3. A researcher has a panel data on n -1000 workers over T-2 years (1995 and 200

Question

3. A researcher has a panel data on n -1000 workers over T-2 years (1995 and 2005) that contains the workers' wages, gender, education, and experience. The researcher is interested in the following regression logwage),- + .male. + .educ., + 3 experit + 4IQ + ui 1) Suppose IQ is correlated with education and experience. Since there is no IQ information in the data, the researcher has to omit it from the regression Which coefficient estimates will be biased using OLS estimation directly? 2) What regression would you estimate in order to avoid the problem stated in question 1)?

Explanation / Answer

1) If IQ is related to education and experience but unrelated to wage, then this is multicollinearity at its worst so we want to exclude IQ.

1, 2, 3, will normally be biased.

The only exception to this is when male, education and experience are uncorrelated.

2)

If IQ is related to education and experience but unrelated to wage, then this is multicollinearity at its   worst so we want to exclude IQ. Adding IQ to the regression won’t reduce bias and won’t reduce the sum of squared residuals, but it will reduce the residual variation in education and experience; that is, the variance inflation factor will scale the denominator towards zero which blows up the variance of the regression coefficient on x. Note: The variance inflation factor (VIF) is:

VIF = 1/ (1-Rj^2)

Use Partial Least Squares Regression (PLS) or Principal Components Analysis, regression methods that cut the number of predictors to a smaller set of uncorrelated components.

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