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

3. Quantitative exploration

The model of the preceding sections has rich implications for both the cross-sectional and time series behavior of labor markets. We now explore these implications quantitatively and confront them with relevant stylized facts that have emerged in recent literature.
An overview of our approach is provided in the tables and figures that follow. Table 1 summarizes our calibration strategy and its implied parameters, expressed at a monthly frequency. Table 2, together with Figures 5 and 6, then report the calibrated model’s implications for a wide range of nontargeted moments, and contrast them with empirical analogues. These are split between cross-sectional implications for measures of imperfect labor market competition and establishment dynamics, and macroeconomic implications for aggregate labor market dynamics. We now describe our approach in detail.
FIGURE 5

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Gross worker and job flows implied by the model
Notes: Application of Davis et al. and JOLTS methodologies to model-generated data simulated over one quarter in Panels A and B, and one month in Panels C and D. Data in Panel B are from Davis et al. (2012). Data in Panels C and D are estimates from Davis et al. (2013) with controls for establishment fixed effects. “Adjusted” model-generated data are based on a model of mismeasurement of vacancies reported in the text.

FIGURE 6

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Transition dynamics of calibrated model
Notes: Based on simulation of the model calibrated as described in Table 1. The figure illustrates the dynamic response to an unanticipated, permanent 1% decline in aggregate labor productivity.


TABLE 1
Parameters and targeted moments of calibrated model (monthly frequency)

Parameter		Value	Reason/moment	Model	Target
A. Externally calibrated
ω0	Flow breakdown payoff	0.488	Normalization	–	–
r	Discount rate	0.004	Annual real interest rate	0.05	0.05
α	Returns to scale	0.64	Cooper et al. (2007, 2015)	–	–
L	Labor force	21.05	Average firm size	20	20
B. Internally calibrated
c	Per-worker hiring cost	1.107	Hiring costs/monthly pay	1	1
σ	Std. dev. x shocks	0.066	Empl. at estabs. with no hires	0.348	0.348
X	Job creation curve shifter	19.68	U-to-E rate	0.25	0.25
ς0	Exogenous separation rate	0.012	Unemployment rate	0.05	0.05
A	Matching efficiency	1.111	Vacancy rate	0.025	0.025
ϵ	Matching elasticity	0.285	Beveridge curve elasticity	−1	−1
s	Employed search intensity	0.148	E-to-E rate	0.032	0.032
β	Worker bargaining power	0.512	Avg. job-to-job wage gain	0.08	0.08

Notes: The rationale and source for each targeted moment are explained in detail in the main text.
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TABLE 2
Nontargeted moments

Moment		Model		Data
A. Imperfect labor market competition
Rent-sharing measures	Pass-through		0.40	0.2 to 0.4
	Elasticity		0.56	0.4 to 0.7
Wage elasticity of quits			–1.55	−1.5 to −2.0
Frictional log wage dispersion	Std. dev.		0.06	—
	90–10 differential		0.15	—
Mean-min wage ratio			1.24	—
Var. of log wages in natural wastage region/total var.			0.75	—
B. Establishment dynamics
			Raw ν	Adj. ˜ν
Employment at estabs. with no vacancies		0.54	0.45	0.45
Vacancies at t at estabs. with no vacancies at t−1		0.17	0.18	0.18
Hires in (t−1,t) at estabs. with no vacancies at t−1		0.09	0.37	0.42
Hires rate elasticity of daily vacancy-filling rate		0.25	0.74	0.82
Std. dev. employment growth	Monthly		0.08	0.08
	Quarterly		0.19	0.29
	Annual		0.49	0.39
C. Aggregate dynamics
Response relative to output per worker			|Elasticity|	Relative sd.
Unemployment rate			7.6	14.0
Vacancy rate			7.6	12.6
U-to-E rate			6.7	11.6
E-to-U rate			1.3	3.6
E-to-E rate			5.5	5.7
Response relative to unemployment rate			Semi-elasticity	Semi-elasticity
Average wage			–1.4	≈−1

Notes: Data ranges are from the following sources. Panel A: Manning (2011); Kline et al. (2019). Panel B: Davis et al. (2012, 2013); Haltiwanger et al. (2013). Panel C: an update and extension of Shimer (2005) for labor market stocks and flows; a summary of Solon et al. (1994) and Elsby et al. (2016) for wages. “Adjusted ˜ν” model outcomes in Panel B are based on a model of mismeasurement of vacancies reported in the text. Model outcomes in Panel C are steady state (semi-)elasticities. Further detail is provided in the main text.
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