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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.

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.