Statistical evaluation of econometric air travel demand models

To use econometric air travel demand models properly and effectively, it is essential to understand the underlying assumptions which lead to the estimation procedure, and to subject these assumptions to rigorous scrutiny before any such models can be used either to forecast air traffic or to assess the impact of policy changes dictated by the airline, the aircraft manufacturer, or the federal government. This paper evaluates the impact of violation of the following assumptions in the regression model: 1) mean of the stochastic disturbance term is zero; 2) variance-covariance matrix of the disturbance vectors is diagonal with constant variance; 3) the disturbance terms are distributed normally; 4) values of explanatory variables are nonstochastic; and 5) matrix X is of full column rank. Methods of detecting the violation of these assumptions, as well as methods of eliminating the severity of these problems, are presented. The paper also contains extensions of the common statistical tests used to evaluate the appropriateness of such models. While at first sight the statistical evaluation procedures discussed here may appear overly complex, the aerospace anlayst is reminded of the multimillion-dollar investments which are sometimes made based on the results of econometric models judged solely on the high R2 values. I. Introduction S INCE econometric models have become common tools for forecasting demand for air transportation, it is important to examine the statistical procedures commonly used in the estimation of parameters in such models. To apply the models properly and effectively, it is essential not only to understand the underlying assumptions and their implications, which lead to the estimation procedure, but also to subject these assumptions to rigorous scrutiny. With careful analysis the model can be used either to forecast air traffic or to assess the impact of policy changes dictated by airline management and the Civil Aeronautics Board. The purpose of this paper is first to discuss the more important theoretical assumptions in determining the best estimators of the unknown parameters of air travel demand models, and second, to present some formal statistical tests to examine the appropriateness of such models. The emphasis is focused on the statistical evaluation of the common econometric methods and the confidence which can be placed in models which often influence large investments in either fleet acquisition or market planning. Often the decision maker is not statistically oriented, and can make the commitment of substantial corporate resources on the results of a model which may be statistically invalid, or at least inappropriate. This discussion is theoretical, since the currently operating air traffic forecasting models have not been published in sufficient detail to perform the formal statistical evaluation discussed in this paper.