In this paper we examine by simulation whether or not unobserved heterogeneity independent of the included regressors is really an issue in nonlinear single index models. We consider logit, probit and loglog models and both binary and fractional data. We found that unobserved heterogeneity: (i) produces an attenuation bias in the estimation of regression coefficients in all cases; (ii) is innocuous for logit estimation of average sample partial effects and relatively unimportant for the calculation of logit population partial effects, while in the probit and loglog cases there may be important biases in the estimation of those quantities; (iii) does not affect substantially the prediction of outcomes, particularly in the logit model; and (iv) is innocuous for the size of Wald tests for the significance of observed regressors but reduces their power substantially, specially in cases where the amount of heterogeneity is large and/or the sample size is small.
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Paper provided by University of Évora, CEFAGE-UE (Portugal) in its series CEFAGE-UE Working Papers with number
2007_08.