Desired work-leisure balance in a partial equilibrium job search model with multiple job holding

Variables	Mean	SD	min	max
Real wage (cent) in current job	452	261	1	1858
Real wage (cent) in new single job offer	517	267	9	1636
Real wage (cent) in new second job offer	434	239	39	1623
Real wage (cent) in post unemployment job offer	409	212	67	1644
Weekly working hours in current job (one job)	36.6	11.7	0	168
Weekly working hours in current jobs (two jobs)	62.1	19.5	0	168
Weekly working hours in new single job	39.1	8.77	1	168
Weekly working hours in new second job	29.8	13.7	1	140
Weekly working hours in post unemployment job	35.0	11.0	1	144
Weekly leisure hours	127	16.0	0	168
Duration (week) for employment spell (one job)	106	133	1	1346
Duration (week) for employment spell (two jobs)	34.2	47.1	1	630
Duration (week) for unemployment spell	49.5	65.6	1	631
Previous work experience (week)	391	197	1	1646
Number of jobs held prior to change in job status	7.25	4.67	1	36
Age	29.2	3.13	25	35
Female (dummy)	0.50	0.50	0	1
White (dummy)	0.51	0.50	0	1
Black (dummy)	0.28	0.45	0	1
Married (dummy)	0.32	0.47	0	1
Parenthood (dummy)	0.72	0.45	0	4
Net worth (thousand dollars)	61	136	−300	600
Non high school qualification or lower (dummy)	0.15	0.35	0	1
Industry - public sector (dummy)	0.22	0.41	0	1
Industry- professional services (dummy)	0.21	0.41	0	1
Real interest rate (percent)	1.80	1.90	0.50	6.02

Table 2

Estimated conditional reservation wages (cent). The proportion of observed accepted wages w′ smaller than the estimated ξ (percent). Estimated offer acceptance rates for single job offers, second job offers, and post-unemployment offers.

q	0.2	0.5	1	2	3	5
Estimated conditional reservation wages, $\bar{ξ}$	57	82	113	158	191	231
Pr(w′ < ξ) - in percent	0.6	0.7	1.0	1.6	2.3	3.4
Acceptance probability of single job offers, $\bar{P_{1}}$	0.89	0.87	0.78	0.61	0.41	0.20
Acceptance probability of second job offers, $\bar{P_{2}}$	0.86	0.84	0.76	0.60	0.53	0.24
Acceptance probability of post-unemployment offers, $\bar{P_{0}}$	0.93	0.90	0.85	0.72	0.54	0.20

Histograms for working hours in single job.

Table 3

Observed offered wages and estimated conditional reservation wages for different types of job, measured in cent q = 2.

Job types	Observed offered wage			Estimated reservation wage
Job types	Single	Second	Post-unemployment	Single	Second	Post-unemployment
Mean	517	434	408	218	154	125
Median	446	355	338	206	139	124
S.D.	268	239	212	121	113	53

Offered wages and reservation wages - Fitted truncated models and histograms.

Table 4

Estimated job offer rates λ_j, separation rates δ_j, and acceptance rates P_j in percent.

Job types	Job offer rates, λ_j			Job separation rates, δ_j		Job acceptance rates, P_j
Job types	Single	Second	Post-unemp	Job 1	Job 2	Single	Second	Post-unemp
Mean	0.78	0.55	2.18	1.24	1.71	61.0	59.8	72.4
1 percentile	0.18	0.10	1.16	0.14	0.40	5.58	7.02	21.6
99 percentile	7.36	5.86	7.62	14.1	5.31	98.9	98.9	99.7

Table 5

Wage rate w₁ (cent), estimated value of leisure a (cent), adjustment factor B and E, wage elasticity of optimal leisure time ɛ_l,w₁ and ɛ_l,w₂, actual working hours h₁ (weekly hour), estimated optimal working hours $h_{1}^{*}$ (weekly hour), and the difference between h₁ and $h_{1}^{*}$ (weekly hour).

	w₁	a	B	E	ɛ_l,w₁	ɛ_l,w₂	h₁	$h_{1}^{*}$	$h_{1} - h_{1}^{*}$
Mean	445	1680	1.02	0.67	−0.26	−0.40	39.0	46.5	−7.50
S.D.	239	410	0.01	0.11	0.12	0.22	8.39	17.4	17.7
1 percentile	126	1101	1.00	0.40	−0.71	−1.27	12	14.4	−57.9
99 percentile	1345	3152	1.08	0.92	−0.08	−0.10	65	97.1	27.7

Histogram for the dierences between actual and optimal working hours, Δh.

Table 6

Estimated values of leisure a (cent), actual working hours h (weekly hours), estimated optimal working hours $h_{1}^{*}$ (weekly hour), and their difference Δh. Different values of q used in quantile regression.

	a	$h_{1}^{*}$	Δh	$\Pr (h_{1} > h_{1}^{*})$	overworked group			underworked group
	a	$h_{1}^{*}$	Δh	$\Pr (h_{1} > h_{1}^{*})$	h₁	$h_{1}^{*}$	Δh	h₁	$h_{1}^{*}$	Δh
q = 0.2	1595	46.6	−7.6	0.36	41.7	32.4	9.3	37.5	54.7	−17.2
q = 0.5	1655	46.6	−7.6	0.36	41.7	32.9	8.8	37.5	54.6	−17.1
q = 1	1655	46.8	−7.8	0.36	41.7	32.6	9.1	37.5	54.7	−17.2
q = 2	1680	46.5	−7.5	0.37	41.5	33.1	8.5	37.5	54.4	−16.9
q = 3	1681	47.5	−8.7	0.34	41.2	33.5	7.8	37.5	54.8	−17.2
q = 5	1693	48.0	−9.2	0.34	41.1	33.8	7.3	37.5	55.2	−17.7

Table 7

Estimated parameter for the value of leisure (measured in e⁻⁶), the estimated partial effect $a_{i}^{2} α_{k}$ - mean, minimum and maximum (measured in cent).

Variables	*α_k*	The partial effect $a_{i}^{2} α_{k}$
		mean	min	max
Constant	−857^**	−2594	−30665	−793
Previous work experience (weeks)	0.06	0.19	0.06	2.31
Number of previous jobs held	−8.90^**	−27.0	−318	−8.23
Age (years)	10.5^**	31.8	9.69	375
Female (dummy)	−27.4^*	−83.1	−980	−25.3
White (dummy)	17.7	53.6	16.3	632
Black (dummy)	−69.5^**	−210	−2486	−64.3
Married (dummy)	4.76	14.4	4.40	170
Parenthood (dummy)	−17.2^*	−52.2	−615	−15.9
Net worth (thousands dollar)	0.30^**	0.92	0.28	10.8
Non high school qualification or lower (dummy)	−146^**	−440	−5202	−134
Industry - public sector (dummy)	115^**	348	106	4124
Industry- professional services (dummy)	63.2^**	191	58.4	2258

Table 8

Estimated value of leisure a (cent), wage elasticity of optimal leisure time ɛ_l,w₁ and ɛ_l,w₂, actual working hours h₁ (weekly hour), estimated optimal hours $h_{1}^{*}$ (weekly hour), working hours mismatches $Δ h = h_{1} - h_{1}^{*}$ (weekly hour). q = 2. Dierent values of ${\tilde{e}}_{i}$ .

	a	ɛ_l,w₁	ɛ_l,w₂	h₁	$h_{1}^{*}$	Δh	$\Pr (h_{1} > h_{1}^{*})$	overwork	underwork
	a	ɛ_l,w₁	ɛ_l,w₂	h₁	$h_{1}^{*}$	Δh	$\Pr (h_{1} > h_{1}^{*})$	Δh	Δh
${\tilde{e}}_{i} = 168$	1680	−0.26	−0.40	39.0	46.5			8.5	−16.9
${\tilde{e}}_{i} = 140$	1508	−0.28	−0.51	39.0	42.1			9.0	−13.7
${\tilde{e}}_{i} = 126$	1485	−0.32	−0.59	39.0	38.3	0.6	0.53	9.9	−10.1

Histograms for the preferred hours and actual hours, original data. SD = 0.

Histograms for the preferred hours and actual hours, simulated data. SD = 4.

Table 9

Actual working hours h₁ (weekly hour), estimated optimal hours $h_{1}^{*}$ (weekly hour), $Δ h = h_{1} - h_{1}^{*}$ (weekly hour). q = 2. Different SD.

	h₁	$h_{1}^{*}$	Δh	$\Pr (h_{1} > h_{1}^{*})$	overwork group			underwork group
	h₁	$h_{1}^{*}$	Δh	$\Pr (h_{1} > h_{1}^{*})$	h₁	$h_{1}^{*}$	Δh	h₁	$h_{1}^{*}$	Δh
SD = 0	39.0	46.5	−7.5	0.37	41.5	33.1	8.5	37.5	54.4	−16.9
SD = 2	39.8	46.5	−7.1	0.37	40.5	33.3	7.2	38.8	54.3	−15.6
SD = 4	39.8	46.5	−6.7	0.38	40.5	34.0	6.4	39.4	54.0	−14.5
SD = 8	40.7	46.5	−5.8	0.38	42.8	36.2	6.6	39.3	52.8	−13.5