ECON 151 Lecture Notes - Lecture 13: Instrumental Variable, Uncorrelated Random Variables, Regression Dilution
11 Nov 2020
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Document Summary
Wage i = 0+ 1si+ ai+ i (6) where ai+ i = unobserved. Error term is captured, will not be uncorrelated. If ability effect is integrated in error, violated assumption so bias result. The structural model is the model of interest. A, ability, is unobserved therefore included in the error term ; A is correlated with s and explains w; A is endogeneous and therefore biases 1 (and 0) A causes the structural model to be biased or non-identified. I is an error term that respect the 0cm assumption i. e. e( |s) = 0. Here endogenous means that part of the error term and correlated with at least one explanatory variable. Relevance/first stage assumption : z is strongly correlated with s, i. e. e(s|z) = 0 and possibly as large as possible; Strong correlations to education = income, family education, health, location. Independence/exogeneity assumption : z is not correlated with a, e(z|a) = 0.
