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

Simon Ming Sum Lo

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

Simon Ming Sum Lo

| Dec 30, 2023

IZA Journal of Labor Economics

Volume 12 (2023): Issue 1 (January 2023)

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Page range: -

Accepted: Feb 06, 2023

DOI: https://doi.org/10.2478/izajole-2023-0006

Keywords
job search model, work-leisure balance, value of time, multiple jobholding, underemployment and overemployment, wage elasticity of labor supply, employment and unemployment duration

© 2023 Simon Ming Sum Lo, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Histograms for working hours in single job.

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

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

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

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

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, $\bar{ξ}$ \bar \xi	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, $\bar{P_{1}}$ \overline {{P_1}}	0.89	0.87	0.78	0.61	0.41	0.20
Acceptance probability of second job offers, $\bar{P_{2}}$ \overline {{P_2}}	0.86	0.84	0.76	0.60	0.53	0.24
Acceptance probability of post-unemployment offers, $\bar{P_{0}}$ \overline {{P_0}}	0.93	0.90	0.85	0.72	0.54	0.20

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

	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

Estimated values of leisure a (cent), actual working hours h (weekly hours), estimated optimal working hours h1* h.1^* (weekly hour), and their difference Δh. Different values of q used in quantile regression.

	a	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	Δh	$\Pr (h_{1} > h_{1}^{})$ {\bf{Pr(}}{{\boldsymbol{h}}_{\bf{1}}}{\boldsymbol{ > h}}_{\bf{1}}^{\bf{}}{\bf{)}}	overworked group			underworked group

					h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	Δh	h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	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

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

	a	ɛ_l,w₁	ɛ_l,w₂	h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	Δh	$\Pr (h_{1} > h_{1}^{})$ {\bf{Pr(}}{{\boldsymbol{h}}_{\bf{1}}}{\boldsymbol{ > h}}_{\bf{1}}^{\bf{}}{\bf{)}}	overwork	underwork

								Δh	Δh
${\tilde{e}}_{i} = 168$ {\tilde e_i} = 168	1680	−0.26	−0.40	39.0	46.5			8.5	−16.9
${\tilde{e}}_{i} = 140$ {\tilde e_i} = 140	1508	−0.28	−0.51	39.0	42.1			9.0	−13.7
${\tilde{e}}_{i} = 126$ {\tilde e_i} = 126	1485	−0.32	−0.59	39.0	38.3	0.6	0.53	9.9	−10.1

Descriptive statistics.

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

Estimated job offer rates λj, separation rates δj, and acceptance rates Pj in percent.

Job types	Job offer rates, λ_j			Job separation rates, δ_j		Job acceptance rates, P_j

	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

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

	w₁	a	B	E	ɛ_l,w₁	ɛ_l,w₂	h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	$h_{1} - h_{1}^{}$ {{\boldsymbol{h}}_{\bf{1}}} - {\boldsymbol{h}}_{\bf{1}}^{\bf{}}
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

Actual working hours h1 (weekly hour), estimated optimal hours h1* h.1^* (weekly hour), Δh=h1−h1* \Delta h = {h.1} - h.1^* (weekly hour). q = 2. Different SD.

	h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	Δh	$\Pr (h_{1} > h_{1}^{})$ {\bf{Pr(}}{{\boldsymbol{h}}_{\bf{1}}}{\boldsymbol{ > h}}_{\bf{1}}^{\bf{}}{\bf{)}}	overwork group			underwork group

					h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	Δh	h₁	$h_{1}^{}$ {\boldsymbol{h}}_{\bf{1}}^{\bf{}}	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

Estimated parameter for the value of leisure (measured in e−6), the estimated partial effect ai2αk a.i^2{\alpha .k} - mean, minimum and maximum (measured in cent).

Variables	α_k	The partial effect $a_{i}^{2} α_{k}$ {\boldsymbol{a}}_{\boldsymbol{i}}^{\bf{2}}{{\bf{\alpha }}_{\boldsymbol{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

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

Published Online: Dec 30, 2023

Page range: -

Accepted: Feb 06, 2023

DOI: https://doi.org/10.2478/izajole-2023-0006

Keywords
job search model, work-leisure balance, value of time, multiple jobholding, underemployment and overemployment, wage elasticity of labor supply, employment and unemployment duration

© 2023 Simon Ming Sum Lo, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

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.

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

Estimated values of leisure a (cent), actual working hours h (weekly hours), estimated optimal working hours h1* h.1^* (weekly hour), and their difference Δh. Different values of q used in quantile regression.

Descriptive statistics.

Estimated job offer rates λj, separation rates δj, and acceptance rates Pj in percent.

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

Actual working hours h1 (weekly hour), estimated optimal hours h1* h.1^* (weekly hour), Δh=h1−h1* \Delta h = {h.1} - h.1^* (weekly hour). q = 2. Different SD.

Estimated parameter for the value of leisure (measured in e−6), the estimated partial effect ai2αk a.i^2{\alpha .k} - mean, minimum and maximum (measured in cent).

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

Published Online: Dec 30, 2023

Page range: -

Accepted: Feb 06, 2023

DOI: https://doi.org/10.2478/izajole-2023-0006

Keywordsjob search model, work-leisure balance, value of time, multiple jobholding, underemployment and overemployment, wage elasticity of labor supply, employment and unemployment duration

© 2023 Simon Ming Sum Lo, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

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.

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

Estimated values of leisure a (cent), actual working hours h (weekly hours), estimated optimal working hours h1* h.1^* (weekly hour), and their difference Δh. Different values of q used in quantile regression.

Descriptive statistics.

Estimated job offer rates λj, separation rates δj, and acceptance rates Pj in percent.

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

Actual working hours h1 (weekly hour), estimated optimal hours h1* h.1^* (weekly hour), Δh=h1−h1* \Delta h = {h.1} - h.1^* (weekly hour). q = 2. Different SD.

Estimated parameter for the value of leisure (measured in e−6), the estimated partial effect ai2αk a.i^2{\alpha .k} - mean, minimum and maximum (measured in cent).

Keywords
job search model, work-leisure balance, value of time, multiple jobholding, underemployment and overemployment, wage elasticity of labor supply, employment and unemployment duration