Evaluation of the effect of stochastic explanatory variables in regression models when the underlying distribution is in the class of elliptical distributions

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1. I obtained the properties of the asymptotic covariance matrix of the LSE of regression parameters, investigated its small sample properties by simulation, and studied asset pricing models as examples, when explanatory variables are random in regression models. In particular, I (1) derived the asymptotic and small sample properties of the covariance matrix of the LSE when the joint distribution of explanatory and dependent variables is elliptical, (2) showed how the asymptotic variances of the LSE of alpha and beta depend on skewness and kurtosis of the joint distribution in the market model in finance without assuming any specific distribution, (3) found there is no effect of nonnormality on the unconditional LSE inference of expected asset returns in K-factor asset pricing models when factors and returns are i.i.d., and (4) studied the small sample properties of the covariance matrix of the LSE when explanatory variables and error term are uncorrelated but not independent and compared them to those when there is heteroskedasticity.2. I proposed a new definition of weak exogeneity when the underlying distribution is nonnormal in the class of elliptical distributions. Based on the new definition, I compared by simulation the joint and conditional MLEs of parameters for the student's t linear heteroskedastic regression model studied by Spanos (1994). The conditional MLE was found to work fine for regression parameters of the conditional model but not for other parameters.