THE ROLE OF THEORY IN ECONOMETRICS

This paper discusses the way that theory is used in applied econometri cs. The traditional strategy of marrying theory and evidence relied on the fact that older theory implied explicit restrictions on the condi tional distribution of observable variables and could be evaluated in terms of the conditional predictions of the model embodying the theore tical restrictions. However, this is not true of newer theories based on dynamic stochastic optimisation of models which are not based on qu adratic objective functions and linear constraints; the so-called 'LQ form'. Because these models do not usually have closed-form solutions, they tend to be calibrated rather than estimated and cannot be readil y evaluated in terms of their conditional predictions. The application of the stochastic version of the Maximum Principle to such models res ults in Lagrange multipliers, often shadow prices corresponding to mis sing markets, which are not observed by the econometrician. Just as ag ents condition their decisions on unobserved expected prices when forw ard markets do not exist, they also condition on unobserved shadow pri ces when particular current or contingent markets do not exist. The ap proach suggested in this paper is to substitute out the Lagrange multi pliers in terms of their determinants, just as is often done with expe ctations. The approach is illustrated in some detail for two examples: consumer behaviour under liquidity constraints, and oil production.