内生性的含义及其处理方法

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1 If X is orthogonal to μthen 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

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2 Errors in variables

Omitted variables

Simultaneous causality

Self-selection bias

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3 Measurement errors β

1 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

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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 persify**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

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5 Cov(z, X)≠0

Strong instrument

?High correlation

Weak instrument

?Low correlation

Problems with weak instruments

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6 Cov(z,μ

)=0

If Cov(z,μ)≠0, the instrument is inconsistent. Y=β0+β1X+μ

X=α0+α1z Cov(z, X)≠0Cov(z,μ)=0X=α0+α1z+v ^^

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7Y=β0+α

1z+(μ-α1e)Cov(z, X*)≠0Cov(z,μ)=0z=δX*+e Y=β0+β1X*+μY=λ0+λ1Z+ε

Y(1-β1α1)=β0α0 +β1α2Z+β1v+μ

Y=β0+β1(α0+α1Y+α2Z+v)+μY=β0+β1X+μX=α0+α1Y+α2Z+v

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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

H 0:σ1=0

X=α0+α1z+v Y=β0+β1X+μ^

^

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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

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10Variable OLS 2SLS educ

0.075(0.003)0.132(0.055)exper 0.085(0.007)0.108(0.024)exper 2

-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 R 23,0100.3003,0100.238Dependent 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.

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11Variable 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)

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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.

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