In recent years the use of Bayesian methods in macroeconometrics has become more and more widespread. Since the early contribution of Doan, Litterman and Sims (1984) and Litterman (1986), advances insimulation methods and computing technology offered a chance to take a Bayesian perspective in severalfields of applied macroeconomics, including the direct estimation of the structural parameters of dynamic stochastic general equilibrium models (Dejong, Ingram andWhiteman (2000), Smets andWouters (2003), Adolfson, Linde and Villani (2005)), the detection of structural changes in the economy (Sims and Zha
(2006)), the estimation of time-varying VAR models (Gambetti (2005)), of Panel VAR models (Canova and Ciccarelli (2004)) and of factor-augmented VARs (Kose, Otrok and Whiteman (2003)). One of the main reasons underlying the recent success of Bayesian techniques is that they provide tools to deal with some of the intractable problems of macroeconometric modelling. Large quantitative models built in the spirit of the simultaneous equation tradition and currently used to guide policy-making have been criticised both with regard to their weak theoretical foundations and to the way they are estimated, which often neglects the nature of joint probability process of the time series used to estimate the model. The search for more appropriate modelling strategies has generated two alternative classes of models, dynamic stochastic general equilibrium models (DSGE) and vector autoregressions (VARs), which still
suffer of a number of difficulties for being used as tools for policy analysis. DSGEs, while being much richer than just a few years ago, still have a too stylized structure and do not match the level of detail and fit of models required for policy-making. Classical hypothesis testing has big difficulties in dealing with this class of models: when applied to highly stylized, and therefore intrinsically false, models it leads to a rejection of DSGEs against more general specifications. As Sims (2004) points out the frequentist
hypothesis testing methodology “is silent ... when all the interesting theories (say DSGE models) are rejected in favor of an uninteresting (say reduced form VAR) model”. On the other hand, the heavy parameterization of VAR models translates quickly in overfitting when the scale of the model increases. Bayesian techniques provide a flexible, rigorous, and relatively simple framework to deal with these issues. In a Bayesian perspective, DSGEs are no longer “accepted” or “rejected” in a classical sense. Instead, it is correctly recognized that they are not the true data generating process and have only a probability of fairly representing the behavior of the actual economy. The aim of a Bayesian estimation is to deliver this probability, conditional on observed data and researcher’s beliefs. The latter are specified in the form of prior distributions, which play a fundamental role in the estimation exercise, by allowing to properly weight different models, improve the curvature of the posterior distributions on dimensions along which the likelihood is flat and impose non-dogmatic restrictions. This flexibility makes the use of prior distributions particularly suitable for the dimensionality problems that arise in the estimation of large VARs. Given the lack of degrees of freedom implied by their rich parameterization, the estimation of these models relies heavily on exclusion restrictions, which may lead to miss potentially important sources of information. Bayesian VARs impose restrictions in probabilistic terms, thus allowing the data to bring a contribution when their information content is substantial. As such, restrictions imposed by prior distributions turn out to be a device to select only the true signals coming from the data.
This thesis is a collection of three essays, representing three separate applications of Bayesian inference techniques to a macroeconometric model.
In the first chapter I estimate a small monetary DSGE model with Bayesian methods, in order to assess whether a non-Ricardian fiscal-monetary policy mix has been in place in the U.S. during the 1970s. The fiscal theory of the price level suggests that a non-Ricardian policy arrangement, in which fiscal policy is set without having regard to the sustainability of the public debt, can be a source of inflation variability, as opposed to the traditional monetary theory, according to which an excessive inflation variability is the outcome of a loose monetary policy. It is found that the data are informative about the structural parameters of the model and, from the analysis of posterior distributions, that a non-Ricardian regime seems to be an implausible hypothesis to explain the determinants of U.S. inflation during the period considered. In the second chapter I examine the transmission of monetary and technology shocks between the U.S. and the euro area, by fitting a time-varying coefficients Bayesian VAR. The identification of the structural shocks is achieved by weak sign restrictions over the response of a set of endogenous variables. I find that the response of the two economic regions is asymmetric, with euro area responding more than the U.S. to shocks originating in the other country. Furthermore, the response of endogenous variables to domestic technology and monetary policy shocks seems to have changed over time, both in size and in volatility. In the third chapter I analyze in a multi-country framework whether the behavior of real and nominal exchange rates after a monetary policy shock has changed over time. Previous empirical studies (e.g. Eichenbaum and Evans (1995)) document a delayed overshooting of U.S. exchange rates conditional on a monetary policy shock, which stands in sharp contrast with the baseline theory, according to which the maximal response to a monetary policy shock should occur on impact. The main finding of the analysis of this chapter is that the U.S. exchange rate response to a domestic monetary policy shock has changed substantially over the last 15 years: the delayed overshooting behavior, which is evident in the impulse responses of the early 1990s, has attenuated continuously during that decade; in recent years the U.S. exchange rates response has become much more in line with the predictions of the overshooting hypothesis. Instead, monetary policy shocks arising in the U.K. and Germany generate delayed overshooting of exchange rates over the whole period.
The contribution of this thesis is twofold: on empirical grounds it brings additional new evidence on some important issues concerning monetary policies and business cycles; on the methodological ground it develops methods to compute dynamic responses of the endogenous variables to exogenous shocks in heavily parameterized structural models.
