Decomposition of co-worker wage gains

István Boza; Virág Ilyés

doi:10.2478/izajole-2020-0008

Figures & Tables

Wage-tenure profiles and referrer presence.Note: The figure displays point estimations and 95% confidence intervals for two sets of estimations. The first set uses the proxy for contact presence upon entry, while in the other one the same indicator is set to zero if the original contact(s) left the firm by the given month. Both graphs present the parameter of eighteen separate regressions on the logarithm of daily earnings of male workers in the given month, for all odd months of the first three year of the employment spells. Female workers are included in the estimations, with a constant gender difference being assumed. Controlling for fixed effects is achieved by including pre-estimated individual and firm effects from the entry month equation. Additional controls are the same as listed in Table 3. Standard errors used for the confidence intervals are clustered at both firm level and individual level.

Number of linked workers over time.Note: The figure displays the number of hires with co-worker links present in each calendar month from 2003 until 2011. The subsample used for the estimation is the same as in Table 2.

Decomposition of co-worker gains by occupations—male results

	θ^OLS$\hat{\theta}_{\text {OLS}}$	θ^TWFE$\hat{\theta}_{T W F E}$	ψ^ind$\hat{\psi}_{i n d}$	ψ^firm $\hat{\psi}_{\text {firm }}$	ξ^ind$\hat{\xi}_{i n d}$	ξ^firm $\hat{\xi}_{\text {firm }}$	ω^ind$\hat{\omega}_{\text {ind}}$	ω^firm $\hat{\omega}_{\text {firm }}$
Manager	−0.0988*** (0.0259)	−0.0030 (0.0310)	−0.0775*** (0.0211)	−0.0183 (0.0142)	−0.0699*** (0.0196)	0.0226 (0.0241)	−0.0076 (0.0092)	−0.0409** (0.0127)
Skilled_W	0.0924*** (0.0274)	0.0551* (0.0235)	−0.0006 (0.0187)	0.0378* (0.0179)	−0.0049 (0.0169)	0.0094 (0.0250)	0.0044 (0.0101)	0.0285 (0.0156)
Unskilled_W	0.0627*** (0.0182)	0.0409* (0.0183)	0.0167 (0.0134)	0.0051 (0.0129)	0.0153 (0.0120)	−0.0113 (0.0172)	0.0013 (0.0076)	0.0164 (0.0108)
Skilled_B	0.0584*** (0.0070)	0.0228** (0.0077)	0.0217*** (0.0050)	0.0140* (0.0055)	0.0128** (0.0044)	0.0123 (0.0065)	0.0089** (0.0034)	0.0016 (0.0047)
Unskilled_B	0.0475*** (0.0081)	0.0118 (0.0075)	0.0340*** (0.0048)	0.0017 (0.0069)	0.0326*** (0.0045)	0.0161 (0.0085)	0.0014 (0.0030)	−0.0144* (0.0056)
N	964,806	501,200	964,806	964,806	943,643	571,442	964,806	964,806
N_i	616,386	197,435	616,386	616,386	616,365	223,021	616,386	616,386
N_j	105,818	61,121	105,818	105,818	84,655	105,778	105,818	105,818
R²	0.327	0.860	0.190	0.200	0.443	0.612	0.052	0.086

Decomposition of co-worker gains by gender

	θ^OLS $\hat{\boldsymbol{\theta}}_{\text {OLS }}$	θ^TWFE$\hat{\theta}_{\text {TWFE}}$	ψ^ind$\hat{\psi}_{\text {ind}}$	ψ^firm $\hat{\psi}_{\text {firm }}$	ξ^ind$\hat{\xi}_{i n d}$	ξ^firm$\hat{\xi}_{\text {firm}}$	ω^ind$\hat{\omega}_{\text {ind}}$	ω^firm$\hat{\omega}_{\text {firm}}$
Male	0.0465*** (0.0055)	0.0213*** (0.0051)	0.0167*** (0.0038)	0.0086* (0.0041)	0.0125*** (0.0034)	0.0118* (0.0049)	0.0041 (0.0023)	−0.0032 (0.0034)
Female	0.0313*** (0.0082)	−0.0024 (0.0096)	0.0254*** (0.0063)	0.0083 (0.0064)	0.0265*** (0.0055)	0.0148 (0.0080)	−0.0010 (0.0038)	−0.0065 (0.0057)
N	964,806	501,200	964,806	964,806	943,643	571,441	964,806	964,806
N_i	616,386	197,435	616,386	616,386	616,365	223,021	616,386	616,386
N_j	105,818	61,121	105,818	105,818	84,655	105,778	105,818	105,818
R²	0.327	0.860	0.204	0.200	0.453	0.612	0.052	0.087

Gains from links, second links, and similar workers

	θ^OLS${{\hat{\theta }}_{\text{OLS}}}$	θ^TWFE${{\hat{\theta }}_{\text{TWFE}}}$	ψ^ind${{\hat{\psi }}_{ind}}$	ψ^firm${{\hat{\psi }}_{\text{firm}}}$	ξ^ind ${{\hat{\xi }}_{\text{ind }}}$	ξ^firm ${{\hat{\xi }}_{\text{firm }}}$	ω^ind${{\hat{\omega }}_{ind}}$	ω^firm${{\hat{\omega }}_{\text{firm}}}$
Linked	0.0484*** (0.0056)	0.0194*** (0.0055)	0.0188*** (0.0038)	0.0102* (0.0042)	0.0152*** (0.0035)	0.0141** (0.0052)	0.0036 (0.0023)	−0.0039 (0.0035)
Similar	0.0131** (0.0050)	0.0072 (0.0050)	0.0150*** (0.0035)	−0.0091* (0.0041)	0.0194*** (0.0032)	0.0013 (0.0047)	−0.0044* (0.0023)	−0.0104** (0.0034)
Second	0.0489** (0.0157)	0.0125 (0.0173)	0.0062 (0.0104)	0.0302** (0.0111)	−0.0074 (0.0098)	0.0238 (0.0142)	0.0136* (0.0056)	0.0064 (0.0091)
N	938,791	479,919	938,791	938,791	917,835	550,362	938,791	938,791
N_i	603,975	189,756	603,975	603,975	603,955	215,546	603,975	603,975
N_j	105,061	60,367	105,061	105,061	84,105	105,022	105,061	105,061
R²	0.326	0.860	0.199	0.198	0.452	0.611	0.050	0.088

Heterogeneity of co-worker gains by relative position of contact

	θ^OLS${{\hat{\theta }}_{\text{OLS}}}$	θ^TWFE ${{\hat{\theta }}_{\text{TWFE }}}$	ψ^ind${{\hat{\psi }}_{ind}}$	ψ^firm${{\hat{\psi }}_{\text{firm}}}$	ξ^ind${{\hat{\xi }}_{ind}}$	ξ^ftrm${{\hat{\xi }}_{\text{ftrm}}}$	ω^ind${{\hat{\omega }}_{ind}}$	ω^frm${{\hat{\omega }}_{\text{frm}}}$
Superior	0.0572*** (0.0110)	0.0210* (0.0106)	0.0331*** (0.0075)	0.0030 (0.0084)	0.0444*** (0.0070)	−0.0073 (0.0110)	−0.0113* (0.0051)	0.0104 (0.0069)
Similar	0.0463*** (0.0058)	0.0163** (0.0058)	0.0167*** (0.0040)	0.0133** (0.0044)	0.0096** (0.0036)	0.0177** (0.0055)	0.0071** (0.0024)	−0.0044 (0.0037)
Inferior	−0.0125 (0.0127)	−0.0002 (0.0130)	−0.0177 (0.0100)	0.0054 (0.0083)	−0.0142 (0.0088)	0.0115 (0.0109)	−0.0035 (0.0054)	−0.0061 (0.0074)
N	964,806	501,200	964,806	964,806	943,643	571,441	964,806	964,806
N_i	616,386	197,435	616,386	616,386	616,365	223,021	616,386	616,386
N_j	105,818	61,121	105,818	105,818	84,655	105,778	105,818	105,818
R²	0.327	0.860	0.204	0.200	0.453	0.612	0.052	0.087

Decomposition of co-worker gains by occupations

	θ^OLS${{\hat{\theta }}_{\text{OLS}}}$	θ^TWFE${{\widehat{\mathbf{\theta }}}_{\text{TWFE}}}$	ψ^Ind${{\hat{\psi }}_{\text{Ind}}}$	ψ^Firm ${{\hat{\psi }}_{\text{Firm }}}$	ξ^Ind ${{\hat{\xi }}_{\text{Ind }}}$	ξ^Firm ${{\hat{\xi }}_{\text{Firm }}}$	ω^Ind${{\hat{\omega }}_{\text{Ind}}}$	ω^Firm ${{\hat{\omega }}_{\text{Firm }}}$
Manager	−0.0849*** (0.0223)	−0.0262 (0.0259)	−0.0508** (0.0183)	−0.0080 (0.0121)	−0.0397* (0.0171)	0.0378 (0.0196)	−0.0111 (0.0079)	−0.0458*** (0.0109)
Skilled_W	0.1146*** (0.0240)	0.0620** (0.0202)	0.0046 (0.0158)	0.0480** (0.0156)	−0.0026 (0.0141)	0.0130 (0.0205)	0.0072 (0.0088)	0.0349* (0.0136)
Unskilled_W	0.0558*** (0.0126)	0.0244 (0.0137)	0.0223* (0.0096)	0.0091 (0.0089)	0.0249** (0.0086)	0.0022 (0.0116)	−0.0026 (0.0056)	0.0069 (0.0076)
Skilled_B Unskilled_B	0.0507* (0.0060) 0.0349* (0.0072)	0.0159* (0.0068) 0.0079 (0.0070)	0.0236* (0.0044) 0.0287* (0.0044)	0.0112* (0.0049) −0.0017 (0.0063)	0.0156* (0.0038) 0.0278* (0.0041)	0.0132* (0.0058) 0.0117 (0.0076)	0.0079** (0.0030) 0.0009 (0.0028)	−0.0020 (0.0043) −0.0134** (0.0051)
N	964,807	501,200	964,807	964,807	943,643	571,443	964,807	964,807
N_i	616,386	197,435	616,386	616,386	616,365	223,022	616,386	616,386
N_j	105,819	61,121	105,819	105,819	84,655	105,779	105,819	105,819
R²	0.327	0.860	0.204	0.200	0.453	0.612	0.052	0.087

Co-worker gains and skill requirements

	Linked	Skill	Interaction
Baseline	0.0172*** (0.0046)	−	−
Manual Dexterity	0.0172*** (0.0047)	−0.0449*** (0.0020)	−0.0026 (0.0052)
Stamina	0.0172*** (0.0047)	−0.0445*** (0.0019)	−0.0066 (0.0055)
Persistence	0.0167*** (0.0046)	0.0441*** (0.0014)	0.0037 (0.0052)
Stress Tolerance	0.0174*** (0.0046)	0.0308*** (0.0014)	−0.0024 (0.0050)
Analytical Thinking	0.0164*** (0.0046)	0.0469*** (0.0015)	0.0053 (0.0050)
Complex Problem Solving	0.0159*** (0.0046)	0.0546*** (0.0016)	0.0056 (0.0048)
Active Learning	0.0167*** (0.0046)	0.0528*** (0.0015)	0.0016 (0.0052)
Coordination	0.0174*** (0.0046)	0.0398*** (0.0014)	−0.0025 (0.0044
Cooperation	0.0171*** (0.0046)	0.0203*** (0.0015)	−0.0022 (0.0052)
Adaptability/Flexibility	0.0170*** (0.0046)	0.0329*** (0.0015)	0.0026 (0.0050)
Originality	0.0163*** (0.0046)	0.0436*** (0.0015)	0.0066 (0.0052)
Innovation	0.0158*** (0.0046)	0.0329*** (0.0014)	0.0081 (0.0048)
Independence	0.0172*** (0.0046)	0.0152*** (0.0015)	0.0020 (0.0049)

Endogenous and exogenous job mobility

	θ^OLS${{\hat{\theta }}_{\text{OLS}}}$	θ^TWFE ${{\hat{\theta }}_{\text{TWFE }}}$	ψ^ind${{\hat{\psi }}_{ind}}$	ψ^ftm${{\hat{\psi }}_{ftm}}$	ξ^ind${{\hat{\xi }}_{ind}}$	ξ^firm ${{\hat{\xi }}_{\text{firm }}}$	ω^ind${{\hat{\omega }}_{\text{ind}}}$	ω^firm${{\hat{\omega }}_{\text{firm}}}$
Endog.	0.0436*** (0.0058)	0.0162** (0.0055)	0.0188*** (0.0041)	0.0086* (0.0044)	0.0161*** (0.0037)	0.0071 (0.0054)	0.0027 (0.0025)	0.0015 (0.0037)
Exog.	0.0620*** (0.0119)	0.0423*** (0.0117)	0.0103 (0.0080)	0.0095 (0.0087)	−0.0003 (0.0072)	0.0366*** (0.0107)	0.0106** (0.0041)	−0.0272*** (0.0073)
N	964,806	501,200	964,806	964,806	943,643	571,442	964,806	964,806
N_i	616,386	197,435	616,386	616,386	616,365	223,021	616,386	616,386
N_j	105,818	61,121	105,818	105,818	84,655	105,778	105,818	105,818
R²	0.327	0.860	0.203	0.200	0.453	0.612	0.052	0.087

Summary of parameters in our model

	Parameter		Interpretation
0.		θ^OLS$\hat{\theta}_{\text {OLS}}$	The wage differential between linked and nonlinked hires, controlling for only observed worker and firm characteristics.
1.		θ^TWFE$\hat{\theta}_{\text {TWFE}}$	The wage differential between linked and nonlinked hires, controlling for unobserved firm and worker heterogeneity (but not match heterogeneity).
	1a.	θ	The pure ‘presence effects’ of having a potential referrer at the firm.
	1b.		Bias arising from the possibility that linked workers are better matched with firms (match selection).
2.		ψ^ind$\hat{\psi}_{i n d}$	The average worker effect differential between linked and nonlinked hires.
	2a.	ξ^ind$\hat{\xi}_{i n d}$	The average worker effect differentials between linked and nonlinked hires within firms.
	2b.	ω^ind$\hat{\omega}_{i n d}$	The average worker effect differential between firms that tend to make linked hires and those that tend to make nonlinked hires.
3.		ψ^firm$\hat{\psi}_{\text {firm}}$	The average firm effect differential between linked and nonlinked hires.
	3a.	ξ^firm $\hat{\xi}_{\text {firm }}$	The average firm effect differentials between linked and nonlinked hires within worker careers.
	3b.	ω^firm$\hat{\omega}_{\text {firm}}$	The average firm effect differential between workers that tend to be hired with and without links.

Summary statistics: job entrants, freshly acquired jobs, and receiving firms

	Subsample		Nonlinked subgroups			Control group
	Linked	Nonlinked	First spell	W/o small firm experience	Control group	Always nonlinked	Nonlinked and linked
No. of observations	20,227	944,579	135,818	147,600	661,161	645,253	15,908
Log of relative daily earnings	−0.470	−0.580	−0.745	−0.468	−0.571	−0.572	−0.552
Monthly earnings (HUF)	128,511	108,053	80,897	127,616	109,264	109,245	110,046
Age	38.0	32.7	25.6	32.3	34.2	34.2	36.2
Elementary education	12%	11%	21%	14%	9%	9%	13%
Secondary education	63%	66%	63%	65%	67%	67%	64%
Tertiary education	25%	23%	16%	22%	25%	25%	24%
Central Hungary	32%	34%	34%	29%	35%	35%	34%
Central Transdanubia	12%	12%	10%	15%	12%	12%	13%
Western Transdanubia	9%	10%	8%	12%	10%	10%	9%
Southern Transdanubia	8%	7%	6%	8%	8%	8%	8%
Northern Hungary	11%	9%	8%	10%	9%	9%	11%
Northern Great Plain	13%	11%	11%	13%	11%	11%	12%
Southern Great Plain	12%	11%	10%	10%	11%	11%	11%
Max. number of workplaces	5.39	5.57	2.58	4.77	6.37	6.35	7.27
Occupation specific experience	70%	47%	–	37%	59%	59%	69%
Length of prev. unemployment	1.5	2.2	–	2.4	2.1	2.2	1.6
Manager	7%	3%	2%	4%	4%	4%	5%
White-collar work	6%	6%	6%	8%	6%	6%	5%
Other white-collar work	16%	19%	24%	20%	18%	18%	14%
Skilled blue-collar work	43%	40%	38%	34%	41%	41%	44%
Unskilled blue-collar work	28%	31%	30%	35%	30%	30%	33%
Relative wage level of firm	0.907	0.877	0.816	1.028	0.856	0.857	0.815
Sector: Agriculture	3%	2%	3%	2%	2%	2%	2%
Sector: Industry	41%	34%	32%	38%	34%	34%	36%
Sector: Trade and services	56%	64%	65%	60%	64%	64%	62%
Foreign firm	18%	20%	20%	27%	19%	19%	16%
Domestic firm	82%	80%	80%	73%	81%	81%	84%
Number of employees	39.2	42.9	44.4	60.0	38.8	39.0	30.8

Heterogeneity of co-worker gains by link and tie characteristics

	θ^OLS${{\hat{\theta }}_{\text{OLS}}}$	θ^TWFE${{\widehat{\mathbf{\theta }}}_{\text{TWFE}}}$	ψ^ind${{\hat{\psi }}_{\text{ind}}}$	ψ^firm${{\hat{\psi }}_{firm}}$	ξ^ind${{\hat{\xi }}_{\text{ind}}}$	ξ^firm ${{\hat{\xi }}_{\text{firm }}}$	ω^ind${{\hat{\omega }}_{ind}}$	ω^firm ${{\hat{\omega }}_{\text{firm }}}$
Linked	0.0382*** (0.0054)	0.0202*** (0.0054)	0.0173*** (0.0038)	0.0008 (0.0041)	0.0142*** (0.0034)	−0.0002 (0.0052)	0.0031 (0.0023)	0.0009 (0.0034)
Seniority	0.0020*** (0.0005)	−0.0005 (0.0005)	0.0012*** (0.0004)	0.0013*** (0.0004)	0.0013*** (0.0003)	0.0009 (0.0005)	−0.0001 (0.0002)	0.0004 (0.0003)
Since	−0.0003 (0.0004)	−0.0001 (0.0004)	−0.0000 (0.0003)	−0.0001 (0.0003)	−0.0003 (0.0002)	0.0001 (0.0004)	0.0002 (0.0002)	−0.0002 (0.0002)
Common	0.0013*** (0.0003)	0.0000 (0.0004)	0.0006* (0.0002)	0.0007** (0.0002)	0.0005* (0.0002)	0.0005 (0.0004)	0.0001 (0.0001)	0.0003 (0.0002)
N	964,806	501,200	964,806	964,806	943,643	571,441	964,806	964,806
N_i	616,386	197,435	616,386	616,386	616,365	223,021	616,386	616,386
N_j	105,818	61,121	105,818	105,818	84,655	105,778	105,818	105,818
R²	0.345	0.860	0.203	0.232	0.453	0.628	0.069	0.059

Decomposition of co-worker gains by occupations - female results

	θ^OLS${{\hat{\theta }}_{\text{OLS}}}$	θ^TWFE ${{\hat{\theta }}_{\text{TWFE }}}$	ψ^ind${{\hat{\psi }}_{ind}}$	ψ^firm${{\hat{\psi }}_{\text{firm}}}$	ξ^ind${{\hat{\xi }}_{\text{ind}}}$	ξ^firm ${{\hat{\xi }}_{\text{firm }}}$	ω^ind${{\hat{\omega }}_{ind}}$	ω^frm${{\hat{\omega }}_{\text{frm}}}$
Manager	−0.0415 (0.0416)	−0.0809 (0.0463)	0.0168 (0.0345)	0.0226 (0.0216)	0.0372 (0.0320)	0.0804** (0.0289)	−0.0204 (0.0141)	−0.0579** (0.0198)
Skilled_W	0.1648*** (0.0425)	0.0784 (0.0403)	0.0157 (0.0293)	0.0706** (0.0253)	0.0015 (0.0264)	0.0208 (0.0352)	0.0142 (0.0152)	0.0498* (0.0227)
Unskilled_W	0.0503** (0.0158)	0.0081 (0.0194)	0.0296* (0.0128)	0.0126 (0.0113)	0.0357** (0.0115)	0.0150 (0.0157)	−0.0061 (0.0074)	−0.0024 (0.0098)
Skilled_B	0.0275* (0.0111)	−0.0107 (0.0140)	0.0343*** (0.0090)	0.0039 (0.0100)	0.0298*** (0.0074)	0.0170 (0.0124)	0.0044 (0.0062)	−0.0132 (0.0089)
Unskilled_B	−0.0097 (0.0140)	−0.0116 (0.0190)	0.0158 (0.0102)	−0.0138 (0.0125)	0.0178* (0.0090)	−0.0115 (0.0158)	−0.0020 (0.0057)	−0.0023 (0.0109)
N	964,807	501,200	964,807	964,807	943,643	571,443	964,807	964,807
N_i	616,386	197,435	616,386	616,386	616,365	223,021	616,386	616,386
N_j	105,818	61,121	105,818	105,818	84,655	105,778	105,818	105,818
R²	0.327	0.860	0.190	0.200	0.443	0.612	0.052	0.086

Decomposition of co-worker wage gains

Figures & Tables

Figure 1

Figure A1

Decomposition of co-worker gains by occupations—male results

Decomposition of co-worker gains by gender

Gains from links, second links, and similar workers

Heterogeneity of co-worker gains by relative position of contact

Decomposition of co-worker gains by occupations

Co-worker gains and skill requirements

Endogenous and exogenous job mobility

Summary of parameters in our model

Summary statistics: job entrants, freshly acquired jobs, and receiving firms

Heterogeneity of co-worker gains by link and tie characteristics

Decomposition of co-worker gains by occupations - female results

Paradigm

My account