IV simulation

We simulate the peer effect model with reflection problem and use OLS and IV method to estimate the peer effect coefficient.

Case 1: No correlation in random errors

True peer effect parameter value: 0.3

• OLS regression

summary(peer_effect_ols)$coefficients

                Estimate Std. Error    t value      Pr(>|t|)
(Intercept) -0.005663086 0.01223560 -0.4628367  6.434969e-01
X_bar        0.535175042 0.02070905 25.8425670 2.916938e-140

• IV regression

summary(peer_effect_iv)$coefficients

                Estimate Std. Error    t value   Pr(>|t|)
(Intercept) -0.008371936 0.01255374 -0.6668877 0.50486755
X_bar        0.312833226 0.18890976  1.6559929 0.09777151

• Correlation Structure

cor(X_bar,epsilon)

[1] 0.1394578

cor(X_bar,Z_bar)

[1] 0.1105915

cor(Z_bar,epsilon)

[1] 0.0008416066

Case 2: Positive correlation in random errors

True peer effect parameter value: 0.3

• OLS regression

summary(peer_effect_ols_positivecorrelation_error)$coefficients

                Estimate  Std. Error   t value      Pr(>|t|)
(Intercept) -0.002809042 0.004495511 -0.624855  5.320851e-01
X_bar        0.682029738 0.017122845 39.831567 3.998173e-315

• IV regression

summary(peer_effect_iv_positivecorrelation_error)$coefficients

                Estimate Std. Error   t value   Pr(>|t|)
(Intercept) -0.006206147 0.00486003 -1.276977 0.20164960
X_bar        0.297493685 0.16350625  1.819464 0.06888026

• Correlation Structure

cor(X_bar,epsilon)

[1] 0.2485498

cor(X_bar,Z_bar)

[1] 0.1081596

cor(Z_bar,epsilon)

[1] -0.0001763668

Case 3: Negative correlation in random errors

True peer effect parameter value: 0.1

• OLS regression

summary(peer_effect_ols_negativecorrelation_error)$coefficients

                 Estimate  Std. Error     t value     Pr(>|t|)
(Intercept) -0.0002696927 0.003359994 -0.08026582 9.360269e-01
X_bar        0.2358328758 0.018053772 13.06280340 8.733062e-39

• IV regression

summary(peer_effect_iv_negativecorrelation_error)$coefficients

                 Estimate  Std. Error     t value   Pr(>|t|)
(Intercept) -0.0002444271 0.003362187 -0.07269883 0.94204674
X_bar        0.3074223709 0.154550567  1.98913778 0.04670408

• Correlation Structure

cor(X_bar,epsilon)

[1] -0.02897125

cor(X_bar,Z_bar)

[1] 0.1168757

cor(Z_bar,epsilon)

[1] 0.0003916712