Notes9 - Lecture Notes 9 Econ 410 Introduction to...

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Lecture Notes 9 Econ 410 – Introduction to Econometrics 1 Assessing Studies based on Multiple Regression We want to investigate whether a study based on the multiple regression model is reliable or unreliable. The concepts of internal and external validity provide a framework for assessing studies based on multiple regression. Internal Validity A statistical analysis is internally valid if its statistical inferences about causal effects are valid for the population from which the sample was drawn (population studied). Ex. We estimated the effect of the level of education on earnings using a sample of workers in Wisconsin. The analysis is internally valid if its statistical inference is valid for the population of workers in Wisconsin. In regression analysis, threats to internal validity can be divided in two groups. The first one includes threats to unbiasedness and consistency of the OLS estimator; the second one includes sources of inconsistency of OLS standard errors. When these threats are eliminated, the OLS estimators are unbiased and consistent estimators of the true parameters of the model, hypothesis tests have the desired significance level and confidence intervals have the desired confidence level. Reasons why the OLS estimator might be biased and inconsistent 1) Omitted variable Bias We already know that omitted variable bias arises when the omitted variable is a determinant of the dependent variable Y and is correlated with one or more of the regressors. Since the bias persists in large samples, the OLS estimator in this case is also inconsistent. Solutions If you have data available, including the omitted variable in the regression would eliminate the bias. However, adding a new variable might also increase the variance of the coefficients of interest (thus making their OLS estimators less precise). A way of solving this tradeoff is to define a base specification including the variables of interest, and then develop a list of candidate alternative specifications as explained in Lecture
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Notes9 - Lecture Notes 9 Econ 410 Introduction to...

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