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Article Excerpt
A CLASSIC CHALLENGE that macroeconomists face is to explain the cyclical fluctuations of output, unemployment, and inflation. Recently, New Keynesian (NK) business cycle models have made important advances in explaining the links between monetary policy and the joint dynamics of output and inflation (see Gall 2003 for a survey). However, the standard NK model abstracts from unemployment as it assumes a neoclassical labor market in which individuals vary the hours that they work, but the number of people working never changes. This of course implies that the model cannot account for evidence regarding the effects of aggregate shocks, in particular monetary policy shocks, on unemployment dynamics. Moreover, when accounting for the joint response of output and inflation to monetary policy shocks, the standard NK model has a great difficulty in replicating the sluggish response of inflation together with the large and persistent response of output. One key reason for this difficulty is that the model has the labor input adjusting along the intensive margin, which makes real wages very responsive over the cycle unless an implausibly high labor supply elasticity is assumed. This in turn induces firms setting prices as a markup over marginal cost to make large price adjustment and causes inflation in the model to fluctuate more than evidence suggests. Based on these and related considerations, several recent papers have argued that labor market frictions are crucial to understanding business cycle fluctuations, as well as the effects of monetary policy shocks and the design of monetary policies (among these see Gall Gertler, and Lopez-Salido 2001, Smets and Wouters 2003, Christiano, Eichenbaum, and Evans 2005, Levin et al. 2005). The search and matching model, along the lines of the work of Mortensen and Pissarides (1994), is a natural way of thinking about these frictions.
In this paper, I develop a dynamic general equilibrium model that integrates labor market search and endogenous job destruction into an otherwise standard NK model with nominal price rigidities. (1) I show that introducing search and matching frictions modifies the nature of real marginal cost faced by firms in a way that lowers the elasticity of marginal cost with respect to output and thus helps to account for the observed inertia in inflation and persistence in output. To gain some intuition, first note that in the model changes in output can be obtained through either changes in the number of hours worked, the intensive margin, or changes in the number of employed people, the extensive margin. With demand-constrained firms, the two margins will adjust to meet demand so that their marginal costs are equalized. Now, although hours worked by each employed worker are chosen through bargaining, the marginal cost of hours is determined by the workers' marginal disutility from supplying labor, much the same way as in a neoclassical labor market. However, while in a neoclassical framework all variation of the labor input occurs at the intensive margin, which is very costly when the labor supply elasticity is not implausibly high, with equilibrium unemployment firms can change employment at the extensive margin. The cost of adjusting output through changes in the number of employed workers in a framework with hiring frictions and long-term employment relationships has two components. The marginal cost increases with the flow cost of having one additional worker employed but decreases with the expected future payoff from continuing the relationship in the following periods. These dynamic considerations make the extensive margin relatively less costly and induce firms to adjust the labor input mostly at the extensive margin, as we observe in the data.
After developing the theoretical model, I estimate a set of the structural parameters that characterize the dynamics of the labor market and on which there is little or no independent evidence. I follow the limited information estimation strategy adopted in Rotemberg and Woodford (1997) and others. Specifically, the structural parameters are chosen so that the impulse responses to a monetary policy shock of a set of endogenous variables in the model match as closely as possible the responses estimated using a vector autoregressive (VAR) methodology. While the minimum distance estimation strategy is widely adopted in the literature on dynamic general equilibrium models with money, no other study, to the best of my knowledge, has used it to estimate the parameters of a labor market characterized by matching frictions and endogenous job destruction.
In order to evaluate the model I proceed in two steps. First, I assess the contribution of labor market frictions in shaping the joint dynamics of output and inflation by comparing the predictions of the model developed in this paper with those of a NK model that does not have search and matching frictions but keeps all other features the same. I show that in the model with labor market search the response of inflation is significantly less volatile and the response of output considerably more persistent than in the baseline NK model. Second, I evaluate the ability of the model to account quantitatively for the response of the U.S. economy to a monetary policy shock. The estimated model does a good job in replicating the observed responses of output, inflation and the labor market (specifically, employment, hours per worker, job creation, and job destruction).
Independent work by Walsh (2005) also studies the interaction between price rigidities and labor-market search. There are three main differences with this paper. First, his work considers only the extensive margin, while I consider the intensive as well as the extensive margin. This allows me to explain the dynamics of hours per worker over the cycle as well as the dynamics of employment and to clarify how the interaction between the two margins shapes real marginal costs. Second, rather than taking a stand on all the possible sources of fluctuations in the economy, I evaluate the empirical performance of the model based on its ability to match conditional second moments, i.e., second moment conditional on a particular source of fluctuations. (2) Third, I provide estimates of a set of the structural parameters that characterize a labor market with search and matching frictions.
The remainder of the paper is organized as follows. Section 1 presents the evidence related to the response of output, inflation, and the labor market to a monetary policy shock; Section 2 describes the model; Section 3 analyses the determination of real marginal costs with search and matching frictions; Section 4 brings the model to the data and discusses the estimation; Section 5 presents the results; Section 6 discusses the alternative approach to modeling labor market frictions, i.e., nominal wage rigidities; and Section 7 concludes.
1. EVIDENCE: OUTPUT, INFLATION, AND THE LABOR MARKET
In this section, I describe a set of stylized facts related to the behavior of output, inflation, and a set of labor market variables in face of a monetary policy shock. The evidence regarding the response of the labor market to a monetary policy shock is new in the literature. More specifically, I use a VAR methodology to estimate the dynamic response of the variables of interest to an identified exogenous monetary policy shock. The short-term nominal interest rate is taken to be the instrument of monetary policy and the identification strategy is based on the recursiveness assumption as in Christiano, Eichenbaum, and Evans (2000). (3)
The variables included in the analysis are measures of output, inflation, and the nominal interest rate, to which I add four labor market variables. The labor market variables that I include are measures of employment, average hours per worker, the job creation rate, and the job destruction rate. I include four lagged values of all variables in the VAR. Estimates are based on quarterly U.S. data from 1972:2 to 1993:4. (4)
The series for the nominal interest rate is the federal funds rate, annualized and averaged over the quarter. The series for output is the log of quarterly real GDP and the series for inflation is the annualized rate of change of the GDP deflator between two consecutive quarters. The series for employment is the log of total employees in nonfarm establishments. The series for average hours per worker is constructed by subtracting the previous variable from the log of total employeehours in nonagricultural establishments. Finally, the series for job creation and job destruction are taken from Davis, Haltiwanger, and Schuh's (1996) "Job Creation and Destruction" database. They are, respectively, the log of the quarterly job creation rate for both startups and continuing establishments in the manufacturing sector and the log of the quarterly job destruction rate for both shutdowns and continuing establishments in the manufacturing sector.
Figure 1 reports the responses over time of output, inflation, and the federal funds rate to a 1% increase in the federal funds rate, and Figure 2 reports the responses of employment, average hours per worker, the job creation rate and the job destruction rate to the same shock. The solid lines display the point estimates of the coefficients. The dashed lines are two standard deviation confidence intervals. The impulse response functions of inflation and the federal funds rate are reported in percentage points. The other impulse responses are reported in percentage deviations from each variable's unconditional mean. The horizontal axes indicate quarters.
The results suggested by Figure 1 are standard in the VAR literature on monetary policy. After a contractionary monetary policy shock there is a large hump-shaped fall in output accompanied by a sluggish persistent decrease in inflation. The peak fall in output is about 0.4% and that of annualized inflation about 0.3%. Existing optimizing monetary general equilibrium models have shown difficulties in explaining this joint dynamic behavior of output and inflation. In their baseline version, unless a large value of the labor supply elasticity is assumed, they predict a much larger response of inflation.
[FIGURE 1 OMITTED]
Figure 2, instead, presents some new results about the response of the labor market to a monetary policy shock. First, the labor input adjusts along both the extensive and the intensive margins. As a consequence of the tightening in monetary policy, both employment and hours per worker fall. However, while the fall in employment is large and persistent, there is only a small transitory decrease in hours per worker. Therefore, the labor input shows a significantly different cyclical behavior at the extensive and the intensive margins. Second, the response of employment is explained by variations at both the job creation and the job destruction margins. The monetary contraction causes a fall in job creation and an increase in job destruction. The decrease in job creation is transitory with a peak response of about 3.4%, while the increase in job destruction is larger and more persistent with a peak response of about 4.5%.
Finally, the tightening in monetary policy has a significant effect on output, employment, hours per worker, job creation, and job destruction only after two quarters. (5) In order to reproduce this feature of U.S. data, following Rotemberg and Woodford (1997) and others, I will introduce in the model informational lags in the decisions to consume, set prices, post vacancies, and endogenously sever a match.
[FIGURE 2 OMITTED]
2. THE MODEL
The proposed model with nominal price rigidities and search and matching in the labor market has four sectors: households, intermediate goods firms, retail firms, and a monetary authority.
2.1 Households
Each household is thought of as a large extended family that contains a continuum of members with names on the unit interval. In equilibrium, some members will be unemployed while some others will be working for intermediate goods firms. Each member has the following period utility function:
u([c.sub.t], [c.sub.t-1]) - g ([h.sub.t], [a.sub.t]), (1)
with
u([c.sub.t], [c.sub.t-1]) = log([c.sub.t] - [ec.sub.t-1]), (2)
and...
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