Short-run equilibrium dynamics of unemployment vacancies, and real wages

In this paper, I study the dynamics of adjustment in a labor market, following an exogenous shock to the real value of output. Some of the stylized facts of business cycles, with which the predictions of the model are consistent, include first, real wages do not fully reflect fluctuations in the real value of labor's marginal product, so real profits fluctuate more than real wages. Second, unemployment responds to output shocks, but its response is slow. Finally, in countries where there are good data on vacancies, like Britain, we observe that vacancies respond more quickly to shocks and with greater amplitude than unemployment. Several authors have constructed models to explain why output shocks are absorbed partly by real wages and partly by unemployment (the empirical regularity in the United States is discussed by Robert Hall, 1980). Implicit contract models (Costas Azariadis, 1979; Oliver Hart, 1983) have successfully explained why real wages may not reflect output shocks, and the models with asymmetric information and severance pay have also had some success in explaining fluctuations in unemployment. Bargaining models (Ian McDonald and Robert Solow, 1981) and efficiency wage models (Janet Yellen, 1984) appear to be more successful in explaining fluctuations in unemployment, but formalizations are still in their infancy. The models have not yet been subjected to the same scrutiny as implicit contract and earlier models. One feature shared by all these models is that they are static. They explain how real wages and employment respond to shocks in a comparative-static framework but say nothing about the adjustment path from one equilibrium to the next. Also, the models say nothing about job vacancies, either in equilibrium or during the adjustment process. By contrast, this paper takes the view that by modeling job vacancies explicitly, one can learn more about the behavior of unemployment and real wages, both in equilibrium and during the adjustment to equilibrium. Thus, the model developed below is explicitly dynamic, and in it job vacancies play a critical role in the transmission of output shocks to real wages and unemployment. A job vacancy indicates a willingness by a firm to hire a worker.' It is equivalent to unemployment of capital, so just as workers move between the states of employment and unemployment, jobs move between the states of occupancy and vacancy. I model the interaction of vacancies and unemployment by using ideas from equilibrium search theory, where there is continuous wage recontracting and perfect anticipation of the adjustment paths of all endogenous variables. Job vacancies enter the model via their influence on job contacts, which depend on the number of firms looking for workers. Some firms may not wish to hire and so they may not be actively engaged in the search process. Only firms with job vacancies are actively engaged in search, so the number of job contacts and