Model formulation to simplify selection when specification is uncertain

Abstract

Although complicated estimators are now routinely computed, rather little empirical research in econometrics seems to be conducted using fully, and correctly, pre-specified models. When data based selection is required from a ‘small’ sample for a range of alternative potential regressors, lag patterns, functional forms, error processes and so on, computational simplicity and model comprehensibility resume positions of importance and require emphasis even at the cost of conceding other desirable attributes: compromises between alternative properties are amost inevitable and much of the ‘art’ of empirical modelling lies in choosing an appropriate balance. To facilitate selection under uncertain specification, the presentation considered ways of reformulating dynamic and disequilibrium models using two illustrations which exhibited many common difficulties, namely: 1. (1) the relationship linking starts to completions of new housing; and 2. (2) ‘min-condition’ disequilibrium supply-demand systems. In the first example, respecification of the lag reactions based on control servomechanisms and of the functional form to allow untruncated error distributional assumptions jointly produce an equation where selection is possible of both dynamics and economic influences on the lag profile. The resulting model offers a parsimonious parametrization, encompasses previous disparate studies and explains the prevalence of serious residual autocorrelation in distributed lag representations. In (2), the inherent lack of identification of the regime probabilities when assuming a bivariate error distribution entails reformulating the min-condition to allow use of univariate distributions. Once this is done, feedbacks from lagged disequilibria can be introduced in the decision equations without much increase in the computational burden. In both cases, constructive critiques were offered of many aspects of ‘conventional’ formulations and emphasis was placed on: 1. (a) formulating agents' plans in terms of conditional expectations about which independent, normal distributions for the observed data are reasonable; 2. (b) eradicating all complications which are not essential to the efficient estimation of the parameters of interest in the relevant conditional sub-models; and 3. (c) using a framework which sustains easy incorporation of additional generalisations such as prior information, endogeneity of certain regressors, common factors in lag polynomials etc. without inducing computational complexities which inhibit the application of appropriate selection techniques.