Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 24

The following equation represents the effects of tax revenue mix on subsequent employment growth for the population of counties in the United States:

growth = ?0 + ?1shareP + ?2shareI + ?3shareS + other factors,

where growth is the percentage change in employment from 1980 to 1990, shareP is the share of property taxes in total tax revenue, shareI is the share of income tax revenues, and shareS is the share of sales tax revenues. All of these variables are measured in 1980. The omitted share, shareF, includes fees and miscellaneous taxes. By definition, the four shares add up to one. Other factors would include expenditures on education, infrastructure, and so on (all measured in 1980).

(i) Why must we omit one of the tax share variables from the equation?

(ii) Give a careful interpretation of ?1.

Step 1 of 2

(i)

By definition, the shares add up to one. If one of the shares is not omitted, then the equation would suffer from perfect multicollinearity. The parameters would not have a ceteris paribus interpretation, as it is impossible to change one share while holding all of the other shares fixed.