The following equation represents the effects of tax revenue mix on subsequent e

Question

The following equation represents the effects of tax revenue mix on subsequent employ-

ment growth for the population of counties in the United States:

growth = B0 + B1 * shareP + B2 shareI + B3 shareS + other factors,

where growth is the percentage change in employment from 1980 to 1990, share P is the

share of property taxes in total tax revenue, share I is the share of income tax revenues, and

share S is the share of sales tax revenues. All of these variables are measured in 1980. The

omitted share, share F , 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 B1 .

Explanation / Answer

i) We should omit one of the tax variable from equation as all of these variables add upto 1. So one variable will be caught in intercept term Bo .Hence there is no need to introduce another variable Share F. As share F will be equal to Bo.If we introduce another variable Share F in model ,then there will be perfect correlation between variables as already share F is caught in intercept leading to high multi collinearity and there by making difficulty for estimating voefficients in the model. This is like dummy variable model where if we require n dummy variables, we add only n-1 dummmy variables as one dummy variable will be equal to intercept.

ii) Interpretation of B1 is For 1% change in ShareP ,i.e propert tax share, how much % growth will be there in employment growth of population

As B1 = dgrowth/dshareP

so it tells us about how much growth is sensitive to share of property tax.

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