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Saturday, November 28, 2015

Sargan Test and Hausman Test

 Sargan Test
 Hausman Test
 H0: Valid Instrument
 H0: X1 exogeneity 
2SLS 
y ~ X 
 e2SLS = y - Xb2SLS
 e = y-Xb
e2SLS ~ Z 
X1 ~ Z 
 m instruments in Z
 v = X- Zb2SLS1
 k explanatory variables in X
e ~ X + v 
nR2 – χ2 (m-k)
nR2 – χ2 (k1) 

Note:


X = (X1, X2)

Z = (Z*, X2)

X1: potentially endogenous variables

X2: exogenous variables
Z:   Instrumental variables

2SLS: Two Stage Least Square Method


Stage 1:  X1 = Z*ϒ1 + X2ϒ2η

Stage 2:  y = fitted_X1β + X2β + ε