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. / Thesis / Doctor of Philosophy (PhD) / This thesis focuses on model averaging, a leading approach for handling model uncertainty, which is the likelihood that one’s econometric model is incorrectly specified. I examine the performance of model averaging compared to conventional econometric methods and to more recent machine learning algorithms in simulations and applied settings, and show how easily model averaging can be applied to empirical problems in economics. This thesis makes a number of contributions to the literature. First, I focus on frequentist model averaging instead of Bayesian model averaging, which has been studied more extensively. Second, I use model averaging in empirical problems, such as estimating the returns to education and using model averaging with COVID-19 data. Third, I compare model averaging to machine learning, which is becoming more widely used in economics. Finally, I focus attention on different approaches for constructing the set of candidate models for model averaging, an important yet often overlooked step.

Cardiac arrest is a major cause of mortality and morbidity including recurring cardiac events, cognitive impairments, and mental health issues. This thesis is on empirical analyses of cardiac arrest patients in Ontario, Canada using administrative health data sources. Chapter 1 is a retrospective population surveillance study, which employs logistic regression analysis to examine short-term and long-term survival trends for adult patients in acute care hospitals. The 1-year adjusted odds ratio for initial successful resuscitation is 1.049 (95% CI: 1.022-1.076) when controlling for demographics, pre-admission comorbidities, and hospital of arrest. In stark contrast, there was no evidence of a trend in survival at discharge, 30 days, or 1 year. Results suggest further research into post-resuscitation care in Ontario care may be useful. However, we also find evidence of measurement error coding in successful resuscitation that is trending in magnitude in way that could bias trend estimates. Chapter 2 takes a serious look at the nonclassical measurement error problem in resuscitation success coding identified in the previous chapter. We employ a combination of credible assumptions from within the partial identification econometrics literature to nonparametrically bound the trend is resuscitation while allowing misclassification rates to trend. We also develop a novel approach which weakly restricts asymmetry between false positive and negative rates. We find that restricting false positives and negative to be within 10% and 90% of misclassified observations, in combination with monotonicity assumptions is enough to identify a trend. Chapter 3 follows survivors of cardiac arrest after discharge and investigates follow-up patterns in primary care. These patients remain at high risk of death, recurrence of cardiac events, cognitive impairment, and mental health issues. They may benefit from ongoing monitoring of cardiac risk factors, early mental health screening, and co-ordination of specialist care. This requires continuity of primary care. Primary care reforms in Ontario, Canada have led to the majority of general practitioners (GP) switching from fee-for-service remuneration to enhanced patient enrolment models, which encourage or require GPs to formally enroll most patients attached to their practice. To understand continuity of care across payment models, we use semi-parametric duration models to analyze time to first GP outpatient follow-up visit, distinguishing visits a patient’s own regular GP, and other GPs. We find enrolled patients visit their own (other) GP earlier (later) compared to patients whose regular GP is fee-for-service. / Thesis / Doctor of Philosophy (PhD)

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This dissertation provides a thorough overview of the use of nonparametric estimation methods for analyzing data collected by complex sampling plans. Applied econometric analysis is often performed using data collected from large-scale surveys, which use complex sampling plans in order to reduce administrative costs and increase the estimation efficiency for subgroups of the population. These sampling plans result in unequal inclusion probabilities across units in the population. If one is interested in estimating descriptive statistics, it is highly recommended that one uses an estimator that weights each observation by the inverse of the unit's probability of being included in the sample. If one is interested in estimating causal effects, a weighted estimator should be used if the sampling criterion is correlated with the error term. The sampling criterion is the variable used to design the sampling scheme. If it is correlated with the error term, sampling is said to be endogenous and, if ignored, leads to inconsistent estimation. I consider three distinct probability weighted estimators: i) a nonparametric kernel regression estimator; ii) a conditional probability distribution function estimator; and iii) a nonparametric instrumental variable regression estimator. / Thesis / Doctor of Philosophy (PhD)

Thesis advisor: Shakeeb Khan / Thesis advisor: Zhijie Xiao / This dissertation consists of three chapters demonstrating how the current econometric problems can be solved by using machine learning techniques. In the first chapter, I propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric transformation, and duration models. A main advantage of my approach is computational. For instance, rank estimation procedures such as those proposed in Han (1987) and Cavanagh and Sherman (1998) that optimize a nonsmooth, non convex objective function are difficult to use with more than a few regressors and so limits their use in with economic data sets. For such monotone index models with increasing dimension, we propose to use a new class of estimators based on batched gradient descent (BGD) involving nonparametric methods such as kernel estimation or sieve estimation, and study their asymptotic properties. The BGD algorithm uses an iterative procedure where the key step exploits a strictly convex objective function, resulting in computational advantages. A contribution of my approach is that the model is large dimensional and semiparametric and so does not require the use of parametric distributional assumptions. The second chapter studies the estimation of semiparametric monotone index models when the sample size n is extremely large and conventional approaches fail to work due to devastating computational burdens. Motivated by the mini-batch gradient descent algorithm (MBGD) that is widely used as a stochastic optimization tool in the machine learning field, this chapter proposes a novel subsample- and iteration-based estimation procedure. In particular, starting from any initial guess of the true parameter, the estimator is progressively updated using a sequence of subsamples randomly drawn from the data set whose sample size is much smaller than n. The update is based on the gradient of some well-chosen loss function, where the nonparametric component in the model is replaced with its Nadaraya-Watson kernel estimator that is also constructed based on the random subsamples. The proposed algorithm essentially generalizes MBGD algorithm to the semiparametric setup. Since the new method uses only a subsample to perform Nadaraya-Watson kernel estimation and conduct the update, compared with the full-sample-based iterative method, the new method reduces the computational time by roughly n times if the subsample size and the kernel function are chosen properly, so can be easily applied when the sample size n is large. Moreover, this chapter shows that if averages are further conducted across the estimators produced during iterations, the difference between the average estimator and full-sample-based estimator will be 1/\sqrt{n}-trivial. Consequently, the averaged estimator is 1/\sqrt{n}-consistent and asymptotically normally distributed. In other words, the new estimator substantially improves the computational speed, while at the same time maintains the estimation accuracy. Finally, extensive Monte Carlo experiments and real data analysis illustrate the excellent performance of novel algorithm in terms of computational efficiency when the sample size is extremely large. Finally, the third chapter studies robust inference procedure for treatment effects in panel data with flexible relationship across units via the random forest method. The key contribution of this chapter is twofold. First, it proposes a direct construction of prediction intervals for the treatment effect by exploiting the information of the joint distribution of the cross-sectional units to construct counterfactuals using random forest. In particular, it proposes a Quantile Control Method (QCM) using the Quantile Random Forest (QRF) to accommodate flexible cross-sectional structure as well as high dimensionality. Second, it establishes the asymptotic consistency of QRF under the panel/time series setup with high dimensionality, which is of theoretical interest on its own right. In addition, Monte Carlo simulations are conducted and show that prediction intervals via the QCM have excellent coverage probability for the treatment effects comparing to existing methods in the literature, and are robust to heteroskedasticity, autocorrelation, and various types of model misspecifications. Finally, an empirical application to study the effect of the economic integration between Hong Kong and mainland China on Hong Kong’s economy is conducted to highlight the potential of the proposed method. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Thesis advisor: Arthur Lewbel / This dissertation comprises three essays on empirical industrial organization (IO) and applied econometrics. The first and third chapters focus on identification approaches in structural models, with the first chapter dedicated to addressing limitations in demand modeling, while the third chapter studies identification in a triangular two-equation system. The second chapter applies modern econometric tools to understand policy-related topics in IO. The first chapter deals with identification in structural demand modeling, and generalizes the current framework in the literature to achieve a more accurate estimation of differentiated products demand. Within the framework of Berry (1994) and Berry, Levinsohn, and Pakes (1995), the existing empirical industrial organization literature often assumes that market size is observed. However, the presence of an unobservable outside option is a common source of mismeasurement. Measurement errors in market size lead to inconsistent estimates of elasticities, diversion ratios, and counterfactual simulations. I explicitly model the market size, and prove point identification of the market size model along with all demand parameters in a random coefficients logit (BLP) model. No additional data beyond what is needed to estimate standard BLP models is required. Identification comes from the exogenous variation in product characteristics across markets and the nonlinearity of the demand system. I apply the method to a merger simulation in the carbonated soft drinks (CSD) market in the US, and find that assuming a market size larger than the true estimated size would underestimate merger price increases. Understanding consumer demand is not only central to studying market structure and competition but also relevant to the study of public policy such as taxation. In the second chapter, we examine household demand for sugar-sweetened beverages (SSB) in the U.S. Our goal is to understand the distributional effect of soda taxes across demographic groups and market segments (at-home versus away-from-home). Using a novel dataset that includes at-home and away-from-home food purchases, we study who is affected by soda taxes. We nonparametrically estimate a random coefficient nested logit model to exploit the rich heterogeneity in preferences and price elasticities across households, including SNAP participants and non-SNAP-participant poor. By simulating its impacts, we find that soda taxes are less effective away-from-home while more effective at-home, especially by targeting the total sugar intake of the poor, those with high total dietary sugar, and households without children. Our results suggest that ignoring either segment can lead to biased policy implications. In the final chapter, we show that a standard linear triangular two equation system can be point identified, without the use of instruments or any other side information. We find that the only case where the model is not point identified is when a latent variable that causes endogeneity is normally distributed. In this non-identified case, we derive the sharp identified set. We apply our results to Acemoglu and Johnson's (2007) model of life expectancy and GDP, obtaining point identification and comparable estimates to theirs, without using their (or any other) instrument. / Thesis (PhD) — Boston College, 2024. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

Thesis advisor: Shakeeb S.K. Khan / Thesis advisor: Zhijie Z.X. Xiao / Binary choice models can be easily estimated (using, e.g. maximum likelihood estimation) when the distribution of the latent error is known, as in Logit or Probit. In contrast, most estimators with unknown error distribution (e.g., maximum score, maximum rank correlation, or Klein-Spady) are computationally difficult or numerically unstable, making estimation impractical with more than a few regressors. The first chapter proposes an estimator that is convex at each iteration, and so is numerically well behaved even with many regressors and large sample sizes. The proposed estimator, which is root-n consistent and asymptotically normal, is based on batch gradient descent, while using a sieve to estimate the unknown error distribution function. Simulations show that the estimator has lower mean bias and root mean squared error than Klein-Spady estimator. It also requires less time to compute. The second chapter discusses the same estimator in high dimensional setting. The estimator is consistent with rate lower than root-n when the number of regressors grows slower than the number of observations and asymptotic normal when the square of the number of regressors grows slower than the number of observations. Both theory and simulation show that higher learning rate is needed with higher number of regressors. The third chapter provides an application of the proposed estimator to bankruptcy prediction. With more than 20 regressors, the proposed estimator performs better than logistic regression in terms of Area Under the Receiver Operating Characteristics using firm data one year or two years prior to bankruptcy, but worse than logistic regression using firm data three years prior to bankruptcy. / Thesis (PhD) — Boston College, 2022. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Economics.

This thesis concerns the asymptotic behaviour of the sequence of 1-step recursive Chow statistics and various tests derived therefrom. The 1-step statistics are produced as diagnostic output in standard econometrics software, and are expected to reflect model misspecification. Such misspecification testing is important in validating the assumptions of a model and so ensuring that subsequent inference is correct. Original contributions to the theory of misspecification testing include (i) a result on the pointwise convergence of the 1-step statistics; (ii) a result on the extreme-value convergence of the maximum of the statistics; and (iii) a result on the weak convergence of an empirical process formed by the statistics. In Chapter 2, we describe the almost sure pointwise convergence of the 1-step statistic for a broad class of time series models and processes, including unit root and explosive processes. We develop an asymptotic equivalence result, and use this to establish the asymptotic distribution of the maximum of a sequence of 1-step statistics with normal errors. This allows joint consideration of the sequence of 1-step tests via its maximum: the sup-Chow test. In Chapter 3, we use simulation to investigate the power properties of this test and compare it with benchmark tests of structural stability. We find that the sup-Chow test may have advantages when the nature of instability is unknown. In Chapter 4, we consider how the test may be adapted to situations in which the errors cannot be assumed normal. We evaluate several promising approaches, but also note a trade-off between robustness and power. In Chapter 5 we analyse an empirical process formed from the 1-step statistics, and prove a weak convergence result. Under the assumption of normal errors, the limiting distribution reduces to that of a Brownian bridge. The asymptotic approximation appears to works well even in small samples.

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