Essays in Macroecometrics: methodological aspects and empirical applications

In the first chapter, I develop a panel no-cointegration test which extends Pesaran, Shin and Smith (2001)'s bounds test to the panel framework by considering the individual regressions in a Seemingly Unrelated Regression (SUR) system. This allows to take into account unobserved common factors that contemporaneously affect all the units of the panel and provides, at the same time, unit-specific test statistics. Moreover, the approach is particularly suited when the number of individuals of the panel is small relatively to the number of time series observations. I develop the algorithm to implement the test and I use Monte Carlo simulation to analyze the properties of the test. The small sample properties of the test are remarkable, compared to its single equation counterpart. I illustrate the use of the test through a test of Purchasing Power Parity in a panel of EU15 countries. In the second chapter of my PhD thesis, I verify the Expectation Hypothesis of the Term Structure in the repurchasing agreements (repo) market with a new testing approach. I consider an "inexact" formulation of the EHTS, which models a time-varying component in the risk premia and I treat the interest rates as a non-stationary cointegrated system. The effect of the heteroskedasticity is controlled by means of testing procedures (bootstrap and heteroskedasticity correction) which are robust to variance and covariance shifts over time. I fi#nd that the long-run implications of EHTS are verified. A rolling window analysis clarifies that the EHTS is only rejected in periods of turbulence of #financial markets. The third chapter introduces the Stata command "bootrank" which implements the bootstrap likelihood ratio rank test algorithm developed by Cavaliere et al. (2012). The command is illustrated through an empirical application on the term structure of interest rates in the US.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Seemingly unrelated linear regression for contaminated data based on Gaussian mixtures

In this thesis, new classes of models for multivariate linear regression defined by finite mixtures of seemingly unrelated contaminated normal regression models and seemingly unrelated contaminated normal cluster-weighted models are illustrated. The main difference between such families is that the covariates are treated as fixed in the former class of models and as random in the latter. Thus, in cluster-weighted models the assignment of the data points to the unknown groups of observations depends also by the covariates. These classes provide an extension to mixture-based regression analysis for modelling multivariate and correlated responses in the presence of mild outliers that allows to specify a different vector of regressors for the prediction of each response. Expectation-conditional maximisation algorithms for the calculation of the maximum likelihood estimate of the model parameters have been derived. As the number of free parameters incresases quadratically with the number of responses and the covariates, analyses based on the proposed models can become unfeasible in practical applications. These problems have been overcome by introducing constraints on the elements of the covariance matrices according to an approach based on the eigen-decomposition of the covariance matrices. The performances of the new models have been studied by simulations and using real datasets in comparison with other models. In order to gain additional flexibility, mixtures of seemingly unrelated contaminated normal regressions models have also been specified so as to allow mixing proportions to be expressed as functions of concomitant covariates. An illustration of the new models with concomitant variables and a study on housing tension in the municipalities of the Emilia-Romagna region based on different types of multivariate linear regression models have been performed.