Model Averaging: Methods and Applications

This thesis focuses on a leading approach for handling model uncertainty: model averaging. I examine the performance of model averaging compared to conventional econometric methods and to more recent machine learning algorithms, and demonstrate how model averaging can be applied to empirical problems in economics. It comprises of three chapters. Chapter 1 evaluates the relative performance of frequentist model averaging (FMA) to individual models, model selection, and three popular machine learning algorithms – bagging, boosting, and the post-lasso – in terms of their mean squared error (MSE). I find that model averaging performs well compared to these other methods in Monte Carlo simulations in the presence of model uncertainty. Additionally, using the National Longitudinal Survey, I use each method to estimate returns to education to demonstrate how easily model averaging can be adopted by empirical economists, with a novel emphasis on the set of candidate models that are averaged. This chapter makes three contributions: focusing on FMA rather than the more popular Bayesian model averaging; examining FMA compared to machine learning algorithms; and providing an illustrative application of FMA to empirical labour economics. Chapter 2 expands on Chapter 1 by investigating different approaches for constructing a set of candidate models to be used in model averaging – an important, yet often over- looked step. Ideally, the candidate model set should balance model complexity, breadth, and computational efficiency. Three promising approaches – model screening, recursive partitioning-based algorithms, and methods that average over nonparametric models – are discussed and their relative performance in terms of MSE is assessed via simulations. Additionally, certain heuristics necessary for empirical researchers to employ the recommended approach for constructing the candidate model set in their own work are described in detail. Chapter 3 applies the methods discussed in depth in earlier chapters to currently timely microdata. I use model selection, model averaging, and the lasso along with data from the Canadian Labour Force Survey to determine which method is best suited for assessing the impacts of the COVID-19 pandemic on the employment of parents with young children in Canada. I compare each model and method using classification metrics, including correct classification rates and receiver operating characteristic curves. I find that the models selected by model selection and model averaging and the lasso model perform better in terms of classification compared to the simpler parametric model specifications that have recently appeared in the literature, which suggests that empirical researchers should consider statistical methods for the choice of model rather than relying on ad hoc selection. Additionally, I estimate the marginal effect of sex on the probability of being employed and find that the results differ in magnitude across models in an economically important way, as these results could affect policies for post-pandemic recovery.

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