With the empirical strategy in place, we can proceed to describing the results and their interpretation. Table 2.2 shows alternative estimates of the ARDL model of the labor 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.
Table 2.2: Estimates based on full sample, 1960-2008
FE PMG MG spacespace Hausman test
Notes: ∗∗∗/∗∗/∗ denotes significance at the 1%/5%/10% level, respectively, according to the two-sided critical values of the Student’s t distribution. Figures in brackets are the standard errors, which are corrected for possible heteroscedasticity in the case of the FE estimates. The figures in brackets for the Hausman tests report p-values according to the critical values from theχ2(1) and theχ2(3) distribution.
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 (heteroscedasticity-corrected) standard error renders the FE estimator insignificant.
It seems as if there is a strong dynamic element in the data that the static FE estimator – by construction – is unable to pick up. According to theory, the negative coefficient sign hints to an average economy-wide elasticity of substitution larger than one, pointing to labor and capital being substitutes. The PMG and MG estimates with values of -0.56 and -0.62 are in line with other estimates in the literature as, for example, in Hutchinson & Persyn (2012) or Bentolila & Saint-Paul (2003). More
suggesting the validity of the pooling assumption in this case - a point emphasized by a Hausman test, which takes the value of 0.13 and therefore does not reject the homogeneity of the ln(k) coefficient according to the critical value of the χ2(1) distribution. A similar picture emerges with regard to total factor productivity.
Estimated coefficients are negative and significant. The PMG and MG estimates turn out to be quite similar in magnitude and the Hausman test does not reject the poolability hypothesis. The FE estimate deviates considerably from the MG estimate, which is the only consistent estimate to summarize the overall effect in the panel if slope coefficients are heterogenous. We take these first two results as a first indication of the weakness of the static fixed effects estimator. Theory tells us that equally signed coefficients for ln(k) and ln(T F P) reveal technological progress to be capital augmenting, to which our results thus lend support (Bentolila
& Saint-Paul 2003). The slope estimates of the trade openness variable are negative but insignificant. Thus, the idea that greater openness lowers the labor share, due to relative factor price effects or through power-shifts in the wage bargaining process to the disadvantage of labor, is not supported by the data if we estimate over the whole period from 1960 to 2008. 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 labor share is best described by a static model.
In order to check the stability of our results, as well as to gain insights into chang-ing impacts on the labor share over time, we split our sample in two subperiods. Table 2.3 reports results of the same estimators as before which are applied for the periods from 1960 to 1980 and from 1980 to 2008. Figure 2.3 shows country specific slope
estimates and their deviations from the MG estimates for the two subperiods. Tables in the appendix provide more detailed results of country specific OLS estimates.
Table 2.3: Estimates based on sample split
1960-1980 1980-2008
FE PMG MG H-test FE PMG MG H-test
ln(k) -0.035 -0.375∗∗∗ -0.887 0.59 -0.082 -0.475∗∗∗ -0.432∗∗∗ 0.14 0.179 0.126 0.677 (0.44) 0.100 0.045 0.125 (0.71) ln(T F P) 0.024 -0.450∗∗∗ -0.195 0.61 -0.370∗∗∗ -0.324∗∗∗ -0.380∗∗∗ 0.20 0.116 0.077 0.336 (0.44) 0.077 0.027 0.130 (0.66) Trade op. 0.044 1.095∗∗∗ 0.864 0.15 -0.103∗∗ -0.143∗∗∗ -0.171 0.08 0.154 0.143 0.614 (0.70) 0.045 0.023 0.101 (0.78)
Joint H-test 2.47 0.65
(0.48) (0.88)
Notes: See notes to table 2.2.
As shown in the left part of table 2.3, both the FE estimates and the MG estimates turn out to be insignificant for the earlier period. The MG estimate for the slope coefficient of the capital output ratio differs quite substantially from the PMG estimate. This difference traces back to the cross-country heterogeneity of the slope estimates, which are illustrated in the upper left part of figure 2.3. The variation of slope estimates across countries is striking. However, only for three economies (France, Italy and the Netherlands), these slope estimates are significant (see table 2.4 in the appendix for details). Table 2.4 provides additional insights into the stability of the estimated relationships. The last column shows estimates of φ, which is the loading coefficient of the underlying error correction representation of the ARDL model. Only if these coefficient estimates are negative and significant, the model succeeds to estimate a stable long-run relationship. This is the case for 7 out of 18 country specific models which implies that for 11 models the hypothesis of a long-run connection between the labor share and its determinants gets rejected by the data for the subperiod between 1960 and 1980. In contrast, if we look at the country specific OLS estimates over the estimation period from 1980 to 2008,
1960-1980 1980-2008
Notes: Dots show the individual estimates of the long-run coefficients. The solid line indicates the MG estimate.
Figure 2.3: Individual vs. MG estimates
we see that for all countries except Portugal the loading parameter estimates are significant and negative (table 2.5). There are also more significant slope estimates
for ln(k), ln(T F P) and trade openness and less “outliers” than in the earlier sample.
Generally, a first main result emerges in that the period between 1980 and 2008 is better explained by the empirical model than the period between 1960 and 1980 for which we find less convincing results.
The coefficients in table 2.3 show some support to the standard model put for-ward in Bentolila & Saint-Paul (2003). Increases in capital intensity and total factor productivity tend to depress labor shares. Yet, the impact of trade – as a prominent shift factor in much of the literature – differs substantially across sample periods.
Indeed, it shows the opposite impact between periods. Higher openness to trade seems like a strong driver of rising labor shares in the 1960s and 70s. Afterwards, however, it played an important role in depressing it. This pattern is all the more interesting as trade openness increased almost equally strong in both sample periods.
In the two decades preceding 1980, average trade openness across the countries in our sample increased by roughly 17 percentage points. From 1980 to 2008, the numbers show a very similar trend – an increase by around 16 percentage points.
It should be noted, however, that the estimated coefficients for the first sample period also differ substantially between models. The FE estimate is rather close to zero and not significantly different from it. The MG estimate is very high but, again, not significant. Only the PMG model yields a positive and significant coefficient.
Taking a look at the country specific estimates in figure 2.3 casts some doubts on this estimate, however. There is clear heterogeneity in the individual coefficients and visual inspection already suggests the PMG and MG estimates to be driven by outliers. From whichever angle one takes a look at those numbers, it does remain clear, however, that trade had a significant and negative influence on the labor share after 1980. Taking the increase in trade openness in combination with the
coefficient from table 2.3, around a third of the fall in the labor share since 1980 can be explained by rising trade openness.
Returning to the numbers showing trade openness to rise similarly in both pe-riods, simple claims, such as trade having been simply not as important and that therefore predictions derived from traditional trade models would not hold for ear-lier periods, do not seem justified. Rather the nature of trade must have changed.
There is indeed ample evidence that this is the case. Prominent contributions such as Hummels et al. (2001) and Yi (2003) show that vertical specialization contributed strongly to the growth of world trade since the 1980s. It seems plausible that this led to a higher degree of specialization in advanced countries towards capital intensive production. Also, many developing and emerging countries became more integrated in world markets throughout the 1980s and 1990s when global trade barriers were brought down. In fact, most of the measured growth in trade openness over the last two or three decades directly stems from increased trade with non-OECD countries.
This led to further possibilities of production sharing across countries. It also in-creased the pressure labor is facing in the wage bargaining process, where workers are now often confronted with the threat of plant closure at home and relocation abroad. Additionally, unions lost support continuously over time thereby being less able to counterbalance the competition from low-cost labor abroad. It remains to be seen, what exactly is the main driving force underlying the impact of trade open-ness on labor shares. Our general measure of trade openopen-ness likely captures all the above aspects to a certain extent. At the same time, it stands for an impact that has become much more homogeneous across countries over time.8 Disentangling the
8The increased similarity in the effect across countries is confirmed by the Hausman test com-paring PMG and MG estimates. This test in unable to reject the hypothesis of equal coefficients across models.
effects underlying this convergence in trade’s impact on the labor share emerges as an interesting topic for further research.