Improved Modelling of Competition among Airports through Flexible Form and Non-Diagonal Demand Structures Explaining Flows Registered within a New Traffic Accounting Matrix

Abstract

Briefly stated, we first provide a new accounting framework that pinpoints the relevant flows to be explained by air demand and airport choice models. We then focus on the critical feature of demand modelling practice that bears particularly on airport competition and hub stability: the built-in IIA-axiom consistency of typical “diagonal” structural demand and itinerary choice procedures. We argue that this core property must be avoided because, always dubious, it is now particularly challenged in modelling the fastest growing component of passenger air demand, non-business trips, and by the clear need for reference alternatives in mode and path or airline company choice representation procedures. Because flows are interdependent, the utility of alternatives cannot be defined only by reference to own (matrix diagonal) transport conditions. On this critical point, we summarize how Standard Box-Cox endogenous form specifications contribute to a much improved representation of the role of transport conditions within prevailing IIA-consistent structures but argue that freedom from “diagonal slavery” requires more, to wit: spatial correlation processes in Generation-Distribution models and Generalized Box-Cox specifications in Mode and Path choice analysis. In both cases, IIA-consistency is avoided in realistic ways by making parsimonious use of off-diagonal terms and permitting in principle the establishment of complementary alternatives, in contrast to the currently forced substitution straightjacket imposed on them. In more detail, we first define a new four-part Traffic Accounting Matrix (TAM) to register all spatial flows of interest for air demand forecasting, effectively extending the scope of classical algebraic input-output analysis by doubling up and reinterpreting the intermediate and final transactions components of two-part Input-Output (IO) matrices. Strictly defined subsets of a TAM can then be matched to, and explained by, the usual procedures pertaining to the distinct generation, distribution, mode choice and assignment steps of traffic demand planning, or to their combinations. We then focus on the key properties of such demand models in order to evaluate their relevance to the explanation of airport or hub competition and consider, among potential remedies, the estimation of form with Box-Cox transformations, but point out that their demonstrated relevance to the measurement of the impact of transport conditions is insufficient to solve the problem at hand. In both Generation-Distribution and Split Choice mode-company-path structural steps, the predominant use of Independence from Irrelevant Alternatives (IIA) consistent cores must be rejected to account properly for competition among destinations in Generation-Distribution models and for the prevailing importance of reference alternatives in Split Choice mode-company-path models. We provide a first partial literature summary of numerous results obtained with endogenous functional forms in both of these structural steps but argue that, because the issue of non separability of utility is not directly addressed by standard Box-Cox transformations, their increased explanatory power and realism as compared to the popular fixed form a priori logarithmic (in Gravity models) and linear (in Logit models) specifications─ is more relevant to the proper measurement of the role of transport conditions (distance, level of service or price) than to the necessary representation of interdependence among alternatives, which mandates the abandonment of “diagonal slavery” in utility formulations. Of course, the proper role of transport conditions still matters decisively in both Generation-Distribution models of transport or trade and in the Mode or company-path Choice splits. In the former class, proper curvature defines the total market reach and data determined forms rectify the demonstrably incorrect use of distance in the many logarithmic pooled time-series and cross-sectional models. In the latter class, allowing for changing marginal utility profoundly modifies the relative sensitivity of longer over shorter length trips, as compared to their behavior in prevailing untested linear constant marginal utility forms of the same functions, never theoretically very credible nor empirically sustainable. But none of these benefits and remedies to current dominant practice allows for interdependence (non separability) of utility, the key future demand modelling challenge if ex ante forecasts are to be of relevance to the air demand question at hand. To point to real remedies, we summarize some recent promising attempts to deal with interdependence in manageable ways expected to yield “diagonal dominant” results: through the use of spatial autocorrelation in Box-Cox GenerationDistribution models and of Generalized Box-Cox specifications in Split models. Separable utility is thereby rejected by the data but without using too many independent off-diagonal terms pertaining to transport conditions: if the denial of any separability has been the scourge of classical demand equation system, its blind imposition has been that of Gravity and Logit demand systems. Considerate and flexible middle ways are now within reach and they matter most to model new interdependent markets, such as tourism.