Mixed Lasso estimator for stochastic restricted regression models

Parameters of a linear regression model can be estimated with the help of traditional methods like generalized least squares and mixed estimator. However, recent developments increased the importance of big data sets, which have much more predictors than observations where some predictors have no impact on the dependent variable. The estimation and model selection problem of big datasets can be solved using the least absolute shrinkage and selection operator (Lasso). However, to the authors’ knowledge, there is no study that incorporates stochastic restrictions, within a Lasso framework. In this paper, we propose a Mixed Lasso (M-Lasso) estimator that incorporates stochastic linear restrictions to big data sets for selecting the true model and estimating parameters simultaneously. We conduct a simulation study to compare the performance of M-Lasso with existing estimators based on mean squared error $ (\textrm{mse}) $ (mse) and model selection performance. Results show that M-Lasso is superior in terms of $ \textrm{mse} $ mse and it generally dominates compared estimators according to the model selection criteria. We employ M-Lasso to estimate parameters of a widely analysed production function under stochastic restrictions raised from economic theory. Our results show that M-Lasso can provide reasonable and more precise estimates of model parameters that are in line with the economic theory.