Local Cuts and Separate Inference

The new concept of a local(cut is shown to lead to natural separate inference in cases where no formal statistical justification for such procedures exists using conventional concepts. Examples include the panel data model with fixed effects, the capital asset pricing model, the cointegration model and the prototypal job search model. An interpretation of local cuts in sufficiently smooth settings in terms of the familiar Edgeworth expansion is provided. In empirical analysis of observed economic phenomena, insights from theory should be incorporated appropriately in the statistical models employed. Although crucial for analysis of structural economic parameters, this approach rarely simplifies the theory of inference. Frequently, economic considerations introduce nuisance parameters, non-smooth likelihoods and the like. Occasionally, ad hoc procedures for dealing with these complications have been devised, but in general, formal statistical justification is missing. Often, inference is drawn only on some of the parameters in a model, leaving others for separate analysis or ignoring them entirely. Examples in econometrics arise in relation to exogeneity, the incidental parameter problem and limited information analysis of simulta- neous systems. Separate inference is justified if a cut exists in the model, so that the model function factorizes in a conditional and a marginal component, each of which is parametrized by a separate subparameter (see sect. 2 below). However, reduction to separate conditional and marginal models may seem natural even when this condition is violated. In this paper we consider a generalized concept, the local cut, and the associated principles of inference. We show that the local cut leads to natural separate inference. During the development, economic examples serve to illustrate the new concepts. We show that conditioning on group means in the panel data model with fixed effects is justified in the generalized framework, although it has only ad hoc justification in standard statistical theory. Thus, the model has no cut, but we show that the group means constitute a local cut. Similarly, in the zero-beta capital asset pricing model, an important model in financial economics, we show that the equal-weighted market return is a local cut. This allows separate inference on the zero-beta rate. In the prototypal job search model it is natural to condition on the minimum observed wage. We show that this is a local cut, hence justifying the procedure. Finally, we illustrate local cuts in the cointegration model and in the orthogeodesic family.