This dissertation is comprised of four chapters. Chapter 1 is a reprint of my job marketpaper “Estimation and Inference with Transfer Learning.” In this chapter we propose and study machine learning algorithms which utilize “transfer learning,” and their application to improving semi-parametric inference in cases of insufficient sample size. We consider multiple machine learning algorithms, including elastic net and deep feedforward neural networks with rectified linear unit (ReLU) activation functions, and allow for transfer through an ℓ1 penalty term in the loss function which shrinks the estimates towards auxiliary estimates. Novel results on error bounds and convergence rates are established to justify the usage of these algorithms as nuisance function estimators for double machine learning. We evaluate the usage of these algorithms in conducting valid inference on treatment effects with Monte Carlo simulations and an empirical application on the Job Corps training program. Our numerical results show that transfer learning can substantially improve estimation in the presence of sizeable missing data.

Chapter two is comprised of an analysis of the effects of minimum wages on unemploymentduration and re-employment outcomes. Using the Survey of Income and Program Participation, we build a sample of unemployment spells to study how the minimum wage affects several outcomes of the unemployed. We establish that the policy matters for the unemployed in two ways. A higher initial level of the minimum wage (at the start of a spell) leads workers to abandon their job search but has mostly null effects on other outcomes. However, being unemployed at the time the minimum wage is raised is associated with longer spells, a higher rate of search quitting, and fewer working hours after re-employment. Chapter three is derived from a joint work of mine with Ying-Ying Lee entitled ”Double Machine Learning Nonparametric Inference with Continuous Treatment.” In this chapter we numerically evaluate the effectiveness and characteristics of the double machine learning continuous treatment estimator discussed in Colangelo and Lee 2020. We conduct simulations using a variety of machine learning algorithms such as lasso, random forests and neural networks (and variations of these), and also provide an empriical application using data from the Job Corps program. The estimator is fairly robust to the choice of machine learning algorithm in the presence of cross-fitting, with all algorithms attaining near perfect coverage rates and unbiasedness. Some algorithms perform well even without cross-fitting, indicating that the procedure can be skipped in particular cases. The empirical results are similar regardless of which algorithm is used, and are consistent with previous research on the Job Corps program.

Chapter 4 discusses a new estimator for estimation and inference in long term panelswith interactive effects. We modify the Common Correlated Effects (CCE) approach of Pesaran (2006) to produce a simpler and more computationally expedient estimator than the original CCE estimator. While CCE substitutes the factors with cross sectional means, the new method which we call Two Way CCE (TWCCE) substitutes out the individual specific factor loadings in addition to the factors themselves. This conveniently reduces the estimation problem to simple least squares without the need to estimate heterogeneous coefficients on each factor. We investigate the performance of TWCEE in comparison with the other most common factor model estimators such as the Interactive Effects Estimator (IFE) of Bai (2009) and the Augmented Mean Group Estimator (AMG) of Eberhardt and Teal (2010). We show that TWCEE has similar performance to the other methods, while also demonstrating the least computation time.