Chapter 8. Stochastic regressors and measurement errors

1. Conditional expectation:
1. definition in case of two discrete random variables
2. the Law of Iterated Expectations, generalized homogeneity, conditioning for two independent variables
2. Assumptions for models with stochastic regressors
3. Finite-sample properties:
1. Unbiasedness of the OLS estimator under independence of regressors and errors
2. Variance of the OLS estimator under independence of regressors and errors
4. Asymptotic properties (consistency, asymptotic normality)
5. The consequences of measurement errors
1. How are measurement errors (in dependent and independent variables) modeled? Derive the asymptotic formula for the bias in case of an error in the dependent variable.
2. What are the consequences?
6. What are the predictions for the bias of the slope estimate in the permanent income hypothesis (Friedman’s critique)? And for that of the intercept? What are the implications for the (expenditures) multiplier?
7. Describe the IV estimation. What are the requirements to instruments?
8. Durbin-Wu-Hausman specification test

Suppose we have two different estimators (for example, OLS and IV) for a given parameter. Suppose that there exists a set of conditions under which both estimators are consistent (when the regressors are not correlated with the error), with OLS being efficient and IV being less efficient. Suppose as well there is another set of conditions under which IV is consistent but OLS is not (when the true regressors are correlated with the error and the instruments are not). Then the Hausman test is a test of the null hypothesis that the event occurs, against the alternative that occurs.

1. Exercises 8.1, 8.2, 8.3, 8.4, 8.7, 8.10, 8.11

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