regional disparities and whether there is a tendency for poor economies to grow faster than richer ones has become a central issue in the growth literature. Different theories and a variety of empirical models using different econometric techniques, have been used to examine the convergence phenomenon without reaching any common consensus on the forces which lead to convergence, on the speed of convergence or even on the existence of a convergence pattern. Most of the empirical analysis is focused on the so-called β convergence which predicts a negative relationship between the growth of per capita income over a certain period and the initial level of per capita income across different economies1. The negative coefficient of the initial per capita income variable is taken as evidence that poor economies are growing faster than richer ones, therefore, predicting convergence in the long run.. This simple equation is extended to include some other structural variables, such as human and physical capital, innovation activity, government expenditures, labour participation, agricultural share, population growth, trade and so on. The augmented equation is used to provide evidence of conditional convergence which is the contribution of “new growth theory”, or endogenous growth theory, to the convergence debate (Barro,1991). Cross-section data are mostly used to test the hypothesis of convergence in per capita income or output per worker across different countries or states or regions. The majority of the empirical studies provide evidence in favour of conditional convergence and they agree that the speed of convergence across countries or regions is slow, at about 2% per annum among the States in the USA and below 2% in Europe (Barro and Sala-i-Martin, 1992, Sala-iMartin,1996). However, there is a dispute among the empirical studies in relation to the set of the conditional variables which plausibly contribute to the convergence process. The main difficulty is to isolate the individual effects of the conditional variables and to avoid statistical problems related to multicolinearity, endogeneity, omitted variable bias, simultaneity, misspecification and error measurement problems, all of which can seriously affect the robustness of the convergence coefficient.2 The cross section results of the conditional convergence approach also suffer from stability problems and sample selection bias. It has The concept of β convergence was first introduced by Barro and Sala-i-Martin(1991) to distinguish it from σ convergence which measures the dispersion of per capita income using the standard deviation or coefficient of variation. 2 Temple (1999) provides a detailed review on the convergence issue, discussing the problems of measuring convergence, the econometric defects involved in the cross-section analysis and the difficulties of choosing the set of structural variables which robustly affect the growth process. 1

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been shown that the speed of convergence is not stable over time (Dewhurst and Gaitan, 1995) and that some groups of countries or regions are more likely to converge but others not, depending on their degree of homogeneity. This is the so-called convergence club hypothesis which identifies spatial or partial convergence (Chatterji, 1992). The convergence evidence of the single equation approach is often contrasted to the so-called σ convergence which shows if the dispersion of per capita income among different economies has declined through time. The σ convergence approach is useful in the sense that it allows to observe the convergence pattern over time and, therefore, to identify periods of convergence or divergence. Empirical studies using the σ convergence approach, based on the coefficient of variation, seem to agree that the differences in per capita income levels between the industrial countries have decreased significantly in the 1960s and early 1970s, remained constant(or increased) in the late 1970s and early 1980s, and increased slightly in the 1990s3. The main difference of the σ convergence approach is that it shows the path of the dispersion of the level of per capita income, as opposed to β convergence approach which simply indicates whether (on average) poor countries are growing faster than rich ones. In this context, β convergence is a necessary but not a sufficient condition for σ convergence (Sala-i-Martin, 1996). In other words, the fact that poor economies are growing faster than rich countries does not necessarily imply that they converge also in their absolute levels. The convergence of the absolute levels of per capita income between countries depends on the magnitude of the initial absolute gap and how fast the poorer economies grow relatively to the richer ones. The higher the initial absolute gap of per capita income between the poor and rich economies the faster the poor economies must grow in relation to the wealthier ones in order to decrease their initial distance. This distinction between the absolute levels and growth rates in per capita income is very relevant in order to be able to interpret correctly the empirical findings in the convergence literature. The evidence of a slow β conditional convergence and the lack of σ convergence since the 1980s indicates that poor countries have not grown sufficiently faster than the richer ones in order to be able to reduce their differences in the level of per capita income. From this comparison it is shown that the use of the two approaches is useful and complementary if one wishes to have a complete picture of the convergence phenomenon. However, the σ convergence approach suffers also from some defects. The coefficient of variation which is used to measure σ convergence is very sensitive to some 3

Parente and Prescott(1993) found that the standard deviation of log per capita incomes has not changed significantly over the last century for 29 countries for which σ convergence is tested.

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outliers of the selected sample and the results can be distorted. If one joins one or two poor economies to the sample of rich economies then the tendency is for the dispersion of per capita income to increase implying divergence. If the poor countries are excluded from the sample then convergence might be the plausible outcome. The unsatisfactory and conflicting results given by the β or σ convergence approaches has led some researchers to use alternative definitions and different approaches to explain the issue of convergence. Recently, a time series approach has been developed as an alternative to cross-section models trying to give a more satisfactory answer to the convergence problem. This methodology analyses the stochastic behaviour of the differences in per capita income among countries and is explained in the next section. 2. A time series approach to convergence.

A number of studies in the empirical literature of the convergence issue use time series rather than cross-section analysis to find if the levels of per capita income of different economies tend to equalise over time. Bernard and Durlauf (1995,1996) provide an innovative method to study the stochastic behaviour of per capita output series across countries which relies on the notions of unit roots and cointegration. According to their definition, country i and j converge if the long-term forecasts of per capita output (y) for both countries are equal at a fixed time t, so that limk→∞ E(yi,t+k-yj,t+kIt)=0 , where It is the set of information available at period t, and k is the forecasting horizon. If y is the log of per capita output then the series of the difference (yi,t+k – yj,t+k) have to be stationary4(with zero mean) in order to satisfy the convergence hypothesis. Stationarity implies that random shocks have only transitory and not permanent effects on the series. A stronger notion of convergence between countries i and j requires that their outputs per head are cointegrated5 with cointegrating vector [1,-1]. From an economic point of view, cointegration between two series on per capita income implies a long run equilibrium relationship between these variables and that they cannot move independently of each other. On the other hand, countries i and j contain a common trend if the long-term forecasts of per capita output are proportional (not equal) at a fixed time t, so that limk→∞E(yi,t+k-αyj,t+kIt)=0. In other words,

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Stationarity implies that the mean, variance and covariances of the series are invariant with respect to time. Two series are cointegrated when they are both stationary of the same order k and a linear combination between them is stationary of order n