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Figure 2 summarises this section in a graphical framework based on Bentolila and Saint-Paul (2003).

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3 Empirical Framework The aim of the remaining sections is to test the explanatory power of the outlined theory. To this end, we have to chose suitable estimators among the many that panel econometrics, in particular for macro panel data, offer. Two principles guide us through this selection process. The first principle is that we take serious account of cross-sectional heterogeneity in the data, i.e. we carefully deal with the question whether to employ pooled or country-specific estimators in order to receive reliable empirical results. The second principle is the preference of estimators based on dynamic rather than static models since our objective is not only to explain cross-country differences in the labour shares but also to gauge the persistence in the evolution over time.

Obeying to the second principle is straightforward by considering an autoregressive distributed lag (ARDL)-Model as in Pesaran et al. (1999)

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in which yit represents country i’s observation on the logarithm of the labour share in period t and xit−j is the vector of the explanatory variables. Slope coefficients to be estimated are given by λij and δij and µi is a time-invariant fixed effect. The indices run from t = 1,... T and i = 1,... N.

By reparameterisation the following error-correction representation of (1) emerges

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These two equations suffice for organising ideas and for demonstrating the parameter restrictions inherent to the estimators we look at.

3.1 Consistency versus efficiency To begin with, we consider the static fixed effects (FE) estimator which is still the model of choice in many empirical studies, in particular the ones that seek to estimate the determinants of the labour share. In terms of our model, the FE estimator imposes the following parameter restrictions

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The PMG estimator restricts the long-run parameters to be the same across countries but leaves the parameters concerning the error correction coefficients φi and the coefficients of the short-run dynamics unrestricted. The set of long-run parameters that maximises the concentrated likelihood function belonging to the panel data model gives the PMG estimator β P M G.

If homogeneity of the β-parameters holds, then the PMG estimator is consistent and efficient, whereas the MG estimator is only consistent. Likewise, if the model is homogeneous and dynamic responses are absent, then the FE estimator is preferable in terms of efficiency. Principally, in choosing among the FE, MG and PMG estimators we face a trade-off between consistency and efficiency. From the outset it is not clear which estimator accurately measures the relationships between the labour share and its determinants. Theory suggests that there might be both heterogenous and homogeneous causes for the parallel movement in the labour shares, but in order to clarify which explanatory variable exerts what effect, we employ Hausman specification tests to check whether homogeneous or heterogeneous parameter estimates are consistent with the observered data.

3.2 Cross-sectional dependence

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and (2). The standard FE, MG and PMG estimation framework assumes that the disturare independently distributed across i and t. A more reasonable assumption is bances it that countries are cross-correlated due to international linkages and common influences such as common macroeconomic shocks. Neglecting such dependencies yields inefficient parameter estimates and is likely to lead to size distortions of conventional tests of significance. A convenient way to incorporate cross-sectional dependence in our framework is to model such dependencies by a factor error structure. Under this assumption, the errors of equation (2) are given by = γi ft + eit (7) it in which ft is a unobserved common effect and eit are independently distributed country-specific errors. Such an empirical specification seems to be more in line with a model of the labour share featuring technological change as an important determining variable that may comprise common components across countries.

Pesaran (2006) shows that, in principle, directly augmenting the panel model with a set of cross-sectional averages of all variables can capture the correlated error component.

However, considering the large time series dimension of such an approach, following Binder and Bröck (2006) we pursue a more parsimonious specification which results in conducting a two-step procedure when estimating equation (8). The basic insight that lies behind the common correlated effects estimator developed in Pesaran (2006) is that a proxy for the unobserved common factor can be obtained as

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This section describes the data and provides details on the calculations of all variables used in the next section’s estimations. The labour share of income is one of the most classical measures in macroeconomics, yet, it is not uniquely defined. We use data provided in the "total economy database" (TED) where the labour share is defined as total labour compensation (LAB) divided by gross value added (VA): LSit = LABit /V Ait.3 It is important to note that labour compensation contains an imputed labour income of the self-employed, thereby providing a better cross-country comparability as stressed by Gollin (2002).

The capital output ratio k is calculated with capital stock data from the EU’s Ameco database as the net capital stock in year t over GDP in the same year.4 Total factor productivity (tf p)data is also taken from TED. Trade openness is calculated as the sum of imports and exports divided by GDP with data from the OECD Economic Outlook database. In order to capture different institutional settings, in particular with respect This database is available at http://www.ggdc.net/databases/ted.htm This database is available at http://ec.europa.eu/economy_finance/db_indicators/db_indicators8646_en.htm. Data for Germany prior to 1991 are calculated based on capital stock growth rates for West Germany.

to the bargaining process, we characterize countries as either having strong unions or weak ones using union density as the principal measures. These data are provided by and described in Visser (2009). All data are at yearly frequency. Table 1 shows summary statistics for our resulting balanced sample of 15 OECD countries over 25 years (1982 The descriptive statistics again clarify the downward movement of labour shares across almost every country in the sample, with the United States being the only exception. At the same time countries have become more open and experienced substantial increases in Total Factor Productivity. The assessment is less clear with regard to the capital output ratio, which has increased for some and decreased for others. In addition, union density is now lower than in the 1980s for all countries except Belgium and Finland.

While the descriptive statistics point to some interesting relationships between variables, it remains for the next section to establish significant links between the labour share and its driving forces.

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With the empirical strategy in place, we can proceed to describing the results and their interpretations in this section. Table 2 shows alternative estimates of the ARDL model of the labour share. The short-run dynamics of the PMG and MG models have been specified with the aid of the Akaike information criterium where we allowed for a maximum lag of order one.

For the log of the capital output ratio ln(k) = ln(K/Y ) the coefficient is negative for all three estimated models - FE, PMG and MG. However, a large (heteroscedasticitycorrected) standard error renders the FE estimator insignificant. According to theory, the negative coefficient sign hints to an average economy-wide elasticity of substitution larger than one, pointing to labour and capital being substitutes. The PMG and MG estimates are also in line with other estimates in the literature as, for example, in Hutchinson and Persyn (2009) or Bentolila and Saint-Paul (2003). More importantly, the MG estimate seems broadly in line with its pooled counterparts, suggesting the validity of the pooling assumption in this case - a point emphasised by a Hausman test, which takes the value of.94 and therefore does not reject the homogeneity of coefficients across the PMG and MG specifications according to the critical value of the χ2 (1) distribution. A similar picture emerges with regard to Total Factor Productivity. Estimated coefficients are negative. Theory tells us that equally signed coefficients for ln(k) and ln(T F P ) reveal technological progress to be capital augmenting (Bentolila and Saint-Paul (2003)). Given that the MG turns out to be insignificant, the homogeneity assumption of the ln(T F P ) coefficient is questionable. We pointed out above that technological developments in the OECD countries are very similar. However, technological change seems to influence the labour share quite heterogeneously across countries. This can be seen clearly in figure 5 were country-specific deviations from the MG coefficient estimates are shown. The individual slope estimates for the ln(T F P ) variable scatter quite a lot around the MG estimate. For several countries the ln(T F P ) coefficient is even positive which suggests that—given the negative sign of the capital/output coefficient— technological progress is neither labour- nor capital augmenting (Australia, Austria, Ireland and the US).

Individual slope estimates of the trade openness variable also fluctuate around the MG counterpart but to a lesser extent. However, we cannot reject the homogeneity assump

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tion on the estimated coefficients based on Hausman tests. Returning to table 2, we find trade openness to negatively and significantly affect the labour share in all three specifications.

We furthermore note that a dynamic specification is preferable over a static one given that for all country specific models at least two of the variables are significant in contemporaneous values as well as when included with one lag. There is not a single country for which the labour share is best described by a static model.

While our results from table 2 establish a decent benchmark, they leave out one important aspect that features in nearly all papers on the topic: institutional arrangements, in particular with relevance for the wage bargaining process. Therefore, we comply with other studies and test whether institutional settings influence our estimates. However, we proceed in a different fashion with respect to the precise way of accounting for institutions. We do not directly include institutional variables in the estimation but divide the sample and test for the stability of the other variable’s coefficients in the split samples.

Note that an approach using the full sample and an interaction term is not feasable when employing the MG estimator. Directly including measures for the relative strength in the bargaining process is not an option either; this is for the following reasons: (i) we need a sufficient amount of variation in the variables over time; (ii) our time series based estimation approach does not allow to estimate models with many variables; and (iii)

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−1.5 −1 −0.5 0 0.5 1 1.5 Notes: Dots show the individual estimates of the long-run coefficients. The solid line indicates the MG estimate. Dotted lines denote MG estimates +/- 2-times the standard error.

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High union density Austria, Belgium, Denmark, Finland, Ireland, Italy, Sweden Low union density Australia, France, UK, Germany, Japan, Netherlands, US, Canada institutional proxies are typically plagued by measurement error, which would result in biased point estimates.

In the following, we divide our sample into two country groups according to whether they can be described as having high or low union density and redo the estimations.

Union density tells us the percentage of the workforce that is member of a union. We define countries that fall into the high union density group if their average value is above the cross-sectional median over the period from 1982 to 2006. Table 3 shows the country groupings based on this classification scheme.

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