Models with Several Regimes and Changes in Exogeneity

In recent years, increasing attention has been devoted to models with a finite (usually) number of regimes. Various strategies have been discussed in the literature to situations where each regime is characterized by a different value of a common vector. See e.g. Barten and Bronsard (1970), Goldfeld and Quandt (1973), (1976),... . It appears however that no satisfactory treatment has yet been given to where the partitioning between " endogenous " and " exogenous " variables changes time. Our objective is therefore to define a class of models with several regimes which flexible enough to cover such situations. convenience, we shall illustrate our argument by reference to an economy which is"controlled " by a policy maker shifting between instruments at some, possibly unknown, of time. For tractability we shall mainly restrict our attention to a class of dynamic models although the concepts we introduce apply in a much broader framework. possibility that the switching times could be endogenous to the model, such as in models will not be investigated here: work in progress indicates however our approach can be extended in such directions. paper is organized as follows: In Section 2 we shall discuss at length the issues to faced by means of a simple example, taken from Goldfeld and Quandt (1973). In 3 we shall introduce the concepts which are needed for our analysis; linear models, LIML estimation and exogeneity. In Section 4, we shall discuss models several regimes and concentrate in particular on imposing appropriate restrictions on parameters characterizing different regimes. It will be shown that it is possible to some of the operational features of LIML procedures.