Instrumental Variables for Dummies January 2011 () IV January - PowerPoint PPT Presentation

Instrumental Variables for Dummies January 2011 () IV January 2011 1 / 4

Instrumental Variables (2SLS) Methodology Hypothesized structural model: Y i = α + β X i + ε i X i = γ + δ Y i + θ Z i + η i , where = Y i dependent variable (e.g. price) X i = key explanatory variable (e.g. quantity) Z i = vector of exogenous instrumental variables (e.g. costs) Reduced form for X i : X i = γ + δα + θ Z i + δε i + η i 1 � δβ () IV January 2011 2 / 4

If Z i is uncorrelated with ε i and η i then we can estimate the “…rst stage regression” X i = a + bZ i + u i using OLS where a = γ + δα θ 1 � δβ and b = 1 � δβ Then run “second-stage regression” Y i = α + β ˆ X i + ε i using the …tted value ˆ a + ˆ X i = ˆ bZ i Estimate of β should re‡ect impact of variations in X i that are due to exogenous variation in Z 0 i s only () IV January 2011 3 / 4

Three key requirements of "good instruments": ! R 2 in …rst stage regression must be reasonably high , , ! must clearly be an exogenous determinant of X i , ! no other theoretical channels through which Z i e¤ects Y i (i.e. Z i is not correlated with ε i in theory) Testing identi…cation restrictions , ! the last requirement can be tested for if the system is “over-identi…ed”: if there are more Z 0 s than X 0 s , ! Sargan test () IV January 2011 4 / 4