Richard Fowles and Peter Loeb studied the interactive effect of drinking and altitude on traffic deaths.8 The authors hypothesized that drunk driving fatalities are more likely at high altitude than at low altitude because higher elevations diminish the oxygen intake of the brain, increasing the impact of a given amount of alcohol. To test this hypothesis, they used an interaction variable between altitude and beer consumption. They estimated the following cross-sectional model (by state for the continental United States) of the motor vehicle fatality rate (Note: t-scores in parentheses):

Where:

F_i = traffic fatalities per motor vehicle mile driven in the ith state

B_i = per capita consumption of beer (malt beverages) in state i

S_i = average highway driving speed in state i

D_i = a dummy variable equal to 1 if the ith state had a vehicle safety inspection program, 0 otherwise

A_i = the average altitude of metropolitan areas in state i (in thousands)

a. Carefully state and test appropriate hypotheses about the coefficients of B, S, and D at the 5-percent level. Do these results give any indication of econometric problems in the equation? Explain.

b. Think through the interaction variable. What is it measuring? Carefully state the meaning of the coefficient of B*A.

c. Create and test appropriate hypotheses about the coefficient of the interaction variable at the 5-percent level.

d. Note that Ai is included in the equation in the interaction variable but not as an independent variable on its own. If an equation includes an interaction variable, should both components of the interaction be independent variables in the equation as a matter of course? Why or why not?

e. When the authors included Ai in their model, the results were as in Equation 7.23 (with t-scores once again in parenthesis). Which equation do you prefer? Explain.