120 ADVERTISING COSTS IN AIRLINE INDUSTRY

described by the auxiliary regression Equation 4. Since all threevariables have grown over time, it is likely that both c1 and c3 will bepositive. To the extent that the estimated model. Equation 4, omits apertinent variable such as the estimated parameters do not giveunbiased estimates of the effects of changes in the explanatory vari-ables. In the example I have cited b1 will be an over-estimate of thecorresponding parameter, B1, in the correctly specified model (Equation3). Similarly, b3 will be larger than B3. Indeed, his parameter estimateswould be unbiased if and only if one of the following two conditionsprevailed: (1) any pertinent excluded variables are statistically in-dependent of both advertising expenditures and lagged revenues, or (2)excluded variables have no effect on current revenues. The possibilitythat either condition truly prevails contradicts intuition about themarket for air transportation. Kraft's defense for omitting these"other variables" is that they produce too formidable a problem ofcollinearity. If collinearity is present the exclusion of the collinearvariables will lead to false conclusions.

One method for handling the problem of collinearity has been sug-gested by Richard Stone. First differences or other statistical trickshave also been used. Until Kraft gives explicit consideration to othervariables affecting an airline's revenues the empirical work will leavemuch to be desired.

Finally, the theoretical justification for the model strongly supportscross-sectional analysis. If relative advertising expenditures do notvary across firms then an empirical analysis cannot hope to succeed.