Explaining labor wedge trends: an equilibrium search approach.

AuthorRojas, Coralia A. Quintero
  1. Introduction

    Over the last few decades, most OECD countries have shown large differences in aggregate hours of market work. The interesting issue of understanding these differences in work effort has resulted in a number of significant contributions. For instance, Prescott (2004) studies the taxes account for differences in labor supply over time and across countries from the early 1970's to the mid-1990's and finds that for acceptable values of labor supply elasticity, the effective marginal tax rate on labor income explains most of the differences at points of time and the large change in relative (to US) labor supply over time. On this line of research, Rogerson (2004) points to the role of taxes and technology as determining factors in the changes from 1956-2000, whereas Rogerson (2006) argues that changes in technology and government are promising candidates to explain the broad changes over the period 1956-2003. Finally, Ohanian, Raffo and Rogerson (2008) emphasize the intensive margin of aggregate hours of work and find that the neoclassical growth model, augmented with taxes, can account for most of the variations over the period 1956-2004.

    However, since the late 1970's, the differences in aggregate hours across countries seem to be largely to quantitatively important differences along the extensive margin. Moreover, the relative change in the employment rate behaves differently than the relative change in hours worked per employee. To stress this point, Langot and Quintero Rojas (2009) construct counterfactuals to quantify the relative importance of the extensive and intensive margins of aggregate hours of market work in the observed differences between Europeans and Americans since the 1970's. They show that the extensive margin explains most of the total-hours-gap between regions, while the intensive margin plays the smallest role. Furthermore, Ljungqvist and Sargent (2007a, 2007b and 2008) suggest that the large decrease in the employment rate in European countries observed after 1980, was an important factor in the dynamics of total hours worked. In addition, there is a bulk of evidence from previous literature on the European unemployment problem regarding the effects of labor market indicators other than taxes on the extensive margin (4).

    This suggests that the basic neo-classical growth model with endogenous labor supply is insufficient to account for the impact of the various labor market institutions on aggregate hours of work. However, when this model is extended to include a search and matching process in the labor market it is able to explain the employment dynamics. An example of this is the study by Quintero Rojas (2009), who examines the incidence of various labor market institutions on the extensive margin to explain the evolution of aggregate hours over the period 1980-2003. However, her model holds the intensive margin constant, thereby neglecting an interesting dimension of the problem.

    Against this rich background, our main contribution is twofold. Firstly, we take into account the differentiated dynamics of the two main margins of aggregate hours of work, i.e., the average hours worked per employee (or intensive margin); and the employment rate (or extensive margin). This enables us to assess the relative effect of taxes on each margin, on the one hand; and that of unemployment benefits and workers' bargaining power on the other. Secondly, the analysis covers the updated period 1980-2013.

    More precisely, we develop a dynamic general equilibrium model with search and matching frictions, wage bargaining, and efficient bargain on the number of hours worked per employee. The model is extended to include a tax/benefit system consisting of taxes on consumption, labor income, and payroll, unemployment benefits, and the workers' wage bargaining power. Since the model distinguishes between the two margins of the aggregate hours of work, we are able to look at the relative contribution of taxes and labor market institutions to each margin. Contrary to Ljungqvist and Sargent (2007a), our "representative family model" incorporates congestion effects through a matching function. This friction leads to a more realistic elasticity of the employment rate to the observed shifts in the unemployment replacement ratio (Ljungqvist and Sargent, 2007b).

    The model builds on the Diamond-Mortensen-Pissarides workhorse (Diamond, 1982; Mortensen, 1970; Pissarides, 1985), though avoids the kind of criticism leveled by Shimer (2005), by taking a long-run approach and through our choice of labor market institutions and the changes that occurred in these (5).

    With respect to methodology, we proceed as follows. First, the observed differences in aggregate hours of work are summarized by the labor wedge (Shimer, 2009), defined as the deviation of the marginal product of labor (MPL) from the marginal rate of substitution between consumption and leisure (MRS). Next, we conduct an accounting procedure inspired by Ohanian et al. (2008). (6) In broad terms, we compute the empirical counterparts of theoretical labor wedges, under various scenarios in order to evaluate the impact of distortions. The closer the empirical wedges are to zero, the better the model accounts for the observed labor behavior. Hence, the reduction of a wedge that results from the introduction of a distortion is interpreted as a measure of the quantitative importance of such distortion.

    We show that; for the ten countries in our sample; the trends of the two margins of the aggregate hours are well explained by our search model; when it includes the observed heterogeneity of both taxes and labor market institutions. Since these empirical results come from a unified framework, they also provide a strong support for the matching models.

    The remainder of the paper is organized as follows. Section 2 present some stylized facts on total hours worked and on the contrasted dynamics of the hours worked per employee (the intensive margin) and the employment rate (the extensive margin). In Section 3, we present a search and matching model in which both margins are endogenous. In Section 4 we quantitatively evaluate the model using an accounting procedure. Section 5 presents the concluding remarks. Finally, the Appendix A is devoted to data.

  2. Empirical Regularities

    In this section we establish a number of facts concerning the allocation of time in ten OECD countries. Our sample includes Austria, Belgium, Finland, France, Italy, the Netherlands, Spain, Sweden, the United Kingdom and the United States. The analysis covers the period 1980-2013. First, we define aggregate hours worked and its two main dimensions. Next, we describe our sample and the main variables and labor market institutions. The full definition of variables and data sources are included in the Appendix A. Finally, we perform a series of empirical exercises.

    2.1 Aggregate hours of work in Western Europe and the U.S.

    Let N, h and L respectively denote employment level, average hours worked per employee and working age population. Thus, the decomposition of the aggregate hours of market work, H, is given by

    H = h x N/L (1)

    The first component of this decomposition is the intensive margin, since it represents the average work effort that each employed person invests. Meanwhile, the second term is the extensive margin, since it refers to the proportion of people who have a job.

    To provide an initial overview of the labor behavior, we compute the sample mean of each variable in equation (1) from 1980 to 2013. We observe notable differences in the total hours worked. Moreover, countries with similar performances (measured by the aggregate hours) show contrasting work efforts and employment rates. For instance, the average total hours worked in Italy and the United States is the same. However, the individual work effort in Italy is higher to compensate the lower employment rate. Similarly, the average aggregate hours worked in Belgium, Spain and France are very similar to one another. However, while employees in Belgium work virtually the same amount of hours as those in Sweden, in Spain the individual work effort is high enough to compensate for its lower employment rate with respect to Belgium and Sweden.

    For a more detailed analysis, we turn to the evolution over time of aggregate hours and its components, shown in Figures 1 to 3.


    Aggregate hours worked. From Figure 1, we can see very varied trend-experiences: Austria (AT) and France (FR) show a steady decline over the whole period. Spain (SP), Belgium (BE), the United Kingdom (UK), the United States (US), Italy (IT), the Netherlands (NL) and Sweden (SW) exhibit similar fluctuations around their means, though these are less marked in the last three countries, and far more marked in Spain and the Anglo-Saxon countries. Moreover, all mainland European countries start and finish the period with a declining trend, whereas the trend in the Anglo-Saxon countries starts to increase by the end. In contrast, Finland (FI) displays a unique pattern with a sharp decline in the middle of the period.


    Average hours per employee. The patterns for the average work effort seem more similar (Figure 2): most countries show a declining trend over the whole period, though that is less marked in Italy, Spain and the Netherlands. The two exceptions are Sweden and the United States. Sweden experienced an increasing trend until the end of the 1990's, followed by a few years of decline, then a slightly longer upward trend before finally decreasing again from 2010 on. In contrast, the United States shows a flat trend at the beginning and then oscillates in a way similar to its aggregate hours.


    Employment rate. In most countries the employment rate (Figure 3) shows a similar but sharper fluctuating pattern than aggregate hours. Two notable exceptions are Austria and France. In the first case, the...

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