Pseudo panel is a relatively new econometric technique to estimate dynamic models using repeated cross sectional data. 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 ownershipmodel. It is organised as follows: The first section discusses 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 with the conventional cross sectional model, the 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 panelmethod has the advantage of (1) Explicitly modelling and estimating saturation level; (2) Can be formulated to be consistent with theory of utilitymaximization. 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 a 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 the two types of model have different scales. 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 includethe 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 modelling. 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 reportsthe 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 thelevel 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. For the covering abstract see ITRD E137145.
Samenvatting