The standard Mortensen and Pissarides (1994) search and matching model of equilibrium unemployment has been argued in many places to be inconsistent with key business cycle facts. In particular, it cannot explain the high volatilities of unemployment, vacancies and market tightness (Shimer, 2005), nor the persistence in the adjustment of these variables to exogenous shocks (Fujita and Ramey, 2007). Subsequent research has focused on whether the lack of internal propagation, both in terms of amplification and persistence, stems from the structure of the model itself or whether it is a question of setting an appropriate calibration.
Firms in these models must expend resources to fill job vacancies, a time-consuming process in the presence of search frictions on labor markets. Under Nash bargaining as a wage mechanism, wages absorb much of the change in the expected benefit to a new worker induced by fluctuations in labor productivity. As a result, Shimer (2005) argues, the incentive to post vacancies changes little over the business cycle. Quite naturally, subsequent research has focused on the dynamics of wages as a means of generating amplification of exogenous innovations. Such studies have either altered the particulars of the wage determination mechanism (e.g. Shimer 2004), or as in Hagedorn and Manovskii (2008), followed an alternative calibration strategy that results in a rigid wage. In order to address the second empirical shortcoming, the persistence in labor market adjustments to productivity shocks, a second strand of research has focused on the structure of vacancy costs. Fujita and Ramey (2007), for example, develop a story about sunk costs to vacancy creation such that the strongest change in market tightness occurs several periods after the original shock. Their approach, however, does not generate any additional amplification.
This paper extends the baseline search and matching model of equilibrium unemployment by assuming that external finance must be called upon to fund part of a firm’s vacancy costs, and that agency problems cause credit markets to be frictional. The thrust of this paper is to show that evolving conditions on credit markets over the business cycle change the opportunity cost of resources used by firms to create new jobs in the face of small changes in the expected benefit to a new worker, simultaneously addressing the lack of amplification and persistence to productivity shocks outlined above. Acemoglu (2001) and Wasmer and Weil (2004) have shown that credit market imperfections lead to higher equilibrium unemployment by restricting firm entry. This paper shows that such frictions matter for the cyclical dynamics of the labor market. This paper also raises a broader case for the role credit market imperfections in understanding aggregate dynamics operating through worker as opposed to investment flows, as has been the focus in models of financial intermediation and agency costs such as Kiyotaki and Moore (1997) or Bernanke et al. (1999).
The model developed in this paper works as follows. Due to a problem of costly state verification in lending relationships, firms write standard debt contracts to fund vacancies over accumulated assets. The higher shadow cost of external over internal funds increases the cost of vacancies, leading to a higher rate of equilibrium unemployment. However, the degree of agency costs is alleviated during economic upturns, lowering the shadow cost of resources allocated to job creation. This opens two channels through which the elasticity of job vacancies to productivity is increased: (i) a cost channel, driving a time-varying wedge in the job creation condition in which the lowered opportunity cost of resources allocated to job creation during an upturn increases the incentive to post vacancies; (ii) a wage channel - under Nash bargaining as a wage mechanism, the lowered opportunity cost of vacancies limits part of the upward pressure of market tightness on wages by improving the bargaining position of firms. Note that the source of wage rigidity is a consequence of frictional credit markets and not an inherent feature of the wage rule or a particular calibration of the model. Finally, the progressive easing of financing constraints as firms accumulate assets induces persistence in the adjustments of labor market variables to productivity shocks. Whereas in standard search models of equilibrium unemployment, or models with increased wage rigidity for that matter, the largest response of market tightness is contemporaneous to the exogenous shock, the height of the response in this setting is reached with a lag after the innovation.
Section 3 details the model’s quantitative results and sets them against a comparable framework without credit frictions. This sections finds the cost channel to be the most important for the model’s ability to replicate the volatility relative to output and persistence of labor market variables observed in the data. For example, the relative volatility of market tightness reaches 12.45 (against 15.41 in the data) while only 3.76 in the standard model with perfect credit markets, and the relative volatility of unemployment, which is 6.82 in the data, rises to 3.26 in the presence of credit frictions compared to 0.82 in the standard model. U.S. quarterly data on market tightness displays a high degree of persistence, measured as positive auto-correlations in the growth rate of 0.67, 0.48 and 0.33 at the first, second and third lags respectively. Allowing for frictional credit markets can generate auto-correlations of 0.62, 0.24 and 0.08 at the first, second and third lags, whereas a standard search model generates virtually no auto-correlation. This criticism is akin to that of Real Business Cycles (RBC) models advanced by Cogley and Nason (1995) in their inability to generated persistence in the growth rate of output. In this last respect, the inclusion of credit frictions allows the model to nearly perfectly match the persistence in the growth rate of output by inducing large variations in employment over the business cycle. Section 3 also examines a series of robustness issues. For one, the results are very robust to an extension to externally funding part of the wage bill over and above recruiting costs. Second, it is shown that the results are driven by a single parameter capturing the degree of credit market imperfection, the resource cost to lenders of monitoring firms’ realized productivity.
The baseline model allows only for exogenous separation of workers out of employment, resulting in an inability of the model to be consistent with observations on gross labor flows. Section 4 extends the model to allow for endogenous labor separation by introducing a job specific productivity shock observed at the beginning of each period, with jobs drawing a productivity below a certain threshold being terminated. However, contrary to Mortensen and Pissarides (1994), some of the separations are inefficient owing to an imposed restriction on current losses that pushes the cut-off productivity above that for which the surplus of the job match is null. The main results regarding propagation are robust to this extension, and the model is then largely consistent with the cyclical properties of gross labor flows. Moreover, contrary to most models allowing for endogenous job separation (see Ramey, 2008), the Beveridge relationship between unemployment and vacancies is not violated by this extension. This is because the increased incentive to post job vacancies from eased credit markets during an upturn dominates the disincentive caused by the drop in the job separation rate.
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