Determinants of long-run unemployment.

• Author: Liu, Haoming
• Position: Trends in labor market and whole economy due to unemployment - Author abstract

1. Introduction

   Although a high rate of economic growth and a low rate of unemployment are two major goals of most governments, the relationship between these two goals is not well understood. For example, Pissarides (1990) shows that the long-run unemployment rate and growth rate are always negatively correlated, whereas Aghion and Howitt (1994) conclude that the former can be an inverted U-shaped function of the latter. More recent studies by Eriksson (1997) and Falkinger and Zweimuller (2000) suggest that growth can either increase or decrease unemployment depending on the sources of economic growth. The empirical evidence on this issue is equally ambiguous. Bean and Pissarides (1993) find that there does not exist any significant relationship between unemployment and growth across OECD countries. Caballero (1993) finds that these two series are weakly positively correlated in the UK and United States. However, Muscatelli and Tirelli (2001) find that though unemployment has a significant negative effect on growth in Canada, France, Germany, Italy, Norway, Japan, and Sweden, its impact is not significant in Australia, Austria, the UK, and the United States.

   Aghion and Howitt (1994) and Pissarides (1990) are two influential theoretical studies that have investigated the long-run effect of growth on employment. (1) In Pissarides (1990), the long-run growth rate is exogenous. Because higher productivity growth raises the rate of return from job creation, and hence increases the exit rate from unemployment, the unemployment rate and growth rate are always negatively correlated in his model. To reconcile the conflict between the model prediction and the empirical evidence, Mortensen and Pissarides (1998) incorporate renovation costs into a model similar to that of Pissarides (1990). (2) They show that the relationship between the unemployment rate and growth rate depends on the renovation costs. That is, they are negatively correlated if the renovation costs are low and positively correlated if the renovation costs are high.

   Aghion and Howitt (1994) identify two competing effects of growth on unemployment. On the one hand, as in Pissarides (1990), an increase in growth increases the returns from job creation, which reduces the unemployment rate (the capitalization effect). On the other hand, an increase in growth shortens the duration of job matches. Because shorter duration of job matches directly raises the job separation rate and indirectly discourages job creation (the creative destruction effect), a higher growth rate could increase the unemployment rate. The results (Propositions 1 and 2) in Aghion and Howitt (1994) suggest that the unique equilibrium unemployment rate can be represented as an inverted U-shaped function of the growth rate whenever the entry cost is positive but sufficiently small.

   Because productivity growth is exogenous in Pissarides (1990) and Mortensen and Pissarides (1998), the cross-country variations in economic growth cannot be explained. In contrast, the long-run growth rate is endogenously determined in Aghion and Howitt (1994). However, they do not explicitly examine the impact of labor market parameters such as unemployment benefits and hiring costs on the unemployment rate and growth rate. (3) Consequently, Aghion and Howitt (1994) cannot answer some important questions such as whether differences in institutional settings between Europe and the United States are accountable for the differences in their unemployment rates. Because, as shown by Mortensen and Pissarides (1998), the relationship between the unemployment rate and growth rate can turn from negative to positive as the renovation costs rise, an explicit examination of the impact of labor market parameters is important to understanding the cross-country differences in the long-run growth rate and unemployment rate.

   To examine the determinants of long-run unemployment and economic growth simultaneously, we extend the endogenous growth framework of Howitt and Aghion (1998) to allow for a more general treatment of the labor market in the spirit of Pissarides (1990). The major distinction between Pissarides (1990) and Mortensen and Pissarides (1998) and our model is whether growth is endogenously determined. (4) Endogenizing economic growth enables us to explicitly analyze the impact on unemployment of factors that are commonly considered as determinants of growth, but are largely overlooked by the unemployment literature, such as the productivity of research and development (R&D) and the speed of technological spillovers. Our model differs from Aghion and Howitt (1994) in that the impact of several important institutional factors, such as unemployment benefits and workers' bargaining power, on growth and unemployment is explicitly examined. Our model generates several interesting findings that are absent from Aghion and Howitt (1994), Mortensen and Pissarides (1998), and Pissarides (1990). (5)

   First, we find that the long-run growth rate depends not only on the regular preference and technology parameters, as in the literature on endogenous growth with full employment, but also on certain labor market parameters; symmetrically, we find that the unemployment rate depends not only on the labor market parameters, but also on other factors that affect growth. Second, consistent with the empirical evidence, our model predicts that a rise in the growth rate can either increase or decrease the unemployment rate, depending on the model's parameters. Third, different types of government policies that directly or indirectly promote long-run growth can have opposite effects on the unemployment rate.

   The remainder of the paper is organized as follows. The next section describes the environment and sets up the model. Section 3 derives the steady-state equilibrium conditions and the major results and discusses the policy implication of these results. Some concluding remarks are given in the last section.

2. The Model

   This section develops the basic model. Our model extends the Schumpeterian endogenous growth model of Howitt and Aghion (1998) to allow for a more general treatment of the labor market in the spirit of Pissarides (1990).

   Technologies

   The economy is populated with a continuum of identical households with measure one. Each household consists of many infinitely lived members whose time endowment is normalized to unity. There are five types of production activities in this economy: final good production, intermediate good production, search in the labor market, physical capital accumulation, and R&D. It is assumed that in the intermediate sectors, producers are assumed to have temporary monopoly power, and in the labor market, wage rates are determined through Nash bargaining.

   Final Good Production

   Following Pissarides (1990), we make the following two assumptions: (i) there is a continuum of identical final-good producing firms with measure one and (ii) each firm employs many workers and is large enough to eliminate all uncertainty about the flow of labor. An individual firm uses a continuum of intermediate goods i [member of] [0, 1] and labor as its inputs subject to the following production technology:

   Y = [N.sup.1 - [alpha]] [[integral].sup.1.sub.0] [A.sub.1][x.sup.[alpha].sub.i] di, 0 < [alpha] < 1, (1)

   where Y is the output; N is the number of workers employed; (6) [x.sub.i] is the flow of intermediate good i used: [alpha] is a parameter that measures the contribution of the intermediate good to the final-good production, and its inverse measures the intermediate-good producer's market power; and [A.sub.i] s the productivity coefficient of intermediate good i that is determined by the technology from R&D.

   Final output is allocated among consumption C, investment in R&D Q, expenditures on hiring in the labor market [GAMMA], and investment in physical capital K:

   Y = C + [??] + Q + [GAMMA]. (2)

   We implicitly assume that each unit of consumption good foregone can be used to produce one unit of capital and that there is no capital depreciation. Throughout this paper, the final good is used as a numeraire.

   Search in the Labor Market

   To produce final output, the final-good producers have to search for workers. Because N is the number of workers that are matched with jobs in the final good sector, 1 - N is the number of unemployed workers. Job-worker pairs are assumed to separate at a constant rate s, with 0 < s < 1. (7) To find a suitable employee, a firm has to incur a hiring cost [GAMMA]. We assume that the hiring cost is proportional to the wage rate W, that is, [GAMMA] = [gamma]W, where [gamma] > 0. The rate at which new jobs and workers match is governed by the constant-returns-to-scale aggregate matching technology

   M (v, 1 - N) = M (v, u), (3)

   where v is the number of vacancies, and u [equivalent to] 1 - N is the number of unemployed workers. Because the labor force is normalized to unity, v and u are also respectively the vacancy rate and the unemployment rate. With the matching technology (3), the instantaneous probability of a vacancy being filled is m([theta]) [equivalent to] M(v, u)/v = M(1, 1/[theta]) with m'(*) < 0, where [theta] [equivalent to] v/u is the vacancy-unemployment ratio that is outside the control of firms. As a result, the employment of an individual firm evolves according to (8)

   N = m([theta])v - sN, (4)

   where a dot over a variable represents the time change rate of that variable. Equation 4 states that the net change of employment N is the difference between the inflow of workers m([theta])v and the outflow of workers sN. Given the matching technology (3), the wage rate determined through Nash bargaining W, and the prices of intermediate goods [p.sub.i], the final-good producer chooses the number of vacancies v and quantities of intermediate inputs [x.sub.i] to maximize its discounted expected profit (9)

   [[integral].sup.[infinity].sub.0] [e.sup.rt][[pi].sub.Y]dt, [[pi].sub.Y] =...