Paolo Giordani

Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models

Time series subject to parameter shifts of random magnitude and timing are commonly modeled with a change-point approach using Chibs algorithm to draw the break dates. We outline some advantages of an alternative approach in which breaks come through mixture distributions in state innovations, and for which the sampler of Gerlach, Carter, and Kohn allows reliable and efficient inference. We show how the same sampler can be used to model shifts in variance that occur independently of shifts in other parameters and how to draw the break dates efficiently when regime durations follow a Poisson process. Finally, we introduce to the time series literature the concept of adaptive Metropolis–Hastings sampling for discrete latent variable models. We develop an easily implemented adaptive algorithm that improves on the work of Gerlach et al. and promises to significantly reduce computing time in a variety of problems including mixture innovation, change-point, regime switching, and outlier detection. The efficien...

Adaptive Independent Metropolis–Hastings by Fast Estimation of Mixtures of Normals

Adaptive Metropolis–Hastings samplers use information obtained from previous draws to tune the proposal distribution automatically and repeatedly. Adaptation needs to be done carefully to ensure convergence to the correct target distribution because the resulting chain is not Markovian. We construct an adaptive independent Metropolis–Hastings sampler that uses a mixture of normals as a proposal distribution. To take full advantage of the potential of adaptive sampling our algorithm updates the mixture of normals frequently, starting early in the chain. The algorithm is built for speed and reliability and its sampling performance is evaluated with real and simulated examples. Our article outlines conditions for adaptive sampling to hold. An online supplement to the article gives a proof of convergence and Gauss code to implement the algorithms.

Reconsidering the Role of Money for Output, Prices and Interest Rates

New Keynesian models of monetary policy assign no role to monetary aggregates, in the sense that the level of output, prices, and interest rates can be determined without knowledge of the quantity of money. We evaluate the empirical validity of this prediction by studying the effects of shocks to monetary aggregates using an identified VAR. Shocks to monetary aggregates are isolated by means of identifying restrictions suggested by this class of models. Contrary to the theoretical predictions, shocks to broad monetary aggregates have substantial and persistent effects on output and prices.

Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios

We demonstrate improvements in predictive power when introducing spline functions to take account of highly non-linear relationships between firm failure and earnings, leverage, and liquidity in a logistic bankruptcy model. Our results show that modeling excessive non-linearities yields substantially improved bankruptcy predictions, on the order of 70 to 90 percent, compared with a standard logistic model. The spline model provides several important and surprising insights into non-monotonic bankruptcy relationships. We find that low-leveraged and highly profitable firms are riskier than given by a standard model. These features are remarkably stable over time, suggesting that they are of a structural nature.

Flexible Multivariate Density Estimation With Marginal Adaptation

This article is concerned with multivariate density estimation. We discuss deficiencies in two popular multivariate density estimators—mixture and copula estimators, and propose a new class of estimators that combines the advantages of both mixture and copula modeling, while being more robust to their weaknesses. Our method adapts any multivariate density estimator using information obtained by separately estimating the marginals. We propose two marginally adapted estimators based on a multivariate mixture of normals and a mixture of factor analyzers estimators. These estimators are implemented using computationally efficient split-and-elimination variational Bayes algorithms. It is shown through simulation and real-data examples that the marginally adapted estimators are capable of improving on their original estimators and compare favorably with other existing methods. Supplementary materials for this article are available online.

Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures

We model a regression density nonparametrically so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the com- ponents changing smoothly as a function of the covariates. The model extends existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need a lot fewer heteroscedastic components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mech- anism that prevents overfitting and makes it feasible to fit high-dimensional nonparametric surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities.

Constitutions and Central Bank Independence: An Objection to McCallum's Second Fallacy

Most of the literature on monetary policy delegation assumes that the government can credibly commit to the delegation contract, an assumption criticized by McCallum. This paper provides foundations for the assumption that renegotiating a delegation contract can be costly by illustrating how political institutions can generate inertia in recontracting, reduce the gains from it or prevent it altogether. Once the nature of renegotiation costs has been clarified, it is easier to see why certain institutions can mitigate or solve dynamic inconsistencies better than others. The paper points to institutions which give Western democracies the technology to make credible delegation commitments, and argues that the ECB is an example of credible delegation.

Stronger Evidence of Long-Run Neutrality: A Comment on Bernanke and Mihov

Few propositions in macroeconomics are less controversial than long-run money neutrality, yet clear and robust empirical support has not been found in time series studies. Bernanke and Mihov (1998) are comparatively successful in this hunt, but their output response to monetary policy shocks remains stubbornly persistent. This paper argues that the omission of a measure of output gap from the VAR estimated by Bernanke and Mihov lies at the heart of this excessive persistence. In the theoretical framework of a New Keynesian model similar to that of Svensson (1997) and Clarida, Gali and Gertler (1999), I prove that this omission induces persistence overestimation under relatively mild assumptions. The inclusion of a proxy for the output gap in the VAR is then shown to drastically increase the evidence for long-run money neutrality on US data, as predicted by the theoretical analysis.

Up the Stairs, Down the Elevator: Valuation Ratios and Shape Predictability in the Distribution of Stock Returns

While a large literature on return predictability has shown a link between valuation levels and expected rates of returns, we document a robust link between valuation levels and the shape of the distribution of cumulative (up to 24 months) total returns. Return distributions become more asymmetric and negatively skewed when valuation levels are high. In contrast, they are roughly symmetric when valuation levels are low. These results shed some light on how equity prices regress back to their means conditional on valuation levels and have important practical implications for risk measurement and asset management.