Richard Paap

Real-Time Inflation Forecasting in a Changing World

This paper revisits inflation forecasting using reduced-form Phillips curve forecasts, that is, inflation forecasts that use activity and expectations variables. We propose a Phillips-curve-type model that results from averaging across different regression specifications selected from a set of potential predictors. The set of predictors includes lagged values of inflation, a host of real-activity data, term structure data, nominal data, and surveys. In each individual specification, we allow for stochastic breaks in regression parameters, where the breaks are described as occasional shocks of random magnitude. As such, our framework simultaneously addresses structural change and model uncertainty that unavoidably affect Phillips-curve-based predictions. We use this framework to describe personal consumption expenditure (PCE) deflator and GDP deflator inflation rates for the United States in the post-World War II period. Over the full 1960-2008 sample, the framework indicates several structural breaks across different combinations of activity measures. These breaks often coincide with policy regime changes and oil price shocks, among other important events. In contrast to many previous studies, we find less evidence of autonomous variance breaks and inflation gap persistence. Through a real-time out-of-sample forecasting exercise, we show that our model specification generally provides superior one-quarter-ahead and one-year-ahead forecasts for quarterly inflation relative to an extended range of forecasting models that are typically used in the literature.

A nonlinear long memory model, with an application to US unemployment

Two important empirical features of US unemployment are that shocks to the series seem rather persistent and that it seems to rise faster during recessions than that it falls during expansions. To jointly capture these features of long memory and nonlinearity, we put forward a new time series model and evaluate its empirical performance. We find that the model describes the data rather well and that it outperforms related competitive models on various measures of fit.

Priors, posteriors and bayes factors for a Bayesian analysis of cointegration

Cointegration occurs when the long-run multiplier matrix of a vector autoregressive model exhibits rank reduction. Using a singular value decomposition of the unrestricted long-run multiplier matrix, we construct a parameter that reflects the presence of rank reduction. Priors and posteriors of the parameters of the cointegration model follow from conditional priors and posteriors of the unrestricted long-run multiplier matrix given that the parameter that reflects rank reduction is equal to zero. This idea leads to a complete Bayesian framework for cointegration analysis. It includes prior specification, simulation schemes for obtaining posterior distributions and determination of the cointegration rank via Bayes factors. We apply the proposed Bayesian cointegration analysis to the Danish data of Johansen and Juselius (Oxford Bull. Econom. Stat. 52 (1990) 169).

Retrieving Unobserved Consideration Sets from Household Panel Data

The authors propose a new model to capture unobserved consideration from discrete choice data. This approach allows for unobserved dependence in consideration among brands, easily copes with many brands, and accommodates different effects of the marketing mix on consideration and choice as well as unobserved consumer heterogeneity in both processes. An important goal of this study is to establish the validity of the existing practice to infer consideration sets from observed choices in panel data. The authors show with experimental data that underlying consideration sets can be reliably retrieved from choice data alone and that consideration is positively affected by display and shelf space. Next, the model is applied to Information Resources Inc. panel data. The findings suggest that promotion effects are larger when they are included in the consideration stage of the two-stage model than in a single-stage model. The authors also find that consideration covaries across brands and that this covariation is mainly driven by unobserved consumer heterogeneity. Finally, the authors show the implications of the model for promotion planning relative to a more standard model of choice.

A Hierarchical Bayes Error Correction Model to Explain Dynamic Effects of Price Changes

The authors put forth a sales response model to explain the differences in immediate and dynamic effects of promotional prices and regular prices on sales. The model consists of a vector autoregression that is rewritten in error correction format, which allows the authors to disentangle the immediate effects from the dynamic effects. In a second level of the model, the immediate price elasticities, the cumulative promotional price elasticity, and the long-term regular price elasticity are correlated with various brand-specific and category-specific characteristics. The model is applied to seven years of data on weekly sales of 100 different brands in 25 product categories. The authors find many significant moderating effects on the elasticity of price promotions. Brands in categories that are characterized by high price differentiation and that constitute a lower share of budget are less sensitive to price discounts. Deep price discounts increase the immediate price sensitivity of customers. The authors also find significant effects for the cumulative elasticity. The immediate effect of a regular price change is often close to zero. The long-term effect of such a regular price decrease usually amounts to an increase in sales. This is especially true in categories that are characterized by a large price dispersion and frequent price promotions and for hedonic, nonperishable products.

Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to U.S. Consumption and Income

Stylized facts show that average growth rates of U.S. per capita consumption and income differ in recession and expansion periods. Because a linear combination of such series does not have to be a constant mean process, standard cointegration analysis between the variables to examine the permanent income hypothesis may not be valid. To model the changing growth rates in both series, we introduce a multivariate Markov trend model that accounts for different growth rates in consumption and income during expansions and recessions and across variables within both regimes. The deviations from the multivariate Markov trend are modeled by a vector autoregression (VAR) model. Bayes estimates of this model are obtained using Markov chain Monte Carlo methods. The empirical results suggest the existence of a cointegration relation between U.S. per capita disposable income and consumption, after correction for a multivariate Markov trend. This result is also obtained when per capita investment is added to the VAR.

Modelling day-of-the-week seasonality in the S&P 500 index

A time series model is proposed that describes the day-of-the-week seasonality in returns as well as in volatility of the daily S&P 500 index. The model is a periodic autoregression with periodically integrated GARCH [PAR-PIGARCH]. With this statistically adequate model, positive (negative) autocorrelation is found in the returns on Monday (Tuesday). Day-of-the-week variation in the persistence of volatility is also found.

What are the advantages of MCMC based inference in latent variable models

Recent developments in Markov chain Monte Carlo [MCMC] methods have increased the popularity of Bayesian inference in many fields of research in economics, such as marketing research and financial econometrics. Gibbs sampling in combination with data augmentation allows inference in statistical/econometric models with many unobserved variables. The likelihood functions of these models may contain many integrals, which often makes a standard classical analysis difficult or even unfeasible. The advantage of the Bayesian approach using MCMC is that one only has to consider the likelihood function conditional on the unobserved variables. In many cases this implies that Bayesian parameter estimation is faster than classical maximum likelihood estimation. In this paper we illustrate the computational advantages of Bayesian estimation using MCMC in several popular latent variable models.

Does seasonality influence the dating of business cycle turning points

The Markov switching regime model is often applied to dating business cycle turning points. Typically, this model is then considered for quarterly seasonally adjusted macroeconomic time series. In this paper we show through simulations and empirical examples that, when the Markov model is applied to quarterly seasonally adjusted data, one may find different peaks and troughs and hence a different characterization of the business cycle. We also find different dynamic relations between macroeconomic variables across the business cycle. In other words, we answer the question in the title affirmatively.

Modelling regional house prices

We develop a panel model for regional house prices, for which both the cross-section and the time series dimension is large. The model allows for stochastic trends, cointegration, cross-equation correlations and, most importantly, latent-class clustering of regions. Class membership is fully data-driven and based on the average growth rates of house prices, and the relationship of house prices with economic growth. We apply the model to quarterly data for the Netherlands. The results suggest that there is convincing evidence for the existence of two distinct clusters of regions with pronounced differences in house price dynamics.