Random Utility Model of Pseudo Panel and Application on Car Ownership Forecast
B Huang, MVA Consultancy and Birkbeck College, UK
This paper reports the recent development on the theoretical aspects of the nonlinear pseudo panel, its empirical application on car demand model, and forecast of car ownership level in Great Britain to year 2026.
Pseudo panel is a relatively new econometric technique to estimate dynamic models using repeated cross sectional data. It has been applied in car ownership analysis in various studies including Dargay and Vythoulkas (1999) and Dargay (2002), which are all linear models. The current research extends the pseudo panel techniques to nonlinear (discrete choice) models and some early empirical results have been presented at this conference (Huang, 2005).
This paper reports the recent development on the theoretical aspects of the nonlinear pseudo panel as well as some substantially improved empirical results of the car ownership model. It is organised as follows:
The first section discuss the pros and cons of nonlinear pseudo panel model and argue for its potential as an effective ?third way? in modelling and forecasting using cross sectional data. Compared to the conventional cross sectional model, nonlinear pseudo panel has the advantages of 1) Consideration of dynamic in modelling; 2) Effective tackling of aggregation bias problem. Its disadvantage are 1) Reduction in data variability; 2) Loss of information on individual decision makers. Compared to its linear counterpart, nonlinear pseudo panel method has the advantage of 1) Explicitly modelling and estimating saturation level; 2) Can be formulated to be consistent with theory of utility maximization. However, it suffers the limitation of 1) ?incidental parameter problem? for fixed effect model; 2) Needing tailored code for estimating advanced models. On Balance, nonlinear pseudo panel model is most suitable for forecasting purpose, and the case is less clear for analytical purpose.
Section 2 introduces a random utility model of pseudo panel. In a standard random utility model of cross sectional data, the utility function consists of a deterministic term and a random term. For pseudo panel model, such deterministic term can be further decomposed into four components: the first is the sample mean observable utility of alternative a for cohort c in year t, which is deterministic and observable; the second is the difference between the sample mean utility and the true mean unobservable utility of alternative a for cohort c in year t, which represents the measurement error; the third is the (time-invariant) unobserved heterogeneity, which includes alternative specific constants and cohort fixed (random) effect; the fourth component represents the unobserved utility of alternative a for individual i in year t, which is the deviation from the mean utility for the cohort. It should be noted that the fourth component is observable to researchers in the cross-sectional models and is ?lost? in the aggregation process of pseudo panel. The fourth decomposed utility component has to be combined with the random utility term in the underlying cross sectional model; consequently two types of model have different scale.
For dynamic model, if there is true state dependence, the choice from the previous period will affect the current utility and it is natural to include the lagged dependent variable in the utility function. However, the lagged dependent variable might appear significant even without true state dependence due to unobserved heterogeneity or series correlation. This has to be taken into account in empirical work.
Section 3 applies the pseudo panel RUM to car ownership modeling. The hierarchical model structure for handling multiple car ownership has been chosen. This model is then extended to take saturation into account. To be consistent with the RUM theory, a Dogit model structure is adopted; this model also ensures the saturation level can be reliably estimated and statistically tested.
Section 4 discusses the consistent estimation of the pseudo panel RUM. The fixed effect estimator is consistent only when the number of time period is sufficiently large, while the random effect estimator requires that the unobserved heterogeneity are uncorrelated with the explanatory variables. The mixed logit model allows all the parameters to be random, thus make the orthogonality assumptions of the random effect model rather irrelevant.
Section 5 reports the empirical results of car ownership model. Separate results are presented for models of one plus cars and those of two plus cars. Selected results for static fixed effect models, random effect models, dynamic fixed effect model, random parameters (mixed logit) models, and Dogit models will be reported.
Section 6 uses the preferred econometric model to forecast the level of car ownership in Great Britain to year 2026. Results will be compared to the observed data in the early forecast years and forecasts from other published studies of car ownership.
Section 7 is a brief conclusion.
Association for European Transport