Firm Dynamics, On-the-Job Search, and Labor Market Fluctuations

3.1. Calibration

We begin with a normalization. Note that, in the limit in which the hiring cost c is zero, optimal labor demand implies that marginal products are equalized across firms at a level m∗≡ω0/(1−ω1)⁠. It follows from (6) that there is a common wage in this case equal to w∗≡ω0/(1−β)⁠. We normalize w∗≡1 or, equivalently, ω0≡1−β⁠. It follows that all flow parameters are expressed in terms of monthly frictionless wages.
The discount rate r⁠, the curvature of the production function α⁠, and the labor force L are calibrated externally to replicate, respectively, an annual real interest rate of 5%, the estimates of Cooper et al. (2007, 2015), and an average firm size of 20 employees, consistent with data from the Small Business Administration.
The remaining parameters are then calibrated internally. Although, of course, all target moments inform all parameters, in what follows we provide an account of the empirical moments that intuitively are most relevant for the calibration of each parameter.
A central ingredient to the frictions in the model is the hiring cost c⁠. In his original study, Oi (1962) reported two early empirical results. First, the majority of hiring costs pertain to training, rather than to recruiting. This provides some empirical justification for our choice to model hiring rather than vacancy costs. Second, hiring costs correspond to approximately one month’s wages.18 In his survey, Manning (2011) notes that, although evidence on the magnitude of hiring costs remains limited, Oi’s initial estimates broadly are borne out in subsequent work. More recently, Gavazza et al. (2018) report estimates of hiring costs compiled by human resources professionals that reinforce this conclusion. Accordingly, we target a hiring cost equal to the average monthly wage.
Hiring costs interact with the presence of idiosyncratic shocks x to determine the size of the natural wastage region. For a given hiring cost c⁠, a higher standard deviation of idiosyncratic shocks σ implies greater dispersion in innovations to firms’ desired labor demand, and a smaller measure of employment in firms with zero hires. We thus discipline σ by targeting the share of employment at establishments with zero hires over a month. Using microdata from the Job Openings and Labor Turnover Survey (JOLTS), Davis et al. (2013) estimate this share at 34.8%.
Next, we target a set of moments relating to labor market stocks and flows. To do so, we adopt a conventional Cobb–Douglas matching function,
M=A[U+s(L−U)]ϵV1−ϵ,
(35)
where A denotes match efficiency. In addition, we augment the model of the preceding sections to incorporate a portion of separations into unemployment that are exogenous. Specifically, we allow such exogenous separations to occur at rate ς0⁠.19
Unemployment stocks and flows are then targeted as follows. Note that any steady-state level of labor market tightness θ∗ and, thereby, of the job-finding rate of unemployed searchers λ(θ∗)⁠, can be supported by an appropriate choice of the job creation curve shifter X in (29). We choose X to replicate a monthly unemployment-to-employment transition rate of 0.25, consistent with Current Population Survey “gross flows” data.20 Given this unemployment outflow rate, we choose the exogenous separation rate ς0 to replicate a steady-state unemployment rate of 5%.
As is standard in search and matching models, matching efficiency A⁠, and the matching elasticity ϵ⁠, then determine respectively the steady-state level of vacancies, and the slope of the Beveridge curve relation between vacancies and unemployment. We choose A to target a steady-state vacancy rate of 2.5% (Davis et al., 2013), and ϵ to target a Beveridge curve elasticity of −1 (Shimer, 2005).
Finally, we use the remaining parameters of the model to target empirical moments relating to the role of on-the-job search in the labor market. The search intensity of employed searchers s naturally shapes the magnitude of direct transitions from one employer to another. We therefore choose s such that the model replicates a monthly job-to-job transition rate of 0.032, as in Moscarini and Thomsson (2007). It remains to determine worker bargaining power β⁠, which we choose to replicate an average wage gain associated with job-to-job transitions of 8%, based on Barlevy (2008). Intuitively, job-to-job transitions in the model involve workers moving up a hierarchy of marginal products. Recalling the wage solution (6), greater bargaining power raises the gradient of wage increases as workers move up this hierarchy through on-the-job search.