Benchmark specification of the cross-sectional wage-type equation and data

Taking logarithms to the wage-type of equation (3.28) and proxying 𝑅𝑀𝑃_𝑖 with 𝐻𝑀𝑃_𝑖, the econometric specification considered in this paper for a cross-sectional regression is:

ln 𝑤𝑖= 𝐶 + 𝛼 ln 𝑘𝑖+ 𝛽 ln ℎ𝑖+_{𝜃𝜎 ln 𝐻𝑀𝑃}1 𝑖+ 𝑢𝑖 (3.36)

which is observationally equivalent to the logarithm of equation (3.30) but they have different underlying assumptions about the values of 𝛼 + 𝛽. This is one of the issues that will be studied in the next sections. Though when using 𝐻𝑀𝑃_𝑖 it is not possible a structural NEG interpretation of the parameters the notation is kept as a reference.

The benchmark specification in this work proxy wages with per capita income, as it is frequent in the NEG literature (Redding and Venables, 2004; Brakman et al., 2009a). Here it is represent- ed by per capita gross value added (GVA). The research focus on the observational equivalence of the NEG makes to try alternative measures for the dependent variable in section 3.4.2. The benchmark Market Potential variable is built with GVA too. Alternative measures are tried in section 3.4.3. The estimations are controlled by per capita capital stock and by a proxy of human capital. The variable chosen to proxy human capital is the share of the population who has suc- cessfully completed education in Science and Technology (S&T) at the third level and is em- ployed in a S&T occupation33. Details about the variables and the sample are provided in Appen- dix A. The sample exclude the regions of Norway and Switzerland because of lack of data on capital stock but those regions are included to calculate the Market Potential variables of the 206 NUTS 2 regions studied here. Table 3.1 and Appendix C show correlations among different vari- ables used in the next sections.

The term 𝑢_𝑖 is supposed to collect the effects of omitted variables and departures from the as- sumptions of the theoretical model, which are assumed to be randomly distributed under OLS estimation. Actually, all the estimations presented in this paper present spatially autocorrelated residuals. However, the models of Spatial Econometrics are avoided to discuss the observational equivalence of the NEG because they provide alternative interpretations and/or channels of inter- action, through spillovers or the other motivations of spatial specifications discussed by LeSage and Pace (2009, chap. 2). Some partial results of the following empirical exercises change when estimating spatial models but the main message about the observational equivalence of the NEG remains the same than using simple OLS regressions.

Market Potential is not instrumented here, contrary to the frequent instrumentation of this vari- able in the NEG empirical literature. Instrumental variables estimation of a wage-type equation involves a number of issues that are out of the scope of this paper. The same can be said about the estimation with panel data and fixed regional effects. However, given the previous discussion about the important role of regional productivity differences it is worthy saying a few words about this.

Panel estimation with fixed individual effects follows a procedure of time-demeaning to pro- duce estimates of the average effects of the variations of the right hand variables on the variations of the dependent variable (within estimator). The procedure can reduce measurement errors in the levels of the Market Potential variable but the resulting estimates are not comparable with those

33

Though this variable is not frequently used in the literature, Niebuhr (2006), Bivand and Brunstad (2006), Artis et al. (2011) or Dreger et al. (2011) have worked with variants of it.

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Chapter 3: The observational equivalence of the NEG wage-type equation

of cross-sectional or pooled estimations (Acemoglu et al., 2008). For instance, estimating with fixed effects human capital tends to be insignificant because of the smooth changes of this varia- ble in Europe. Additionally, given that panel estimation with fixed effects just eliminates the time invariant individual factors, the results are going to dependent on the variations of the variables omitted from the regression and related with changes in 𝐴_𝑖. If capital stock is not included in the estimation, the results are sensitive to the omitted short-term variations of capital stock.

Again the time horizon of the theoretical model to be estimated is the key issue and therefore, the econometric techniques and samples to be used in the estimation. This paper does not analyz- es how trade interactions are able to explain short term effects on the income of a region after variations of variables in the neighboring regions. The strategy of this paper is to keep the estima- tion procedure simple, cross-sectional OLS, and control the estimation for capital stock, though some of the tests exclude this variable. This strategy allows the discussion about one of the sides of the NEG observational equivalence: cross-sectional estimations of wage-type equations are driven by general characteristics of the variables in levels. Therefore, the definition of the sample is crucial both because of the geographical location of the observations and because their relative wealth.

The following figures make this last point clearer. First, Figure 3.1 provides a first intuition about the role of a Market Potential variable on a wage-type equation. It shows quantile maps of the logarithms of per capita gross value added and Market Potential in the year 2008. The values of are divided in seven quantiles and darker colors are associated with higher values of the varia- bles. In spite of the visual limitations of cloropheth maps, Figure 3.1 is enough two distinguish the core-periphery spatial pattern of the logarithm of per capita GVA, with just a few high per capita income regions out of the geographical center of Europe, particularly those in Nordic countries. Given the spatial structure of GVA in Europe, the logarithm of a Harris’s measure of Market Potential built with GVA shows an even more concentrated distribution and a clearer core-periphery pattern. Therefore, in the context of a wage equation a variable of Market Poten- tial is able to collect the global core-periphery pattern of per capita GVA.

Figure 3.1. Cloropleth maps of the logs of per capita GVA and Market Potential (year 2008)

Fernando Bruna, University of A Coruña

Figure 3.2. Log of per capita GVA in year 2008: Countries and regions

Figure 3.2 compares from a different perspective the levels of the benchmark dependent varia- ble, the logarithm of per capita GVA on two samples of countries at two different NUTS dis- aggregation levels (see details in Appendix A). The top plot of Figure 3.2 shows the variable for 25 countries of the European Union (excluded Malta and Cyprus). The left central plot shows 260 regions from this broad sample. The points in the lower band of this last plot are the regions from the Eastern European countries, which are relatively poor. Those 54 regions are suppressed in the right central plot. The omission of this 20% of the observations of the broad sample reduces to coefficient of variation of the cross-sectional log of per capita GVA from 7.5 % to 3.3%. Howev- er, because of the higher heterogeneity of the sample with the Eastern European regions all the correlations shown in Table 3.1 are higher than 0.9 for the broad sample: the variables collect approximately in the same way the dispersion of per capita income in a sample including the

Chapter 3: The observational equivalence of the NEG wage-type equation

Eastern regions. The tests presented in this paper were repeated for the broad sample and are available upon request. The main conclusions about the observational equivalence do not change so the results presented later will use the restricted sample of 206 regions.

The broad sample is shown in Figure 3.2 to illustrate the role of sample heterogeneity. Many regional variables can collect the heterogeneous levels of income of a sample including the East- ern European regions. If a variable of Market Potential is included in the regression the issue of the relative wealth of the Eastern European regions get mixed with their particular location, some of them relatively close to the economic center of Europe. Too this mix of explanation affects the restricted sample, as shown in the bottom plot of Figure 3.2, which just zooms the right central plot. Now the lower band of points mainly represents regions from the following Mediterranean countries: Spain (ES), Greece (GR), Italy (IT) and Portugal (PT). Of course, the NEG explanation is that these countries have lower income and physical and human capital due to their lower Mar- ket Potential. However, the results presented later show that the main explanatory variable is cap- ital stock. Therefore it is necessary to translate the NEG explanation of wages to an explanation of capital accumulation what take us to the same type of conclusion discussed before. At the end all is about explaining differences of total factor productivity. What it is studied here is the role of Market Potential to explain the cross-sectional dispersion of per capita income after controlling the estimation for the effects of human and physical capital stocks on factor productivity. How- ever, some conclusions do not depend on the inclusion of control variables.