内生性含义及其处理方法

6/13/2011 1 € If X is orthogonal to μ then OLS will provide the best linear unbiased estimate of β1 € If X is correlated with μ then OLS will provide a biased estimate of β1, thus we have endogeneity. Y=β0+β1X+μ 6/13/2011 2 € Errors in variables € Omitted variables € Simultaneous causality € Self-selection bias 6/13/2011 3 € Measurement errors € β1 estimated by OLS will be biased towards zero+ Example € Standard Industrial Classification (SIC) system € Participants optimistically report the industries they participate in.++ +Woodbridge, 2006. ++Bascle, 2008 € An explanatory variable that is correlated with other explanatory variables and the dependent variable, yet is omitted from the regression.* Example € In a wage- education regression the variable ability is often omitted yet affects both wage and education. *Bascle, 2008 6/13/2011 4 € Causality runs in both directions € Explanatory variable affects dependent variable and latter affects former. * Example € Diversification affects a firm’s performance but the firm’s performance affects the decision to diversify* *Bascle, 2008 € When the data are selected non- randomly. € Estimating only a subset of the true population will lead to bias. Example € Link between test scores and classes skipped 6/13/2011 5 € Cov(z, X)≠0 € Strong instrument › High correlation € Weak instrument › Low correlation € Problems with weak instruments 6/13/2011 6 € Cov(z,μ)=0 € If Cov(z,μ)≠0, the instrument is inconsistent. Y=β0+β1X+μ X=α0+α1z Cov(z, X)≠0 Cov(z,μ)=0 X=α0+α1z+v ^ ^ 6/13/2011 7 Y=β0+α1z+(μ-α1e) Cov(z, X*)≠0 Cov(z,μ)=0 z=δX*+e Y=β0+β1X*+μ Y= λ0+λ1Z+ε Y(1- β1α1)= β0α0 +β1α2Z+β1v+μ Y=β0+β1(α0+ α1Y+α2Z+v)+μ Y=β0+β1X+μ X=α0+ α1Y+ α2Z+v 6/13/2011 8 € Corrects for non-random selection bias € Selection equation › Probit model € Outcome equation € Heckman two-step procedure will transform your sample into one that functions as randomly selected. € X is exogenous with Y if v is uncorrelated with μ € μ=σ1v+e € Y=β0+β1X+ σ1v+e € H0: σ1=0 X=α0+α1z+vY=β0+β1X+μ ^^ 6/13/2011 9 € Card (1995) estimated returns to education for men in 1976. € Used the dummy variable, nearc4, if the man grew up near a college that offered a 4 year program. € =α0+α1nearc4+…+v € log(wage)=β0+β1 +…+μ 6/13/2011 10 Variable OLS 2SLS educ 0.075 (0.003) 0.132 (0.055) exper 0.085 (0.007) 0.108 (0.024) exper2 -0.023 (0.003) -0.023 (0.003) black -0.199 (0.018) -0.147 (0.054) smsa 0.136 (0.020) 0.112 (0.032) south -0.148 (0.026) -0.145 (0.027) Observations R2 3,010 0.300 3,010 0.238 Dependent Variable: log(wage) € Levitt (1997) estimated the elasticity of crime rates with respect to hired police officers. € Does an increase in the number of police reduce the crime rate? € Endogeneity between number of police and the crime rate. € Instrument used is mayoral elections as a measurement of when police are hired. 6/13/2011 11 Variable OLS 2SLS Sworn officers per capita 0.28 (0.05) -1.39 (0.55) State unemployment rate -0.65 (0.40) -0.00 (0.36) Public welfare spending per Capita -0,03 (0.02) -0.03 (0.02) Education spending per capita 0.04 (0.07) 0.02 (0.07) Percent ages 15-24 in SMSA 1.43 (1.00) -1.47 (4.12) Percent black 0.010 (0.003) -0.034 (0.015) Percent female-headed households 0.003 (0.006) 0.040 (0.030) Variable OLS 2SLS Sworn officers per capita 0.21 (0.05) -0.38 (0.83) State unemployment rate 1.40 (0.46) 1.04 (0.55) Public welfare spending per Capita 0.01 (0.03) -0.02 (0.04) Education spending per capita 0.51 (0.08) 0.01 (0.11) Percent ages 15-24 in SMSA 1.43 (1.00) -1.47( 4.12) Percent black -0.002 (0.003) -0.029 (0.018) Percent female-headed households 0.007 (0.006) 0.025 (0.039) 6/13/2011 12 € What are the four sources of endogeneity? € When would you use the Heckman two step procedure? € Give an example of omitted variable endogeneity. € What are the two characteristics an IV must have? € Bascle, G. (2008). ‘Controlling for endogeneity with instrumental variables in strategic management research’. Strategic Organization. Vol 6(3), 285-327. € Heckman, J. (1979). ‘Sample Selection Bias as a Specification Error’. Econometrica. Vol 47(1), 153-161. € Levitt, S. (1997). ‘Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime’. The American Economic Review. Vol 87 (3), 270-290. € Wooldrige, J. (2006). Introductory Econometrics, 3rd ed. United States of America: Thompson South-Western.