Introduction

‘The march of science is towards unity and simplicity’, Poincaré ([1903] 1952, p. 173) wrote. In econometrics, this march threatens to become lost in a maze of specification uncertainty. There are many different ways to deal with specification uncertainty. Data-mining invalidates traditional approaches to probabilistic inference, like Fisher's and Neyman-Pearson's methodology. A theory of simplicity is helpful to get around this problem.

Fisher (1922, p. 311) defined the object of statistics as ‘the reduction of data’. The statistical representation of the data should contain the ‘relevant information’ contained in the original data. The decision, about where to draw the line when relevant information is lost is not trivial: Fisher's own methodology is based on significance tests with conventional size (usually, 0.05). At least, Fisher had relatively sound a priori guidelines for the specification of the statistical model. This luxury is lacking in econometrics. Fisher could rely on randomization, to justify his ‘hypothetical infinite population’ of which the actual data might be regarded as constituting the random sample. Chapter 6 shows that economic metaphors referring to this hypothetical infinite population are unwarranted.

Another effort to justify Fisher's reduction can be found in structural econometrics, where the model is based on a straitjacket imposed by economic theory. This provides the a priori specification of the econometric model.