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Lecture Notes 8 Econ 410 – Introduction to Econometrics 1 Model Specification Linear models: which variables should we include? In the linear regression model, an important question is: which variables should we include in the regression? The answer to this question we should take into consideration: economic theory and the knowledge of the problem under analysis; the presence of omitted variable bias. Omitted variable bias In the multiple regression model, the conditions for omitted variable bias to arise are the same as in the model with one regressor. These conditions are: the omitted variable influences the dependent variable i Y the omitted variable is correlated with at least one of the regressors. When both conditions are present, the error term is correlated with at least one of the regressors and the conditional mean assumption does not hold: ( ) 1 | ,..., 0 i i ki E u X X . If this is the case, the OLS estimator is biased and inconsistent. In order to eliminate omitted variable bias, we should include all possibly omitted variables into the regression. In practice, however, we often don’t have data available and including a large number of regressors in the model is not always the best solution. Therefore, deciding whether to include a particular variable becomes a matter of judgment. Usually the best way to proceed is the following: 1) Using economic theory, information of how the data was collected and your judgment, decide a base set of regressors. This will be your base specification . 2) Using the data that you have available, decide alternative sets of regressors. These will be your alternative specifications . If the value of the coefficient (or coefficients) you are interested in is similar in the baseline and in the alternative specifications, then the estimates from the baseline specification are likely to be reliable. On the other hand, if the estimates of the coefficient of interest change substantially across specifications, then this might indicate that the original specification had omitted variable bias. Important : We know that a value of 2 R or 2 R close to 1 implies that the regressors are good in predicting i Y in the sample. However, deciding which variables to include in the regression line based exclusively on 2 R and 2 R might be deceiving for the following reasons:

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Lecture Notes 8 Econ 410 – Introduction to Econometrics 2 1) An increase in 2 R or 2 R does not necessarily mean that the added regressor is statistically significant. 2) A high 2 R or 2 R does not mean that the regressor are a true cause of the dependent variable. 3) A high 2 R or 2 R does not mean that there is no omitted variable bias. 4) A high 2 R or 2 R does not mean that the set of regressor is the most appropriate; as it doesn’t tell it is not appropriate.
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