Time series econometrics is essential to empirical studies in macroeconomics, finance, and many other areas.While the canonical models in this literature are small, parametric, and linear, there is growing interest in models in which the data generating process is either nonlinear or of a flexible, adaptive form. This dissertation proposes several new models and techniques in the area of flexible and nonlinear time series econometrics.

Chapter 1 proposes a novel methodology for determining the specification of factor-augmentedvector autoregression (FAVAR) models. Without strong a priori beliefs about the set of possible models, the complexity of the problem renders traditional model selection techniques infeasible. By contrast, my proposed solution only requires the estimation of a single model. This makes the process easy to scale in both the cross-sectional and time series dimensions. An efficient optimization algorithm for model estimation is developed. Monte Carlo studies show the technique to be highly effective in small samples, even in the presence of a low signal-to-noise ratio and missing data. Applications to large datasets of monthly and quarterly U.S. macroeconomic variables identify observed factors not normally considered in the FAVAR literature. The methodology is then used to analyze the asset-pricing model of Fama and French (1993). I find that their constructed factors for firm size and book-to-market equity ratio are likely observed components, but excess market return is not.

Chapter 2 proposes a regime-switching linear model with time-varying transition probabilities,endogenous switching, and a nonparametric error distribution. The last two qualities are achieved by letting the conditional mean of the normalized observation errors be a potentially nonlinear function of the errors in the state equation. We demonstrate that this specification permits a very flexible marginal distribution for the observation error. A Markov Chain Monte Carlo algorithm for sampling from the posterior distribution of parameters is developed. A simulation study demonstrates that existing parametric switching models yield biased parameter estimates when the data is generated by a model with nonlinear endogenous switching. We apply the model to US quarterly output growth. The proposed model is shown to fit the data better than parametric switching models.

Count data models are at the core of a large and diverse empirical literature in the socialand natural sciences. A key component in this class of models is the mean function, which defines the relationship between the covariates and the conditional expectation of the count process. Chapter 3 considers a general approach for representing the mean function that is adaptable, tractable, and dispenses with problematic facets of count data models such as explosive covariate effects and restrictive time series properties. The methodology is broadly applicable in cross-sectional, longitudinal, and time-series settings, with likelihood-based, generalized linear, copula and other models. We provide theoretical results that distinguish our methodology from existing work and implement it in two examples that demonstrate its relevance and practical appeal.

This dissertation comprises three chapters that expand upon Bayesian econometrics and game theory. Chapter 1 integrates heteroskedasticity into various models including regression discontinuity design, the Rubin causal (Roy-type) model, propensity score matching, and inverse probability weighting within a Bayesian framework. The practical adequacy of our modeling techniques is assessed through formal Bayesian model comparisons. Simulation studies evaluate the impact of neglected heteroskedasticity and the efficacy of our proposed methods, while their practical applicability is examined through three applications. Specifically, we investigate the impact of academic probation on subsequent academic performance, the effect of Medigap on healthcare expenditures, and the influence of COVID-19 vaccination on mental well-being. These applications highlight the consequences of misspecification and underscore the importance of addressing risks associated with omitted heteroskedasticity. Chapter 2 introduces a Bayesian treatment model that incorporates self-selection and multiple outcomes. We discuss marginal likelihood estimation for formal model comparison and validate our approach through simulation results. We then apply the model to two datasets, examining the influence of insurance on healthcare utilization. In particular, we analyze the impact of Medigap policies on healthcare expenditure using 1987 National Medical Expenditure Survey (NMES) data and the effect of types of private insurance on healthcare utilization using 1996 Medical Expenditure Panel Survey (MEPS) data. Our analysis indicates weak evidence supporting selection bias in both applications. In Chapter 3, we delve into the analysis of a price signaling game that integrates consumer learning. The chapter delineates the perfect Bayesian equilibrium for sellers and employs the undefeated equilibrium refinement to determine optimal choices. Furthermore, our analysis encompasses comparative statics, examining how variations in the probability of type revelation, initial customer review scores, and the quality of both high and low-quality seller products impact the expected return for sellers. Collectively, these chapters offer methodological advancements in Bayesian econometrics and game theory, and provide insights into real-world phenomena across various industries.

We describe a method for estimating the marginal likelihood, based on CHIB (1995) and CHIB and JELIAZKOV (2001), when simulation from the posterior distribution of the model parameters is by the accept reject Metropolis-Hastings (ARMH) algorithm. The method is developed for one-block and multiple-block ARMH algorithms and does not require the (typically) unknown normalizing constant of the proposal density. The problem of calculating the numerical standard error of the estimates is also considered and a procedure based on batch means is developed. Two examples, dealing with a multinomial logit model and a Gaussian regression model with non-conjugate priors, are provided to illustrate the efficiency and applicability of the method.

This dissertation is comprised of three chapters. Chapter 1 is a reprint of my job market. The chapter considers the efficient estimation of opinion pools in the Bayesian paradigm and extends their application to cases where the number of competing models exceeds the number of observations. An appropriate Bayesian formulation and estimation algorithm is proposed which 1) accommodates any proper scoring rule and 2) allows the weights to shrink towards any possible combination. This flexibility makes the Bayesian opinion pool relevant for applications related to model averaging and model selection and improves stability compared to the ones estimated using scoring rules in a small sample setting. Results from a simulation study reveal that the proposed Bayesian opinion pool methodology improves prediction accuracy. An application involving the Survey of Professional Forecasters demonstrates that the Bayesian opinion pool's inflation forecast competes well with the equal-weight aggregated inflation forecast published by the Federal Bank of Philadelphia. The application showcases the usefulness of the Bayesian solution in situations where traditional opinion pools fail.

Chapter two introduces a non-parametric vector autoregressive model with dynamic factor (DF-NPVAR) through a hierarchical Bayesian approach. The chapter considers the specification, identification and estimation of the DF-NPVAR model, allowing it to be efficiently fit via MCMC algorithms. The model aims at effectively capturing dynamic relationships among variables and enabling the incorporation of extensive information sets. Issues related to model comparison and extensions to settings with autocorrelated errors and qualitative variables are also considered. In an application employing post-war US data, the DF-NPVAR model successfully identifies non-linear associations between macroeconomic variables and the dynamic factor captures the business cycle component, which aligns with officially declared recession periods.

Chapter three discusses a Bayesian estimation for the FAVAR models using the precision-based algorithm. The model is fully identified under the identification restrictions of \cite{bai2016estimation}. The approach increases the efficiency of the Gibbs sampler and avoids slow convergence and poor mixing (\cite{chan2009efficient}). This article then contrasts the Bayesian approach with the one-step and two-step estimation techniques proposed in \cite{bernanke2005measuring}. The simulation study finds that the Bayesian approach recovers the unobservable factor in a simple FAVAR framework compared to estimation techniques proposed in \cite{bernanke2005measuring}.

This dissertation features a selection of Bayesian estimation frameworks for a variety of data and modeling scenarios. Economists seldom work with data arising from a prototypical linear regression model. In reality, data may be discrete, mixed, or missing; the true model may be semiparametric or nonparametric; effects may be nonadditive, or it may be heterogeneous across sampling units; observational data may be subject to sample selection and endogeneity issues; and the data might be coming from a sequential process. We discuss estimation methodologies for multifaceted data arising from complex processes. Special emphasis is placed on computational and mixing efficiency.

The first chapter develops a class of Markov process smoothness priors for potentially nonadditive multivariate mean functions. The proposed class of priors is incorporated into a larger semiparametric estimation framework that allows for endogeneity and sample selection, and is used to study how age and population density jointly affect car use in Japan. We find that an increase in density leads to a reduction in car use, and that this effect is smaller for elderly drivers than for young drivers. We also uncover interesting nonlinearities in the relationship between age and car use. Our empirical findings highlight the importance of allowing for nonlinear and nonadditive effects in our models.

The second chapter develops an econometric framework for estimating the effect of the built environment on transportation mode choice and usage when a large fraction of the population under study is nonlicensed. We use a multivariate ordinal outcomes model with a binary selection component to allow for heterogeneity in built environment effects and indirect effects urban form has on mode usage via license choice. Our exposition focuses on the joint modeling of correlated and discrete outcomes (binary and ordinal), strategizing with identification restrictions and nonidentification, and the efficient estimation of model parameters. A separate contribution this paper makes to the urban/transportation economics literature is the cross entropy index for land use imbalance, which we propose as a replacement to the entropy index for land use mix/balance. Using data from the 5th Nationwide Person Trip Survey (NPTS), we investigate whether the built environment is a policy-relevant determinant of travel behavior in the Japanese elderly. Effects are found to be nonzero but modest at best. Our results and conclusions are broadly consistent with those based on the United States.

In the third chapter, we design a Bayesian estimation method for the binary logit model with fixed and random effects. To this end, we develop a Gibbs procedure that uses sparse matrix algorithms, vectorization (parallelization), and collapsing to achieve computational and mixing efficiency. The method is fully Gibbs in that it does not involve a Metropolis-Hastings step anywhere. We also discuss the computation of the marginal likelihood, which is used to compare and select models. A detailed simulation study shows that the proposed methodology works well.

This thesis is concerned with specifying and estimating multivariate models in discrete data settings. The models are applied to several empirical applications with an emphasis in banking and monetary history. The approaches presented here are of central importance in model evaluation, policy analysis, and prediction.

The first chapter develops a framework for estimating multivariate treatment effect models in the presence of sample selection. The methodology deals with several important issues prevalent in program evaluation, including non-random treatment assignment, endogeneity, and discrete outcomes. The framework is applied to evaluate the effectiveness of bank recapitalization programs and their ability to resuscitate the financial system. This paper presents a novel bank-level data set and employs the new methodology to jointly model a bank's decision to apply for assistance, the central bank's decision to approve or decline the assistance, and the bank's performance. The article offers practical estimation tools to unveil new answers to important regulatory and government intervention questions.

The second chapter examines an important but often overlooked obstacle in multivariate discrete data models which is the proper specification of endogenous covariates. Endogeneity can be modeled as latent or observed, representing competing hypotheses about the outcomes of interest. This paper highlights the use of existing Bayesian model comparison techniques to understand the nature of endogeneity. Consideration of both observed and latent modeling approaches is emphasized in two empirical applications. The first application examines linkages for banking contagion and the second application evaluates the impact of education on socioeconomic outcomes.

The third chapter, which is joint work with Professor Ivan Jeliazkov, studies the formulation of the likelihood function for simultaneous equation models for discrete data. The approach rests on casting the required distribution as the invariant distribution of a suitably defined Markov chain. The derivation resolves puzzling paradoxes highlighted in earlier work, shows that such models are theoretically coherent, and offers simple and intuitive linkages to the better understood analysis of continuous outcomes. The new methodology is employed in two applications involving simultaneous equation models of (i) female labor supply and family financial stability, and (ii) the interactions between health and wealth.

This dissertation contains essays that address questions related to banking policy and regulation by developing original Bayesian econometric methods that address unobserved heterogeneity.

In the first chapter, I study the resolution of failed financial institutions by regulators in the U.S. over the period 1984-1992, which was characterized by concurrent crises in the banking and Savings and Loans (S & L) industries. Economic theory indicates that regulators best serve the public interest when they act to discourage moral hazard and preserve channels of financial intermediation. I determine whether regulators in the two industries conformed to norms of optimal resolution by developing a Bayesian latent class algorithm to uncover their decision rules. The results show that whereas the banking regulator's actions were consistent with optimal resolution norms recommended by theory, the S & L regulator deviated from such norms.

The second chapter examines the moral hazard effects of lax regulatory and resolution standards on thrift institutions during the Savings and Loans crisis. I make use of the natural policy experiment arising from the closure of the Federal Savings and Loans Insurance Corporation (FSLIC) and the Federal Home Loan Bank Board (FHLBB) in 1989 and the ensuing regime of stringent regulation of thrift institutions. The paper develops a Bayesian method for causal inference by incorporating the difference-in-difference strategy into the potential outcome framework. I find that thrifts facing a high probability of failure increase their composition of safe assets and reduce the share of high-risk loans on their balance sheet relative to thrifts at a low probability of failure following the policy change. These results provide evidence of moral hazard in the thrift industry prior to the introduction of enhanced regulation and oversight in 1989.

The third chapter examines the nature of heterogeneity in consumer expectations by utilizing random coefficient models, which are proven to be effective tools to address unobserved heterogeneity in panel data settings. The estimation method utilized in this study extends the method developed by Chen and Dunson (2003) for the selection of random effects in linear models to a model with ordered categorical outcomes. The application of this algorithm on responses pertaining to credit access and financial position from the Survey of Consumer Expectations provides evidence in favor of a random intercept. However, the findings do not support the presence of other random coefficients. This shows that unobserved heterogeneity exists in the expectation-formation mechanism but does not manifest in the responses to changes in demographic and economic characteristics of households.

In this paper, we consider the analysis of models for univariate and multivariate ordinal outcomes in the context of the latent variable inferential framework of Albert and Chib (1993). We review several alternative modeling and identification schemes and evaluate how each aids or hampers estimation by Markov chain Monte Carlo simulation methods. For each identification scheme we also discuss the question of model comparison by marginal likelihoods and Bayes factors. In addition, we develop a simulation-based framework for analyzing covariate effects that can provide interpretability of the results despite the nonlinearities in the model and the different identification restrictions that can be implemented. The methods are employed to analyze problems in labor economics (educational attainment), political economy (voter opinions), and health economics (consumers’ reliance on alternative sources of medical information).