Figure 6 also displays how the firm reduces its demand for temporary workers but maintains a certain number of skilled and permanent workers during the recession. Since the firm shrinks its stock of permanent workers only slowly, the labor hoarding effect leads to a moderate variation of output in the short run. Specifically, the calibrated model predicts that a 1 percent decline in TFP brings about a 3.39-percent decrease in temporary employment as well as a 0.18 percent decrease in the permanent counterpart. Meanwhile, output drops by 1% upon the arrival of the negative shock and the figure is around 50% lower than the decline in output as the economy reaches another steady state (i.e., -1.5%). This result suggests that the loss of the stock of permanent workers has a persistent impact on the output in the long run.
5 Conclusion
The data for the US labor market reveal the following stylized facts involving temporary and permanent employment: (i) a much higher volatility of temporary employment than of per-manent employment; (ii) a strong pro-cyclicality of the share of temporary employment; (iii) the lagged behavior of permanent employment; and (iv) a stronger correlation between tempo-rary employment and output than in the case of the permanent counterpart. Given that the
standard RBC model does not draw an explict distinction between temporary and permanent employment, it is unable to provide a plausible explanation for these observed facts.
This paper proposes three channels related to distinguishing temporary employment from permanent employment. The first channel has to do with the substitutability between tempo-rary and permanent workers. The second channel is concerned with the time-to-build mecha-nism for job training, which leads new recruits to become productive permanent workers. The third channel relates to the costs of training permanent workers. By incorporating these three channels into into the standard RBC model, this paper finds that the modified model is able to explain the above stylized facts in the US labor market. Moreover, this paper also finds that the modified model provides a plausible explanation for the firms’ decision to hoard labor when the economy experiences a recession.
Table 1: Cyclical behavior of temporary and permanent employment in the US economy Moments
Standard deviation of output std(ˆyt) 1.10
Standard deviation of share of temporary employment std(ˆet) 5.79
Standard deviation of temporary employment std(ˆht) 6.66
Standard deviation of permanent employment std(ˆnt) 1.10
Correlation of coefficient between the share of temporary employment and output corr(ˆet, ˆyt) 0.89 Correlation of coefficient between temporary employment and output corr(ˆht, ˆyt) 0.91 Correlation of coefficient between
permanent employment and 3-period lagged output corr(ˆnt+3, ˆyt) 0.81 permanent employment and 2-period lagged output corr(ˆnt+2, ˆyt) 0.87 permanent employment and 1-period lagged output corr(ˆnt+1, ˆyt) 0.84 permanent employment and output (contemporaneous) corr(ˆnt, ˆyt) 0.75 permanent employment and 1-period lead output corr(ˆnt−1, ˆyt) 0.56 permanent employment and 2-period lead output corr(ˆnt−2, ˆyt) 0.34 permanent employment and 3-period lead output corr(ˆnt−3, ˆyt) 0.12
Table 2: Parametrization of the benchmark model Panel A: Calibrated parameters
Category Parameter value
Preference Intertemporal elasticity of substitution in consumption (1/θ) 1
Subjective discount rate (β) 0.99
Inverse of the Frisch elasticity of labor supply (χ) 0.0546 (varied) Disutility of temporary labor supply (ψ) 1.1633 (varied)
Technology Share of physical capital (α) 0.3
The productivity of temporary relative to permanent workers (γ) 0.3969 (varied)
Capital depreciation rate (δ) 0.025
Job separation rate (µ) 0.0849
Persistence parameter of the auto-regressive process (ρ) 0.99 The number of periods required for job training (b) 4
Panel B: Estimated parameters by SMM
σ ϕ1 ϕ2 σ2ε J χ20.05(1)
0.9249 11.6754 6.0124 0.8315
0.97 3.84
(0.0024) (0.6010) (0.8353) (0.0238)
Note: Based on the statistics for the targeted moments in Panel A of Table 2, the reported values of the SMM parameters with the standard deviations in the parentheses are computed by using the 500 replications of the estimation procedure. The variance of the technology shock is reported in percentage terms.
Table 3: Calibration of the parameters
Moments Data Model
Targeted
std(ˆyt) 1.10 1.08
std(ˆct) 0.79 (0.72) 0.75 (0.69)
std(ˆht) 6.66 (6.05) 6.29 (5.82)
corr(ˆht, ˆyt) 0.91 0.83
corr(ˆnt, ˆyt) 0.75 0.74
Non-targeted (selected)
std(ˆit) 4.15 (3.77) 1.74 (1.61)
std(ˆnt) 1.10 (1.00) 0.73 (0.68)
std( ˆNt) 1.17 (1.06) 0.76 (0.70)
std(ˆet) 5.79 (5.26) 5.97 (5.53)
corr( ˆNt, ˆyt) 0.78 0.81
corr(ˆet, ˆyt) 0.89 0.77
Note: The sampling period is 1990:Q1–2014:Q4. All of the variables (for gt = ˆNt, ˆht, ˆnt, ˆet) are de-trended by the HP-filter and the smoothing parameter is set to 1600. The standard deviations of output, temporary employment, consumption, in-vestment, permanent employment, aggregate employment, and the share of temporary employment are displayed in order. In addition, the values in the parentheses are the ratios of the standard deviations of the variables to the standard deviations of output.
The simulated moments are averages of variables across 1000 replications and over 100 periods.
Table 4: Coefficients of correlation between de-trended output and employment variables
Source Data Model
Coef. of Corr. Nˆt ˆht nˆt ˆet Nˆt hˆt nˆt ˆet corr(gt+3, ˆyt) 0.80 0.52 0.81 0.44 0.74 0.03 0.78 -0.06 corr(gt+2, ˆyt) 0.87 0.73 0.87 0.67 0.83 0.27 0.84 0.18 corr(gt+1, ˆyt) 0.86 0.88 0.84 0.84 0.86 0.53 0.83 0.45 corr(gt, ˆyt) 0.78 0.91 0.75 0.89 0.81 0.83 0.74 0.77 corr(gt−1, ˆyt) 0.60 0.83 0.56 0.83 0.57 0.62 0.51 0.58 corr(gt−2, ˆyt) 0.38 0.68 0.34 0.70 0.39 0.48 0.34 0.46 corr(gt−3, ˆyt) 0.16 0.48 0.12 0.51 0.26 0.41 0.21 0.40
Note: All the variables are expressed in quarterly frequencies. Then, the HP-filter is applied with respect to all variables to remove the effects of the trend compo-nents. Each amount represents the coefficient of correlation between a de-trended (lagged or lead) variable and output. For example, the correlation between the one-quarter lead aggregate employment and output of the data equals 0.86.
Table 5: Sensitivity analysis Panel A: simulated moments
Moments Data Benchmark. σ = 0.01 b = 1 ϕ1 = ϕ2 = 0
std(ˆht) 6.66 6.29 0.81 5.06 8.23
std(ˆnt) 1.10 0.73 0.74 1.08 1.81
std(ˆet) 5.79 5.97 0.37 4.70 6.78
corr(ˆht, ˆyt) 0.91 0.83 0.97 0.78 0.22 corr(ˆnt, ˆyt) 0.75 0.74 0.76 0.86 0.76 corr(ˆet, ˆyt) 0.89 0.77 0.57 0.63 0.06
Panel B: Coefficients of correlation between de-trended output and employment variables
Source Data Benchmark σ = 0.01 b = 1 ϕ1 = ϕ2 = 0
Coef. of Corr. ˆht nˆt ˆht nˆt ˆht ˆnt ˆht nˆt ˆht nˆt corr(gt+3, ˆyt) 0.52 0.81 0.03 0.78 0.52 0.78 -0.08 0.83 -0.25 0.15 corr(gt+2, ˆyt) 0.73 0.87 0.27 0.84 0.61 0.84 0.13 0.92 -0.10 0.31 corr(gt+1, ˆyt) 0.88 0.84 0.53 0.83 0.77 0.85 0.41 0.94 0.06 0.52 corr(gt, ˆyt) 0.91 0.75 0.83 0.74 0.97 0.76 0.78 0.86 0.22 0.76 corr(gt−1, ˆyt) 0.83 0.56 0.62 0.51 0.68 0.54 0.74 0.67 0.30 0.68 corr(gt−2, ˆyt) 0.68 0.34 0.48 0.34 0.45 0.38 0.67 0.47 0.42 0.65 corr(gt−3, ˆyt) 0.48 0.12 0.41 0.21 0.31 0.26 0.58 0.29 0.58 0.68
Note: See the note to Table 3.
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 Year
0 0.5 1 1.5 2 2.5 3 3.5
%
Share by SIC-7360 Share by SiC-7363 Share by NAICS-56132
Figure 1: The share of temporary employment measured by different industry classifications (source: BLS)
1990 1995 2000 2005 2010 2015 Year
-20 -15 -10 -5 0 5 10
%
Output Share of temporary employment
Figure 2: The HP-filtered cyclical components of output the share of temporary employment (sources: BLS and FRED)
1990 1995 2000 2005 2010 2015 Year
-5 -3 -1 1 3
%
Permanent employment Output Temporary employment (right scale)
-25 -15 -5 5 15
%
Figure 3: The HP-filtered cyclical components of permanent and temporary employment (on the right scale) along with output (sources: BLS and FRED)
1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 Year
10 13 16 19 22 25
Value
Temporary Aggregate
Figure 4: The hourly wage rates of temporary and total private-sector workers in US dollars (source: OES)
1990 1995 2000 2005 2010 2015 Year
0.74 0.76 0.78 0.8 0.82 0.84 0.86 0.88
Ratio
Figure 5: The ratio of hourly earnings of temporary to total private-sector workers (source:
BLS)
2 4 6 8 10
Figure 6: The impulse responses of the main variables to 1% positive (negative) TFP shock
2 4 6 8 10 0
0.5 1 1.5 2
%
2 4 6 8 10
0 2 4 6 8
%
2 4 6 8 10
0 0.5 1 1.5
%
2 4 6 8 10
0 0.05 0.1
Figure 7: The impulse responses to an 1% positive TFP shock given σ = 0.96 (benchmark) and σ = 0.01
2 4 6 8 10 0
0.5 1 1.5 2 2.5
%
2 4 6 8 10
0 2 4 6 8
%
2 4 6 8 10
0 0.5 1 1.5 2 2.5
%
2 4 6 8 10
0 0.05 0.1
Figure 8: The impulse responses to an 1% positive TFP shock given b = 4 (benchmark) and b = 1
2 4 6 8 10 0
1 2 3
%
2 4 6 8 10
0 3 6 9
%
2 4 6 8 10
0 1 2 3
%
2 4 6 8 10
0 0.05 0.1
Figure 9: The impulse responses to an 1% positive TFP shock given ϕ1 = 11.7 and ϕ2 = 6.0 (benchmark) and ϕ1 = ϕ2 = 0
Appendix A
This appendix provides a brief derivation of the stationary values of essential macro vari-ables. The competitive equilibrium for the economy is composed of 16 conditions (A1)–(A16).
The endogenous variables are the sequences of quantities{yt, ct, ht, nt, xt, vt, l1,t, It, kt, zt, dt} and prices {wh,t, wn,t, ηt, λt, pt}. Given A = 1 at the steady state, the stationary relationship at the competitive equilibrium can be stated as:
z = 1, (A1)
I = δk, (A10)
l1 = µx, (A11)
v = bl1, (A12)
n = x + v, (A13)
d = (
1− ϕ1+ ϕ2
2 µ2 )
(1− α) y − whh− wnn, (A14)
p = β
1− βd, (A15)
λ = [
c− ψ
1 + χ(n1+χ+ h1+χ) ]−θ
. (A16)
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