My thesis consists of three chapters. The first chapter uses the Factor-augmented Error Correction Model in model averaging for predictive regressions, which provides significant improvements with large datasets in areas where the individual methods have not. I allow the candidate models to vary by the number of dependent variable lags, the number of factors, and the number of cointegration ranks. I show that the leave-h-out cross-validation criterion is an asymptotically unbiased estimator of the optimal mean squared forecast error, using either the estimated cointegration vectors or the nonstationary regressors. Empirical results demonstrate that including cointegration relationships significantly improves long-run forecasts of a standard set of macroeconomic variables. I also estimate simulation-based prediction intervals for six real and nominal macroeconomics variables. The results are consistent with the point estimates, which further support the usefulness of cointegration in long-run forecasts.<div><br></div><div>The second chapter is a Monte Carlo study comparing the finite sample performance of six recently proposed estimation methods designed for large-dimensional regressions with endogeneity. The methods are based on combining shrinkage estimation with two-stage least squares (2SLS) or generalized method of moments(GMM), where both the number of regressors and instruments can be large. The methods are evaluated in terms of bias and mean squared error of the estimators. I consider a variety of designs with practically relevant features such as weak instruments and heteroskedasticity as well as cases where the number of observations is smaller/larger than the number of regressors/instruments. The consistency results show that the methods using GMM with shrinkage provide smaller estimation errors than the methods using 2SLS with shrinkage. Moreover, the results support the use of cross-validation to select tuning parameters if theoretically derived parameters are unavailable. Lastly, the results indicate that all instruments should correlate with at least one endogenous regressor to ensure estimation consistency.<br></div><div><br></div><div>The third chapter is coauthored with Mohitosh Kejriwal. We present new evidence on the nexus between democracy and growth employing the dynamic common correlated effects (DCCE) approach advanced by Chudik and Pesaran (2015), which is robust to both parameter heterogeneity and cross-section dependence. The DCCE results indicate a positive and statistically significant effect of democracy on economic growth, with a point estimate between approximately 1.5-2% depending on the specification. We complement our estimates with a battery of diagnostic tests for heterogeneity and cross-section dependence that corroborate the use of the DCCE approach.<br></div>

<div>This thesis has three major chapters. Structural estimation of non-homothetic demands is the element that is the most common across the three papers in which structural parameters from the data.<br></div><div><br></div><div><b>First Chapter</b>: Preference structures in applied general equilibrium models are commonly in favor of the family of linear expenditure system (LES) due to the desire for global regularity and applicability, while other emerging preference functions include the constant-elasticity-of-substitution (CES) forms that are used as sub-utility functions to fulfil regularity conditions with additional flexibilities. Hanoch (1975) introduces indirect, implicit additive relationships—a generalization of the CES—to obtain more flexible demand relationships that are globally regular. These preference relationships unlink substitution effects from income effects in ways that go beyond relaxation of homotheticity, and are more flexible than their direct dual. However, the estimation of these models as demand systems has proven to be challenging, and most published work in this area has focused on estimation approaches that involve approximations or that cannot fully identify parameter values in the preference relationships. Essay one introduces a direct approach which avoids approximations and allows parameters to be identified. We demonstrate the estimation using the readily accessible Global Trade Analysis Project (GTAP) and the confidential World Bank (International Comparison Program) databases, estimating the constant difference of elasticity or CDE directly in a maximum likelihood framework. In doing this, we show that the global regularity conditions stated in Hanoch (1975) can be slightly relaxed, and that the relaxed parametric conditions facilitate estimation. We introduce a normalization scheme that is beneficial for the scaling of the parameter values and which appears to have little impact on the economic performance of the estimated system. We develop a numerical test that justifies the normalization scheme. The series of procedures developed in this paper applied to this empirical example is generalized to solve many other econometric problems of general demand models of the Bergson family and those that are under-identified using reduced-form approaches. </div><div><br></div><div><b>Second Chapter</b>: This paper presents a general equilibrium gravity model of trade based on the constant difference of elasticities of substitution preferences. Hanoch (1975) illustrates these preferences' advantages in terms of parsimony and flexibility. This paper introduces a parsimonious, non-homothetic and globally well-behaved demand model into the gravity model that both separates substitution effects from income effects and has non-constant substitution elasticities. These features of the demand model---together with the structural estimation procedure devised in this paper---allow nesting several prominent theoretical motivations for the gravity model, and exploring the merits of this more general model. They also allow identification of the elasticity of trade costs with respect to distance and asymmetric border coefficients from the elasticity of trade flows with respect to trade costs. Most previous studies cannot separately identify these structural parameters. </div><div><br></div><div><b>Third Chapter</b>: The primary advantage of structural approaches to estimating the gravity model of trade is that they allow a transparent mapping of regression coefficients to structural parameters. Unfortunately, as shown in essay two, existing structural estimation methods are unable to separately identify trade costs and the trade elasticity without incorporating external data. We demonstrate that theoretical structure is alone sufficient for identifying all of the structural parameters of the canonical constant elasticity of substitution (CES) gravity model. We accomplish this by adopting an implicitly indirect representation of utility and estimating structurally using a mathematical program with equilibrium constraints. Our estimate of the elasticity of substitution is much smaller than in much of the rest of the literature, an outcome that we attribute to Pigou's Law, which ties income and substitution elasticities together in demand systems that assume additive preferences. This restriction is undesirable in demand systems, generally, and is a critical weakness for the canonical gravity model, a model that is commonly used to interpret the geographic trade pattern and to infer the welfare gains from trade. We demonstrate a non-homothetic CES model that both achieves identification and relaxes this restriction. Our counterfactual results based on the model suggest that the combination of a lower elasticity and lower trade costs generate a larger welfare change due to border removal compared to the CES model.<br></div>