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«Der Open-Access-Publikationsserver der ZBW – Leibniz-Informationszentrum Wirtschaft The Open Access Publication Server of the ZBW – Leibniz ...»

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P (Mj ) is a weighting factor to correct for the model size, i.e. for the number of explanatory variables. k is the prior model size, K is the total number of available explanatory factors, and kj is the number of explanatory variables included in model j. Models with a size close to the prior model size is given a higher weight. In doing so, I correct for the fact, that models with a large number of explanatory variables per se achieve a better fit than models with only few explanatory factors.7 It is also possible to calculate the probability that a coefficient has the same sign as its mean conditional on inclusion. This can serve as a check for the reliability of the results delivered by the posterior inclusion probability. A sign certainty probability value close to one means that the coefficient sign of a variable is independent of the model specification.

For a detailed description of the method I refer to Sala-i-Martin et al. (2004).

Note, that I only report the estimation coefficients unconditional on inclusion. Magnus et al. (2010) argue that the conditional estimates overstate the impact of the explanatory factors on the dependent variable.8

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4.1 Baseline Estimation Applying the model averaging approach gives me the posterior inclusion probability and the (weighted) coefficient as well as the (weighted) standard deviation for each factor.

Variables with a higher inclusion probability are more likely to be significant explanatory factors of the dependent variable. In other words, the posterior inclusion probability gives a measure of the model fit containing this variable compared to models estimated without this variable. A posterior inclusion probability above the prior inclusion probability complies with a recommendation for including this variable. A value below the prior probability means omission.

I include 3 indicators concerning taxation, 1 measure for employment protection, 5 indicators of the bargaining system, 2 for product market regulation, and 4 measures for the unemployment benefit system. An indicator for credit constraints is included as a control variable. I specify the prior model size to be equal to 6, i.e. I expect that the model consists of 6 variables. Thus, the prior inclusion probability is 16. The corresponding estimation output can be found in Table 1, where the variables are sorted in descending order regarding their posterior inclusion probabilities in column (1). The weighted coefficients and standard deviations are displayed in columns 2 and 3, while the sign certainty probability can be found in the fourth column. The employment protection legislation, the payroll tax, the consumption tax, and the fourth and fifth year benefits are highly robust with a posterior inclusion probability close to 1. Similarly, the first year benefits, the public ownership, the barriers to entry and the bargaining coordination also have posterior inclusion probabilities above the prior. If I additionally include a measure for benefit duration, the fourth/fifth year benefits lose significance while the newly introduced duration measure is significant. Hence, the later year benefits can, to some extent, be In their paper, Magnus et al. compare different model averaging techniques and proposes a new method called weighted averaged least squares (WALS). However, to my knowledge, it is questionable whether this method outperforms the BACE approach applied in this paper in terms of reliability of the results. One crucial advantage of the WALS method is its computational simplicity. Since I only rely on up to 18 explanatory variables, the estimations are computationally feasible within the BACE framework which is why I refrain from using the WALS method.

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seen as a proxy for the benefit duration. Whether the later year benefits or the benefit duration indicator is included does not affect the remaining indicators.

Turning to the direction of influence, one can see that the majority of robust variables has a negative impact on unemployment. An increase in the employment protection legislation, the bargaining coordination, the access to credits, the barriers to entry, the consumption tax as well as in the fourth and fifth year benefits tends to lower the unemployment rate.

In contrast, the payroll tax, the public ownership, and the first year benefits are positively related to the unemployment rate. Note that the sign certainty probability measures conform to the posterior inclusion probabilities. Significant variables concerning the latter measure have sign certainty probabilities close to 1.9

4.2 Alternative Prior Model Sizes and Other Modifications The prior model size is a factor which serves as a sensitivity check. Such a check has to focus on the comparison of results produced assuming distinct prior model sizes. In the baseline specification I have relied on a prior model size of 6. Now I perform the same estimations for prior model sizes of 2, 4, 8 and 10. Running this kind of sensitivity check for the baseline estimation shows that most of the outcomes are insensitive to the variation of the prior model size. I have considered 16 institutional indicators in the analysis,

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so far. However, there are some more institutional variables available. More specifically, One might argue that possible endogeneity can bias the outcomes. I set up a model containing all significant variables with respect to the model averaging procedure, and carried out a two-stage least squares regression with the lagged variables of the endogenous explanatory factors as instruments. The results provided in section 4.3, Table 3, show that the results do not change considerably when endogeneity is taken into account.

I have indicators for the overall unemployment benefits, the tax wedge, the benefit duration, and the overall product market regulation. I have neglected these indicators in order to avoid multicollinearity in the estimation. This might occur since the mentioned indicators are products of some other indicators which I have already considered in the estimations. For example, the tax wedge is just the sum of the payroll, the income, and the consumption tax. Including them might vary the findings concerning the indicators of the same category, while the remaining indicators should show similar results.

Indeed, the inclusion of the four additional variables has only a small impact. Merely the tax wedge shows robustness with a positive coefficient. The overall benefits, the overall product market regulation as well as the benefit duration are not significant. Note that when including the benefit duration the fourth and fifth year benefits inclusion probability drops independently of the prior model size. Apart from that, the same indicators are robust, only the inclusion probabilities for some variables fall such that only 4 factors have an inclusion probability close to 1. This can be explained by the larger number of models to be estimated. For the model with 16 explanatory variables, I estimate 216, i.e. 65536 different models. The setup with 20 variables and 1048576 models lowers the relative model quality of each model compared to the remaining models and, consequently, the posterior inclusion probabilities.

Furthermore, one might argue that the shocks which are included in each single model have an impact which lasts more than one year. Hence, I extended the set of fixed regressors by taking into account the lagged values of the shock variables. This reduces the estimation period to 1983 to 2005. Again, I can only report slight changes in the findings.

The inclusion probabilities of the bargaining coordination and the first year benefits drop considerably but are still clearly above the prior.

Additionally, according to Baccaro and Rei (2007) I included the change in the ination rate and the lagged labor productivity growth as macroeconomic controls. The results hold independent of the inclusion of both variables. Only the bargaining coordination posterior inclusion probability drops from 0.88 to 0.63.10

4.3 Single Model Estimation

The model averaging approach serves to identify significant variables. However, it is not appropriate to allow for several extensions of the econometric model. Hence, I set up a model consisting of those institutional variables which have been identified as signifThe construction of the TFP shock might be exposed to measurement error. Hence, I use a different factor for this shock, namely the TFP growth rate from the Total Economy Database provided by the Conference Board. Including this alternative variable has no impact on the results.

icant in the model averaging framework, additional to the usual shock variables. Once a reasonable number of institutional indicator is selected, the single model approach is more flexible. In this single model, I can allow for cross-section heteroscedasticity and endogeneity. The endogeneity problem is tackled by applying instrumental variable estimation. I use the lagged values of the endogenous variables as instruments. However, I first have to check whether the lagged values are adequate instruments for the endogenous factors. I assume that all 8 institutional variables are endogenous and use the two-stage least squares estimation as my instrumental variable approach. The F-statistic of the first stage regression of the endogenous variables on the exogenous ones to test for joint significance of the instruments are displayed in table 3.

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Obviously, the F-statistics of the first stage regressions are above a value of 10 what is usually seen as the threshold level for weak instruments (see Stock and Staiger 1997).

According to this, by using the lagged values of the endogenous variables as instruments I can take the endogeneity problem into account. Table 4 presents the results of this single model estimation.

Specification (2) is estimated with the heteroskedasticity-consistent White estimator.

Specification (3) uses two-stage least squares with the lagged values of the endogenous variables as instruments. Specification (4) additionally includes the output gap as a control variable. This has been done to test whether the shock variables are indeed able to completely capture business cycle dynamics of the unemployment rate. Although the output gap is highly significant, the institutional results do not change substantially.

Table 4: Single model estimation Independent variable: Unemployment rate (1) (2) (3) (4)

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As a further robustness check, I successively exclude 5 year periods from the sample, starting with the period from 1982 to 1986, then 1987 to 1991, and so on. This sample reduction has only an impact on the first year benefits which become insignificant for the panel from 1987 to 2005.

Another check is to leave out each country at a time in specification (2). While the results for the payroll and the consumption tax, the bargaining coordination, the public ownership, the barriers to entry, and the credit constraints still hold, the first year benefits turn out to be insignificant if I exclude Canada. The effect on the fourth and fifth year benefits is even more severe. When excluding one of the following countries, Denmark, the Netherlands, Norway, Spain, or Switzerland, the fourth and fifth year benefits are insignificant. I interpret this finding as a sign for the heterogeneous impact of the unemployment benefit system in different countries. One reason could be the dependence on other institutional or macroeconomic conditions.

4.4 Discussion

I expect the tax system to be positively correlated with the unemployment rate. In fact, I estimate a positive coefficient for the payroll tax rate and for the tax wedge. The income tax is not significant. Furthermore, the consumption tax is negatively related to the unemployment rate, i.e. the higher the consumption tax, the lower the unemployment rate.

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