The Distribution, When the Residuals Are Small, of Statistics Testing Overidentifying Restrictions

Joseph B. Kadane

No 251, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: In the estimation of simultaneous equation econometric models, overidentifying restrictions improve estimates of the remaining parameters. Natural test statistics for the hypothesis that an equation is overidentified have been developed by Anderson and Rubin and by Basmann. If the residuals are jointly normal, serially uncorrelated, and small, both the above overidentification test statistics have the Snedecor F distribution asymptotically as the variance of the residuals get small. This gives analytic confirmation of Monte Carlo results of Basmann. The results given apply to linear models in which predetermined variables can be exogenous or lagged endogenous.

Pages: 10 pages
Date: 1968
Note: CFP 326.
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Published in Journal of the American Statistical Association (March 1970), 65(329): 182-184

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