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Table 8 shows the results of the decomposition analysis. Disregarding welfare
changes for the capitalist has a general level eﬀect on optimal tax progressivity:
Optimal tax progressivity is higher than in the base case, because capitalist need not to be compensated for the income losses they suﬀer when we move away from the labour-input-maximising point in Figure 1. In the “average OECD” model, the utility of the employed through the adjustments of ta necessary to compensate the public budget L for unemployment beneﬁt payments. It turns out that with lower valuation of unemployed time, the reductions in unemployment through higher tax progressivity are slightly lower than in the main variant. This pushes the eﬀect in the opposite direction.
optimal CRIP is now at 0.85 (compared to 0.93 in the base case with compensation).
Interestingly, this is almost exactly equal to the actual CRIP of 0.87.
The partial eﬀects of Table 8 are in a similar range to the base case (Table 2). Some quantitative changes need comment, however. The coeﬃcient of the value share of labour (sL ) is now positive. This is plausible, because the higher the share of labour, the lower proﬁts and the smaller the external eﬀect on capitalists, which works in favour of high tax progressivity. The partial eﬀects of the tax rates (tC, ta, and, for the ﬁrst time, tπ itself) are stronger. This is a tax-base eﬀect. We are L farther away from the labour-input maximum. The tax base for the wage tax is therefore smaller. A given tax revenue loss from shrinking economic activity (which is the higher the higher the tax rates) now requires a larger adjustment of the average wage tax. This makes additional tax progressivity, which produces tax revenue losses, less attractive.
Table 9 shows the decomposition for the individual countries. sL and tπ now enter the picture with contributions to the explanation of deviations from the OECD average. However, as their coeﬃcients are not particularly large and cross-country variation is moderate for these variables, the overall qualitative pattern remains unchanged.
Table 9: Cross-country diﬀerences
The model of the paper is used to analyse the determinants of optimal tax progressivity in a labour market with collective wage bargaining and ﬂexible labour supply.
The framework chosen is simple enough to keep an overview over the basic mechanisms, but has suﬃcient complexity to be calibrated to a number of behavioural and macroeconomic parameters, partly universal, partly country-speciﬁc.
In particular, the following parameters are used to adjust the model to countryspeciﬁc conditions: factor shares in value added, important macroeconomic tax quotas (consumption tax, labour tax, capital tax), unemployment rates, tax progressivity and replacement rate. In addition, three behavioural parameters were taken into account: wage elasticity of labour supply at the intensive and at the extensive margin, and income elasticity of labour supply.
When calibrated to average OECD values, the model produces the following
• Optimal tax progressivity is lower than actual progressivity. Moving to the optimal point would mean a ﬁve percent cut in the marginal wage tax, which would allow for half a percent compensating decrease in the average wage tax.
• The optimal tax structure is located in the region where increasing the marginal labour tax produces negative tax revenue.
• The optimal tax structure is considerably far away from the point of maximum labour input. This is because an labour input gain through lower unemployment has more value (in welfare terms) than labour input losses at the hours-of-work margin.
There is considerable cross-country variation both in actual and optimal tax progressivity.
A decomposition approach shows that approximating the general eﬀect by linear additive eﬀects of the seven country-speciﬁc parameters gives a reasonable ﬁt, where:
• Higher initial unemployment leads to higher optimal tax progressivity, because unemployment reduction eﬀects are approximately proportional to the initial level.
• A higher general tax level leads to lower optimal tax progressivity, because the tax revenue losses when departing from the employment maximum, which must be compensated through a higher average labour tax, are higher.
• Initial tax progressivity aﬀects optimal progressivity. The extent of this eﬀect depends on the exogeneity assumptions in the calibration. If labour supply elasticities are assumed to be exogenous and constant across countries, the eﬀect it large. If the elasticity of substitution between consumption and leisure is considered a “deep”, constant parameter, the eﬀect is considerably smaller.
This last point may be translated into a ﬁrst indication of where the results may be reﬁned in future work. A careful meta-study on labour supply elasticities could explore which parameters of an underlying utility function should most reasonably be considered to be “deep” constants. Such an approach could re-establish the calibration-simulation dichotomy, which becomes blurred in the alternative labour supply calibration of Section 4.1.
There are other points where the analysis of this paper potentially can be improved upon. The wage bargaining model used does not have a suﬃcient number of parameters25 to be calibrated to empirical estimates of wage equations. There are problems at the other end of the model-empirics match as well. Empirical wage curve estimates turn out to be very unstable, so that it is diﬃcult to ﬁnd a good standard of comparison (Folmer, 2009). Nevertheless, it could be illuminating to replace the wage bargaining equation in the model with wage curves that are more similar to empirical speciﬁcations. Other aspects that could be integrated in the model in a straightforward manner are interactions between diﬀerent skill types of workers and international capital mobility, which both are likely to have an impact on the results.
However, here we approach the grey area of “real” applied models. These focus on institutional detail at the cost of more and more intertwined economic eﬀects that can only be disentangled with great eﬀort. For a recent example of such a model with diﬀerent skill types, labour supply reactions at the micro level, a diﬀerentiated sectoral structure and mobile capital, see Boeters and Feil (2009).
Finally, if we put aside all doubts about the working mechanisms of the model and take the levels of optimal tax progressivity that we obtain at face value, we may proceed to a question of political economy: What might explain the deviations of actual tax progressivity from the level characterised as “optimal” in this study?
Given that there are deviations in both directions, this is not an easy question to answer. The results of the paper apply to a representative ex-ante worker and do not capture distributional considerations. Governments with large redistributive ambitions are likely to choose more progressive tax schedules than the “optimal” ones of this paper. On the other hand, if the actual tax policy in a country is determined by labour market insiders, whose unemployment risk is lower than the average unemployment rate, this would lead to less tax progressivity than the reference values Actually, there is one free parameter, the value of involuntarily unemployed time. The eﬀect of this parameter on the results is small (see Section 4.2), so that it cannot be used to tune the bargaining equations to empirically estimated wage curve elasticities.
of this paper. It might be an interesting line of research to see whether empirical indicators of redistribution willingness or insider power in unions are better correlated with deviations between actual and optimal tax progressivity than with actual tax progressivity itself. But considering the small size of the potential dataset and the many additional assumptions that enter the calculations of the optimal tax rates, it would be a surprise if such an empirical analysis produced strong, signiﬁcant results.
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