Essays on Models with Time-Varying Parameters for Forecasting and Policy Analysis
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The aim of this thesis is the development and the application of econometric models with time-varying parameters in a policy environment. The popularity of these methods has run in parallel with advances in computing power, which has made feasible estimation methods that until the late ‘90s would have been unfeasible. Bayesian methods, in particular, benefitted from these technological advances, as sampling from complicated posterior distributions of the model parameters became less and less time-consuming. Building on the seminal work by Carter and Kohn (1994) and Jacquier, Polson, and Rossi (1994), bayesian algorithms for estimating Vector Autoregressions (VARs) with drifting coefficients and volatility were independently derived by Cogley and Sargent (2005) and Primiceri (2005). Despite their increased popularity, bayesian methods still suffer from some limitations, from both a theoretical and a practical viewpoint. First, they typically assume that parameters evolve as independent driftless random walks. It is therefore unclear whether the output that one obtains from these estimators is accurate when the model parameters are generated by a different stochastic process. Second, some computational limitations remain as only a limited number of time series can be jointly modeled in this environment. These shortcomings have prompted a new line of research that uses non-parametric methods to estimate random time-varying coefficients models. Giraitis, Kapetanios, and Yates (2014) develop kernel estimators for autoregressive models with random time-varying coefficients and derive the conditions under which such estimators consistently recover the true path of the model coefficients. The method has been suitably adapted by Giraitis, Kapetanios, and Yates (2012) to a multivariate context. In this thesis I make use of both bayesian and non-parametric methods, adapting them (and in some cases extending them) to answer some of the research questions that, as a Central Bank economist, I have been tackling in the past five years. The variety of empirical exercises proposed throughout the work testifies the wide range of applicability of these models, be it in the area of macroeconomic forecasting (both at short and long horizons) or in the investigation of structural change in the relationship among macroeconomic variables. The first chapter develops a mixed frequency dynamic factor model in which the disturbances of both the latent common factor and of the idiosyncratic components have time varying stochastic volatility. The model is used to investigate business cycle dynamics in the euro area, and to perform point and density forecast. The main result is that introducing stochastic volatility in the model contributes to an improvement in both point and density forecast accuracy. Chapter 2 introduces a nonparametric estimation method for a large Vector Autoregression (VAR) with time-varying parameters. The estimators and their asymptotic distributions are available in closed form. This makes the method computationally efficient and capable of handling information sets as large as those typically handled by factor models and Factor Augmented VARs (FAVAR). When applied to the problem of forecasting key macroeconomic variables, the method outperforms constant parameter benchmarks and large Bayesian VARs with time-varying parameters. The tool is also used for structural analysis to study the time-varying effects of oil price innovations on sectorial U.S. industrial output. Chapter 3 uses a bayesian VAR to provide novel evidence on changes in the relationship between the real price of oil and real exports in the euro area. By combining robust predictions on the sign of the impulse responses obtained from a theoretical model with restrictions on the slope of the oil demand and oil supply curves, oil supply and foreign productivity shocks are identified. The main finding is that from the 1980s onwards the relationship between oil prices and euro area exports has become less negative conditional on oil supply shortfalls and more positive conditional on foreign productivity shocks. A general equilibrium model is used to shed some light on the plausible reasons for these changes. Chapter 4 investigates the failure of conventional constant parameter models in anticipating the sharp fall in inflation in the euro area in 2013- 2014. This forecasting failure can be partly attributed to a break in the elasticity of inflation to the output gap. Using structural break tests and non-parametric time varying parameter models this study shows that this elasticity has indeed increased substantially after 2013. Two structural interpretations of this finding are offered. The first is that the increase in the cyclicality of inflation has stemmed from lower nominal rigidities or weaker strategic complementarity in price setting. A second possibility is that real time output gap estimates are understating the amount of spare capacity in the economy. I estimate that, in order to reconcile the observed fall in inflation with the historical correlation between consumer prices and the business cycle, the output gap should be wider by around one third.
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