SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

Contributions: Abstract

Detecting social interactions in bivariate probit models: some simulation results

Johannes Jaenicke
University of Osnabrueck
Germany

This paper analyzes the possibility of detecting observable andnon-observable 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. Thenon-observable part of the social interactions is tested by thesignificance of the residual correlation structure r. Hence,we analyze the power of the usual z-coefficient test concerningthe parameters of the observable and non-observable interactionsin the bivariate probit model.

The main result is that in small samples, we only find a lowprobability of detecting observable and non-observable 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 r-coefficients and 22.6 percentof the true observable social interaction-coefficients aresignificantly different from zero at the 5-percent significancelevel. In large samples, however, we find the z-parameter testto be very powerful.

References

Gordon, D.V., Lin, Z., Osberg, L. & Phipps, S. (1994)Prediction probabilities: Inherent and sampling variability in theestimation of discrete-choice models. Oxford Bulletin of Economicsand Statistics 56, 13-31.

Greene, W. (1998) Gender economics courses in liberalart colleges: further results. Journal of Economic Education 29,291-300.