Jesus Crespo Cuaresma
email: jesus.crespo-cuaresma@univie.ac.at

Maria Antoinette Silgoner
email: maria.silgoner@oenb.at

Jesús Crespo-Cuaresma

Doris Ritzberger-Grünwald
email: doris.ritzberger-gruenwald@oenb.at

Economics, F43 -Economic Growth of Open Economies < F4 -Macroeconomic Aspects of International Trade and Finance < F -International Economics, C23 -Models with Panel Data < C2 -Econometric Methods: Single Equation Models < C -Mathematical and Quantitative Methods

Keywords: convergence, economic growth, European integration, threshold panel regression convergence, economic growth, European Union, threshold panel data regression JEL codes: F15, F43, C23

published or not. The documents may come

Growth, convergence and EU membership

Introduction

For the last 50 years there has been widespread discussion about the economic consequences of European integration. The basic questions are: Is economic integration growth enhancing? Are the rich getting richer and the poor getting poorer, or will the income levels of the EC/EU member countries converge as a consequence of integration? Furthermore, which countries will profit most from intensified trade among the members? The discussion on the growth effects of EU membership has gained momentum since the last enlargment round on May 1, 2004 when ten countries became new member states of the European Union, expanding the EU's population by 20%.

The theoretical literature on economic growth has gone through several phases, and the answers to the above questions depend on the specification of the respective growth model.

From the late 1950s to the mid-1980s the simple Solow-Swan exogenous growth model dominated the literature (Solow, 1956). According to the neoclassical theory, the economy converges towards a steady state due to diminishing returns to investment in physical capital. Assuming a constant population, the long-run growth rate is solely determined by the rate of technological change, which is assumed to be exogenous. As the growth rate is therefore independent of any economic behavior, economic policy changes will only have a temporary effect on economic activity.

The same is true for economic integration (in the sense of an increase of the market size). Technological change is considered a public good common to all countries, so that they all share the same long-run growth rate determined by technological progress only. Therefore the integrated economy will expand along this unchanged steady state growth path in the long run, and the reallocation of resources will only temporarily have an influence on the growth rate. Hence according to the neoclassical view of growth, European integration should not have a lasting effect on growth rates. However the income levels should converge perfectly.

In the mid-1980s the so-called endogenous growth theory revolutionized the literature on economic growth (Romer, 1990). Technology that was formerly considered a public good and exogenous now became endogenous and subject to decision-making processes at individual firms. According to this concept, enterprises have an incentive to invest in research, as the development of new technologies assures them of the possession of temporary monopoly power. But the absorption of monopoly rents is limited, as knowl-F o r P e e r R e v i e w edge is only partially excludable. Patent protection is limited in time, and inventions can be used as input to further research and new technological innovations. These knowledge spillovers prevent the firms from collecting the full monopoly rent for their new inventions.

The aspect of the new growth theory according to which technological progress depends on the research activities of individual firms which seek to collect monopoly rents opens a new view on the issue of economic growth in an integrated region: now an increased scale of the economy will have a lasting positive effect on growth. On the one hand, knowledge spillovers imply increasing returns to scale to capital accumulation. On the other hand, the monopoly rent increases with the number of consumers while the costs for research and development are independent of the size of the economy. The prospect of higher profits increases the incentive for further research and hence spurs economic growth. These two factors together imply that the long-run growth rate increases with the size of the economy. [START_REF] Andrews | Optimal tests when a nuisance parameter is present only under the alternative[END_REF] To sum up, the consequences of European integration are fundamentally different within the framework of endogenous growth. The more countries join the Economic Union and hence the larger the scale of the integrated economy is, the higher the incentive for R&D is and, accordingly, the higher the growth rate is. Enhanced growth is now not only a transitory, but a permanent phenomenon from which all countries profit in the long run.

In this sense, testing for a growth effect due to European integration could be seen as a strategy to prove the superiority of one of these two theoretical frameworks. There are, however, possibilities to allow for the existence of integration-driven growth effects within the neoclassical paradigm of exogenous growth, just by modelling the process of technological growth in a more complex manner (for example, by letting the growth rate of technology be a function of the overall size of the integrated unit). Therefore, evidence for integration related growth effects could thus be seen as a motivation for a more complex modelling of the technological progress variable.

Most empirical papers on economic growth aim at detecting the main determinants of long-run growth without referring explicitly to regional integration or deal with convergence and divergence across European regions (see

F o r P e e r R e v i e w
for example Button and Pentecost, 1995, Sala-i-Martin, 1996, Quah, 1996 or Magrini, 1996). The first papers dealing with the question of a possible growth bonus associated with European integration were all cross-country studies. Basically, they compare EU members with other countries that have not joined the European Union, mostly countries at a similar stage of development. The basic question is whether there exists a global growth benefit from being a EU member. Most of the studies do not find any such growth bonus (see e.g. De Melo et al., 1992 or Landau, 1995).

However, panel data regression techniques opened up a new way to deal with the question of possible growth benefits associated with EU membership. Focusing exclusively on the current EU member states the basic question then can be whether in retrospect they profited from regional integration.

The line of research we will follow is based on the estimation of growth regressions using panel data methods. The superiority of panel data methods over cross-country growth regressions has been highlighted often in the empirical literature (see e.g. Islam, 1995). The main advantage of pooled estimation is the explicit modelling of country-specific effects, removing thus part of the problem caused by the unobservability of initial levels of technical efficiency.

There are two studies which ask questions similar to the ones discussed in our paper, although they look at a wider set of countries and do not exclusively focus on EU members. Vanhoudt (1999) tests the validity of the neoclassical implication that regional integration has no impact on long-term growth against the alternative model based on endogenous growth theory. He carries out panel data regressions on 23 OECD countries to check whether EU membership had a positive impact on growth compared to developed countries which have not joined the European Union. He does not find evidence of a significant long-run growth bonus associated either with EU membership or with membership length. Also, the results do not support the hypothesis of a scale effect on growth. The author concludes that the neoclassical hypothesis cannot be rejected by the data. Henrekson et al. (1997), who focus on EC as well as on EFTA member countries, find the opposite result: EC/EFTA membership may increase growth rates significantly, by around 0.6 to 0.8 percentage point per year. However, apparently it does not matter whether a country is an EC or an EFTA member. Their results support the hypothesis that regional integra-4 F o r P e e r R e v i e w tion in Europe can have significant growth effects and suggest that further regional integration may be growth enhancing in the long run. However, the results of the paper are not completely robust with respect to changes in the model specification.

Both these studies and the present paper deal with the question of whether European integration had a positive impact on long-term growth in the member countries. Our study, however, deviates from the other two in that it exclusively focuses on EU member states2 and in that it deals with the issue of convergence within the integrated European economy. Focussing on the 15 EU member states as of January 2004 our questions are: Have per capita income levels in European countries converged towards each other since the 1960s? And if EU membership had a favorable impact on growth in these countries, can we detect subsets of countries that profited more than average from EU membership? Can we conclude from these asymmetric gains in growth that convergence was also a consequence of intensified economic involvement due to European integration?

The paper is organized as follows. Section 2 gives a short overview of the different concepts of convergence and presents some first results. In section 3 we introduce the specific econometric form of our growth model and its extensions and report the empirical results. Section 4 concludes and makes propositions for further research. Details about the data and the econometric specification can be found in the appendix.

Convergence and growth in the EU -concepts and first results

The term β-convergence was coined by Barro and Sala-i-Martin (1992) and refers to the negative correlation between initial levels of real GDP per capita and its average yearly growth rate either after conditioning for certain control variables (conditional β-convergence) or without conditioning (unconditional β-convergence). For a complete survey on the empirical literature dealing with evidence on β-convergence, see e.g. Durlauf and Quah (1998). [START_REF] Badinger | Growth effects of economic integration -The case of the EU member states[END_REF] To-

F o r P e e r R e v i e w
gether with the concept of β-convergence, Barro and Sala-i-Martin (1992) introduce the complementary concept of σ-convergence, which refers to the decrease of the dispersion of real GDP per capita across economic units through time. It should be noted that β-convergence is a necessary but not sufficient condition for σ-convergence.

Figure 1 shows a scatter plot aimed at checking for (unconditional) βconvergence in the European Union for the period 1960-98: on the x axis, the initial (log) level of real GDP per capita in 1960 is represented, while the y axis shows the average yearly growth of real GDP per capita in the period 1960-98. A visual inspection points at a negative relationship between both variables. This first indication of convergence is confirmed by dividing the data for the EU-15 countries into four subperiods (1961-70, 1971-80, 1981-90, 1991-98) [START_REF] Baltagi | Econometric analysis of panel data[END_REF] and estimating the β parameter in the error-components model

[ln(y T t,i ) -ln(y 0t,i )]/n t = α + βln(y 0t,i ) + u t,i , (1)
where y T t,i refers to the real GDP per capita in the last year of period t (t = 1, 2, 3, 4 stands for each of the subperiods described above) for country i, y 0t,i refers to the value of real GDP per capita in the initial year of period t and n t is the number of years in period t. Equation (1) has been estimated based on different assumptions for the error term, and the results are presented in Table 1, together with the test statistic for equality of β parameters across subperiods. [START_REF] Barro | Economic growth in a cross section of countries[END_REF] The first column shows the result for the assumption that the error term is independent of the cross-sectional units (countries) and iid normal (that is, the panel is estimated as if it were a cross-country regression).

The second column shows the results for the assumption of fixed country effects, that is,

u t,i = µ i + t,i ,
where µ i is a country-specific constant and t is white noise. Finally, the third column shows the estimated β under the assumption of fixed country and time effects, that is,

u t,i = µ i + λ t + t,i ,
where µ i and t are defined as above, and λ t is an exclusively time-dependent constant effect. All specifications reported in Table 1 point at the existence of very significant unconditional β-convergence across EU members for the period 1960-98, and the null of equality of convergence parameters across subperiods cannot be rejected as long as country fixed effects are included in the regression. [START_REF] Barro | Inflation and economic growth[END_REF] Figure 2 shows the evolution of the cross-country coefficient of variation of per capita GDP for the period 1960-98 for the 15 EU countries in our analysis, as well as for subsets of countries grouped by cronology of EU entry: EU-6 (Germany, France, Italy, Belgium Netherlands and Luxembourg), EU-10 (EU-6 plus United Kingdom, Ireland, Denmark and Greece) and EU-12 (EU-10 plus Spain and Portugal). By visual inspection the trend is clearly decreasing for the full sample and the subgroups EU-10 and EU-12, indicating σ-convergence. Whether the standard deviation in the final period is significantly different from that of the first period can be tested using the T 2 test statistic developed by Carree and Klomp (1997), [START_REF] Barro | Determinants of economic growth: A crosscountry empirical study[END_REF] which is χ 2 (1) distributed under the null hypothesis of no σ-convergence. The value of T 2 for the EU-15 data is 4.46, which indicates rejection of the null of no σ-convergence at a 5% significance level. The value for EU-12 is 3.80, also significant at a 10% level. Two clear regimes can be identified in the dynamics of the dispersion of GDP per capita for the EU-6 (formed by countries which tend to be above EU-15 average in terms of GDP per capita) and, to a lesser extent, in the EU-10 group. The dispersion of income across EU-6 countries had a negative trend until the beginning of the 1980s, which reversed in the late 1980s and 1990s. The difference between the dispersion in 1960 and in 1998 has been positive, although it is not significant at any reasonable significance level, with a T 2 test statistic of 0.05. The results for EU-10 are an intermediate case, with a decrease in dispersion of income between 1960 and 1998 which [START_REF] Barro | Inflation and economic growth[END_REF] Notice that while the common intercept specification hypothesizes convergence to a common steady state, the use of country fixed effects assumes potentially different steady states. This issue will be dealt with in more depth below. [START_REF] Barro | Determinants of economic growth: A crosscountry empirical study[END_REF] The T 2 test statistic is defined as

T 2 = (N -2.5) ln 1 + σ2 0 -σ2 T 4(σ 2 0 σ2 T -σ2 0T )
,

where N refers to the number of countries, σ2 0 and σ2 T are the cross-country variances of real GDP per capita in the initial period and the final period, respectively, and σ0T is the covariance between initial and final real GDP per capita.

7

F o r P e e r R e v i e w appears insignificant using the T 2 test, with a test statistic of 1.93. [START_REF] Barro | International data on educational attainment: updates and implications[END_REF] 3 Growth and EU membership

The basic model and some extensions

In order to study explicitly the determinants of long-term growth in Europe in the last four decades, equation (1) will be extended by including an augmented set of explanatory variables. The obvious candidates to form part of the group are those variables which are explicitly implied by economic theory and which have been used in virtually every empirical study on economic growth: the initial (log) level of per capita GDP -evaluated in our case at the first year of each subperiod -, the investment share -subperiod averageand some proxy for human capital -average years of education of population over 25, evaluated at the first year of the subperiod.

Together with these basic variables others which are considered to be relevant to economic growth have been included in the econometric specification. The specification in which all the estimated models presented in Table 2 are nested is:

[ln(y T t,i ) -ln(y 0t,i )]/n t = β 1 ln(y 0t,i ) + β 2 ln(INV t,i ) + β 3 ED t,i + β 4 INF t,i + +β 5 GOV t,i + β 6 OP t,i + β 7 Y EA t,i + u t,i , (2)
where ln(y 0t,i ) is the (log) initial GDP per capita of country i in subperiod t, ln(INV t,i ) is the (log) investment share, ED t,i refers to the years of education, INF t,i is the subperiod-average inflation rate, GOV t,i is government consumption over GDP, OP t,i is openness of the economy defined as trade over GDP, 9 and Y EA t,i is the average length of EU membership (in years) [START_REF] Barro | International data on educational attainment: updates and implications[END_REF] Notice that the remarkable change in trend experienced since the end of the seventies could represent a structural break in the process underlying the dynamics of σ-convergence. We test this hypothesis by implementing the test procedure proposed by Hansen (1997) on the first differences of the variation coefficient for EU-15, which were assumed to be represented by an AR(1) process. The results give evidence for a break in the parameters of the data generating process around 1978, notwithstanding the fact that the results of the test should be interpreted with care, as the data is actually generated out of the crosssection variability of the sample. This would give room for further investigation, that goes beyond the scope of this paper. [START_REF] Barro | Convergence[END_REF] Due to the multidimensional nature of the concept of trade, there are many different measures for openness, most of which are found to be almost uncorrelated (see e.g. Pritchett, 1996). The openness index developed in Sachs and Warner (1995), which has been widely used in the empirical literature on economic growth, would be of little use in this study, as the variable they propose is a dummy that would take a value of one for practically the whole sample used here. for country i in subperiod t. [START_REF] Bernard | Convergence of international output movements[END_REF] The error term u t,i is assumed to be composed by a constant country-specific effect and a common constant time effect, although in the estimation the latter will only be included if found significant.

The specification given by ( 2) can be seen as a log-linearization in a neighborhood of the steady state of the Solow model augmented with human capital à la Hall and Jones (1999), as derived in Mankiw et al. (1992). They suggest the use of the logarithm in the investment share and the level of school enrollment (the human capital function put forward by Hall and Jones, 1999, is exponential on the education variable) as additional variables to initial GDP. The rest of the controls could thus be seen as explaining the growth rate of technological progress (assumed constant in the basic Solow specification). [START_REF] Bernard | Interpreting tests of the convergence hypothesis[END_REF] Table 2 shows the results of the estimation of the different specifications of our growth model.

In a first step, growth is regressed on initial GDP, the investment share and the years of education. All coefficients in the first column have the expected signs. Growth depends negatively on initial GDP, indicating βconvergence. The investment share enters positively (see e.g. Barro, 1991, Levine and Renelt, 1992), although not significant at the 10% significance level. Turning to education, most authors find that the overall level of education is growth enhancing (see e.g. Barro, 1991). [START_REF] Bernard | Productivity across industries and countries: Time series theory and evidence[END_REF] Our positive and significant coefficient for the average years of education seems to support this result.

In a second step, the inflation rate, government consumption over GDP and openness of the economy are added to the model as explanatory variables. The inclusion of these three variables does not change the signs of the first three factors, as can be seen in the second column. Inflation enters [START_REF] Bernard | Convergence of international output movements[END_REF] For Germany we use data for West Germany until 1991, and for the unified Germany from 1991 onwards. Initially, an additional dummy variable was included in order to account for the German unification, but it appeared insignificant in all specifications. For further details on the data, see the appendix.

11 Empirical studies dealing with a more heterogeneous set of countries tend to include population growth on the right hand side of the growth equation, as implied by the original Solow model (see e.g. Mankiw et al., 1992). In our case, the variable appeared insignificant in every specification in which it was included and was therefore not added to final specification. The same occurred when a socio-demographic variable like female participation in the labor market was used. A possible explanation of the lack of significance of labor participation would be the high correlation between this variable and initial GDP. [START_REF] Bernard | Productivity across industries and countries: Time series theory and evidence[END_REF] There is, however, some indication that primary education has a negative impact on growth, see e.g. Barro (1997). the equation with a negative sign, indicating the growth-hampering effect of high increases in the price level (for a detailed study on this relationship, see Barro, 1995). The minus sign of the coefficient for the government consumption ratio implies a negative relationship between government expenditures and growth. Other empirical studies, e.g. Barro (1991) and Barro (1997) also found this result. The intuition is that government spending has only a temporary influence on growth, while in the long run the growth-hampering impact of high debt levels as a consequence of excessive government spending as well as possible allocative inefficiencies predominate. In our case, however, the coefficient is not significant (a result also found by Levine and Renelt, 1992). Finally the coefficient for the openness of the economy is significant and shows the expected positive sign, supporting the view that trade stimulates growth. This result is also found by Harrison (1995), Sachs and Warner (1995).

In the final step, the model is modified by inclusion of the subperiodaverage number of years since a country's accession to the European Union. The choice of this specification of the membership variable aims at reflecting the potentially time-varying nature of the growth effect of integration and it fits to the long-term orientation of EU membership. It is also aimed at modelling the fact that those countries that have been EU members for a longer time will have adapted their institutional setting in order to be grasp more benefits of the enlarged economic area. Notice that, having controlled already for openness and initial GDP per capita, the EU membership variable will reflect growth effects of regional integration different from those directly related to trade and pure convergence à la Solow. [START_REF] Button | Testing for convergence of the EU regional economies[END_REF] The positive and significant coefficient in column 3 indicates that the longer a country has been a member of the EU, the more it profits from membership. The inclusion of this new variable leaves the signs of the other coefficients unchanged. The coefficient for education is still positive, but it is now significant at the 5% level. This extended model explains approximately 78% of the variation in growth.

If the results are to be interpreted under the light of the parametrization in Mankiw et al. (1992), the point estimate of the implied factor share of physical capital (assuming a Cobb-Douglas function with labour augmenting [START_REF] Button | Testing for convergence of the EU regional economies[END_REF] The fact that our openness variable is defined as trade over GDP implies that traderelated technology absorption is already partly captured by the positive coefficient for OP t,i . This is expected to actually reduce the size of our coefficient for the impact of the EU membership variable and reinforces the importance of technological spillovers as a driving force for growth. In order to ensure the validity of our results several robustness checks were carried out. First, the model is also estimated without government consumption, as the coefficient proved insignificant in models 2 and 3. The other coefficients remain practically unchanged, some of them becoming even more significant. This strengthens the robustness of our previous results.

Another source of concern in terms of adequacy of the estimation method could be the potential endogeneity of right-hand side regressors. The usual suspects would be the investment share, education attainment and openness, which have sometimes been claimed to depend upon the growth rate of GDP per capita. In order to account for this possibility, the specification in (2) was reestimated using instrumental variables. The results of the Sargan test for validity of instruments supports the use of population growth, government consumption and the initial sub-period levels of investment and openness as instruments for the investment share (the Sargan test statistic takes a value of 0.95, and therefore cannot reject that these are valid instruments at any reasonable significance level). The Durbin-Wu-Hausman test cannot reject the null hypothesis of no endogeneity for the regressors considered, validating thereby the use of OLS as an estimation method (the fitted values of the investment share from the first stage appear highly insignificant when added to the final specification, with a t-statistic of -0.21) .

The effect represented by the coefficient of the variable Y EA t,i affects only countries that have been members of the EU for at least one year in a given subperiod. It could be the case, however, that a larger regionally integrated space has an effect also on the growth rates of countries that do not form part of it yet. In order to check for this possibility and to shed a light on whether membership is actually required for gaining growth benefits from regional integration, the model was reestimated by replacing Y EA t,i with a scale variable common to all countries but variable in time, which captures the size of the regionally integrated unit. We used three different specifications of the scale variable (aggregate population, aggregate GDP and aggregate labor force), and the coefficient always appeared positive, but insignificant. Therefore, the growth benefits associated with regional integration seem to be due to formal participation in the union.

Another objection to our conclusion could be that it is not EU member- ship itself that enhances growth, but that the accompanying stability measures for nominal macroeconomic variables had a positive impact on growth performance. Partly this was already accounted for by including the inflation rate as an explanatory variable. To check in addition for the impact of a potential decrease in the exchange rate volatility caused by EU membership, the standard deviation of the exchange rate against the US dollar for each country was included as an additional independent variable. However, its coefficient appeared insignificant in all specifications. This indicates that exchange rate policy does not explain the existence of a growth bonus associated with EU membership.

We tried several other specifications in order to capture potential decreasing returns to EU membership, however models with the log or square root of Y EA t,i did not improve upon the model with a linear Y EA t,i variable. Including a squared term of Y EA t,i improves the estimation in terms of adjusted R 2 and renders a (10%) significant negative parameter for the quadratic term. This model is presented in column 5. Notice that the size of the parameter estimates imply that the quantitative effect is relatively small and tends to matter only for countries after very long periods of membership.

To sum up, our model so far explains a considerable part of the variation in growth, and the results strongly support the hypothesis of (conditional) β-convergence: poorer countries have caught up with the richer ones since the 1960s, and the rate of convergence is found to be approximately 4% and 6%, depending on the specification used. [START_REF] Carree | Testing the convergence hypothesis: A comment[END_REF] This rate of convergence appears significantly higher than convergence rates reported in cross-country studies due to the use of fixed country effects, and should thus be interpreted as the common convergence rate to country-specific steady states. Furthermore, the coefficient estimates support the hypothesis of a positive impact of investment, education and openness on growth, as well as a negative impact of high inflation rates. Finally the results not only point at a growth-enhancing effect of EU membership, but they also show that this effect gained importance over the duration of membership, with some evidence of decreasing returns to EU membership. [START_REF] Carree | Testing the convergence hypothesis: A comment[END_REF] The rate of convergence, λ, has been computed using nonlinear least squares on each specification, replacing the coefficient corresponding to initial GDP per capita by the term -[1-exp(-λT )]/T , where T is the subperiod length. This expression for λ results from the log linearization around the steady state in the Solow model as in Mankiw et al. (1992). The smallest estimate of λ is obtained in the simplest model (including only investment and education variables) and equals 0.04, with a standard error of 0.007. The estimate for the model including the Y EA t,i variable equals 0.06, with standard error 0.015.

Who profits most from EU membership?

One interesting extension to the basic models is to look in more detail at the finding that EU membership is growth enhancing and furthermore becomes even more so the longer a country belongs to the confederation. A particularly interesting question is whether a subgroup of countries profited more from EU membership than other countries. The idea is to divide the sample of countries into subsets with respect to one of the other variables and to investigate whether the coefficient for the years of membership differs significantly across subgroups. The evidence of decreasing growth returns to EU membership reported above could actually be masking different effects across countries, and could arise from the variation in timing of EU entry.

One basic way to do that would be to split the sample according to a priori defined rules. For example one could define poor, medium and rich countries by setting the borderline income levels. The threshold panel data technique, however, offers a more neutral approach. It allows to test whether such subgroups can be found at all and how many subsets are appropriate. Furthermore, it estimates explicitly the borderline income levels. The main advantage of this approach is that it avoids ad hoc definitions of subgroups, but tests the hypothesis of the existence of subsets against the alternative of no division of the sample.

In our extension of the basic model we test whether countries with a lower initial per capita income level profited more or less from EU membership than more developed countries. If subsamples according to initial income levels can be identified and the coefficient for the years of EU membership is significantly higher for initially poorer countries, this would be an indication of increased economic convergence as a consequence of European integration. If, however, we get the opposite result, this would indicate that the initially richer countries are also the ones which profit most from intensified economic involvement.

Table 3 gives the results of the threshold estimation, and Table 4 presents the parameter estimates of the threshold model, where the nonlinear effect has been built upon the Y EA t,i variable. For the details concerning the threshold panel data technique, see the appendix. The estimation procedure identifies exactly one threshold at a level of (log) initial GDP per capita equal to 9.8 (approximately, USD 18,000). A 95% confidence interval around the threshold estimate computed using the empirical likelihood function is [9.79, 9.93]. The test for linearity rejects the null of no threshold effect at a 5% significance level, and the null of one threshold cannot be rejected when Looking at the original data set, we see that at the beginning of our sample, that is in 1960, all countries had an initial income level below the threshold. In 1970 Denmark and Sweden had broken through the threshold. Ten years later, six more countries had followed and only the incomes of Greece, Ireland, Italy, Portugal, Spain and the United Kingdom remained below the threshold. In 1990, finally, the income levels in Italy and the UK exceeded the threshold income level, so that the subgroup of less developed countries was now limited to the classical catching-up countries Greece, Ireland, Portugal and Spain. Towards the very end of our data set, the income level of Ireland, which recently experienced two-digit growth rates, exceeded the threshold level. The next step is to divide the sample in each period according to this threshold and rerun the panel regressions. The results are shown in Table 4, where we now have a separate coefficient for the length of EU membership for each subgroup. The coefficient for the years of EU membership is positive and significant for both subgroups. Furthermore we find that the coefficient differs significantly across groups and is significantly higher for the countries with lower initial income levels. All the other coefficients show the expected signs. The new model, which splits the countries into two subgroups according to their initial income levels, explains around 83% of the variation in growth. [START_REF] Melo | L'integration regionale hier et aujourd'hui[END_REF] A similar type of effect of initial GDP per capita levels on the parameter attached to the EU membership variable could have been attained by including an interaction term between initial GDP per capita and the Y EA t,i variable in the specification given by (2). If the specification with an interaction term is estimated, the coefficient of the product of Y EA t,i with the initial GDP per capita variable appears significant and negative (the estimate equals -0.07, with a robust standard error of 0.03), indicating that countries with a lower level of development (in terms of GDP per capita) benefitted from higher growth rates due to EU membership. It should be pointed out that the model with an interaction term assumes that the coefficient of Y EA t,i decreases linearly with the level of initial GDP per capita of the country, while the threshold model assumes the existence of two coefficients for Y EA t,i , depending on the level of development of the country. [START_REF] Melo | L'integration regionale hier et aujourd'hui[END_REF] To check for robustness the model was reestimated using Switzerland as an external control country. The coefficients remained similar in terms of sign, range and significance. The goodness of fit, furthermore, improved considerably. The results are not reported in the tables and are available upon request from the authors. Although qualitatively the conclusions of both models are similar, the goodness of fit (as measured by the adjusted R 2 ) of the model with a threshold effect is relatively better than that of the model with an interaction (77% against 83% of the variation of growth rates are explained by, respectively, the model with an interaction term and the model with a threshold effect).

We also checked the residuals of the final model for normality using the Jarque-Bera (JB) test. The JB test statistic, χ 2 distributed with two degrees of freedom under the null hypothesis of Gaussian distribution of the residuals, takes a value of 15.69, and therefore rejects the null hypothesis of normally distributed residuals at any reasonable significance level. The lack of normality seems to be caused by a single observation, corresponding to Ireland during the last subperiod of the sample, for which our model strongly underestimates the growth rate of GDP per capita. Including a dummy for this single observation does not change our results qualitatively, and improves enormously the fit of the model. The JB test cannot reject now normality at any sensible significance level. The estimates of this model are presented in column 4B in Table 4. The estimate of the parameter on Y EA t,i for the lower regime of countries is obviously smaller than before, as we have dummied out an observation of extreme positive growth performance belonging to that regime, but remains significantly higher than the coefficient for the higher regime.

Hence while we find that, ceteris paribus, countries with a higher level of development grew faster the longer they were member of the EU, this effect is even more pronounced when it comes to the subgroup of less advanced countries. [START_REF] Durlauf | The new empirics of economic growth[END_REF] This finding can be interpreted as another indication for a catching-up process of poorer towards richer countries in Europe in the sense that with two countries entering the EU at the same point in time the growth bonus is larger for the less advanced country. [START_REF] Ederveen | Fertile soil for Structural Funds? A panel data analysis of the conditional effectiveness of European cohesion policy[END_REF] Not only do our results show that countries with lower initial incomes grew faster than the more advanced countries (β-convergence), [START_REF]Allocation of 2000 EU operating expenditure by member states[END_REF] the estimates also imply that [START_REF] Durlauf | The new empirics of economic growth[END_REF] The exercise was repeated using the relative level of GDP per capita with respect to the average of current member states as a threshold variable. However, the test for linearity could not reject the null of linearity at any reasonable significance level. This suggests that it is the absolute level of development of the country that determines the asymmetric effect of EU membership on long term growth. [START_REF] Ederveen | Fertile soil for Structural Funds? A panel data analysis of the conditional effectiveness of European cohesion policy[END_REF] This, however, does not imply that this growth bonus alone has actually led to absolute convergence of the EU member states. The different entry dates and the cumulative nature of the growth bonus has lead to several more advanced economies profiting relatively more from integration. [START_REF]Allocation of 2000 EU operating expenditure by member states[END_REF] An F-test for equality of β-convergence parameters across time results in an insignificant test statistic of 0.55, backing up the results presented for the case of unconditional 15 F o r P e e r R e v i e w countries that exhibit per capita income levels below the threshold profit more from long-term EU membership than richer countries.

A theoretically sound interpretation of the results would be that it is the relatively less developed countries that profit most from access to the broader technological framework offered by the regionally integrated unit. The variable referring to the duration of EU membership would then be interpreted as one of the variables explaining technological progress in a theoretical framework such as in Mankiw et al. (1992).

Conclusions and prospects for further research

The empirical study performed in this paper shows that EU membership has had a positive and asymmetric effect on long-term economic growth. As the model specification uses openness as a control variable, the growth effect picked up by the regional integration variable differs from that resulting from intensified trade and would relate to the improvements in the transmission of technological knowledge among the EU member states. The results would imply that it is the relatively less developed countries that profit most from access to the broader technological framework offered by the regionally integrated unit. Given that the estimates of the effect of EU membership are retrieved after conditioning upon the initial levels of GDP per capita, this effect acts on top of the usual convergence dynamics implied by neoclassical growth models.

It could be argued that technology diffusion is not the only factor explaining the growth bonus associated with EU membership. One argument that may as well be used to interpret the results relies upon the assumption that financial help from the EU to relatively poorer members actually does have an effect on long-term growth. In fact the EU budget generated major net financial transfers to the four cohesion countries -Greece, Portugal, Ireland and Spain. [START_REF] Fölster | Growth effects of government expenditure and taxation in rich countries[END_REF] In 2000, these net transfers accounted for 3.6% of Greek GNP, 1.9% of Portuguese GNP, 1.8% of Irish GNP and 0.9% of Spanish GNP. To a lesser extent, Finland, Denmark and Italy also showed positive net balances (see European Commission 2001). The European Commission runs several β-convergence, and confirming the stability of the convergence parameters across time. [START_REF] Fölster | Growth effects of government expenditure and taxation in rich countries[END_REF] The cohesion fund was established in 1993, after the Mediterranean countries Greece (1981) and Spain and Portugal (1986) had joined the European Union. Cohesion countries are EU member countries whose GDP per capita is lower than 90% of the EU average. macroeconomic models (for an overview see the 6th Periodic Report of the European Commission 1999) in order to assess the effectivity of these transfers. The Beutel model, for instance, is used to investigate how much of the economic growth in the member states covered can be attributed to EU co-funded programs and EU grants. According to the model, EU transfers during the two programming periods (1989 to 1993 and 1994 to 1999) are found to have increased GDP growth in the four cohesion countries by an average of 0.5 percentage points in the first period and 0.7 percentage points in the second period. The overall result of a number of macroeconomic models is that one third of the reduction in disparities in GDP per capita is due to the Structural Funds (Moucque 2000).

In order to assess this question directly, we also collected comparable data from the European Commission on financial assistance in form of structural funds for the countries in our sample (as a percentage of GDP) for the period 1992-2000, roughly corresponding to the last subperiod in our sample. The cross-country correlation between the average structural fund receipts (as percentage of GDP) and the growth bonus for this subperiod computed for the model with a threshold effect, although positive, is only approximately 0.23 (and therefore insignificant using Fisher's z-transform). The membership bonus we are capturing includes thus other factors which dominate the pure effect of structural funds, and that may as well be related to institutional quality and its evolution through time. In a recent contribution, Ederveen et al. (2002) offer solid empirical evidence concerning the importance of institutional quality in order to grasp the benefits of structural funds.

A different potential explanation for the growth bonus could be related to fiscal policy. Fölster and Henrekson (2001) find a robust and negative relationship between government size and economic growth. This could provide another possible explanation for our result that EU membership had a positive impact on growth, as due to liberalization measures inherent to the integration process the size of the government in EU member states has decreased rapidly in the last decade (an EU-average decrease of around 6% in government expenditure over GDP between 1991 and 2000, according to the OECD's Main Economic Indicators Database). [START_REF] Hall | Why do some countries produce so much more output per worker than others?[END_REF] Possible other sources of the growth bonus could be the stabilization of expectations in the context of the European Exchange Rate Mechanism or the change in the institutional framework due to European integration (the results in Tsionas and Christopoulos, 2003, point One interesting question would be whether our results allow implications for the last enlargement round on May 1st, 2004. In terms of pure GDP per capita levels, some of the new EU member countries (Slovenia, the Czech Republic, Hungary and Slovakia) have already reached a GDP per capita level (in % of the EU-15) which is similar to or even above the one Greece showed at its EU entry in 1981. As our study is based on historical data for the EU-15 member states, it would be adventurous to directly apply the findings to the new members and potential future entrants. The structural and institutional differences in these economies as compared to the current member states are sometimes very significant, and even the fact that the income levels of all candidate countries currently lie below our estimated threshold does not allow for the straightforward conclusion that these countries will indeed profit more than average from EU membership. Additionally, one should take into consideration that the transformation process that these countries had to undergo during the last decade makes their growth experience hardly comparable with that of the countries in our sample and limits the applicability of our results. -Openness: trade in % of GDP, taken from the World Development Indicators 2001 -World Bank -except the data for West Germany (1960-91), which were taken from the Penn World Table 5.5.

F

Threshold panel data models: estimation and testing

Inference in threshold panel data models has been recently developed by Hansen (1999). Let y t,i be the dependent variable for cross-section i at time t, which depends on a set of explanatory variables {x j t,i , j = 1, . . . , k} according to the following specification

y t,i = µ i + k j=1 α 1 j x j t,i + u t,i if x r t,i ≤ γ µ i + k j=1 α 2 j x j t,i + u t,i if x r t,i > γ , (3)
for i = 1, . . . , N and t = 1, . . . , T ; where u t,i is white noise with variance σ 2 . The model is, thus, a piecewise-linear one, where the α parameters depend on whether the value of x r t,i -the threshold variable -exceeds γ or not. The threshold value, γ, is treated as a parameter to be estimated. Notice that, for a given value of γ, equation ( 3) can be easily estimated by dividing the sample into the observations corresponding to x r t,i ≤ γ and those in the regime x r t,i > γ. The parameters can then be estimated using the Within method (see e.g. Baltagi, 1995). Estimating γ implies choosing the estimator γ which together with its corresponding α parameters, { α1 j (γ), α2 j (γ), j = 1, . . . , k}, minimize the sum of squared residuals of model (3). The parameter γ only needs to be sought among the actually realized values of x r t,i after trimming the initial and final tail of the distribution for identification reasons, as for a given ordered sample of the realizations of x r for all countries {x r 1 , x r 2 , . . . , x r N ×T } and a threshold γ ∈ [x r f , x r f +1 ) for some f ∈ {1, . . . , N × T }, then { α1 j (γ), α2 j (γ)} = { α1 j (γ * ), α2 j (γ * )} for all j and for every γ * ∈ [x r f , x r f +1 ).

A most important issue in threshold models is that of testing for α 1 j = α 2 j ∀j. The likelihood ratio test would take the usual form

F (γ) = [S 0 -S 1 (γ)]/σ 2 ,
where S 0 refers to the sum of squared residuals under the null of no threshold effect and S 1 (γ) is the sum of squared residuals of the model with threshold γ. However, F 1 does not have a standard asymptotic distribution, as the parameter γ is not identified under the null of linearity. [START_REF] Hansen | Inference when a nuisance parameter is not identified under the null hypothesis[END_REF] However, the distribution of F (γ) under the null can be replicated by bootstrapping, as proposed by Hansen (1999) based on Hansen (1996): Using the empirical distribution of the residuals by cross-section, a sample of T values is drawn for each one of the N cross-sections and, given those values of the error term and the observations on the x j t,i variables, the bootstrap values of y t,i are recovered. With the bootstrap sample, the linear and the threshold model for γ are estimated and the test statistic F 1 (γ) is computed as indicated above. This procedure is repeated H times, the values {F h , h = 1, . . . , H} are obtained and the p-value of F (γ) is taken to be the number of times that F h (γ) exceeds F (γ), divided through H. Hansen (1996) proves that the procedure renders asymptotically valid p-values.

  in Hall and Jones, 1999) from the model specification with the Y EA variable is approximately 0.46. The implied return to human capital formation is 0.035. Both values are in line with those reported inMankiw et al. (1992) andHall and Jones (1999).

13

 13

  alternative of two thresholds.

14

 14

16 Page 16 of 27 Editorial

 1627 Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

19

 19

Figure 1 : 25 Page 25 of 27 Editorial

 12527 Figure 1: GDP per capita in 1960 versus growth: EU-15 countries 1960-1998

  in this direction).

Table 1 :

 1 * * * (0.20) -3.02 * * * (0.37) -4.88 * * * (1.41) Unconditional β-convergence in the EU-15 * * (0.45) -3.84 * * * (0.52) -4.74 * * * (0.75) -4.82 * * * (0.78) -4.83 * * * (0.92) countries included (except Luxembourg, data for West Germany until 1991, unified Germany afterwards), with data ranging from 1961 to 1998, divided into four periods: 1961-70, 1971-80, 1981-90 and 1991-98. All data in percentage points except initial GDP, years of education and years in the EU. White heteroskedasticity/serial correlationcorrected standard errors in parentheses. Fixed effects estimation with period-specific time dummies included if jointly significant.

	Obs.	56	56		56
	R 2 adj F-test 7.12 * * * 51.3%	62.3% 1.42	62.4% 0.80
	* * * ( * * )[ * ] stands for 1% (5%) [10%] significant.
	MODEL	1	2	3	4	5
	Initial GDP -3.39 Investment share 0.45 (1.09)	3.16 * * * (0.90)	4.03 * * * (0.96)	4.11 * * * (0.88)	4.23 * * * (1.05)
	Years of education 0.24 * * (0.10)	0.24 (0.16)	0.36 * * (0.16)	0.36 * * (0.17)	0.33 * (0.19)
	Inflation rate		-0.13 * * * (0.02)	-0.12 * * * (0.02) -0.12 * * * (0.03) -0.12 * * * (0.03)
	Government cons.		-0.06 (0.09)	-0.01 (0.10)	-	-
	Openness		0.06 * * (0.03)	0.07 * * (0.03)	0.07 * * (0.03)	0.06 * (0.03)
	Years in the EU			0.03 * (0.02)	0.04 * * (0.01)	0.11 * * (0.04)
	(Years in the EU) 2					-0.002 * (0.001)
	Observations	56	56	56	56	56
	R 2 adj (in %)	61.1%	76.2%	76.9%	77.5%	79.2%
	EU-15

* * * * ( * * )[ * ] stands for 1% (5%) [10%] significant.

Table 2 :

 2 Growth panel data regressionsBootstrap p-values based on 1000 replications. Threshold values found by grid search in the central 50% of the distribution of the threshold variable.

		Single threshold Double threshold
		γ	γ1	γ2
	Initial GDP per capita (logged)	9.81	9.25	9.80
	Bootstrap p-value	0.007		0.296

Table 3 :

 3 Testing for linearity * * (0.72) -4.57 * * * (0.68) -3.99 * * * (0.54)

	26

*

Table 4 :

 4 Threshold panel data regressions

	0.5
	0.45
	0.4
	0.35
	0.3
	0.25
	0.2
	0.15
	1 9 6 0 1 9 6 2 1 9 6 4 1 9 6 6 1 9 6 8 1 9 7 0 1 9 7 2 1 9 7 4 1 9 7 6 1 9 7 8 1 9 8 0 1 9 8 2 1 9 8 4 1 9 8 6 1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8

Variation coefficient of per capita income EU 15 EU 6 EU 12 EU 10

	Page 27 of 27
	Figure 2: Real GDP per capita dispersion: EU-15 countries 1960-1998
	27

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

Submitted Manuscript

A countervailing effect of integration which could work in the opposite direction to the one described in the text refers to the fact that, in a larger market, competition is more intense and monopoly rents are smaller and more short-lived. However, empirical research on the effect of trade integration on growth suggests a dominant role of the growth enhancing effect. See below for some references.

Another recent contribution to this branch of literature,[START_REF] Badinger | Growth effects of economic integration -The case of the EU member states[END_REF], focuses exclusively on European countries using a somehow different approach and finding again no evidence for a growth bonus of EU membership.

Notice that this approach is not free from criticism. For a critical view and alternative concepts of convergence based on the time series properties of real GDP per capita, see e.g.Bernard and Durlauf (1995,1996) or[START_REF] Bernard | Productivity across industries and countries: Time series theory and evidence[END_REF].

A minimum amount of eight years seems reasonable for studying long-term growth features, because thus business cycle fluctuations are eliminated. In the literature the estimates for the average business cycle length in European countries deviate substantially across countries and depending on the detrending method. In general, however they do not tend to exceed 8 years but remain within a range of around 3 to

years. For recent estimations on the euro area as well as on selected European countries see e.g.[START_REF] Harding | Extracting, analysing and using cyclical information[END_REF] or[START_REF] Artis | Dating the euro area business cycle[END_REF].[START_REF] Barro | Economic growth in a cross section of countries[END_REF] Throughout the study (with the exception of the exercise on σ-convergence across European countries) Luxembourg was excluded from the estimations for two reasons: It is typically considered an outlier, and no data on average education years is available for this country in[START_REF] Barro | International data on educational attainment: updates and implications[END_REF].

The only countries that experienced an increase in this measure of government size are the ones that received substantial resources from EU structural funds. The co-financing requirement by itself would lead to an increase in government expenditure.

The testing problem when there is a nuisance parameter which is only identified under the alternative has been studied by e.g.[START_REF] Andrews | Optimal tests when a nuisance parameter is present only under the alternative[END_REF] and[START_REF] Hansen | Inference when a nuisance parameter is not identified under the null hypothesis[END_REF].

Acknowledgments

We would like to thank Peter Backé, Uwe Dulleck, Jarko Fidrmuc, Neil Foster, Jakob de Haan, Helmut Hofer, Sylvia Kaufmann, Robert Kunst and Dennis C. Mueller, as well as the participants at the "East-West Conference 2001" of the Oesterreichische Nationalbank in Vienna, at the workshop "The European Macroeconomy: Integration, Employment and Policy Coordination" in Antwerp, at the Ryerson University Conference "Exchange Rates, Economic Integration and the International Economy" in Toronto, at the XIV Villa Mondragone International Economics Seminar "Institutions and Growth: The Political Economy of International Unions and the Constitution of Europe" in Rome, at the 17th Annual Congress of the European Economic Association in Venice and at internal seminars at the IMF, the European Central Bank, the Institute for Advanced Studies in Vienna and the Oesterreichische Nationalbank the for many helpful comments and discussions.

Appendix


C33 -Models with Panel Data < C3 -Econometric Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods, E27 -Forecasting and Simulation < E2 -Consumption, Saving, Production, Employment, and Investment < E -Macroeconomics and Monetary

Keywords: Efficiency, Expectations, Investment, Survey

Introduction

Business fixed investment in manufacturing constitutes a sizeable component of total demand and therefore exerts a significant impact on economic activity. In addition, apart from its contemporaneous effect on the level of income, it also exerts a longerlasting effect, since it directly impacts on the future production capabilities of manufacturing. Thus, studying various aspects of the underlying investment decision making process is of paramount importance both for academics and policy makers.

For these reasons the Directorate General of Economic and Financial Affairs of the Commission of the European Communities conducts a survey where managers state their plans about future investment, which the European Commission then uses for multiple purposes such as forecasting output growth and employment in Euroland. In other words, managers state their expectations regarding future investment and essentially provide a quantitative forecast. It is apparent that the quality of the survey responses will ultimately affect their usefulness for policy making decisions. Although planned investment will probably differ from actual investment, one expects that differences will be random. This forecast would be valuable to the extent that it contains significant predictive power over future investment. Moreover, having obtained direct observations on investment plans, it is possible to investigate empirically the nature of expectations formation.

Thus, in this study we mainly focus on two issues. First, test whether the particular survey-based expectations are compatible with rationality. Second, in the event rationality is rejected, explore the properties of the expectations formation mechanism. The remainder of the paper is structured as follows. Section 2 provides a brief review of the literature on testing Rational Expectations. Section 3 describes the dataset used in our analysis. Section 4 discusses the empirical methodology adopted. Section 5 presents the empirical results. Finally, major findings are summarised in Section 6.

Testing Rational Expectations: A Brief Literature Review

The introduction of the notion of Rational Expectations Hypothesis (REH, hereafter) by [START_REF] Muth | Rational Expectations and the Theory of Price Movements[END_REF] and its further development by [START_REF] Lucas | Expectations and the Neutrality of Money[END_REF], and [START_REF] Sargent | Rational Expectations and the Theory of Economic Policy[END_REF] has produced a so-called revolution in economics as a science, which has dramatically altered the way economic modelling is done as well as policy is conducted [START_REF] Goodwin | Testing the Rational Expectations Hypothesis in an Agricultural Market[END_REF][START_REF] Pesaran | The Limits to Rational Expectations[END_REF]Keane andRunkle, 1990, 1993;[START_REF] Dominitz | Using expectations data to study subjective income expectations[END_REF]. Early studies investigated whether forecast errors possessed properties that were compatible with rationality, as an indirect way of testing the validity of REH [START_REF] Mullineux | On Testing Rationality: Another Look at the Livingston Price Expectation Data[END_REF].

A major drawback of testing the REH is that it is very often based on ex post observed data, which are then used to form forecast (expectation) errors. For this reason, there is a growing literature that tests the REH using survey data, which by definition correspond to agents' stated expectations. Thus, directly observing market participants expectations allows the econometrician to assess their rationality, and in cases the expectations are quantitative rather than qualitative, to also study the evolution of expectations. The forecasting accuracy, predictive content and rationality of survey-based expectations are of paramount importance in various markets.

A number of studies have found expectations to contain useful information and in general conclude that macroeconomic models perform better when survey-based expectations are utilised instead of model-constructed rational expectations [START_REF] Batchelor | Quantitative vs. Qualitative Measures of Inflation Expectations[END_REF][START_REF] Lee | Formation of Price and Cost Inflation Expectations in British Manufacturing: A Multi-Sectoral Analysis[END_REF][START_REF] Holden | Combining Forecasts, Encompassing and the Properties of UK Macroeconomic Forecasts[END_REF][START_REF] Lee | Expectations Formation and Business Cycle Fluctuations: An Analysis of Actual and Expected Output in UK Manufacturing Industries, 1975-1993[END_REF][START_REF] Smith | Alternative Procedures for Converting Qualitative Response Data to Quantitative Expectations: An Application to Australian Manufacturing[END_REF][START_REF] Roberts | New Keynesian Economics and the Phillips Curve[END_REF][START_REF] Roberts | Is Inflation Sticky?[END_REF][START_REF] Mankiw | Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve[END_REF]. [START_REF] Madsen | Formation of Inflation Expectations: from the simple to the Rational Expectations Hypothesis[END_REF][START_REF] Thomas | Rational Expectations and macroeconomic Forecasts[END_REF][START_REF] Mehra | Survey Measures of Expected Inflation: Revisiting the Issues of Predictive Content and Rationality[END_REF] consider the issue of formation of inflation expectations and its implications for the efficiency of macroeconomic policy. The rationality of participants in the foreign exchange market, and its implications for exchange rate behaviour and management has also been a prominent application [START_REF] Tagaki | Exchange Rate Expectations: A Survey of Survey Studies[END_REF][START_REF] Ito | Short-Run and Long-Run Expectations of the Yen/Dollar Exchange Rate[END_REF][START_REF] Sobiechowski | Rational Expectations in the Foreign Exchange Market? Some Survey Evidence[END_REF][START_REF] Dutt | Are Experts' Expectations Rational? A Multicurrency Analysis[END_REF][START_REF]Testing the Rationality of Exchange Rate and Interest Rate Expectations: An Empirical Study of Australian Survey-Based Expectations[END_REF][START_REF] Moosa | Expectation Formation Mechanisms, Profitability of Foreign Exchange Trading and Exchange Rate Volatility[END_REF]. Finally, the rationality of participants in financial markets has also attracted considerable attention [START_REF] Fraser | The Efficiency of CAC Expectations: A Survey Based Perspective[END_REF][START_REF] Pieroni | Testing Rational Expectations in Primary Commodity Markets[END_REF].

Considerable amount of research effort has also been committed on testing whether income expectations predict future income, in the context of micro-level data studies [START_REF] Flavin | The Joint Consumption/Assets Demand Decisions: A Case Study in Robust Estimation[END_REF][START_REF] Dominitz | Subjective Expectations on Unemployment, earnings and Income[END_REF][START_REF] Alessie | Saving and Income Smoothing: Evidence from Panel Data[END_REF][START_REF] Das | A Panel Data Model for Subjective Information on Household Income Growth[END_REF][START_REF] Delorme | Consumer Confidence and Rational Expectations in the United States Compared with the United Kingdom[END_REF]. Finally, an extensive literature focuses on the efficiency of betting markets by testing the rationality of market participants' in forecasting [START_REF] Gray | Testing Market Efficiency: Evidence from the NFL Sports Betting Market[END_REF][START_REF] Boulier | Testing the Efficiency of the National Football League Betting Market[END_REF]. Basically, a questionnaire is sent to managers twice a year in order to provide information regarding their current and planned (fixed) investment decisions. In particular, the first survey is conducted on March/April, while the second on October/November and respondents answer the following questions:

Data Description and Definitions of Variables

The timing of responses is crucial in this context since it affects the time horizon (span) of responses as well as their nature (backward or forward looking). The October/November Q1 is clearly backward-looking since respondents, at about the end of the fiscal year, state the percentage change of investment relative to last year. Responses on this question are used in our analysis as the (reported) realised change in investment, and are denoted as: ( )

1 t
. Notice that we denote conditioning on t % in order to emphasize that although responses are given in year ( )

t ,
this is done when only three months of this year have elapsed.

The two alternative forecasts, ,1 1,

i t t F and ,2 , i t t
F % , differ in terms of timing. The first is an expectation for investment growth (change) in year ( ) t , which is formed 3 months before year ( )

1 t
has ended. The second is an expectation for investment growth in year ( ) t , which is formed 3 months into year ( )

t . Thus, ,2 , i t t F % should be a more accurate forecast in comparison to ,1 1, i t t
F since the former is based on a superior information set.

Graphs 1 and 2 offer a pictorial representation of the direction of movements between expectations and actual (as reported) investment changes.

[Graphs 1 & 2]

Both expectations measures exhibit a strong positive relationship with actual investment change, providing informal evidence that each one of them contains some explanatory power over actual investment growth. Note that ,2 , i t t F % tends to be more We also constructed the scatter diagram between the two forecast measures, provided below.

[Graph 3]

The two conditional expectations are very closely linked, as expected, and their scatter diagram almost coincides with the 45 0 line. Any deviations from the unit-slope curve may primarily be attributed to the asynchronous timing in forming these expectations and therefore, reflect differences in the information sets.

Empirical Methodology and Testable Hypotheses

Efficiency of Expectations

One interpretation of rationality of expectations is that survey measures are unbiased forecasts of actual future outcomes. Under rational expectations, the unbiasedness hypotheses are given by: ( )

,1 1, 1 i i t t t t F E I = (1) and ( ) ,2 , i i t t t t F E I = % % (2)
Where ( ) where ' s are the expectations' forecast errors and under rational expectations should, at least, satisfy the following properties [START_REF] Sheffrin | Rational Expectations[END_REF]:

( ) , 1 0 i j t E = and ( ) , , 1 0 i j i j t t k t E + = 0 k .
The unbiasedness of survey measures can be tested in a simple regression framework, where the observed outcome is the dependent variable and the conditional forecast measure is the explanatory variable:

( ) ( ) ,1 ,1 1 1 1 , i i i i t tt t I F u = + + (5) and ( ) ( ) ,2 ,2 2 2 , i i i i t t t t I F u = + + % (6)
Where ' u s are white noise disturbance terms.

Under the null hypothesis of unbiasedness a set of restrictions are imposed on the parameters of the above regressions as follows [START_REF] Lovell | Tests of Rational Expectations Hypothesis[END_REF][START_REF] Bernheim | How Do the Elderly Form Expectations? An Analysis of Responses to New Information[END_REF]:

0 1 1 : 0 1 H = = , and 0 2 2 : 0 1 H = = .
Rejection of these hypotheses would provide prima facie evidence against the unbiasedness hypothesis and consequently against rationality.

Evolution and Formation of Expectations

By exploiting the different timing of forming the two forecasts, one may test some further fruitful hypotheses regarding the evolution of expectations. In particular, using the law of iterated expectations, the two expectations formed should differ by the amount of any information that became available between ( ) Any differences between the two forecasts may only be attributed to the 'arrival of news'. Hence, if expectations were rational, then any revisions or changes in them should be uncorrelated with all previously available information. The difference between expectations is essentially a revision of expectations, and should reflect the arrival of new information and by default should be non-autocorrelated and furthermore should be orthogonal to any member of the information set 1 t . Let us denote the revision process as follows:

,2 ,1 1, , 1 ,

i i i t t t t t t REV F F = % % (8)
Rationality of expectations can also be tested using the properties of the revision process. In particular, current revision should be unrelated to past revisions. Thus, the slope parameters of the following model should be jointly equal to zero:

( ) ( ) 1 2 , 1 1, 2 2, 2 i i i i i t t t t t t t REV REV REV = + + + % % % (9)
While the above analysis allows us to comment on the nature and the efficiency of expectations it is not informative about how the expectations are formed. In order to find the type of expectation formation mechanism that underlies the evolution of expectations, assume first that expected changes in investment are a weighted average of the current change in investment and some other element, t x :

( ) ( ) ( ) ,2 1 1 , 1 i i t t t t F wx w I = + % (10)
Where 1 w is a weighting factor.

If 1 0 w = then (10) would describe static expectations. Having (10) as a starting point we may consider two alternative expectation mechanisms. First, Regressive Expectations, where t x g = , and g denotes the sample mean of ( ) i t I . Regressive Expectations imply that agents adjust their expectations a certain fraction of last year's deviation from the distribution mean of the underlying variable. In other words, agents believe that the variable of interest will tend to move towards its mean. Then one may reparameterise (10) as:

( ) ( ) ,2 ,2 ,2 * 1 , 1 , 1 , i i i i t t t t t t t t F F F g I u = + % % % % (11)
Where * t u % is a white noise error term and is an estimable parameter that measures the rate of adjustment to deviations from the mean, which is expected to lie in the ( ) Where ** t u % is a white noise error term and is an estimable parameter that measures the rate of adjustment to last period's expectation error, which is expected to lie in the ( )

1, 0 interval.

Empirical Results

We estimate the parameters of equations ( 5) and ( 6) in a panel framework, which will allow us to exploit variation both cross-sectionally (across countries) as well as time.

Estimation is conducted applying Fixed and Random Effects, and including a set of year dummies in order to allow for time heterogeneity. The choice between Fixed and Random Effects is based on the Hausman test [START_REF] Hausman | Specification Tests in Econometrics[END_REF]. In particular, significant values of the test qualify the Fixed Effects estimator. The relevant estimation results are reported in Table 2.

[Table 2]

For both cases the preferred specification is given by Fixed Effects. Both forecast measures explain a statistically significant portion of the variation in actual investment growth. Furthermore, both slope parameters are positive suggesting that both forecast measures correctly predict the direction of movement. In addition, the second forecast measure accounts for 60 percent of actual investment growth's variation while the first forecast measure explains 49 percent. The difference, as discussed earlier, is attributed to the fact that the second forecast measure is based on a superior information set and consequently constitutes a more accurate forecast. Notice that the slope parameter associated with the second forecast measure is larger and closer to unity (0.58) than that obtained from the first forecast measure (0.48), although both are statistically different from unity, which enables the rejection of efficiency (unbiasedness) of expectations.

Overall, our findings indicate that expectations, on average, predict accurately the direction of movement in investment growth and furthermore contain significant explanatory power over its variation. However, strictly speaking efficiency (rationality) is rejected since expectations do not represent unbiased predictors of investment growth.

We now turn our attention to the evolution of expectations and in particular focus on the orthogonality conditions regarding expectation revisions. As discussed earlier, revisions of expectations should be uncorrelated with any member of the information set that was know at the time of expectation formation. The simplest orthogonality test one may perform is to investigate whether expectations revisions' behaviour exhibits any autoregressiveness. This is one by employing equation ( 9) whose estimated parameters are reported in Table 3.

[Table 3]

Again the Fixed Effects estimator is in order. The AR(2) model explains an insignificant 5 % of the variation in revisions and furthermore we were able to reject that revisions show any first-order autocorrelation. In contrast, highly significant secondorder dependence is uncovered, with the relevant coefficient carrying a negative sign. In other words, the orthogonality condition fails providing us with further evidence against rationality of expectations.

We proceed by exploring the process that more adequately describes the expectation formation mechanism. In particular, we consider two competing specifications; Regressive Expectations and Adaptive Expectations whose performance is assessed by the means of estimating equations ( 11) and ( 12) respectively. The relevant results are summarised in Table 4.

[Table 4]

Based on the Fixed Effects estimation results, we observe that both estimated slope parameters are consistent with their a priori expected signs. In particular, the slope parameter associated with the Regressive Expectations is positive, suggesting that when last period's actual investment growth was above (below) its average, agents expect that in the current period it will move downwards (upwards), showing a tendency to approach its mean value. Similarly, the parameter of the Adaptive Expectations is negative, indicating that if in the last period agents had overestimated (underestimated) the actual investment growth they will adjust downwards (upwards) their expectations for the current period. As far as the speeds of adjustment (i.e. the slope parameters) are concerned, under the validity of Regressive Expectations agents are found to 'clear' about 90 percent of the observed 'disequilibrium', while under Adaptive Expectations only 53 percent is 'cleared'. In addition, we also tested whether the speed of adjustment parameters, as estimated, (i) are indeed different from zero and therefore non-trivial, and

(ii) are significantly different from their maximum theoretical values (+1 for Regressive Expectations and -1 for Adaptive Expectations). The null of zero (trivial) speed of adjustment was emphatically rejected for both cases, while we were not able to reject the hypothesis that the coefficient associated with Regressive Expectations is equal to unity, and therefore represents full adjustment within a single period. Finally, both equations explain a significant part of expectations' formation, although the Regressive Expectations mechanism exhibits almost double explanatory power when compared to the Adaptive Expectations. All in all, our results qualify the Regressive Expectations as the mechanism that more adequately describes the behaviour of expectations' formation.

Conclusion

According to our findings expectations predict accurately the direction of movement in investment growth and furthermore, contain significant explanatory power over its variation. However, strictly speaking efficiency (rationality) is rejected since expectations do not represent unbiased predictors of investment growth. As far as the evolution of expectations is concerned, we report highly significant second-order dependence which provides further evidence against rationality of expectations. Finally, Notes: Numbers in parenthesis denote heteroscedasticity-adjusted standard errors. The hypothesis is tested using applying a chi-square test. One, two or three asterisks denote significance at the 10, 5 or 1 percent level respectively. 2 R stands for the coefficient of determination. Hausman denotes the [START_REF] Hausman | Specification Tests in Econometrics[END_REF] test and its significance qualifies the Fixed Effects estimator as the appropriate model. Notes: Numbers in parenthesis denote heteroscedasticity-adjusted standard errors. The hypothesis is tested using applying a chi-square test. One, two or three asterisks denote significance at the 10, 5 or 1 percent level respectively. 2 R stands for the coefficient of determination. Hausman denotes the [START_REF] Hausman | Specification Tests in Econometrics[END_REF] test and its significance qualifies the Fixed Effects estimator as the appropriate model.

  We utilise data from the Investment Survey (part of Business Surveys) conducted twice a year by the European Commission Directorate General for Economic and Financial Affairs. The survey covers a wide range of industrial sectors and firms of various sizes (in terms of number of employees). Our sample covers the 1985-2003 periods and includes Austria, Belgium, Denmark, Finland, France,

  by (i) the steepness of the scatter diagram, and (ii) the smaller dispersion.

  Given the structure of the survey, one may device two alternative conditional forecasts for ( ) . The first is based on responses to the October/November Q2, where respondents are asked to state their investment plans for the coming year. Let us call this forecast ,1 based on responses to the March/April Q2, where respondents are asked to state their planned investment the year ( )

	i
	t
							1, t t i F , which utilises
	responses on this question from the year prior to ( ) t . The second forecast, call it ,2 , i t t F % for
	symmetry, is
	March/April Investment Survey • March/April Q1: State percentage change in investment last year ( ) 1 t investment two years ago ( ) 2 t . F o	on
	r
	P
	e e r t . R e v i e w
	i t I , where	and i stand for the first-difference operator and
	country index respectively. More formally,	( ) i t I	=	i t I I	i t	1	, evaluated on
	October/November of year ( ) t .

• March/April Q2: State percentage change in investment this year ( ) t on investment last year ( ) 1 t . October/November Investment Survey • October/November Q1: State percentage change in investment this year ( ) t on investment last year ( ) 1 t . • October/November Q2: State percentage change in investment next year ( ) 1 t + on investment this year ( ) I based on information available prior to ( ) t t relative to year ( )

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	our results qualify Regressive Expectations as the mechanism that more adequately
	describes the formation of expectations.
	F o
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of 25 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

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	F o F o F o F o
	r r r r
	P P P P
	e e r e e r e e r e e r
	R e v i e w R e v i e w R e v i e w R e v i e w

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		Submitted Manuscript
	Tables
	Table 1 Descriptive Statistics and Sample Correlations
		Mean	Std. Deviation	Min	Max
	Actual	4.53	12.82	-30	51
	Forecast-1	8.24	13.65	-17	94
	Forecast-2	10.00	14.36	-31	77
	Revision	1.20	8.99	-28	26
		Sample Correlations
		Actual	Forecast-1	Forecast-2
	Actual Forecast-1 Forecast-2	1.00 0.56 o F 0.69	1.00 0.79	1.00
		r
		P
		e e r
			R e v i e w

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	F o
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Table 2 Testing Efficiency of Expectations (Panel estimation, with time dummies)

 2

					Forecast-1	Forecast-2
	Coefficient	Fixed	Random	Fixed	Random
	(standard error)	Effects	Effects	Effects	Effects
					15.89	0.67	-0.60	-0.266
					(3.10) ***	(3.19)	(2.45)	(2.58)
					0.485 ***	0.398 ***	0.580 ***	0.537 ***
					(0.056)	(0.052)	(0.046)	(0.044)
					Diagnostics
		R	2		49 %	50 %	60 %	61 %
	Wald test	13.51 ***	231.30 ***	21.97 ***	375.01 ***
	Hausman test	15.79 ***	32.77 ***
					Hypotheses testing
	H	0 :	=	1	81.96 ***	130.54 ***	81.76 ***	107.78 ***

Table 3 AR(2) model for Expectations Revisions (Panel estimation, with time dummies)

 3 Numbers in parenthesis denote heteroscedasticity-adjusted standard errors. The hypothesis is tested using applying a chi-square test. One, two or three asterisks denote significance at the 10, 5 or 1 percent level respectively. 2 R stands for the coefficient of determination. Hausman denotes the[START_REF] Hausman | Specification Tests in Econometrics[END_REF] test and its significance qualifies the Fixed Effects estimator as the appropriate model.

	Coefficient	Fixed Effects	Random Effects
	(standard error)
			1			0.029	0.265 ***
							(0.075)	(0.075)
			2			-0.251 ***	-0.031
							(0.079)	(0.08)
						Diagnostics
			R	2			5 %	15 %
	Wald test	1.83	29.80 ***
	Hausman test	66.14 ***
						Hypothesis testing
	H	0	:	1	=	0	0.15	12.31 ***
	H	0	:	2	=	0	10.00 ***	0.16
	Notes:

Table 4 Expectation Formation Mechanisms (Panel estimation, with time dummies) Regressive expectations Adaptive expectations

 4

	Coefficient	Fixed	Random	Fixed	Random
	(standard error)	Effects	Effects	Effects	Effects
							0.908 ***	0.808 ***	-	-
							(0.097)	(0.092)
							-	-	-0.530 ***	-0.381 ***
							(0.132)	(0.105)
							Diagnostics
			R	2			44 %	44 %	26 %	26 %
	Wald test	9.29 ***	148.20 ***	4.01 ***	67.49 ***
	Hausman test	3.88 **	5.94 **
							Hypothesis testing
	H	0 :	=	0	86.55 ***	-
	H	0 :	=	0	-	16.14 ***
	H	0 :	= +	1	0.88	-
	H	0 :	=	1	-	12.60 ***

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