Real-time inflation forecasting in a changing world

This paper revisits inflation forecasting using reduced form Phillips curve forecasts, i.e., inflation forecasts using 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 of the individual specifications 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 certainty that unavoidably affects Phillips curve forecasts. We use this framework to describe PCE deflator and GDP deflator inflation rates for the United States across the post-WWII period. Over the full1960-2008 sample the framework indicates several structural breaks across different combinations of activity measures. These breaks often coincide with, amongst others, policy regime changes and oil price shocks. In contrast to many previous studies, we find less evidence for autonomous variance breaks and inflation gap persistence. Through a \\textit{real-time} out-of-sample forecasting exercise we show that our model specification generally provides superior one-quarter and one-year ahead forecasts for quarterly inflation relative to a whole range of forecasting models that are typically used in the literature.Bayesian model averaging;structural breaks;real-time data;model uncertainty;Phillips correlations;inflation forecasting

Common large innovations across nonlinear time series

We propose a multivariate nonlinear econometric time series model, which can beused to examine if there is common nonlinearity across economic variables. Themodel is a multivariate censored latent effects autoregression. The key featureof this model is that nonlinearity appears as separate innovation-likevariables. Common nonlinearity can then be easily defined as the presence ofcommon innovations. We discuss representation, inference, estimation anddiagnostics. We illustrate the model for US and Canadian unemployment and findthat US innovation variables have an effect on Canadian unemployment, and notthe other way around, and also that there is no common nonlinearity across theunemployment variables.Nonlinearity;Censored latent effects autoregression;Common features

Bayes estimates of Markov trends in possibly cointegrated series: an application to US consumption and income

Stylized facts show that average growth rates of US per capita consumption and income differ in recession and expansion periods. Since 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, which 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 autoregressive 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 US per capita disposable income and consumption, after correction for a multivariate Markov trend. This results is also obtained when per capita investment is added to the vector autoregression.Cointegration;MCMC;Permanent income hypothesis;Multivariate Markov trend

Analyzing the effects of past prices on reference price formation

We propose a new reference price framework for brandchoice. In this framework, we employ a Markov-switching processwith an absorbing state to model unobserved price recall ofhouseholds. Reference prices result from the prices households areable to remember. Our model can be used to learn how many pricesobserved in the past are used for reference price formation.Furthermore, we learn to what extent households have sufficientprice knowledge to form an internal reference price. For A.C.Nielsen scanner panel data on catsup purchases, we find that theprices observed at the previous purchase occasion have an averagerecall probability of about 20%. Furthermore, the averageprobability that a household has sufficient price knowledge toform a reference price is estimated at about 30%. Even thoughprice recall is very limited the impact of reference priceformation on brand choice is substantial, and it is stronger thantwo popular alternative models in the literature suggest.Moreover, contrary to the two alternative models, our model doesnot suggest asymmetry between price gains and losses.brand choice;household scanner panel data;Markov switching process;reference price

Do experts incorporate statistical model forecasts and should they?

Experts can rely on statistical model forecasts when creating their own forecasts.Usually it is not known what experts actually do. In this paper we focus on threequestions, which we try to answer given the availability of expert forecasts andmodel forecasts. First, is the expert forecast related to the model forecast andhow? Second, how is this potential relation influenced by other factors? Third,how does this relation influence forecast accuracy?We propose a new and innovative two-level Hierarchical Bayes model to answerthese questions. We apply our proposed methodology to a large data set offorecasts and realizations of SKU-level sales data from a pharmaceutical company.We find that expert forecasts can depend on model forecasts in a variety ofways. Average sales levels, sales volatility, and the forecast horizon influence thisdependence. We also demonstrate that theoretical implications of expert behavioron forecast accuracy are reflected in the empirical data.endogeneity;Bayesian analysis;expert forecasts;model forecasts;forecast adjustment

Modeling dynamic effects of promotion on interpurchase times

In this paper we put forward a duration model to analyze the dynamic effects of marketing-mix variables on interpurchase times. We extend the accelerated failure-time model with an autoregressive structure. An important feature of our model is that it allows for different long-run and short-run effects of marketing-mix variables on interpurchase times. As marketing efforts usually change during the spells, we explicitly deal with time-varying covariates. Our empirical analysis of purchases in three different categories reveals that, for some segments of households, the short-run effects of marketing-mix variables are significantly different from the long-run effects.Dynamic duration model;Error-correction model;Time-varying covariates;Unobserved heterogeneity

Incorporating Responsiveness to Marketing Efforts When Modeling Brand Choice

In this paper we put forward a brand choice model which incorporates responsiveness to marketing efforts as a form of structural heterogeneity. We introduce two latent segments of households. The households in the first segment are assumed to respond to marketing efforts while households in the second segment do not do so. Whether a specific household is a member of the first or the second segment at a specific purchase occasion is described by household-specific characteristics and characteristics concerning buying behavior. Households may switch between responsiveness states over time.We compare the in- and out-of-sample performance of our model with various versions of the MNL model. We conclude that, while using the smallest amount of parameters, our model outperforms all MNL variants on forecasting. This, together with the face validity of our parameter results, leads us to believe that incorporating responsiveness seems to be a worthwhile exercise.mixtures;Marketing-instrument effectiveness;multinomial logit;state dependence;structural heterogeneity

Performance of Seasonal Adjustment Procedures: Simulation and Empirical Results

In this chapter we use a simulation experiment to examine whether theseasonal adjustment methods Census X12-ARIMA and TRAMO/SEATS effectivelyremove seasonality properties from time series data, while preserving otherfeatures like the stochastic trend. As data generating processes we use avariety of processes that are actually found in practice. These processesinclude constant seasonality, changing seasonal patterns due to seasonalunit roots and processes with periodically varying parameters. To check forseasonality, we consider tests for seasonal unit roots, for deterministicseasonality, for seasonality in the variance, and for periodicity in theparameters. Our simulation results show that both adjustment methods areable to remove stochastic seasonal patterns from the data with the exceptionof changing seasonal patterns due to periodicity in the parameters. Onaverage, the two methods perform equally well.

The Bayesian Score Statistic

We propose a novel Bayesian test under a (noninformative) Jeffreys’ prior speciï¬ca- tion. We check whether the ï¬xed scalar value of the so-called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standard- ized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothe- sis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys’ priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspeciï¬cation in linear and cointegration models.bayesian statistics

The Bayesian Score Statistic

We propose a novel Bayesian test under a (noninformative) Jeffreys' prior specification. We check whether the fixed scalar value of the so- called Bayesian Score Statistic (BSS) under the null hypothesis is a plausible realization from its known and standardized distribution under the alternative. Unlike highest posterior density regions the BSS is invariant to reparameterizations. The BSS equals the posterior expectation of the classical score statistic and it provides an exact test procedure, whereas classical tests often rely on asymptotic results. Since the statistic is evaluated under the null hypothesis it provides the Bayesian counterpart of diagnostic checking. This result extends the similarity of classical sampling densities of maximum likelihood estimators and Bayesian posterior distributions based on Jeffreys' priors, towards score statistics. We illustrate the BSS as a diagnostic to test for misspecification in linear and cointegration models.