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# slides_lecture15c - ECON 103 Lecture 15C Instrumental...

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ECON 103, Lecture 15C: Instrumental Variables III Maria Casanova June 2nd (version 1) Maria Casanova Lecture 15C

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Requirements for this lecture: Chapter 12 of Stock and Watson Maria Casanova Lecture 15C
0. The general IV regression model (reminder) The equation of interest is: Y i = β 0 + β 1 X 1 i + ... + β k X ki + β k +1 W 1 i + ... + β k + r W ri + ε i where: Y i is the dependent variable X 1 i , ..., X ki are the endogenous regressors (potentially correlated with ε i ) W 1 i , ..., W ri are the included exogenous regressors (uncorrelated with ε i ) β 0 , ..., β k + r are the unknown regression coefficients Z 1 i , ..., Z mi are the instrumental variables (or excluded exogenous regressors) Maria Casanova Lecture 15C

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0. The general IV regression model (reminder) The population first-stage regression relates X to the exogenous variables, i.e. the Z ’s and the W ’s: X i = π 0 + π 1 Z 1 i + ... + π m Z mi + π m +1 W 1 i + ... + π m + r W ri + v i where: π 0 , ..., π m + r are the unknown regression coefficients When there are multiple endogenous regressors X 1 i , ..., X ki , each endogenous regressor requires its own first-stage regression. Each of these first-stage regressions includes as independent variables all the instruments ( Z ’s) and all the included exogenous variables ( W ’s) Maria Casanova Lecture 15C
1. The IV regression assumptions The IV regression assumptions modify the least squares assumptions that we covered in lecture 6 and lecture 7. Under the IV regression assumptions, the TSLS estimator ... 1 ... is consistent 2 ... is approximately normally distributed in large samples. Maria Casanova Lecture 15C

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1. The IV regression assumptions Ass1: The conditional distribution of ε i given W i has zero mean. E ( ε i | W i ) = 0 Notice that the first least squares assumption required that all regressors had a conditional mean of 0; while the first IV assumption only requires that the included exogenous variables have mean zero. Maria Casanova Lecture 15C
1. The IV regression assumptions Ass2: The ( X i , W i , Z i , Y i ) variables are independently and identically distributed. Ass3: Large outliers are unlikely. Ass4: There is no perfect collinearity between two included exogenous regressors (e.g. W 1 and W 2 ). Assumptions 2 and 3 are the same as the second and third least squares assumptions. Assumption 4 doesn’t require that there isn’t perfect collinearity among two of the endogenous regressors ( X ), but this will be implicit in assumption 5 (see next slide).

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