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Econometric modelling of economic time series requires discovering sustainable and interpretable relationships between observed economic variables. Critical and constructive aspects are distinguished, and the roles of theories, instruments, and evidence discussed. A simple statistical mechanism, which could generate data with many of the salient features of observed time series, is analysed. An inconsistency between that and models fitted to the observed data, highlights the ease of critical evaluation, as against the difficulty of constructive progress. The concept of an empirical model is introduced.

Addresses the issue of testing, and reveals some intrinsic problems pertaining to hypothesis testing beneath the achievements of formalizing econometrics. Theory verification through applied studies forms one of the main motives for formalizing methods of model estimation and identification, and the statistical theory of hypothesis testing was accepted without much dispute quite early as the technical vehicle to fulfil this desire. However, during the adoption of the theory into econometrics in the 1940s and 1950s, the achievable domain of verification turned out to be considerably reduced, as testing in econometrics proper gradually dwindled into part of the modelling procedure and pertained to model evaluation using statistical testing tools; in the applied field, empirical modellers took on the task of discriminating between and verifying economic theories against the model results, and carried this out in an ad hoc and often non‐sequitur manner. Describes how the desire to test diverged into model evaluation in econometric theory on the one hand, and economic theory verification in practice on the other, as econometric testing theory took shape. The story begins with the early period prior to the formative movement in the first section of the chapter; the following section looks at the period in which the theme of hypothesis testing was introduced, and the first test emerged in econometrics; the last two sections report, respectively, on how model testing in applied econometrics and test design in theoretical econometrics developed and moved apart.

Records the fundamental event of the probability revolution in econometrics. Focuses upon how probability theory was brought into econometrics in relation to the main econometric modelling issues, such as estimation, identification, and testing, and shows that this laid the basis for the formalization of those issues, which is reported in later chapters. The first section sketches the eve of the probability revolution. An introduction to probability methods follows in the second section, and the third section is dedicated to the ‘Haavelmo revolution’: the thorough adoption of probability theory in econometrics. The following section turns to alternative approaches to the adoption of probability theory, and the final section discusses the after‐effect and especially the incompleteness of the probability revolution.

Looks at problems associated with econometric model construction for the period immediately after the formative phase, and tries to link up the previous chapters and to show what has been left unsolved in the formation of econometrics. The structural modelling procedure explained only how to estimate and identify a priori given structural models, while many of the empirical studies involved searching for the appropriate structural models from the given data. This mismatch of the two sides gave rise to many problems and disputes, mostly in connection with the roles that modellers attributed to individual tools of testing, identification, and estimation in the integrated process of empirical model construction, as the procedure and the associated techniques spread and formed the core of orthodox econometrics. Revisits the issue of model construction with particular respect to the roles of testing, identification, and estimation, depicting how controversies arose as econometricians were swung back to more data‐based positions, away from the emphasis on a priori considerations; back to statistical results, away from reliance on economic theory; and back to dynamics, away from concerns over contemporaneous interdependency. The first section looks at modelling issues associated with hypothesis testing; the second examines problems about model formulation with respect to identification; the third turns to the estimation aspect of modelling; and the fourth leads the discourse to the focal issue of the probability approach underlying established econometrics by illustrating that most of the problems could be viewed as due to the incompleteness of the probability approach (as suggested in Chapter 1).

This chapter recounts the evolution of econometric models up to the 1940s, discussing the common criteria and principles used for model choice, and the generalization of model construction as econometrics focused on the structural modelling procedure. The first section reviews the pre‐model period, and the second looks at the emergence of models and the structural method of model construction. The initial generalization (formalization) efforts of the model‐building strategy and criteria are dealt with in the third section. Concludes with the establishment of the structural modelling procedure (the maturity of simultaneous‐equations model formulation).

Narrates the process of how estimation was formalized. Estimation can be seen as the genesis of econometrics, since finding estimates for coefficients of economically meaningful relationships has always been the central motive and fulfilment of applied modelling activities. The process therefore became separated out as one of the basic steps along with model construction, identification, and testing. Subsequent research activities in estimation were confined to technical development of new optimal estimators for increasingly complicated model forms. The first section of the chapter describes the early developments in estimation methods centring around the least squares (LS) principle; how this led to the maximum‐likelihood (ML) method in a simultaneous‐equations system is the content of the second section; the third section turns to look at special problems in the context of time‐series analysis; other developments concerning errors‐in‐variables models are summed up in the fourth section; and the final completion of basic estimation theory in orthodox econometrics takes up the final section.

Narrates the process of how identification was formalized in econometrics. The issue of identification stemmed from the quest to know the attainability of economically meaningful relationships from statistical analysis of economic data in early estimation attempts. It arose out of the ‘correspondence’ problems ‘between economic activity, the data that activity generates, the theoretical economic model and the estimated relationship’ (Morgan, 1990). When identification theory was eventually formalized, its purpose became focused on the conditions under which a certain set of values of structural parameters could be uniquely determined from the data among all the permissible sets embodied in a mathematically complete theoretical model, usually composed of a simultaneous‐equations system. These conditions are most commonly known as the order and rank conditions in the context of linear, simultaneous‐equations models in present‐day econometrics textbooks. The emergence of identification theory played a key role in the formal establishment of the structural approach of orthodox econometrics through its links to model testing and model specification. Traces the formalization of identification theory around two interwoven themes: how the identification problem was perceived and described in connection with the other issues in econometric modelling; and how the problem was formalized and tackled with mathematical and statistical means. The first section outlines the early appearance of the identification problem and some ad hoc solutions for particular cases and model forms before the mid‐1930s; the second centres upon the initial systematic work on the issue around 1940; the third is devoted to the contribution of the Cowles group; and the completion of the theoretical framework and its overlaps with other modelling issues form the subject of the last section.

Mainstream econometric research in the 1960s and the 1970s comprised primarily technical refinements and extensions of the structural modelling procedure. The author, therefore marks an end‐point around 1960 in the historical study of the formation of econometrics, and asks in this concluding chapter of the book what should and can be learnt from this period of history with respect to present and future econometric research. She has seen during the historical investigation presented that the key points of historic significance are the junctures at which economic thinking and mathematical statistics merged to match economics with data information. In the light of this, she tries to draw some more concrete lessons from these junctures, hoping to provide some useful points, particularly with respect to issues pertinent to present econometric developments. The prime impression of the history is that most important econometric advances have resulted from ingenious interfusion of statistical ideas with economic thinking, in regard to applied problems of interest, with the single most significant event of this sort being, perhaps, the acceptance of probability theory.