Download Labor Supply with Social Interactions

Empirical Model of Labor Supply with Social
Interactions: Econometric Issues and Tax
Policy Implications
Andrew Grodner
Department of Economics
East Carolina University
Thomas Kniesner
Center for Policy Research
&
Department of Economics
Syracuse University,
Outline
1. Literature Review
2. Theory of SI in Labor Supply
3. Econometric model
3a. Identifying reference group
3b. Identifying endogenous social interactions
4. Results
5. Conclusion
2
Summary
Importance - correct wage elasticity crucial for
optimal taxation, deadweight loss calculation,
welfare simulations
Theory - workers believe that they are judged by
others
Identification
- create economic distance
- create and use instrument using assumed
neighborhood structure (IV)
Results:
- spillover effect in labor supply both economically
and statistically significant
- total wage elasticity 0.22: exogenous part 0.08,
endogenous part 0.14
- elasticity without interactions underestimated by
70% (0.13)
3
1. Literature review
Theory - Importance:
Social multiplier (Glaeser et al (2002), Becker and
Murphy (2000)), Irrational behavior in experiments (Fehr
and Schmidt (1999), Falk and Fischbacher (2001))
Theory - Models of Interactions:
Social norms (Lindbeck, Nyberg, and Weibull, 1999),
peer group effects (de Bartolome Charles, 1990),
neighborhood effects (Durlauf, 1996), etc. (session at
2005 AEA)
Empirical - general
Mostly in Urban Economics settings with
Neighborhood effects (Journal of Applied Econometrics,
Special Issue: Empirical Analysis of Social Interactions,
2003, September/October, Vol. 18, No. 5)), Durlauf
(2004). (session at 2005 AEA)
Empirical - in labor supply
Neighborhood characteristics and job proximity
(Weinberg et al, 2004), Taxes and labor supply
(Aronsson et al, 1999), Female labor force participation
(Woittiez and Kapteyn, 1998)
Major challenge: distinguish endogenous from
exogenous interactions (Reflection problem in Manski,
1993)
4
1. Literature: Identification solutions
Non-linearity of interactions (Brock and Duflauf
2001, Manski 1993)
Policy Intervention (Moffitt, 2001)
Spatial GMM regression (Kalejian and Prucha
1998)
Within-Between Variation (Graham and Hahn
2005)
Simulations-based (Krauth forthcoming)
Structural modeling (Weinberg 2005)
5
2. Theory of SI in Labor Supply
Set up:
Workers gain total utility from:
1. individual utility associated with direct and
positive effect of consumption, and direct and
positive effect of leisure,
2. social disutility associated with workers'
beliefs about how others perceive his hours
worked.
Assumptions:
* workers believe that they are going to be
judged more by their reference group when others
in the group work more,
* workers experience lower disutility of being
compared to others when they work harder at a
decreasing rate.
Result:
If social interactions are present an increase in
hours worked in the reference group induces
workers to work more hours to decrease social
disutility.
6
3. Econometric model of SI in Labor Supply
General











 i  g 






yig  0 1xig 2 f y











 i  g 






3h x
4ug  ig
Labor supply version
h         x   h1  1h(i) g  2 x(i) g  
Data
PSID married men 1976, anchors to Hausman
Two crucial empirical ancillary findings
Crucial to instrument reference group h(i ) g
Crucial to control for heterogeneity (h1)
7
3a. Identifying the Reference Group
People close in economic distance
Combine personal/family/location characteristics
Factor analysis deals naturally with our problem
Use the two factors as social coordinates
All independent variables from labor supply
Physical coordinates center of the county
Correlations of factors with variables
KIDSU6 FAMSIZ AGE45 HOUSEQ BHLTH lat
SocCoord1
-0.77
-0.45
0.75
0.44
0.18
0.11
0.00
0.00
0.00
0.00
0.00
0.00
SocCoord2
0.10
0.63
0.11
0.67
-0.28
0.26
0.00
0.00
0.00
0.00
0.00
0.00
* p-value below the correlation
- Demographic factor
- Physical distance factor
(same pattern with three factors)
8
lon2
0.02
0.61
0.27
0.00
Factor Loadings
Variable |
1
2
Uniqueness
-------------+-------------------------------KIDSU6 | -0.52395
0.03592
0.72419
FAMSIZ | -0.30675
0.23363
0.85132
AGE45 |
0.50557
0.04114
0.74271
HOUSEQ |
0.29731
0.24827
0.84997
BHLTH |
0.12031
-0.10413
0.97468
lat |
0.07530
0.09772
0.98478
lon2 |
0.01043
0.09996
0.98990
9
Problem: selecting radius for group
We use spatial econometric result
Coefficient on endogenous social interactions
tends to minus infinity (Kelejian and Prucha, 2002)
Social interactions present at a certain group size
Upward bias in the endogenous variable at some
point overcomes statistical tendency for the
coefficient to become negative (Anselin 1988)
As radius grows N  13, 44*, 89, 143, 204, 271
OLS coefficient on group h most positive (biased)
Table 1. Selection of the reference group using
simple regression: coefficient on Annual hours in
the reference group
radius
δ1
on
N
h(i ) g
0-0.1
0-0.2
−0.1978
0.0626
(0.0867)** (0.1432)
13.33
44.53
0-0.3
−0.2042
(0.2411)
89.19
10
0-0.4
0-0.5
0-0.6
−0.4982
−0.9685
−1.5021
(0.3231) (0.3566)*** (0.4709)***
142.56
204.13
271.21
Spatial Moran Test results:
Moran's I spatial correlogram
AnnualHours
--------------------------------------Distance bands
|
I
p-value*
--------------------+-----------------(0-.1]
| -0.013
0.224
(.1-.2]
| 0.018
0.035
(.2-.3]
| 0.009
0.117
(.3-.4]
| 0.005
0.202
(.4-.5]
| -0.002
0.426
(.5-.6]
| -0.003
0.380
--------------------------------------*1-tail test
Moran's I spatial correlogram
AnnualHours
0.02
I
0.01
0.00
-0.01
-0.02
0-.1
.1-.2
.2-.3
.3-.4
Distance bands
11
.4-.5
.5-.6
Coefficient goes to minus infinity: intuition
Consider example:
y
2000
2000
1000
2000
2000
2000
ybar5
1800
1800
2000
1800
1800
1800
ybar4
1750
1750
2000
1750
1750
1750
ybar3
ybar2
1666.67
1500
1666.67
1500
2000
2000
1666.67
1500
1666.67
2000
1666.67
2000
Regression results:
y = -5.00 * ybar5
y = -4.00 * ybar4
y = -3.00 * ybar3
y = -0.67 * ybar2
1. Coefficient is negative because lower "y" values
increase the mean of neighbors more than for
other observations.
2. Coefficient increases in magnitude because with
larger reference group "ybar" has less variation
and the coefficient need to make up for it.
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3b. Identification - Instrumenting the Reference
Group Outcome
Social Coordinate 2
Graph 1. Demonstration of the identification strategy for the endogenous social interactions.
Boundary for
reference group g1
Boundary for
reference group g2
y0g1
y1g1
y3g2
y2g1g2
Inner Boundary for
instrument group
Outer boundary for
instrument group
Social Coordinate 1
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Table 2. Regressions with Social Interactions, Habit Formation, and Various Sets of Instruments
Dependent
Var:
Annual Hours
Worked
AfterTaxWage
(1)
(2)
(3)
Baseline
Full
66.6982
(35.5604)*
−0.0031
(0.0058)
Only habit
formation
30.5734
(28.1246)
0.0011
(0.0045)
0.5940
(0.0265)***
(4)
Only social
interactions
81.6429
(37.3766)**
−0.0055
(0.0061)
38.5373
(28.6798)
VirtualIncome
0.0000
(0.0047)
AnnualHours75
0.5950
(0.0270)***
AnnHours_0_2
0.6379
1.3128
(0.2689)**
(0.3532)***
Observations
910
910
910
910
Sargan test
0.212
0.081
P-value
0.64502
0.77653
Instruments
WageRate75
WageRate75
WageRate75
WageRate75
NonLaborIncome75 NonLaborIncome75 NonLaborIncome75 NonLaborIncome75
AnnHours_2_6
AnnHours_2_6
IndepVar_2_6
IndepVar_2_6
Standard errors in parentheses
Endogenous variables in bold
* significant at 10%; ** significant at 5%; *** significant at 1%
14
4. Labor Supply Results
Focus on
h  w 1h  h  1 w
11
1/ 11   global social multiplier



h / w      1
11
11

exogenous effect
1  / 11   endogenous effect



 

15
Key Findings: elasticity decomposition
  [1 /(11)]
ˆ1  0.6 [] 1.5
0.22 = 0.08 + 0.14
Putting the Results in Context
  usual elasticity  0.13
total elasticity underestimated
  1.7 (.22/.13)
exogenous elasticity overestimated
  1.6 (.13/.08)
16
5. Conclusion
- Social interactions both statistically and
economically significant
- Total wage elasticity is 0.22, with endogenous
part 0.14, and exogenous part 0.08
- Wage elasticity (total) 70% larger due to
interactions
- Usual wage elasticity (exogenous) estimate
overestimated in baseline by 60%
17