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Erschienen in: International Tax and Public Finance 1/2017

09.06.2016

Optimal unemployment benefit policy and the firm productivity distribution

Erschienen in: International Tax and Public Finance | Ausgabe 1/2017

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Abstract

This paper provides a novel justification for a declining time profile of unemployment benefits that does not rely on moral-hazard or consumption-smoothing considerations. We consider a simple search environment with homogeneous workers and low- and high-productivity firms. By introducing a declining time profile of benefits, the government can affect the equilibrium wage profile in a manner that enhances the sorting of workers across low- and high-productivity firms. We demonstrate that optimal government policy depends on the dispersion and skewness of the firms’ productivity distribution.

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Fußnoten
1
Mortensen (2003) provides evidence whereby wage dispersion for observationally equivalent workers can be explained by more productive firms paying higher wages. For detailed empirical work, see Davis et al. (1996), Abowd et al. (1999), Haltiwanger et al. (1999, (2007) and Bartelsman et al. (2013).
 
2
Note as well that the much discussed skewness of the distribution of firm size (Luttmer 2007) is consistent with our model as declining unemployment benefits imply that the expected number of workers per firm increases with firm productivity.
 
3
See Tatsiramos and van Ours (2014, Table 2), and for updated statistics, the following Web site http://​www.​oecd.​org/​els/​benefitsandwages​statistics.​htm.
 
4
Suppose that firms can enter by incurring a fixed entry cost, that an entering firm’s productivity is determined by a random draw (productivity is high with a probability p and low with a probability \(1-p\)) and that entry is determined by a zero discounted expected profit condition. We then conjecture that if the entry cost is sufficiently high, in equilibrium, the total measure of high-productivity firms will be lower than the total measure of the work-force, so that our qualitative results will remain valid.
 
5
Instead of assuming that there is a measure pM of high-productivity firms, each being able to employ at most one worker, we could assume, alternatively, that there is less than pM high-productivity firms, each being able to employ more than one worker. Ultimately, what matters for our analysis is that the measure of high-productivity jobs is given by pM and that firms post vacancies at a specified wage.
Notice that we are invoking a tractable wage determination mechanism which assigns the entire bargaining power to the firm. We conjecture that our qualitative results will remain valid under alternative wage determination mechanisms (such as Nash bargaining).
 
6
For empirical evidence on random matching, see Petrongolo and Pissarides (2001). The random matching assumption seems an appropriate way of capturing labor market frictions. These underlie the potential gain from government intervention discussed below.
 
7
To ensure that the fiscal system is sustainable, we assume that capital markets are perfect implying that there are no binding liquidity constraints. Without loss of generality we also assume that the government has no revenue needs.
 
8
Note that the subscript of H refers to the length of the current unemployment spell and not to absolute time.
 
9
Fully differentiating equations (19) and (20) with respect to s we can obtain an expression for \(\partial U^{P}/\partial s\). For technical reasons we assume that \(\lim _{s\rightarrow 0}(\partial U^{P}/\partial s)<\infty \). This property holds for a large class of matching functions.
 
10
Maximizing aggregate output is a common assumption in the search literature (e.g., Albrecht and Axell 1984). Given the linearity of utility in income, an allocation is second-best efficient (given the matching friction) if and only if it maximizes the sum of utilities.
 
11
Given that the government objective is to maximize aggregate output, and hence sets aside redistributive concerns, a flat regime whereby the benefit level is set so low such that all firms are active, coincides with the benchmark regime without unemployment benefits.
 
12
US data on monthly separation rates indicate an average of about 1.5 %, which is consistent with the example worked out in the next section [see, for example, Yashiv (2007, Table 1b) and Elsby et al. (2013, Figure 2)].
 
13
When no sorting is optimal, there is no need for unemployment benefits. In contrast, when full sorting is optimal, a flat regime with sufficiently high unemployment benefits is warranted.
 
14
The constant-returns-to-scale Cobb–Douglas matching function has wide empirical support (see Petrongolo and Pissarides 2001). Yashiv (2000) and Borowczyk-Martins et al. (2013) provide detailed estimates and discussion. Of course, the matching function can only take the form \(0.1*U^{0.5}V^{0.5}\) in the range where \(0.1*U^{0.5}V^{0.5}\le \min (U,V)\). Since \(V=U+30\), the relevant range is \(30/99\le U\).
 
15
If it were the case that \(\lim _{s\rightarrow 0}\left( \partial \overline{V}/\partial s\right) <0\), then \(\overline{V}<0\) for sufficiently small \(s>0\), which contradicts that \(\overline{V}\ge 0\).
 
16
The constant-returns-to-scale implies that
$$\begin{aligned} m_{U}(U^{P},V^{P})U^{P}+m_{V}(U^{P},V^{P})V^{P}=m(U^{P},V^{P}). \end{aligned}$$
As \(M-V^{P}=L-U^{P}\) and \(M>L\) it follows that \(V^{P}>U^{P}\ge m(U^{P},V^{P})\). Therefore, \(m_{U}(U^{P},V^{P})+m_{V}(U^{P},V^{P})<1\) and hence \(\lim _{s\rightarrow 0}\left[ m_{U}(U^{P},V^{P})+m_{V}(U^{P},V^{P})\right] \le 1\).
 
17
When \(s\rightarrow 0\), there is no frictional unemployment so that employment equals the smaller of the measure of workers and the measure of active firms. Thus, employment is L in the no- and partial-sorting configurations, and is pM in the full-sorting configuration.
 
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Metadaten
Titel
Optimal unemployment benefit policy and the firm productivity distribution
Publikationsdatum
09.06.2016
Erschienen in
International Tax and Public Finance / Ausgabe 1/2017
Print ISSN: 0927-5940
Elektronische ISSN: 1573-6970
DOI
https://doi.org/10.1007/s10797-016-9408-1

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