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The chapter begins with a discussion of the status of bridge principles in empirical analyses in which the data generating process does not appear. Then it contrasts the ideas of encompassing and congruence in present-day econometrics and formal econometrics, and explicates how the notions of encompassing and congruence can be used to determine the status of bridge principles in formal econometrics. The chapter concludes with a discussion of present-day and formal econometric prescriptions for the use of theory in the book’s case studies, and with a commentary on three problematic aspects of present-day econometric methodology. The results of a case study with the methods of present-day econometrics differ from the results which the same case study yields with the methods of formal econometrics. The chapter attributes the differences to the respective researchers’ different understanding of theory, and describes how a researcher’s understanding of theory affects the inference about social reality that he can draw from statistical analyses. The three methodological problems concern analysis of positively valued time series, empirical irrelevance of qualitative response models, and the search for theoretically meaningful cointegrating relations. The discussion suggests solutions to problems and good reasons for concern about a misguided search for cointegrating relations.

The chapter presents Ragnar Frisch and Trygve Haavelmo’s vision of a science of economics, explicates in simple terms the meaning of a formal theory-data confrontation, and describes and resolves an interesting riddle in applied econometrics. Frisch and Haavelmo’s idea of a unified theoretical-quantitative and empirical-quantitative approach to economic problems can be realized in two ways. In one the researcher identifies his theory variables with Haavelmo’s true variables and carries out his empirical analysis the way present-day econometricians do. In the other the researcher identifies his theory variables with variables in Frisch’s model world and carries out his empirical analysis the way formal econometrics prescribes. As exemplified in a formal data confrontation of a simultaneous-equations model of a perfectly competitive commodity market, the empirical analyses in the two scenarios may end in different descriptions of the dynamics of data variables and yield different statistical inferences about social reality. The chapter concludes with a discussion of the mentioned riddle in applied econometrics. The riddle elicits a clear view of the kind of knowledge about social reality that an applied econometrician can obtain.

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.

Chapter VII has two purposes. One is to study the methodological problems that arise in analysing positively valued time series in foreign exchange. The other is to contrast the analysis of time series in formal econometrics with the analysis of such data in present-day econometrics. The chapter presents an axiomatic data confrontation of a theory of spot and forward exchange in foreign currency markets. In the formulation of the axioms, actual and auxiliary theory and data variables interact in such a way that the problem that usually arise in the analysis of positively valued time series disappears. The data for the empirical analysis comprise observations on spot and forward exchange rates in the market for Swiss Francs and US Dollars. In the empirical analysis, the given data are analysed, first, with the prescriptions of formal econometrics and, then, with the prescriptions on which present-day econometric time-series analysis insist. The statistical results yield different descriptions of the dynamics of foreign exchange and different inferences about the economics of social reality. In doing that the two contrasting empirical analyses provide interesting ingredients for the discussion of how best to incorporate economic theory in empirical analyses.