Suppose you have specified the following regression model of Y: 2i Suppose also

Question

Suppose you have specified the following regression model of Y: 2i Suppose also that you believe instrumental variables, Z1 and Z2 for X2. What are the tests that you can run to check the validity of the instrumental variables, Z1 and Z2? Multiple answers can be true. X2 is endogenous in this model and you are considering two O Hypothesis test on the first stage regression of 2SLS O Hypothesis test on the regression of X2 on Z1 and Z2. O Hypothesis test on the regression of X2 on X1, X3, Z1, and Z2. Overidentification test if one of the instrument variable is known to be valid. ? Test whether residual U and ZI are correlated. O Test whether residual U and Z2 are correlated.

Explanation / Answer

1) The Instrumental variable chossen must be correlated with the endogenous variable but not with the error term. so the options 1,2, and 5,6 are valid

2) The right option is c, Z3. where the instrumental variable must be correlated with the endogenous variable, and not correlated with the error term U (so that does not suffer from measurement error and also is not correlated with any unobservable factors influencing the dependent variable)

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