One of the prominent features of econometric analysis is the incorporation of economic theory into the analysis of numerical and institutional data. Economists, from León Walras onwards, perceive the economy as a coherent system. The interdependence of sectors of an economy is represented by a set of functional relations, each representing an aspect of the economy by a group of individuals, firms, or authorities. The variables entering into these relations consist of a set of endogenous (or joint dependent) variables, whose formations are conditional on a set of exogenous variables that economic theory regards as given. Two approaches have been proposed to model a system of economic behaviors – the structural equation approach and the reduced form approach. The structural approach constructs the system of behavioral equations from a priori assumed “theory,” based on behavioral hypotheses and institutional and technological knowledge. However, different theoretical models may generate the same observed phenomena. To ensure the one-to-one relationship between the specified model and the observed phenomena, a priori restrictions need to be imposed to exclude other “observationally equivalent” models (e.g., Dufour and Hsiao 2008, Hsiao 1983). The resulting statistical inference is conditioning on the hypothesized theoretical model. The statistical inference could be grossly misleading if the hypothesized model is not compatible with the data-generating process of the observed sample. Sims (1980) has criticized that many models are identified because of the “incredible” prior restrictions. Liu (1960), Sims (1980), etc. have therefore favored the reduced form approach.
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