Introduction

Throughout this study we have stressed the idea that the statistician, whether he (or she) is a dominant player or one insignificant player among many, is part of the system that he is studying; that his is a view from within. In this, the last chapter, we shall review some of the implications of this principle as we have established them in previous chapters and take the opportunity to add a little here and there in the interests of rounding off. Section 8.2 is concerned with the statistical problems arising in the identification of equilibrium structures. The existence of phases of disequilibrium, perhaps during learning or temporary breakdowns of cooperative behavior, will result in argument instability, which implies that the specified disturbances (in, say, a regression context) will not exhibit invariant or stable behavior. The most that one can then hope for is the applicability of conclusions based upon large-sample theory. In such circumstances, the statistical profession's passion for small-sample (or “exact”) results may be misplaced. Section 8.3 looks at the problem of structure, reviewing the conclusions that we have arrived at concerning the existence of a stable invariant structure and the pitfalls of a naive positivist methodology in hoping to identify such a structure if it does exist. Section 8.4 turns to the problem of observer-dependent systems, both in the structural aspect (as in rational-expectations models with heterogeneous information) and in the dominant-player mode, the characteristic modus operandi of the professional statistician.