Econometrica: Sep, 1974, Volume 42, Issue 5

Testing Structural Specification Using the Unrestricted Reduced Form

https://doi.org/0012-9682(197409)42:5<869:TSSUTU>2.0.CO;2-3
p. 869-883

R. P. Byron

In the first section of this paper the overidentifying restrictions on a system of linear simultaneous equations are expressed in terms of restrictions on the reduced form parameters. These restrictions provide the basis of a test of the structure using only the unrestricted reduced form parameter estimates. Under Ho the test proposed is asymptotically equivalent to a likelihood ratio test. The test may be applied as a single equation or complete system procedure and it may be presented as either a @?2 or an F statistic. The case is also made here for system overidentification tests rather than single equation procedures, the arguments being drawn from the statistical literature on hypothesis testing by induction. The computational advantages of the present proposals are substantial when compared to FIML based likelihood ratio tests and Monte Carlo experiments confirm that a system version of the test performs well in large samples. The system version of the test behaves like the FIML likelihood ratio test in large sample situations both under H0 and H1. However, the Monte Carlo studies indicate that both the single equation and system versions of the test perform poorly in small samples.