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Chapter III explains and illustrates what it means for an economic theory to be empirically relevant. A theory’s empirical relevance depends on the empirical context in which it is tested and on the explication of empirical relevance. In present-day econometrics the empirical context of a test is determined by the characteristics of the data generating process. Also, the theory is empirically relevant if and only if the test gives the researcher no reason to reject the theory. In formal econometrics the empirical context of a test is determined by a probability distribution of the data - the MPD - that is induced by the probability distribution of the theory variables and the bridge principles. Also, the theory is empirically relevant if and only if there is a model of its axioms and a model of the bridge principles that determine a model of the MPD that belongs to a 95% confidence band around a meaningful statistical estimate of the MPD. Examples from experimental economics, consumer choice, simultaneous equations, and choice among safe and risky assets illustrate the contrasting characteristics of the notion of empirical relevance in present-day and formal econometrics.

Chapter I begins by describing the salient parts of a formal science of economics that the author has put together in this book and in earlier works (B.P. Stigum 1990 and 2003). The parts comprise a unitary methodological basis for a science, an explication of the meaning of facts and fiction in econometrics, and a confrontation of the methods of present-day applied econometrics with the methods that a formal science advocates. Next the chapter discusses interesting ways in which the axiomatic method and the model-theoretic method of developing theories are used in mathematical economics and statistics, and describes the underlying ideas of a formal theory-data confrontation. Thereafter follows a discussion of three controversial aspects of formal econometrics: (1) the essence of an economic theory; (2) the double role of theory in applied econometrics and the need for bridge principles; and (3) why theory is required both for the design of an empirical analysis and for the interpretation of its results. The chapter ends with a brief description of the contents of the remaining nine chapters.

Chapter IV discusseseconometric analyses of qualitative response models. A qualitative response model is an econometric modelin which the dependent variable is either discrete or half continuous and half discrete. Each proto-type of such models appears in two forms – a standard model and a latent-variable model. Both forms suffer from a serious defect: they fail to provide 1a researcher with the means he needs to ascertain the empirical relevance of his parameter estimates. That is a serious defect since the relations between dependent and explanatory variables that an empirically irrelevant estimate of a qualitative response model describes are meaningless. In a case study of 1980 US females’ participation in the labor force the chapter uses a Probit version of the two models to contrast present-day econometric analysis of the standard model with a formal econometric analysis of the latent-variable model. The empirical analysis reveals that the Probit versions of the two qualitative response models are not empirically relevant in the given empirical context. The empirical analysis also reveals that a present-day analysis of the standard model may deem it empirically relevant while a formal econometric analysis of the latent-variable model deems the latter empirically irrelevant and vice versa.