Bayesian applications in dynamic econometric models

The purpose of this thesis is to provide a few new ideas to the field of Bayesian econometrics. In particular, the focus of the thesis is on analyzing dynamic econometric models. In the first essay, we provide an easily implementable method for the Bayesian analysis of a simple hybrid DSGE model of Clarida et al. (1999). The forecasting properties of the model are tested against commonly used forecasting tools, such as Bayesian VARs and naïve forecasts based on univariate random walks. In particular, the predictability of three key macroeconomic-variables, inflation, short-term nominal interest rate and a measure of output gap, are studied using quarterly ex post and real-time U.S. data.Our posterior evidence implies that the simple hybrid model captures the predictable behavior of the three U.S. key macroeconomic variables very well. The result is very interesting, since several recent Bayesian papers have suggested different ways to improve the forecasting performance of DSGE models at the cost of increasing the complexity of model mechanisms, thus decreasing the practicability of these approaches. In the second essay, using GARCH-in-Mean models based on the following Intertemporal Capital Asset Pricing Model Et-1(rt) = μ0 + μ1Vart-1(rt) for the expected excess return rt, we study the robustness of the risk-return relationship in U.S. stock market returns. The issue is important, since unnecessarily including μ0 in the previous expression is known to distort conclusions, while restricting μ0 to zero forces the expected excess return to equal the risk-free interest rate under the hypothesis μ1 = 0. The latter is in conflict with the stock premium puzzle literature. To check the empirical relevance of the theoretical restriction μ0 = 0, we assume a zero mean normal prior distribution for μ0 with several alternative plausible values for its prior variance to see how the tightness of this prior assumption affects the estimation results.Our evidence indicates that the existence of a risk-return relationship is fairly robust in that it does not strongly depend on the prior beliefs concerning the intercept, especially when the true value of μ0 is sufficiently close to zero. In the third essay, we expand Kleibergen and Zivot’s (2003) Bayesian Two Stage (B2S) model by allowing for unequal variances. To the best of our knowledge there is no single Bayesian study of instrumental variable (IV) models with unequal variances, although from the Bayesian point of view modelling heteroscedasticity should improve the precision of estimates and the quality of predictive inference. As an application we present a cross-country Cobb-Douglas production function estimation, since the problems of endogeneity and heteroscedasticity are well documented in the cross-country growth literature. In the fourth essay, we provide a simple epidemiology model where households, when forming their inflation expectations, rationally adopt the past release of inflation with certain probability rather than the forward-looking newspaper forecast as suggested in previous literature. The posterior model probabilities based on the Michigan survey data strongly support the proposed model.We also extend the agent-based epidemiology model by deriving for it a simple adaptation, which is suitable for estimation. Our results show that this model is able to capture the heterogeneity in households’ expectations very well. In the fifth essay, the Bayesian structural vector autoregressive model and the Finnish aggregate infrastructure capital series from 1860 to 2003 are used to explore how government infrastructure policy affects long-run output growth. The Finnish data is used, since to our knowledge the Finnish land and water construction investments series is the best available sufficiently long time series on aggregate infrastructure investments. We base our conclusions on posterior analysis, since it allows us to draw exact inference on parameters with near non-stationary data. We find strong and robust support in the Finnish data to indicate that permanent changes in government infrastructure policy can have permanent effects on the growth rate of output