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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 h1 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 (h1) 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. 12 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 13 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 11 1/ 11 global social multiplier h / w 1 11 11 exogenous effect 1 / 11 endogenous effect 15 Key Findings: elasticity decomposition [1 /(11)] 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