Abstract
It is common econometric practice to propose a system of equations, termed the “structure,” estimate each endogenous variable in the structure via a linear regression with all of the exogenous variables as arguments, and then employ one of variety of regression techniques to recapture the coefficients in the (Jacobian) arrays of the structure. A recent literature, e.g., [1], has shown that a qualitative analysis of a model’s structural and estimated reduced form arrays can provide a robust procedure for assessing if a model’s hypothesized structure has been falsified. This paper shows that the even weaker statement of the model’s structure provided by zero restrictions on the structural arrays can be falsified, independent of the proposed nonzero entries. When this takes place, multi-stage least squares, or any procedure for estimating the structural arrays with the zero restrictions imposed, will present estimates that could not possibly have generated the data upon which the estimated reduced form is based. The examples given in the paper are based upon a Monte Carlo sampling procedure.
Highlights
As early as [2], if not before, it was pointed out that economic theory often only specified the directions of influence among the endogenous and exogenous variables of an economic model, as represented by a proposed sign pattern for a model’s structural arrays
The structure hypothesized by the theory could only be falsified if the proposed structure placed limits on the sign pattern of the corresponding reduced form that could be estimated directly from the data, usually by a linear regression
[1], [4], and [5] showed that even if particular signs in the reduced form were not required by an hypothesized structure, limits on the estimated reduced form were always implied and any model so specified could be potentially falsified by the sign pattern of the estimated reduced form
Summary
As early as [2], if not before, it was pointed out that economic theory often only specified the directions of influence among the endogenous and exogenous variables of an economic model, as represented by a proposed sign pattern for a model’s structural arrays. The structure hypothesized by the theory could only be falsified if the proposed structure placed limits on the sign pattern of the corresponding reduced form that could be estimated directly from the data, usually by a linear regression. This paper shows that the zero restrictions on the hypothesized structure can be falsified independent of the characteristics of the nonzero entries When this happens, the estimated structure with the zero restrictions imposed could not possibly have generated the data upon which the estimated reduced form is based. Without conducting a qualitative analysis, current econometric practice can estimate structural arrays that are impossible, given the outcome of the estimated reduced form. This paper presents the basis for this circumstance and an algorithmic procedure for detecting such circumstances when they occur
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