Prior elicitation in multiple change-point models

This paper discusses Bayesian inference in change-point models. Existing approaches involve placing a (possibly hierarchical) prior over a known number of change-points. We show how two popular priors have some potentially undesirable properties (e.g. allocating excessive prior weight to change-points near the end of the sample) and discuss how these properties relate to imposing a fixed number of changepoints in-sample. We develop a new hierarchical approach which allows some of of change-points to occur out-of sample. We show that this prior has desirable properties and handles the case where the number of change-points is unknown. Our hierarchical approach can be shown to nest a wide variety of change-point models, from timevarying parameter models to those with few (or no) breaks. Since our prior is hierarchical, data-based learning about the parameter which controls this variety occurs

Are apparent findings of nonlinearity due to structural instability in economic time series?

Many modelling issues and policy debates in macroeconomics depend on whether macroeconomic times series are best characterized as linear or nonlinear. If departures from linearity exist, it is important to know whether these are endogenously generated (as in, e.g., a threshold autoregressive model) or whether they merely reflect changing structure over time. We advocate a Bayesian approach and show how such an approach can be implemented in practice. An empirical exercise involving several macroeconomic time series shows that apparent findings of threshold type nonlinearities could be due to structural instability

Prior Elicitation in Multiple Change-point Models

This paper discusses Bayesian inference in change-point models. The main existing approaches either attempt to be noninformative by using a Uniform prior over change-points or use an informative hierarchical prior. Both these approaches assume a known number ofchange-points. We show how they have some potentially undesirable properties and discuss how these properties relate to the imposition of a …xed number of changepoints. We develop a new Uniform prior which allows some of the change-points to occur out-of sample. This prior has desirable properties, can reasonably be interpreted as “noninformative” and handles the case where the number of change-points is unknown. We show how the general ideas of our approach can be extended to informative hierarchical priors. With arti…cial data and two empirical illustrations, we show how these di¤erent priors can have a substantial impact on estimation and prediction even with moderately large data sets.

Forecasting and Estimating Multiple Change-point Models with an Unknown Number of Change-points

This paper develops a new approach to change-point modeling that allows the number of change-points in the observed sample to be unknown. The model we develop assumes regime durations have a Poisson distribution. It approximately nests the two most common approaches: the time varying parameter model with a change-point every period and the change-point model with a small number of regimes. We focus considerable attention on the construction of reasonable hierarchical priors both for regime durations and for the parameters which characterize each regime. A Markov Chain Monte Carlo posterior sampler is constructed to estimate a change-point model for conditional means and variances. Our techniques are found to work well in an empirical exercise involving US GDP growth and inflation. Empirical results suggest that the number of change-points is larger than previously estimated in these series and the implied model is similar to a time varying parameter (with stochastic volatility) model.Bayesian; structural break; Markov Chain Monte Carlo; hierarchical prior

Understanding Liquidity and Credit Risks in the Financial Crisis

This paper develops a structured dynamic factor model for the spreads between London Interbank Offered Rate (LIBOR) and overnight index swap (OIS) rates for a panel of banks. Our model involves latent factors which reflect liquidity and credit risk. Our empirical results show that surges in the short term LIBOR-OIS spreads during the 2007-2009 fi…nancial crisis were largely driven by liquidity risk. However, credit risk played a more signi…cant role in the longer term (twelve-month) LIBOR-OIS spread. The liquidity risk factors are more volatile than the credit risk factor. Most of the familiar events in the fi…nancial crisis are linked more to movements in liquidity risk than credit risk.

Modeling the Dynamics of Inflation Compensation

This paper investigates the relationship between short-term and long-term ination expectations using daily data on ination compen- sation. We use a exible econometric model which allows us to uncover this relationship in a data-based manner. We relate our …ndings to the issue of whether ination expectations are anchored, unmoored or contained. Our empirical results indicate no support for either unmoored or …rmly anchored ination expectations. Most evidence indicates that ination expectations are contained.

On Identification of Bayesian DSGE Models*

In recent years there has been increasing concern about the identification of parameters in dynamic stochastic general equilibrium (DSGE) models. Given the structure of DSGE models it may be di¢ cult to deter- mine whether a parameter is identi?ed. For the researcher using Bayesian methods, a lack of identi?cation may not be evident since the posterior of a parameter of interest may di¤er from its prior even if the parameter is unidentified. We show that this can even be the case even if the priors assumed on the structural parameters are independent. We suggest two Bayesian identification indicators that do not su¤er from this difficulty and are relatively easy to compute. The first applies to DSGE models where the parameters can be partitioned into those that are known to be identified and the rest where it is not known whether they are identi?ed. In such cases the marginal posterior of an unidenti?ed parameter will equal the posterior expectation of the prior for that parameter conditional on the identified parameters. The second indicator is more generally applicable and considers the rate at which the posterior precision gets updated as the sample size (T) is increased. For identi?ed parameters the posterior precision rises with T, whilst for an unidentified parameter its posterior precision may be updated but its rate of update will be slower than T. This result assumes that the identified parameters are pT-consistent, but similar differential rates of updates for identified and unidentified parameters can be established in the case of super consistent estimators. These results are illustrated by means of simple DSGE models.Bayesian identification, DSGE models, posterior updating, New Keynesian Phillips Curve.

The Dynamics of UK and US Inflation Expectations

This paper investigates the relationship between short term and long term inflation expectations in the US and the UK with a focus on inflation pass through (i.e. how changes in short term expecta tions affect long term expectations). An econometric methodology is used which allows us to uncover the relationship between inflation pass through and various explanatory variables. We relate our empirical results to theoretical models of anchored, contained and unmoored inflation expectations. For neither country do we …find anchored or unmoored inflation expectations. For the US, contained inflation expectations are found. For the UK, our fi…ndings are not consistent with the speci…c model of contained inflation expectations presented here, but are consistent with a broader view of expectations being constrained by the existence of an inflation target.

Bayesian analysis of endogenous delay threshold models

We develop Bayesian methods of analysis for a new class of threshold autoregressive models: endogenous delay threshold. We apply our methods to the commonly used sunspot data set and find strong evidence in favor of the Endogenous Delay Threshold Autoregressive (EDTAR) model over linear and traditional threshold autoregressions