Conclusion

In this chapter, we have examined the determination of equilibrium unemployment in a matching model on the labor market. In this model, employers are investing to create job vacancies, and the process of creating jobs involves matching firms that have vacancies with unemployed job seekers.

At each instant, there are two flows: into and out of unemployment. Some workers lose their jobs and move from jobs to unemployment, and some of the unemployed find jobs, through the matching process, with firms that have vacancies.

In the simpler versions of the model, the probability of job destruction is exogenous. This parameter describes the structural or cyclical shocks affecting the economy and leading to the destruction of jobs.

The probability of filling a vacancy, and the probability of an unemployed job seeker to find a job, are endogenous variables. They depend on the degree of labor market tightness, which is defined by the ratio of vacancies to the number of unemployed. The higher the tightness of the labor market is, the greater the probability that an unemployed job seeker will find a job, and the lower the probability that a firm will fill a vacancy.

In the steady state, the flows to and from unemployment are equalized, and the equilibrium unemployment rate (also known as the natural rate) depends positively on the exogenous probability of termination of a job and negatively on the endogenous probability of an unemployed job seeker finding a job. The equilibrium unemployment rate therefore depends negatively on labor market tightness and is, of course, determined endogenously. The negative relationship between the equilibrium unemployment rate and the vacancy rate implied by this dependence is known as the Beveridge curve.

Firms and the unemployed make their decisions rationally, maximizing the expected present value of their profits and income.

The job creation condition implies a negative relationship between the wage that the firm is willing to pay and labor market tightness. The higher labor market tightness is, the lower will be the probability of filling a vacancy and the greater the total cost of maintaining a vacancy, because vacancies remain unfilled for longer.

In contrast, an unemployed job seeker will agree to a job offer if the expected present value of income of an employed worker is greater than the expected present value of income of an unemployed job seeker. This condition is satisfied in this model, as long as the real wage is higher than unemployment benefits.

Real wages are determined in equilibrium by decentralized bargaining between firms that have vacancies and unemployed job seekers. The equilibrium real wage is the result of this negotiation, and it depends positively on the relative bargaining power of the unemployed, the level of unemployment benefits, labor productivity, the cost of maintaining a vacancy, and labor market tightness. The equilibrium real wage depends positively on labor market tightness, because this increases the average recruitment cost per unemployed person, thereby increasing the threat point of prospective employees versus prospective employers and weakening the effective bargaining position of prospective employers.

The positive relationship between real wages and labor market tightness (resulting from the negotiation between firms with vacancies and the unemployed) and the negative relationship between real wages and labor market tightness (implied by the job creation condition for firms) jointly determine the equilibrium real wage and equilibrium labor market tightness. For given equilibrium labor market tightness, the equilibrium unemployment rate is then determined by the Beveridge curve, which implies a negative relationship between the unemployment and vacancy rates.

In the equilibrium of this model, the unemployed are worse off than the employed. Consequently, unemployment is an undesirable and involuntary condition and is not the result of choice by the unemployed, as in competitive models of the labor market without frictions.

If unemployment benefits are proportional to the real wage, labor productivity does not affect the equilibrium unemployment rate in this model.

However, the higher the percentage of real wages paid out as unemployment benefits is, the higher will be the equilibrium real wage and the equilibrium unemployment rate. The reason is that higher real wages reduce incentives for creating new jobs, thus reducing the number of vacancies, reducing labor market tightness, and increasing unemployment.

Higher real interest rates also have a positive impact on unemployment in this model, because they increase the cost of maintaining a vacancy, resulting in the creation of fewer job vacancies, lower labor market tightness, and higher unemployment.

A higher exogenous probability of job destruction has a positive impact on unemployment for two reasons: first, because it directly increases the flows from existing jobs to unemployment; and second, because it indirectly reduces the flows from unemployment to jobs. The second effect takes place because the expected profit from the creation and filling of a vacancy decreases, resulting in fewer vacancies and reduced flows from unemployment to jobs.

In this model, equilibrium unemployment depends both on cyclical and structural factors. Moreover, unlike the new classical model of real economic cycles (but like some versions of new Keynesian models), unemployment is involuntary in the sense that the unemployed would always prefer to be in jobs at prevailing real wages.

The adjustment path predicted by the model is stable, because following shocks to the determinants of equilibrium unemployment, the unemployment and vacancy rates follow a unique and stable adjustment path toward the new equilibrium.

Matching models have been incorporated in business cycle models with nominal rigidities, but the resulting models are quite complicated and can only be solved through the use of numerical methods.

1. See Pissarides [1985], Mortensen [1986], Mortensen and Pissarides [1994], and Pissarides [2000]. Pissarides [2011] provides a historical overview of the development of this approach.

2. The presentation of this model follows Pissarides [2000].

3. Mortensen and Pissarides [1994] have generalized this model to make the job termination rate endogenous. This does not fundamentally change the properties of the model. In the interests of simplicity, we shall thus stick to the model with an exogenous job destruction rate λ.

4. See Beveridge [1944], who first empirically identified this relationship.

5. See Pissarides [2000] on how the real interest rate can become endogenous.

6. In a symmetric bargain, as the one we analyze here, a reasonable value of β would be 1/2, but it is not necessary to assume this particular value.

7. Note that for the parameter values used in our reference simulation in subsection 18.8.2, the speed of adjustment is equal to 0.49, implying that it takes approximately 1 year to close half of the gap between current and equilibrium unemployment.