بهره برداری بیکاری تعادل: تعادل عمومی رویکرد اقتصاد خارجی

This paper presents a new formulation of equilibrium unemployment that is inspired by job search or matching models. Unlike those approaches, however, this formulation does not rely on an explicit stochastic process. The matching process is incorporated through external economies in the labor market such that market expansions reduce the unemployment rate and contractions increase it. The model gives intuitively appealing results in both its static and dynamic versions with relatively little modeling overhead. Conceptually, this formulation represents a modest revision of the standard Arrow–Debreu model, and it builds on the external economies literature. To illustrate the formulation in an applied model, results are presented from an analysis of the United States’ commitment to reduce carbon emissions under the Kyoto Protocol.

There are several informative theories of unemployment. Among these, equilibrium models of job search (‘matching models’) are particularly appealing, yet these ideas have not yet found their way into applied general equilibrium models. The purpose of this paper is to introduce a practical method by which job search can be incorporated in economy-wide models. The starting point for this exercise is to think about unemployment as the result of a process by which willing individuals are transformed into employed workers. This process involves an external effect through which the economy-wide vacancy rate and the unemployment rate alter the job matching probability of individual workers. This paper presents this simple theory of equilibrium unemployment and its operation in a general equilibrium model. There are two compelling aspects of this formulation. First, the model is quite tractable as it relies on a well established technique for representing external economies. Second, there are some very appealing qualitative properties of the model. When placed in a dynamic context, the formulation captures the magnified short-run unemployment reactions consistent with the business cycle. The dynamic model offers a practical strategy for incorporating equilibrium unemployment in large-scale general equilibrium models. Current applied models often center on long-run efficiency and welfare impacts. Although these considerations are probably of most importance, many policymakers find them intangible. Modeling unemployment bouts and other transitional adjustment dynamics builds a modeling procedure's credibility in the eyes of policymakers and weakens the persistent influence of disequilibrium models. The model presented here can deliver insights on short-run dynamic issues that are not available in existing frameworks. Unemployment should be modeled as a natural feature of equilibrium, and fluctuations in the unemployment rate should be tracked as rational responses by agents to the opportunities they face.1 An empirically acceptable theory should provide a positive rate of unemployment but, more importantly, the theory should postulate sensible responses to shocks. Current theories of equilibrium unemployment rely on a real wage equation in which there is a premium on the reservation wage. This paper exploits this equation in a general form as an equilibrium condition for workforce participation. Consistent with the unemployment literature, the specification here of external economies results in an unemployment rate that is inversely related to labor market expansions. Pissarides (1990) offers a theory of equilibrium unemployment with appealing properties. As in a standard general equilibrium model, wages are free to adjust; however, the stochastic and inherently costly nature of searching for a job requires that wages cannot fall to the point that all willing workers are hired. Furthermore, an increase in the ratio of the unemployment rate to the vacancy rate decreases the probability that an unemployed worker will find a matching vacancy. These features are preserved in the model presented here through a reduced form of the job matching opportunities that determine individual labor supply. Consistent with Pissarides’ formulation, the model predicts a positive unemployment rate that reacts to exogenous shocks in the intuitive manner. One substantial application of the equilibrium job search literature is found in the MIMIC model (Gelauff and Graafland, 1994). The MIMIC model is a large-scale applied general equilibrium model of the Netherlands that captures many of the important characteristics of that labor market. The high proportion of unemployment and a general lack of workforce participation in the Netherlands precluded the standard general equilibrium assumption of an efficient labor market, especially considering MIMIC's goal of analyzing welfare state reform and the incentive effects of social programs. MIMIC includes an explicit representation of the stochastic job matching process. The complexity of this approach dictated a number of compromises that are manifested in general inconsistencies among the model's component blocks. For example, within the job matching submodel the reservation wage is exogenous, and unemployed workers are assumed to behave according to a utility function that is fundamentally different from the one that determines labor supply. The inconsistencies within MIMIC are well documented by the authors and are certainly justified within the scope of that project. The approach taken in this paper directly models the externality associated with job matching in a fully consistent representative agent model, and thus suppresses the complexities found in MIMIC. This study incorporates external economies in a process that transforms workforce participants into employed workers. The external effect is the result of search and congestion externalities in the labor market. The externalities arise because, although individuals may view the cost of unemployment as given and demand a compensating wage premium (above their reservation wage) to enter the market, in aggregate this cost will likely depend on the depth and congestion in the market.2 A key characteristic of the model is that the cost to an individual of participation in the workforce falls as the ratio of the vacancy rate to the unemployment rate increases. The model gives intuitively appealing results in both its static and dynamic versions with relatively little modeling overhead. Conceptually, this formulation represents a modest revision of the standard Arrow-Debreu model, and it builds on a rich literature in external economies.3 In addition to being consistent with the stylized fact that labor market expansions are accompanied by dips in the rate of unemployment, the model presented here is logically consistent with the stochastic matching model. Pissarides shows that increases in the marginal product of labor increase the ratio of the job vacancy rate to the unemployment rate (increased market ‘tightness’), which results in a new lower level of equilibrium unemployment and higher real wages. It is important to note that, when the demand for labor increases, total wages increase but the wage premium falls because the chance of becoming unemployed falls. In a dynamic context in which consumption decisions include a consideration of optimal capital accumulation, the model produces short-run adjustments in the unemployment rate that overshoot the steady-state rate. Capital stock adjustments necessitate changes in consumption, and this alters the marginal utility of leisure in a way that magnifies the unemployment reaction through the transition to steady state. These short-run adjustment costs become more dramatic when we include an assumption that some current employees maintain employment across periods. Similar to the matching model, there is a process that separates workers from employment at a given rate. In a dynamic growth model, this implies that a growing proportion of the workforce passes through the employment process or matching technology over time. This larger base of individuals decreases the relative importance of changes in the matching externality. When distortions are placed on capital, the model predicts a long-run rate of unemployment in the neighborhood of the initial steady-state rate. Consistent with empirical findings for the U.S., the unemployment rate moves in step with the business cycle, but tends to a relatively small long-run range. However, when distortions are directly imposed on the labor supply decision, the model predicts a relatively large move to a new steady-state level of unemployment, which might be more consistent with European data. The following section presents the specification of external economies in employment and its incorporation in a simple static general equilibrium. Included is a computation of the model that illustrates how it can be represented as a system of equations and to highlight the welfare implications of the competitive equilibrium. In Section 3 a dynamic equilibrium version is introduced that describes how the model can be implemented within a fully intertemporal framework. Capital stock adjustments result in responses consistent with the stylized business cycle pattern of magnified initial unemployment impacts that dissipate over time. To increase the saliency of the formulation, Section 4 presents an application of the formulation in a large-scale model that analyzes the impacts of carbon emissions abatement in the United States. Concluding remarks are given in Section 5. The attached appendices detail the GAMS computer models that generated the simulation results.

This study presents a unique formulation of equilibrium unemployment and shows its operation in general equilibrium models. The foundations for this representation come from two previously unrelated literatures. First, matching models of equilibrium unemployment identify an externality associated with individual labor supply and the costly nature of job search. Importantly, these models explain movements in the unemployment rate that depend on the depth or size of the labor market. The second literature in external economies of scale represents a very similar externality as a technological restriction on production. Applying the external economies technology on the workforce maintains the key features of the matching model while adding minimal complication to the standard general equilibrium. The simplicity and transparency of this formulation are useful for application to large-scale computable models that currently ignore labor market fluctuations. Unemployment might be particularly important as a transitional phenomenon in dynamic models. These dynamic models offer a theoretically more appealing alternative to traditional macroeconometric forecasting models, but lack an adequate treatment of labor-market adjustments. To illustrate such an application, the formulation was applied to a large-scale model of U.S. carbon abatement policy. The dynamic model produces sensible adjustment dynamics that are flexible with respect to different parametric assumptions. The wage equation (or, more specifically, the wage premium) presented here produces intuitively appealing results that are generally consistent with the matching models; it depends only on the number of workers employed and the unemployment rate. However, the formulation is flexible and might be expanded to include more complex wage equations that are consistent with any number of equilibrium unemployment theories. Implementing any wage premium within the MCP framework is relatively straightforward as long as it is well specified in the context of the model. The specification here would benefit from any empirical literature that deals directly with the wage equation because, although the formulation is flexible, the quantitative results are shown to be sensitive to parameterization. Turnover rates are key to quantifying the short-run impacts. More important, however, is an empirical decomposition of the change in labor supply into a change in leisure versus a change in unemployment. Traditionally, micro-based studies that examine labor supply do not consider involuntary unemployment or changes in the unemployment rate as legitimate reactions to changes in the wage, and most macro studies do not consider leisure — only relating unemployment to historically important drivers. Neither approach is adequate in explaining labor market reactions to structural changes. The general formulation presented here offers a bridge between unemployment and the labor-leisure choice, and would benefit greatly from a similar econometric approach.