اصطکاک های جستجو، انعطاف ناپذیری دستمزد واقعی و طراحی بهینه ی بیمه بیکاری

In this paper, we study the optimal unemployment benefits financing scheme when the economy is subject to labor market imperfections characterized by real wage rigidities and search frictions. The US unemployment insurance financing is such that firms are taxed proportionately to their layoffs to finance unemployment benefits. Using DSGE methodology, we investigate how policy instruments should interact with labor market imperfections. It is shown that wage rigidities in a search and matching environment cause welfare costs, especially in the absence of an incentive-based unemployment insurance. This cost is mainly due to the distorting effect of wage rigidities which generate inefficient separations. We show that the optimal unemployment benefits financing scheme – corresponding to the Ramsey policy – offsets labor market imperfections and allows implementation of the Pareto allocation. The second-best allocation brings the economy close to the Ramsey allocation. The implementation of the optimal policies clearly highlights the role of labor market institutions for short-run stabilization.

What is the optimal level of unemployment benefits and how should they be financed? This question is often discussed without taking into consideration labor market rigidities or the potential role of labor market institutions for short-run stabilization, leaving the job to macroeconomic policy, and especially monetary and budget policy. Indeed, the labor market is characterized by search frictions and wage rigidities which distort agents' job acceptance behavior and firms' job postings. This may generate inefficiencies and affect labor market performance as well as social welfare. Furthermore, it influences the response of macro-economic variables to aggregate shocks and can magnify fluctuation costs. The question of using labor market policy to reduce fluctuation costs and to offset labor market imperfections naturally arises. Taking inspiration from the US unemployment insurance (UI hereafter) system, we wonder if firms should be taxed in proportion to their layoffs to finance the costs incurred by the unemployment benefits fund. This paper investigates the optimal design of an unemployment benefits financing scheme in a DSGE framework. While it is often argued that labor market institutions can affect long-run labor market performance, they have received little attention in the field of short-run stabilization. The marked intensity of business cycles in the US and the high volatility of unemployment and vacancies highlights the usefulness of stabilization policies based on the search for an optimal design of the UI. Moreover, the existence of labor market rigidities gives rise to a complementary motivation. These rigidities can be summed up as two categories: those which limit quantity adjustments and those which limit price adjustments. Matching frictions typically represent the first category. They capture the time-consuming search process and generate congestion externalities. They influence the average duration of unemployment and therefore the fiscal cost associated with a dismissal. The second category corresponds to real wage rigidities. These have been pointed out by many authors (Hall, 2005, Shimer, 2005 and Christoffel and Linzert, 2010) as a means of solving the unemployment volatility puzzle. They prevent wages from adjusting instantaneously to economic fluctuations. Consequently, shocks translate into quantities such as employment, job creations and job destructions. Furthermore, they capture rigidities arising from wage norms. They reduce the ability of firms and workers to use taxes and benefits as a threat in wage bargaining. Following Abbritti and Weber (2008), the nature of adjustments in the US labor market may be linked to its institutions which allow strong quantity adjustments associated with significant real wage rigidities.1 The idea that matching frictions and wage rigidities could interact arises. These labor market rigidities introduce some inefficiencies and leave room for policy instruments to reduce inefficiencies and stabilize labor market fluctuations. There is a growing literature about fluctuation stabilization and labor market imperfections. However, most of this literature is centered on the design of the optimal monetary policy (see Christoffel and Linzert, 2010, Blanchard and Gali, 2010 and Abbritti and Weber, 2008). Zanetti (2011), Joseph et al. (2004) and Faia (2008) introduce some labor market institutions such as unemployment benefits, firing costs or a minimum wage in a DSGE model and study their implications for business cycle dynamics. Krause and Lubik (2007) show that labor market frictions and real wage rigidities explain the negative correlation between vacancies and unemployment. However, their contribution in explaining inflation dynamics is small. Campolmi and Faia (2011) show that labor market institutions, and especially the heterogeneity of the replacement ratios, help to explain inflation differentials between the countries of the euro area. From a positive point of view, labor market institutions matter to explain labor market dynamics and inflation volatility differences in the euro area. Krause and Lubik (2007) and Campolmi and Faia (2011) focus on monetary policy issues but none of them characterizes the optimal design of these institutions. The scope of our paper slightly departs from these studies as we only focus on unemployment dynamics and on the design of unemployment benefits financing. In the US, the rapid increase in unemployment after bad shocks can be related to the weakness of the employment protection legislation and the extent to which firms can layoff workers at no cost. Intuition suggests that if firms do not pay the entire cost of their dismissals, their incentive to fire is higher. The role of unemployment insurance in magnifying permanent and temporary layoffs has been illustrated by a large body of papers (Feldstein, 1976, Topel, 1983 and Card and Levine, 1994). In this system based on the experience rating principle, individual employers' contribution rates are varied on the basis of the firm's history of generating unemployment. Basically, more dismissals result in a higher contribution by firms to unemployment insurance. Blanchard and Tirole (2008) highlight the question of the design of unemployment insurance and its link with employment protection. The respective levels of the layoff tax and of the unemployment benefits may play a key role in achieving an optimal allocation. In order to characterize the optimal UI financing scheme, we build a DSGE model with search and matching frictions and where job creations and job destructions are both endogenous. It has been widely recognized that as firms bear a small share of the total cost of job destructions (due to imperfect experience rating), the UI induces too many layoffs. Moreover the existence of search frictions and wage rigidities can strongly affect the firm's hiring and firing behavior. Then we wonder how much firms should be taxed in proportion to their layoffs to finance the fiscal cost induced by their redundancies. Using the DSGE methodology we compute the Ramsey policy. Under this setup we study (i) how the optimal policy can offset labor market imperfections (ii) how it reduces the welfare cost and (iii) how it affects the business cycle. We show that an optimal combination of unemployment benefits and layoff taxes is welfare-enhancing and can improve labor market performance. Wage rigidities in a search and matching environment have a strong impact on the welfare cost, especially in the absence of an incentive-based unemployment insurance. This cost is mainly due to the distorting effects of wage rigidities which generate inefficient separations. The optimal unemployment benefits financing scheme corresponding to the Ramsey policy allows the implementation of the Pareto allocation. As the Ramsey policy may not be easily implementable in the present labor market institutions, we define a second-best allocation. The replacement rate and an experience rating degree are chosen in order to minimize the welfare cost. This policy brings the economy close to the Ramsey allocation. The implementation of the optimal policies clearly highlights the role of labor market institutions for short-run stabilization. The rest of the paper is organized as follows. Section 2 presents the model and the unemployment insurance system. The equilibrium and the optimal policies are defined in Section 3. Section 4 is devoted to simulation exercises and Section 5 concludes.

In this paper, the properties of the optimal unemployment benefits financing schemes are studied using a search and matching DSGE model calibrated on the US economy. There exists an unemployment insurance system approximating to that of the US. Our crucial assumption is the existence of real wage rigidity. In the absence of search frictions, we evaluate how the distortive effect of wage rigidity may be offset by means of an appropriate unemployment insurance policy. Furthermore, through a sensitivity analysis, we evaluate how search frictions impact the design of the UI financing scheme. Our numerical investigations show that wage rigidities are distortive and generate important welfare costs. Indeed, the wage norm reduces wage dispersion and increases the average wage. It results in inefficient separations characterized by too high a separation rate and too heavy wage pressure. The optimal unemployment benefits financing scheme corresponding to the Ramsey policy allows the policy maker to offset this distortion and to implement the Pareto allocation. The optimal layoff tax should be positive to reduce the turnover rate. When the Hosios condition is satisfied (search externalities of the standard matching model with a Nash wage bargaining are eliminated) the optimal unemployment benefits tend to be a little bit negative to reduce the wage pressures. This can be interpreted as a decrease of the workers' outside option (the sum of the home production and the unemployment benefits). We also investigate a particular case in which the Hosios condition does not hold (search externalities characteristic of the standard matching model are introduced). If the bargaining power is in favor of firms and if there are real wage rigidities, it is optimal that the firms pay an amount greater than the expected fiscal cost of an unemployed worker. In this case, unemployment benefits are positive and in the neighborhood of their institutional counterpart. We provide a way to implement a reform of the unemployment insurance. Numerical experiments suggest the second-best allocation appears to be a good approximation of the Ramsey allocation. An appropriate modification of the experience rating degree and the replacement rate brings the economy closer to the optimum. Real wage rigidities magnify the fluctuations of employment and unemployment over the cycle. An optimal design of the unemployment insurance allows the policy maker to reduce labor market fluctuations. As a whole, an optimal combination of unemployment benefits and layoff taxes is welfare-enhancing and improves labor market performance. Our study may be extended in several directions. First, throughout the paper we assume that incomes pooled by family members are equally redistributed. The assumption of perfect risk sharing limits the results. Indeed, considering individual risks would magnify welfare costs and give to the policy instruments a more important role. An extension in a heterogeneous agent framework would be worthwhile. Second, our study shows that the design of the unemployment insurance can contribute to fluctuation stabilization, which completes the results obtained in the optimal monetary policy literature. In a more general model, other sources of distortions, such as imperfect competition and nominal rigidities, could be introduced. A greater number of distortions would require the use of other policy instruments. In this case, the optimal joint design of unemployment insurance and monetary policy could be studied.