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"multicollinearity" problem

Suppose you want to estimate a model of women's earnings at age 50. You have data for a sample of employed women, provided by the alumni associations of Mills College and Smith College, on:
? A woman's salary at age 50
? Her age
? Year of graduation
? Her high school GPA
? Her college GPA
? Her college major
? Her job tenure (how many years she has been with employer)
? The fraction of her household income that she earns
The question below violate assumptions of the classical model

1.Say that your regression results include a large, positive coefficient on ECON MAJOR, and you tell all your fellow students about it. Why might this coefficient be an overestimate of the average gain in future salary that your fellow students should expect just by switching their major to economics?

2. If you notice that virtually all the Econ majors in your sample are from Mills College, what problem will you have with the following regression model?

3.Suppose that you run two versions of your model. In the first, SALARY is expressed in thousands of dollars. In the other, it is expressed in dollars. Will this affect the size of your coefficients? The size of the standard errors? The adjusted R2? Explain


Solution Preview

1. Apparently, this question has more to do with economic theory rather than econometrics. The reason why this coefficient might be an overestimate of the future salary if you tell all your fellows about it is that the supply of people with a major in Economics will increase, thereby lowering the equilibrium wage that firms will pay to higher them. In other words: the result of the regression tells you that, currently, people with a major in Economics are earning a high salary. Now, if you tell everybody about this finding, many people will start studying Economics. Therefore, in the future there will be more people with Economics studies, and if demand for them does not increase, their price (ie, the salary) will tend to fall. We conclude that the fact that people with a major in Economics are earning high salaries today (which what the regression tells us) doesn't necessarily imply ...

Solution Summary

Investigate a "multicollinearity" problem.