This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Lecture Notes 6 Econ 410 Introduction to Econometrics 1 The multiple regression model Omitted Variable Bias In the linear regression model with just one regressor, we focused on the effect of the variable i X on i Y and we included all the other determinants that have an effect on i Y in the error term. Ex.: i Y is the random variable earnings and i X is the random variable years of schooling. Some omitted variables are: the person IQ, his/her family and regional background, the schools he/she attended, age, working experience, etc. Omitted variables can make the OLS estimator biased (omitted variable bias). In particular, the bias happens when the omitted variable is a determinant of the dependent variable i Y and it is correlated with the included regressor i X . Omitted variable bias means that the first least square assumption doesnt hold, that is: ( )  i i X u E . Indeed, if the omitted variable influences i Y , then it must be included in the error term, and if the omitted variable is correlated with i X , then the error term will be correlated with i X . So: If you suspect that a variable you did not include in your regression has an influence on i Y , then check the data. In particular, check the correlation between your regressor and this omitted variable. If you find a nonzero correlation, then the OLS estimator is biased because the mean of the sampling distribution of the OLS estimator might not equal the true effect on i Y of a unit change in i X . Ex.: Consider the omitted variable IQ. It is plausible to think that this omitted variable is correlated with the level of education of a person, and it is also plausible to think that this variable can affect his/her earnings. So, omitting the IQ might introduce omitted variable bias. Important: Why there is no omitted variable bias if the omitted variable is uncorrelated with the included regressor i X ? Why there is no omitted variable bias if the omitted variable does not affect the dependent variable i Y ? Because in both cases the OLS estimator would not incorrectly incorporate the influence of the omitted variable in predicting the effect on i Y of a unit change in i X . Lecture Notes 6 Econ 410 Introduction to Econometrics 2 Measuring the omitted variable bias If the omitted variable bias is present, than it is possible to show that: X u Xu p + 1 1 where: ) , ( i i Xu u X corr = This formula implies that, in large samples, 1 is close to X u Xu + 1 with high probability. It follows that, if the omitted variable bias is present: 1 is not a consistent estimator of 1 . 1 is a biased estimator of 1 ; X u Xu is the bias that persists even in large samples....
View Full
Document
 Fall '08
 Staff
 Econometrics

Click to edit the document details