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Why is there only one single paper that tries to quantify the optimal tax progressivity in a labour market with collective wage bargaining? This is most probably explained by the fact that to do so, we are forced to leave the area of general and clear-cut analytical results. No-one has so far come up with illuminating analytical expressions that characterise the optimal point. For an optimal tax analysis that involves two tax rates (in our case: the marginal and the average tax on labour income), we need two indicators per tax: its marginal eﬀect on utility, and its marginal eﬀect on the public budget. The latter soon becomes involved once we include the indirect eﬀects through the changes in the tax bases of other taxes (which is necessary in general equilibrium). It remains possible to derive analytical expressions for these eﬀects, but they no longer provide an insight in the economic mechanisms. Hence the shift to numerical models. Here we lose generality, but we may focus directly on parameters that are quantitatively relevant in the situation at hand. Nevertheless, the choice in this paper is to limit the analysis to a simple numerical model. The reason is that once we have identiﬁed a parameter that is quantitatively important, we do not want to stop at this point, but explain why it is important, and why the eﬀect was qualitatively to be expected, even if we could not foresee that it would quantitatively drive the results.
In my attempt to exploit the quantitative potential of the model presented in this paper, I calibrate it both to unweighted averages of the institutional and macroeconomic parameters of eight large OECD economies and to the individual country constellations. A decomposition exercise is executed by varying one of the parameters at a time. This allows us to identify the key drivers of the diﬀerences in optimal tax progressivity.
The most remarkable simulation result is that both at the level of average OECD parameters and for most of the individual countries, optimal tax progressivity is considerably lower than actual progressivity. At the country level, however, we do not get a uniform picture. In a few countries optimal progressivity is even higher than actual progressivity. The between-country diﬀerences can be traced back to diﬀerences in the initial conditions. The eﬀect of the initial unemployment rate is particularly strong. The higher initial unemployment, the higher optimal tax progressivity. Another important driver is the general tax level. High taxes in the initial situation lead to a lower optimal level of tax progressivity. The initial level of tax progressivity plays a signiﬁcant role as well. It aﬀects the optimal progressivity through the interaction with labour supply elasticities. This eﬀect is discussed in detail in the body of the paper.
The model of this paper is set up to focus on one particular trade-oﬀ connected with tax progressivity, at the cost of a number of other aspects that are not included. These should be kept in mind when interpreting the results. First, the quantitative results of the paper do not automatically carry over to other theories of unemployment (search-and-matching and eﬃciency wage theories). However, Pissarides (1998) and Sørensen (1999) show that these approaches produce results similar to the collective bargaining model when they are calibrated to plausible parameter values and applied to taxation issues. The focus on the collective bargaining model is therefore not overly restrictive.
Second, there are other distortions, apart from the eﬀect on labour supply, that run counter to the wage moderating eﬀect of tax progressivity. Examples are Fuest and Huber (1998), who focus on the distortionary eﬀect on human capital formation, Kleven and Sørensen (2004), who describe the eﬀects on dual labour markets, where only one sector is characterised by imperfections, and Koskela and Schöb (2007), who stress the negative eﬀect on workers’ eﬀort.
Third, the paper focuses on eﬃciency issues and abstracts from one core aspect in the early literature on optimal taxation (Mirrlees, 1971; Tuomala, 1990): nonobservable productivity diﬀerences of heterogeneous agents. This can be seen as an analogue to the Ramsey (1927) approach to indirect taxation, where distributional concerns are ignored as well, in order to get a clear picture of the eﬃciency dimension.
Finally, the model of this paper remains at the aggregate level and captures labour market institutions and the tax and transfer system only by a small set of macro indicators. Micro econometricians argue that such models miss the very essence of the labour market: heterogeneity. In fact, there are examples of models that combine microeconomically founded mechanisms of involuntary unemployment and demographic as well as institutional heterogeneity in the labour market: Sørensen (1997), Graaﬂand et al. (2001), Aaberge et al. (2004), Arntz et al. (2008). Due to their complexity, the outcomes of such models are often diﬃcult to explain and to decompose into eﬀects that are qualitatively known from the theoretical literature.
This interpretation work is simpliﬁed through a condensed and simpliﬁed “model of the model” (e.g. “Mini-MIMIC” (Bovenberg et al., 2000) as a complement to Graafland et al., 2001). It is in this tradition that the present paper is most appropriately placed.
The plan for the rest of the paper is as follows. In Section 2, I present the diﬀerent parts of the model, my approach to labour supply calibration, the welfare criterion and the OECD parameters used for the simulations. Sections 3 covers the simulations for the OECD average, diﬀerent country speciﬁcations and systematic parameter variations that make a decomposition of the tax progressivity eﬀect possible. In Section 4, I perform a sensitivity analysis, before Section 5 concludes. The appendix contains the algebraic details of the labour supply calibration and a list of data sources.
2 The model
We consider a small, representative production sector with monopolistic competition in a closed economy. The wage is determined through collective wage bargaining, which produces involuntary unemployment. The government collects taxes on consumption, proﬁt and labour income. In this situation, the progressivity of the labour income tax is chosen so as to maximise the expected utility of a representative worker.
Tax progressivity is captured by a marginal wage tax rate, tm, which in general L will diﬀer from the average rate, ta, and has a direct impact on the hours-of-work L decision.3 This is the “calibrated share form” of the CES function (Rutherford, 1998), which simpliﬁes calibration by linking the parameters directly to observable values. In the following, a variable with a bar generally means the value in the initial situation, which is a calibration constant in the counterfactual simulations.
Throughout the paper, the tax schedule is only characterised locally by the average and marginal tax rate. The global form of the schedule (linear progressive, exponential etc.) is left unspeciﬁed.
The share parameter in (2) is expressed relative to extended income, YE,
Appendices A.1.1 and A.1.2 describe how this function is calibrated to empirical values of labour supply elasticities with respect to income and wage.
Households are assumed homogeneous with respect to their labour-leisure choice, but they diﬀer with respect to their participation decision. This is modelled by heterogeneity in their ﬁxed cost of taking up work, which generates the separation between participating and non-participating individuals. Those with low ﬁxed costs enter the labour market, whereas those with high ﬁxed costs stay at home.4 The two step labour-supply decision (participation, hours of work) is solved backwards: First, individuals determine the optimal choice of hours assuming that they participate. Second, they compare their ﬁxed cost of working with the outcome of the optimal hours choice, taking the presence of involuntary unemployment into account. In particular, the unemployment-weighted (u) expected utility of supplying labour, Ul, is relevant for the comparison,
Ul = (1 − u)Ue + uUu, (5)
which is the same for all individuals. They compare it with their individual ﬁxed cost of supplying labour, U0, and supply labour if Ul U0. The calibration of the distribution of U0 to an empirical participation elasticity is explained in Appendix A.1.3.
See Kleven and Kreiner (2006a) for a general discussion of this approach.
The production sector consists of a large and ﬁxed number, n, of symmetrical ﬁrms.
Firms are small in the sense that repercussions from their production decisions on the economy-wide aggregate output and price index may be neglected. All ﬁrms interact in Dixit-Stiglitz type monopolistic competition (Dixit and Stiglitz, 1977).
Each ﬁrm faces a demand curve with elasticity η (see Section 2.1).
Wage formation is modelled as collective bargaining between a trade union and a representative ﬁrm. More speciﬁcally, I assume (i) that bargaining is only about the wage, not about employment (“right-to-manage” approach)5, (ii) that the trade union is only concerned with the utility of its employed members (“insider model”)6 and (iii) that hours of work are chosen individually according to the optimisation in Section 2.2, and are not subject of the collective bargain.7 Wage formation is conceptualised as the maximisation of a Nash function, Ω, where trade unions are represented by the utility mark-up over the fallback option, Ue − Ua, and ﬁrms by proﬁts, π. The relative bargaining power of the trade union, λ, is an unobservable parameter to be determined in the calibration.
The fallback option of the union, Ua, is composed of possible employment in another ˜ sector, Ue (with a probability that equals the employment rate), and unemployment (receiving unemployment beneﬁts, see Section 2.3):
˜ Ua = (1 − u)Ue + uUu Sørensen (1999) shows that for the type of numerical analysis intended, the choice between right-to-manage and eﬃcient bargaining (where bargaining extends also to the number of employed workers) hardly matters.
Appendix A.1.4 shows that the results are identical to those obtained with a utilitarian union as long as the value shares and the elasticities of labour demand and hours supply are constant.
In the Sørensen (1999) model, it hardly matters quantitatively whether collective bargaining includes hours of work or not. In the model of this paper – with a CES utility function instead of additively separable preferences –, including hours of work in the bargaining set-up would mean a considerable complication of the ﬁrst-order conditions.
The welfare criterion used to determine the optimal degree of tax progressivity is the ex-ante expected utility of workers who do not yet know whether they will be employed or unemployed. This is exactly the same indicator that also governs labour supply at the extensive margin (equation 5),
Ul = (1 − u)Ue + uUu.
The focus on the utility of workers is justiﬁed by the fact that all other magnitudes relevant for a welfare assessment – consumption of the capitalists and the consumptive part of the public budget – are kept at their initial level during the simulations. In the sensitivity analysis, I look also at the case that tπ is ﬁxed and the welfare of capitalists is disregarded (Section 4.3).
2.9 Calibration to OECD economies
The basic model of Section 2 is calibrated to a set of macroeconomic and institutional parameters for a number of OECD countries in 2004/5. The data set contains the six largest European economies: France (FRA), Germany (GER), Great Britain (GBR), Italy (ITA), Spain (ESP) and the Netherlands (NLD), plus the USA and Japan (JPN).