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lecture15_new_version - ECON 103 Lecture 15A Instrumental...

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ECON 103, Lecture 15A: Instrumental Variables I Maria Casanova May 26th (version 0) Maria Casanova Lecture 15A
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Requirements for this lecture: Chapter 12 of Stock and Watson Maria Casanova Lecture 15A
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0. Introduction In lecture 12 we covered 5 threats to internal validity of linear regression model. The 5 threats to internal validity arose because the error term was correlated with the regressor, which caused OLS estimator of unknown population coefficients to be biased. 2 of those threats to validity are: Omitted variable bias Simultaneous causality bias Instrumental variables (IV) regression can be used to obtain a consistent estimator of the unknown coefficients in the presence of omitted variable bias or simultaneous causality bias. Maria Casanova Lecture 15A
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0. Introduction How does IV work? - Intuition Consider the following model: Y = β 0 + β 1 X + ε Think of the variation in X as having two sources: One part that is correlated with the error term One part that is not correlated with it IV uses one or more additional variables Z called instrumental variables or instruments to isolate the variation in X that is not correlated with ε . In this way the source of bias is avoided so that consistent estimates of β 1 can be obtained. Maria Casanova Lecture 15A
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0. Introduction Example 1: omitted variable bias Consider the following model for the average test score in class j : Av test score j = β 0 + β 1 Size j + ε Income would be an omitted variable in this model if: Income had an effect of average test scores AND Income was correlated with class size. If income increases average test scores and is negatively correlated with class size, the the OLS estimate of β 1 would be biased downwards. Maria Casanova Lecture 15A
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0. Introduction Example 1: omitted variable bias (contd.) Now imagine that we can isolate two different sources of variation in class sizes: On the one hand, there is some variation in class sizes that is due to income (richer neighborhoods can afford more teachers, i.e. smaller classes). But class size can also vary for other reasons. For example, imagine that in year 2000 county A and county B have two state schools each, one in a poor and one in a rich neighborhood: Table: Average number of students per class in 2000 County A County B Rich neighborhood 17 17 Poor neighborhood 25 25 Maria Casanova Lecture 15A
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0. Introduction Example 1: omitted variable bias (contd.) While the two counties have the same budget, in 2000 County A makes some lucky investment decisions that produce an unexpected windfall in 2001. This allows county A to hire extra teachers in 2001.
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