Some Recent Developments in Linear Models: A Short Survey

The linear model is — in conjunction with the OLS estimation method — one of the most popular models for statistical analysis. First, the linear model is considered as a model generator for more realistic models such as generalized linear models and threshold models. Second, different kinds of misspecification of the linear model such as non-normal errors, general heteroscedasticity and errors correlated with the regressors are considered and some guidance to deal with such misspecifications is given. Third, the consistency of the parameter estimates is considered if the true dependent variable has been transformed in some unknown non-linear way or if the wrong error distribution has been chosen in limited dependent variable models. The results are illustrated with some limited Monte Carlo studies. Fourth, some implications of the results for sample design are discussed.