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Contributions: AbstractDetecting social interactions in bivariate probit models: some simulation results
This paper analyzes the possibility of detecting observable andnonobservable social interactions in a bivariate probit model viaMonte Carlo simulation. Gordon, Lin, Osberg & Phipps (1994) conclude from their empiricalestimation of logit and probit models that it would be desirableto have at least 10,000 observations in order to maintainparameter stability. However, some applications of bivariateprobit models, e.g. Greene (1998), only have small data sets. Our intention is to find out whether, in the presence of socialinteractions in the data, it is possible to detect theseinteractions in a bivariate probit model. In our model, theobservable part of the social interactions, i.e. the observableinfluence of the decision of the peer, is tested by thesignificance of the endogeneous dummy regressor. Thenonobservable part of the social interactions is tested by thesignificance of the residual correlation structure r. Hence,we analyze the power of the usual zcoefficient test concerningthe parameters of the observable and nonobservable interactionsin the bivariate probit model. The main result is that in small samples, we only find a lowprobability of detecting observable and nonobservable socialinteractions. Furthermore, we find that the power of these testsvaries with the residual correlation r. For example, in thecase of T = 100 observations and a correlation of r = 0.1,only 13.6 percent of the true rcoefficients and 22.6 percentof the true observable social interactioncoefficients aresignificantly different from zero at the 5percent significancelevel. In large samples, however, we find the zparameter testto be very powerful. References
