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

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)

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

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

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

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

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.

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

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)

−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.

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.