Joseph B. Kadane Publications

Reports have been published indicating striking regularities in the distribution of participation in group discussions, regularities potentially important in the understanding of small group processes. Several attempts to explain the form of the regularity contain implications for many sociological analyses. These attempts to explain the regularity are found to be inadequate; at the same time, the regularity is found to be somewhat doubtful.

A recent mathematical model by Horvath which predicts the process of participation in group discussions is compared to several alternative models. The models can be applied to data for which the basic unit is the act and to data for which the basic unit is a continuous sequence of acts. In both cases, when statistical tests of significance are employed, most of the more restrictive models are rejected.

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.