This dissertation consists of four chapters that study estimation and inference in systemof equations and panel data under model uncertainty. In Chapter 2, I consider model uncertainty in a panel data model, and introduce a Stein-like shrinkage estimator that is a weighted average of an unrestricted estimator and a restricted estimator. The restricted estimator represents a belief about where the parameters of the model are likely to be close. Chapter 3 considers the estimation uncertainty from choosing different number of lagged dependent variables as instruments in dynamic panel data models. Generalized method of moments (GMM), the typical estimation method, can produce efficient estimators when all lagged dependent variables are used as instruments. However, estimation using all instruments can cause substantial bias. Conversely, the GMM estimators that use one lag as instrument are asymptotically unbiased under forward demeaning transformation, but at the cost of losing efficiency. Therefore, I introduce an averaging estimator which is a weighted average of the two GMM estimators where the averaging weight is proportional to a quadratic loss function that minimizes the asymptotic risk. In Chapter 4, I consider simultaneous equations models (SEM), and develop an estimator to deal with the model uncertainty about the magnitude of endogeneity. Ordinary least squares (OLS) estimators are the most efficient estimators, however, may suffer from substantial bias when the degree of endogeneity is substantial. On the contrary, two-stage least squares (2SLS) estimators are consistent but not efficient. Therefore, I consider a Stein-like shrinkage estimator which is a weighted average of the OLS and 2SLS estimators, where the weight is inversely related to a Wu-Hausman statistic that measures the magnitude of the endogeneity. Chapter 5 considers latent group structures to model uncertainty resulting from unobserved heterogeneity in panel data models. Basically, I consider a panel data model where the slope parameters are heterogenous across groups but homogenous within a group, and the group identity is unknown. I provide a framework for estimation and identification of the latent group structure using a pairwise fusion penalized approach.

My dissertation consists of six essays which contribute new theoretical results

to two econometrics frontiers: nonparametrics and finite sample econometrics. Chapters 2 to 3 discuss the estimation and inference of the nonparametric and semiparametric models. In chapter 2 an efficient two-step estimator is developed in single nonparametric regression model with a general parametric error covariance. By fully utilizing the information incorporated in the error covariance into estimation, the newly developed method is more efficient compared to the conventional local linear estimator (LLLS) and some other two-step estimator. The corresponding asymptotic theorems are derived. Monte Carlo study shows the relative efficiency gain of the newly proposed estimator. Chapter 3 systematically develops a new set of results for seemingly unrelated regression (SUR) analysis within nonparametric and semiparametric framework. We study the properties of LLLS and local linear weighted least squares (LLWLS) estimators, provide an efficient two-step estimation for the system and establish the asymptotic theorems under both unconditional and conditional error variance-covariance cases. The procedures of estimation for various nonparametric and semiparametric SUR models are proposed. In addition, two nonparametric goodness-of-fit measures for the system are given. Chapter 4 applies the estimation method developed in chapter 2 and 3 to an empirical analysis on return to public capital in U.S.

Chapters 5 to 6 study the finite sample properties of the mean reversion parameter estimator in continuous time models. In chapter 5 we approximate the bias of the estimator for the Levy-based Ornstein-Uhlenbeck (OU) process, and propose bias corrected estimators. In chapter 6 the exact distribution of the MLE is investigated under different scenarios: known or unknown drift term, fixed or random start-up value, and zero or positive . The numerical calculations demonstrate the remarkably reliable performance of the proposed exact approach.

In chapter 7 we study the efficiency of the coefficient of determination based on

final prediction error and compare it with conventional goodness-of-fit measures

in linear regression models with both normal and non-normal disturbances. The

efficiency results show that R2 based on

final prediction error has practical use in empirical analysis, for examples,

panel data analysis and time series analysis.

Nowadays, with advanced technology, it is easier to obtain data like never before. With more available data, comes new information that economists can extract to uncover relationships between economic variables. By using new state of the art machine learning algorithms and techniques that can handle data efficiently and can identify trends and patterns easily, we can help solve economic problems, theoretically and empirically. The primary goal of this dissertation is to help bridge the gap between machine learning and econometrics. With powerful machine learning models that exhibit great predictive ability, it would be useful to further explore machine learning methods and add them to our econometrics toolbox. In addition, we wish to extend these models to incorporate problems often faced in econometric models, including partial effects estimation using first derivatives, evaluating concavity of various economic functions using second derivatives, and allowing for heteroskedastic and autocorrelated errors in an econometric model. These issues are clearly often faced in economics, but not so much in machine learning. To incorporate machine learning techniques, machine learning estimation of nonparametric models and marginal effects are established throughout the dissertation. A derivative estimation procedure of smoothing weighted difference quotients based on random forest is proposed. The procedure of smoothing weighted difference quotients based on random forest is then used to estimate second derivatives. Lastly, a generalized framework for Kernel Regularized Least Squares that incorporates information in the error covariance when estimating the regression function is proposed.

Nonparametric approaches have widely been used due to their advancement in not making assumptions on the distribution of the data. Even with their extensive development, nonparametric hypothesis testing has not been developed as much as a nonparametric estimation even though it is one of the key components of the econometric analysis. This dissertation has mainly two parts. I first explore the systematic development of the current nonparametric tests and provide results on testing linearity as an illustration. Then I develop new nonparametric tests for detecting endogeneity in cross-sectional data and panel data respectively.

Elaborating each test's performance can be meaningful in that we can decide which test to use depending on the hypothesis and even construct a new test based on such a relationship. Under the hypotheses for linearity, Chapter 2 will categorize the types of nonparametric tests and discuss the analytical relationship of those tests. By imposing some conditions, I can compare the local power of each test asymptotically. While examining the analytical relationship, I develop a nonparametric Rao-Score test and show it to be equivalent to the Su and Ullah (2013) test.

Once analyzing the analytical relationship of the current nonparametric tests, I focus on developing a new nonparametric test for endogeneity. Since endogeneity is commonly observed in many economic contexts, detecting its presence is a preliminary step for choosing an estimation strategy. In Chapter 3, I construct a test using the control function approach under a triangular simultaneous equations model. My test can be summarized as being simple to implement as a test and being able to capture the locally nonlinear correlation with kernel weighting. Furthermore, I will apply these tests to the empirical analyses and show the contradicting results with the parametric test.

Not only in triangular simulation equations model, but also is endogeneity important model specification issue in panel data setting. The estimation strategy differs depending on the presence of endogeneity between the individual specific effects and the variable. I propose a new estimation method for the nonparametric panel random effects model and construct a new test for endogeneity using the residuals from the proposed estimation method. By obtaining the individual specific effects in the random effects model, I construct a test over the i index instead of the i index and time. With a large T, the test performs well in terms of size and power.

This dissertation is composed with 4 essays. They explore modelling uncertainty following two major directions. The former 2 contains topics on ordinary and general ridge-type shrinkage estimation developed from model averaging and kernel density estimation. The third one critically reviews recent literature in the areas of model averaging and model selection both parametrically and nonparametrically and proposes topics for future work. The last one focuses on nonparametric panel data estimation with random effects. In chapter 2, ordinary ridge-type shrinkage estimation is extensively studied, where a class of well-behaved ordinary ridge-type semiparametric estimators is proposed. Monte Carlo simulations, theoretical derivations, as well as empirical out-of-sample forecasts are all investigated to prove their usefulness in reducing mean squared errors, i.e. risks. Chapter 3 develops the works in Chapter 2 to the general ridge regressions. By connecting general ridge regression with kernel density estimation, an asymptotically optimal semiparametric ridge-type estimator is built. By connecting general ridge regression with model averaging, a class of model averaging ridge-type estimators are obtained. These estimators are observed to have different improvements upon the feasible general ridge estimators when model uncertainties, i.e., the error variances are different. To encourage better understanding on model averaging and model selection, Chapter 4 gives a comprehensive literature review and analysis on these topics from a frequentist's point of view. Parametric and nonparametric procedures in the recent developments are explored. Chapter 5 starts investigating panel data estimation by introducing nonparametrics in the picture. The proposed two-stage estimator shows good behaviors in Monte Carlo simulation. In addition, illustrative empirical examples in health economics and environmental economics are also introduced.

The first chapter establishes a way of inferring risk aversion in a first-price auction (FPA) model when an entry decision is endogenous. Bidders' risk aversion is captured by a parameter in constant relative risk aversion utility functions and the parameter is then partially identified in a set under a "monotonicity" condition. The recovery of

the partially identified risk aversion parameter is concluded in a confidence set (CS). The CS is constructed by inverting a test dealing with many inequality restrictions of quantiles. In the spirit of Andrews and Shi (2013), we implement quantile selection to address possible slackness. Asymptotic results show desired properties of size and power against fixed (and some local) alternatives. Confidence sets perform fairly well in finite samples and the comparison of results highlights the necessity of quantile selection. The inference is illustrated by using US Forest Service timber auction data and detects considerable risk aversion.

Exogenous entry is a convenient assumption to make for identification and inference in auction models. The second chapter examines this assumption and develops a test against endogenous entry in first-price auctions with risk aversion. The approach also takes auction observed heterogeneity into account. The desirable property of asymptotic size and consistency of the test is proven, and Monte Carlo simulations approve the test at finite samples. The application to US Forest Service timber auctions brings in interesting implication: entry is exogenous with lower entry level but is endogenous with higher entry level. The result also suggests a relatively stronger risk aversion attitude than what is obtained in the literature.

The third chapter shows nonparametric identification and estimation of private value distribution and density functions in first-price auctions with endogenous entry. In the model, symmetric bidders face a nontrivial entry cost and a binding reserve price. We identify latent structures by solving a two stage game, and estimate density

functions (point-wisely) by using and comparing two different methods. Monte Carlo experiments show good performance of our estimators.

My dissertation is comprised of three independent empirical chapters. Below is a brief description of each.

The first Chapter is titled Infant Mortality Rates in India: District-Level Variations and Correlations". This paper examines the correlates of infant mortality in India using district-level data from the 1991 and 2001 Census of India. While infant mortality rates have dropped across districts over this ten year period, there still remains a lot of heterogeneity across districts and hence across the states. Using a panel data set of 666 districts, the analysis seeks to determine which of socio and or economic factors play an important role in reducing infant mortality rates. In our empirical work, the explanatory variables used are male and female literacy, male and female labor force participation, the level of poverty, urbanization and other socio-economic variables. We use quantile regression analysis to determine which of these factors impact infant mortality. Quantile regression is preferred over OLS because it allows us to estimate models for the conditional median function, and the full range of other conditional quantile functions and therefore provides a more complete statistical analysis of the stochastic relationship among random variables. The analysis brings out the powerful in influence of woman's characteristics on infant mortality, especially literacy and labor force participation. Increases in both of these variables significantly reduce child mortality at the district level. Improvements in male laborers in non-agricultural work and reductions in poverty also reduce child mortality, but their quantitative impact is weak in comparison. Further the non-parametric analysis reinforces the results found in the parametric section. They indicate that the action or the impact of the covariates is strongest in the districts which lie in the center of the conditional distribution, rather than those at the extreme. This analysis allows us to determine in which districts the impact of additional target policies would yield the greatest reduction in infant mortality.

The second paper is titled Same-sex siblings and their affect on mothers labor supply in South Africa". This study aims to look at the labor-supply consequences of childbearing for women in South Africa. However due to the endogeneity of fertility, the research question becomes complicated. Using parental preferences for a mixed sibling-sex composition I construct instrumental variables (IV) estimates of the eect of childbearing on labor supply of all women aged 15-35 years having more than two children. The data used for the study is the 10% household sample from the 2001 census. The covariate of interest in the labor supply model is the indicator More than two children. Demographic variables include mother's age, age of the mother at first birth, years of schooling, indicators for race, and an urban dummy. Labor-supply variables include hours worked per week, worked for pay and total income. Unlike previous studies which restrict their sample to include only female household heads or spouse of male household heads, this study expands the sample size to include all childbearing women in the household aged 15-35. The IV estimates that exploit the fertility consequences of sibling sex do not conrm the OLS estimates showing that more children lead to lowering of female labor supply. While OLS estimates exaggerate the causal effect of children, children seem to have a smaller effect on the labor supply of college-educated women. I find that labor market outcomes of childbearing are more severe for married women in South Africa.

The third paper is on The effect of Immigration on Ethnic Composition and Occupational Reallocation". Over the last 30 years, the U.S. labor market has been transformed by the 'second great migration'. Much of this immigration has been among the lower skilled; the share of High School Dropout (HSD) workers who are foreign born increased from 12% in 1980 to 44% in 2007. At the same time, native born HSD workers grew more slowly than any other educational category, falling by nearly 6%. These two outcomes have inevitably lead to much speculation that immigrants depress the wages of similarly skilled natives. The labor economics literature, however, has found little empirical evidence to support this claim. We aim to assess whether the impact of immigration is mitigated by occupational transition of natives. Being over represented among HSDs, we focus on the labor market outcomes for Black workers. We use data from the 5% public use sample of the census (1980, 1990 and 2000) as well as the 1% sample of the population from the American Community Survey (2005, 2006 and 2007) to estimate the effect of occupational reallocation on the wages of Black workers as well as the eect of immigration on reallocation. A shift-share analysis reveals that occupational transitions caused wages for Blacks to rise by 46% more than they would have with a static occupational distribution. However, we find that these occupational shifts were due to crowding out effect of Hispanics on Black occupations: a 10 percentage point increase in the share of workers in an occupation who are Hispanics leads to a 5 percentage point decrease in the share of Black workers in that occupation. This is significantly large to explain substantially, occupations that declined in importance for Blacks during the period of study. We nd a strong correlation between importance of occupations to Hispanic and Blacks, suggesting that most occupational transition for these two groups has not only been driven by outside factors such as trade and technological change, but that these shocks are affecting the two groups similarly.

The theme of this dissertation is the risk and return modeling of financial time series. The dissertation is broadly divided into three chapters; the first chapter focuses on measuring risks and uncertainty in the U.S. stock market; the second on measuring risks of individual financial assets; and the last chapter on predicting stock return. The first chapter studies the movement of the S&P 500 index driven by uncertainty and fear that cannot be explained by economic fundamentals. A new measure of uncertainty is introduced, using the tone of news media coverage on the equity market and the economy; aggregate holding of safe financial assets; and volatility in S&P 500 options trading. Major contributions of this chapter include uncovering a significant non-linear relationship between uncertainty and changes in the business cycle. An increase in uncertainty is found to be associated with drastic but short-lived falls in stock prices; while economic fundamentals have a small but prolonged effect on the stock market prices. The second chapter proposes a new Value at Risk (VaR) and Expected Shortfall (ES) estimation procedure that involves estimating the variance of return using conditional semiparametric approach introduced by Mishra, Su and Ullah (2010). Thus, estimation of variance is independent from the assumed distribution. Monte Carlo simulations are used to compare the performance of these new estimates using normal, Student-t, laplace, ARCH, GARCH, and GJR GARCH distributions. VaR and ES for Amazon, SP500, Microsoft, Nasdaq, USD/GBP and USD/Yen are estimated and the performance of each estimation method is further tested using a battery of tests. The third chapter explores whether non-parametric and semi parametric methods can reduce the bias in predictive regressions in the presence of high persistence in the predictive variables and non-linear relationship with the dependent variable. The predictive performance of the independent variables suggested in the literature to predict stock returns are re-evaluated in sample and out of sample using two step non-parametric and semi parametric models. Empirical RMSE are used to compare the proposed models with the historical average, OLS and non-parametric regression models.

This dissertation covers topics in estimation and forecasting under structural breaks, in

time-series and panel data models.

Chapter two considers the linear structural breaks model with m breaks (m + 1

regimes), and aim in improving the estimation of the parameters within each regime. We

form an optimal combined estimator of regression parameters based on combining restricted

estimator under the restriction of no breaks in the parameters, with unrestricted estimator

which considers the observations within each regime separately. We derive the analytical

finite sample risk and asymptotic risk and show that the risk of the combined estimator is

less than the unrestricted estimator. The simulation study and the empirical example of

forecasting the U.S. output growth confirm our theoretical findings.

Chapter three develops an optimal combined estimator to forecast out-of-sample

under structural breaks. We propose the combined estimator of the post-break estimator

with the full-sample estimator which uses all observations in the sample. Using a local

asymptotic framework, we obtain the asymptotic risk for the combined estimator and show

that it is strictly less than the risk of the post-break estimator, which is a common solution

for forecasting under structural breaks. We also introduce a semi-parametric estimator. Using a discrete kernel, this estimator assigns full weight of one to the post-break observations

and down-weights the pre-break sample observations. The kernel is found by cross validation. Simulation study and the empirical example of forecasting equity premium confirm

our analytical findings.

Chapter four proposes an efficient Stein-like shrinkage estimator for estimating the

slope parameters in the heterogeneous panel data models with cross-sectional dependence.

We combine the unrestricted estimator with the restricted one. The unrestricted estimator

estimates the parameters by considering the break points and only uses the observations

within each regime, while the restricted estimator estimates the parameters under the restriction of no breaks in the coefficients. We show analytically that the asymptotic risk of

the combined estimator is less than the unrestricted estimator. We also show the superiority of the combined estimator over the unrestricted estimator in terms of the mean square

forecast error. Simulation study verifies the main results of this chapter.

In the first two essays of this dissertation, I construct a dynamic stochastic production frontier incorporating the sluggish adjustment of inputs, measure the speed of adjustment of output in the short-run, and compare the technical efficiency estimates from such a dynamic model to those from a conventional static model that is based on the assumption that inputs are instantaneously adjustable in a production system. I provide estimation methods for technical efficiency of production units and the speed of adjustment of output for cases when they are time-invariant and when they vary with time. I also apply the methods to a panel dataset on private manufacturing establishments in Egypt.

The dynamic frontiers with time-invariant and time-varying technical efficiency are estimated using the System Generalized Method of Moments estimator and the Generalized Least Squares estimator with instrumental variables, respectively. The results for the Egyptian private manufacturing sectors show that the speed of adjustment of output is significantly lower than unity, the static model underestimates technical efficiency on average, and the dynamic model captures more variation in the time pattern of technical efficiency. Further, the ranking of production units based on their technical efficiency measures changes when the lagged adjustment process of inputs is taken into account.

In another essay, I characterize a class of rules for decision-making under the type of non-probabilistic uncertainty that was first axiomatically analyzed by Arrow and Hurwicz (1972). In this framework, the agent knows the possible states of the world and the outcome of each of her actions for each state, but does not have any information about the probabilities with which each state occurs. The decision-making rules characterized in this essay focus on the outcome(s) which occupy the middle position(s), when all outcomes of an action under different states of the world are arranged according to the agent's preference ordering defined over the outcomes. The existing literature in the Arrow-Hurwicz framework has mainly considered `max'-based or `min'-based rules and their variants, which reflect rather extreme forms of optimism or pessimism on the part of an agent. In contrast, the results of this essay characterize a decision rule that reflects a more `balanced' attitude of the agent.