http://repub.eur.nl/res/aut/397/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/38711/ 2013-01-28T00:00:00Z This article revisits the accuracy of inflation forecasting using activity and expectations variables. We apply Bayesian model averaging across different regression specifications selected from a set of potential predictors that includes lagged values of inflation, a host of real activity data, term structure data, (relative) price data, and surveys. In this model average, we can entertain different channels of structural instability, by either incorporating stochastic breaks in the regression parameters of each individual specification within this average, or allowing for breaks in the error variance of the overall model average, or both. Thus, our framework simultaneously addresses structural change and model uncertainty that would unavoidably affect any inflation forecast model. The different versions of our framework are used to model U.S. personal consumption expenditures (PCE) deflator and gross domestic product (GDP) deflator inflation rates for the 1960–2011 period. A real-time inflation forecast evaluation shows that averaging over many predictors in a model that at least allows for structural breaks in the error variance results in very accurate point and density forecasts, especially for the post-1984 period. Our framework is especially useful when forecasting, in real-time, the likelihood of lower-than-usual inflation rates over the medium term. This article has online supplementary materials. http://repub.eur.nl/res/pub/38803/ 2012-12-01T00:00:00Z http://repub.eur.nl/res/pub/38708/ 2012-12-01T00:00:00Z This article examines the influence of the business cycle on expenditures of three major types of legalized gambling activities: Casino gambling, lottery, and pari-mutuel wagering. Empirical results are obtained using monthly aggregated US per capita consumption time series for the period 1959. 01-2010. 08. Among the three gambling activities only lottery consumption appears to be recession-proof. This series is characterized by a vast and solid growth that exceeds the growth in income and the growth in other gambling sectors. Casino gambling expenditures show a positive growth during expansions and no growth during recessions. Hence, the loss in income during recessions affects casino gambling. However, income shocks which are not directly related to the business cycle do not influence casino gambling expenditures. Pari-mutuel wagering displays an overall negative trend and its average growth rate is smaller than the growth in income, especially during recessions. The findings of this article provide important implications for the gambling industry and for local governments. http://repub.eur.nl/res/pub/37689/ 2012-11-01T00:00:00Z Dynamic effects of marketing-mix variables on interpurchase times can be analyzed in the context of a duration model. Specifically, this can be done by extending the accelerated failure-time model with an autoregressive structure. An important feature of the model is that it allows for different long-run and short-run effects of marketing-mix variables on interpurchase times. The error-correction specification of the model contains parameters which measure the direct effect of a temporary change in a marketing-mix variable on interpurchase times and parameters which measure the long-run (cumulative) effect of a temporary change in a marketing-mix variable on current and future interpurchase times. As marketing efforts usually change during the spells, time-varying covariates are explicitly dealt with. Heterogeneity of individual behavior is allowed for through a mixture approach. An empirical analysis of purchases in three different categories reveals, for some segments of households, that the short-run effects of marketing-mix variables are significantly different from the long-run effects. The decay in the effect of changes in marketing-mix variables over time is larger in categories with large interpurchase times, and price has the largest long-run effect for the perishable product. Finally, ignoring dynamic effects leads to erroneous results about the effectiveness of marketing instruments. http://repub.eur.nl/res/pub/32870/ 2012-09-01T00:00:00Z This paper investigates the selling process of firms acquired by private equity versus strategic buyers. In a single regression setup we show that selling firms choose between formal auctions, controlled sales and private negotiations to fit their firm and deal characteristics including profitability, R&D, deal initiation and type of the eventual acquirer (private equity or strategic buyer). At the same time, a regression model determining the buyer type shows that private equity buyers pursue targets that have more tangible assets, lower market-to-book ratios and lower research and development expenses relative to targets bought by strategic buyers. To reflect possible interdependencies between these two choices and their impact on takeover premium, as a last step, we estimate a simultaneous model that includes the selling mechanism choice, buyer type and premium equations. Our results show that the primary decision within the whole selling process is the target firm's decision concerning whether to sell the firm in an auction, controlled sale or negotiation which then affects the buyer type. These two decisions seem to be optimal as then they do not impact premium. http://repub.eur.nl/res/pub/37687/ 2012-08-01T00:00:00Z To study preferences, respondents to a survey are usually asked to select their most preferred option from a set. Preferences can be estimated more efficiently if respondents are asked to rank all alternatives. When some respondents are unable to perform the ranking task, using the complete ranking may lead to a substantial bias. We introduce a model which endogenously describes the ranking capabilities of individuals. Estimated preferences based on this model are more efficient when at least some individuals are able to rank more than one item, and they do not suffer from biases due to ranking inabilities of respondents. http://repub.eur.nl/res/pub/26749/ 2012-01-01T00:00:00Z This article addresses heterogeneity in determinants of economic growth in a data-driven way. Instead of defining groups of countries with different growth characteristics a priori, based on, for example, geographical location, we use a finite mixture panel model and endogenous clustering to examine cross-country differences and similarities in the effects of growth determinants. Applying this approach to an annual unbalanced panel of 59 countries in Asia, Latin and Middle America and Africa for the period 1971-2000, we can identify two groups of countries in terms of distinct growth structures. The structural differences between the country groups mainly stem from different effects of investment, openness measures and government share in the economy. Furthermore, the detected segmentation of countries does not match with conventional classifications in the literature. http://repub.eur.nl/res/pub/31226/ 2011-12-15T00:00:00Z We propose a new and simple methodology to estimate the loss function associated with experts' forecasts. Under the assumption of conditional normality of the data and the forecast distribution, the asymmetry parameter of the lin-lin and linex loss function can easily be estimated using a linear regression. This regression also provides an estimate for potential systematic bias in the forecasts of the expert. The residuals of the regression are the input for a test for the validity of the normality assumption. We apply our approach to a large data set of SKU-level sales forecasts made by experts and we compare the outcomes with those for statistical model-based forecasts of the same sales data. We find substantial evidence for asymmetry in the loss functions of the experts, with underprediction penalized more than overprediction. http://repub.eur.nl/res/pub/30685/ 2011-12-15T00:00:00Z We propose a new and simple methodology to estimate the loss function associated with experts' forecasts. Under the assumption of conditional normality of the data and the forecast distribution, the asymmetry parameter of the lin-lin and linex loss function can easily be estimated using a linear regression. This regression also provides an estimate for potential systematic bias in the forecasts of the expert. The residuals of the regression are the input for a test for the validity of the normality assumption. We apply our approach to a large data set of SKU-level sales forecasts made by experts and we compare the outcomes with those for statistical model-based forecasts of the same sales data. We find substantial evidence for asymmetry in the loss functions of the experts, with underprediction penalized more than overprediction. http://repub.eur.nl/res/pub/26863/ 2011-10-01T00:00:00Z This paper examines whether the Conference Board's Leading Economic Index (LEI) can be used for modeling and forecasting a more refined business cycle classification beyond the usual distinction between expansions and contractions. Univariate Markov-switching models for monthly coincident variables and the LEI show that a three regime model is more appropriate than a model with only two regimes. Interestingly, the third regime captures `severe recessions' contrasting the conventional view that the additional third regime represents a 'recovery' phase. This is confirmed by means of Markov-switching vector autoregressive models that allow for phase shifts between the cyclical regimes of LEI and industrial production. Results indicate that a three regime model with a severe recession phase describes the cyclical dynamics in these series better than a two regime model (with only recession and expansion regimes) and a three regime model with a recovery phase. T he timing of the third regime mostly corresponds with periods of substantial credit squeezes and dramatic increases in the default spread as in the recent recession of 2007-2009. These findings provide empirical evidence for the theory of 'financial accelerator'. The severe recession regime of the LEI leads that of IP by 6.5 months whereas for mild recessions this lead time increases to one year. http://repub.eur.nl/res/pub/26660/ 2011-09-30T00:00:00Z 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 three questions, which we try to answer given the availability of expert forecasts and model forecasts. First, is the expert forecast related to the model forecast and how? 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 answer these questions. We apply our proposed methodology to a large data set of forecasts and realizations of SKU-level sales data from a pharmaceutical company. We find that expert forecasts can depend on model forecasts in a variety of ways. Average sales levels, sales volatility, and the forecast horizon influence this dependence. We also demonstrate that theoretical implications of expert behavior on forecast accuracy are reflected in the empirical data. http://repub.eur.nl/res/pub/25708/ 2011-07-13T00:00:00Z This paper examines which macroeconomic and financial variables are most informative for the federal funds target rate decisions made by the Federal Open Market Committee (FOMC) from a forecasting perspective. The analysis is conducted for the FOMC decision during the period January 1990 - June 2008, using dynamic ordered probit models with a Bayesian endogenous variable selection methodology and real-time data for a set of 33 candidate predictor variables. We find that indicators of economic activity and forward-looking term structure variables as well as survey measures have most predictive ability. For the full sample period, in-sample probability forecasts achieve a hitrate of 90 percent. Based on out-of-sample forecasts for the period January 2001 - June 2008, 82 percent of the FOMC decisions are predicted correctly. http://repub.eur.nl/res/pub/22551/ 2011-02-07T00:00:00Z We propose a new approach to deal with structural breaks in time series models. The key contribution is an alternative dynamic stochastic specification for the model parameters which describes potential breaks. After a break new parameter values are generated from a so-called baseline prior distribution. Modeling boils down to the choice of a parametric likelihood specification and a baseline prior with the proper support for the parameters. The approach accounts in a natural way for potential out-of-sample breaks where the number of breaks is stochastic. Posterior inference involves simple computations that are less demanding than existing methods. The approach is illustrated on nonlinear discrete time series models and models with restrictions on the parameter space. http://repub.eur.nl/res/pub/22658/ 2011-02-01T00:00:00Z We propose a new periodic autoregressive model for seasonally observed time series, where the number of seasons can potentially be very large. The main novelty is that we collect the periodic coefficients in a second-level stochastic model. This leads to a random-coefficient periodic autoregression with a substantial reduction in the number of parameters to be estimated. We discuss representation, parameter estimation, and inference. An illustration for monthly growth rates of US industrial production shows the merits of the new model specification. http://repub.eur.nl/res/pub/22208/ 2011-01-01T00:00:00Z 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. http://repub.eur.nl/res/pub/21924/ 2010-12-01T00:00:00Z Although several aspects of gambling have been thoroughly investigated, little is known about the effect of seasonality on gambling. This study investigated the seasonal patterns in slot-machine usage, based on a unique data set of slot-machine usage from a German gambling centre using time series analysis. Knowledge of seasonal slot-machine usage patterns provides useful insights for researchers, gambling centre managers and legal authorities. Slot-machine gambling activity appears to be highest in November, when poor weather is compounded with lack of entertainment activities and lowest in December, when ample entertainment possibilities may distract people from gambling. The estimated daily and weekly seasonal patterns support the self-control literature, which suggests that self-regulatory failures are more likely when people are more tired; after work, or late in the evening. The high variation in gambling during winter implies that the availability of alternative entertainment activities may have an important influence on slot-machine usage. http://repub.eur.nl/res/pub/22327/ 2010-12-01T00:00:00Z This paper develops a Markov-Switching vector autoregressive model that allows for imperfect synchronization of cyclical regimes in multiple variables, due to phase shifts of a single common cycle. The model has three key features: (i) the amount of phase shift can be different across regimes (as well as across variables), (ii) it allows the cycle to consist of any number of regimes J is larger than or equal to 2, and (iii) it allows for regime-dependent volatilities and correlations. In an empirical application to monthly returns on size-based stock portfolios, a three-regime model with asymmetric phase shifts and regime-dependent heteroscedasticity is found to characterize the joint distribution of returns most adequately. While large- and small-cap portfolios switch contemporaneously into boom and crash regimes, the large-cap portfolio leads the small-cap portfolio for switches to a moderate regime by a month. http://repub.eur.nl/res/pub/20741/ 2010-09-22T00:00:00Z This paper studies the economic development process, measured by Gross Domestic Product (GDP), for a large panel of countries. We propose a methodology that identifies groups of countries (convergence clubs) that show similar GDP structures, while allowing for changes in club memberships over time. As a second step we analyze the short-run and long-run effects of financial development (measured by financial intermediary development and stock market development) on the GDP process, and the composition of the convergence clubs. We find that the club memberships are quite persistent, but still their compositions change substantially over time. In particular, several EU member countries and East Asian countries are found to belong to a higher GDP club in recent times compared to the beginning of the 1970s. In terms of the effects of financial development indicators on the GDP process, our results partially confirm the theoretical basis for different effects of financial development indicators in the short-run and the long-run. In the long-run, financial development is found to affect the countries’ GDP level positively. The short-run effects of financial development indicators however are found to be less clear, in the sense that we do not find a negative short-run effect of financial intermediary development on GDP levels, while the short-run effect of stock market development is found to be negative. http://repub.eur.nl/res/pub/19533/ 2010-02-01T00:00:00Z 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. http://repub.eur.nl/res/pub/18651/ 2009-10-01T00:00:00Z We develop a novel Markov switching vector autoregressive model to investigate the possibility that leading indicators have different lead times at business cycle peaks and at troughs. In this model, coincident and leading indicators share a common Markov state process, but their cycles are nonsynchronous, with the nonsynchronicity varying across regimes. An application shows that on average the Conference Board’s Composite Leading Index leads the Composite Coincident Index by nearly 1 year at peaks but by only 1 quarter at troughs. Allowing for asymmetric lead times yields improved real-time dating and forecasting of business cycle turning points. http://repub.eur.nl/res/pub/16709/ 2009-09-10T00:00:00Z 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 full 1960-2008 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. http://repub.eur.nl/res/pub/16314/ 2009-05-01T00:00:00Z http://repub.eur.nl/res/pub/15564/ 2009-04-21T00:00:00Z In applied economic research computable general equilibrium [CGE] models in which the behavior of economic agents are modeled, are widely used. In many CGE models, the Linear Expenditure System [LES] is used to model behavior of the household sector. The disadvantage of LES is that the Engel curves, describing the relationship between expenditure on a certain commodity and total expenditure, are straight lines. Moreover, the LES does not allow for the existence of inferior commodities, elastic demand and gross substitution. An alternative model for the household block is the Indirect Addilog System [IAS] which is as simple to implement as LES, but which does not suffer from these theoretical deficiencies. Consequently, IAS provides a theoretically richer description of household behavior than LES, while it is as easy to implement. In this paper we test the LES specification against the IAS specification in case one disposes of a budget survey. It is not possible to use a standard likelihood ratio test as both models are not nested. We propose to use the likelihood ratio test for non-nested hypotheses due to Vuong (1989), or, alternatively, the distribution-free test due to Clarke (2007). We apply both tests to the Palestinian Expenditure and Consumption Survey (PECS, 2005) and find that there is overwhelming evidence that the IAS specification is to be preferred to the LES specification. http://repub.eur.nl/res/pub/18318/ 2009-04-01T00:00:00Z Purchase timing of households is usually modeled at the category level. However, many potential explanatory variables are observed at the brand level. To explain interpurchase times one has to either construct category-level measures of marketing efforts, or integrate the model with a model for brand choice. In this paper we pursue the latter where we use latent brand preferences to capture the relevance of the marketing mix of an individual brand. We compare our new model with several standard approaches on in-sample and out-of-sample fit and on the interpretation of the estimates of key parameters. http://repub.eur.nl/res/pub/15112/ 2009-03-16T00:00:00Z We develop a new Bayesian approach to estimate the parameters of a latent-class model for the joint clustering of both modes of two-mode data matrices. Posterior results are obtained using a Gibbs sampler with data augmentation. Our Bayesian approach has three advantages over existing methods. First, we are able to do statistical inference on the model parameters, which would not be possible using frequentist estimation procedures. In addition, the Bayesian approach allows us to provide statistical criteria for determining the optimal numbers of clusters. Finally, our Gibbs sampler has fewer problems with local optima in the likelihood function and empty classes than the EM algorithm used in a frequentist approach. We apply the Bayesian estimation method of the latent-class two-mode clustering model to two empirical data sets. The first data set is the Supreme Court voting data set of Doreian, Batagelj, and Ferligoj (2004). The second data set comprises the roll call votes of the United States House of Representatives in 2007. For both data sets, we show how two-mode clustering can provide useful insights. http://repub.eur.nl/res/pub/16160/ 2009-01-01T00:00:00Z Contains household level purchase histories Variables: id household identifier date date of purchase vol purchased volume in ounces brand brand number The data we use are based on the so-called ERIM database, which is collected by A.C.Nielsen. The data span the years 1986 to 1988, and the particular subset we use concerns purchases of detergent by households in Sioux Falls (South Dakota, USA). For our purposes, the data are aggregated to the brand level. Brand coding: 1=Cheer 2=Oxidol 3=Surf 4=Tide 5=Wisk 6=Rest http://repub.eur.nl/res/pub/16161/ 2009-01-01T00:00:00Z Contains household characteristics Variables: hh id household identifier hh income household income category hhsize number of household members insample 0/1 variable indicating whether this household was used f or the in sample data outofsample 0/1 variable indicating whether this household was used for the out of sample data http://repub.eur.nl/res/pub/16312/ 2009-01-01T00:00:00Z We estimate the empirical bimodal cross-section distribution of real Gross Domestic Product per capita of 120 countries over the period 1960–1989 by a mixture of a Weibull and a truncated normal density. The components of the mixture represent a group of poor and a group of rich countries, while the mixing proportion describes the distribution over poor and rich. This enables us to analyse the development of the mean and variance of both groups separately and the switches of countries between the two groups over time. Empirical evidence indicates that the means of the two groups are diverging in terms of levels, but that the growth rates of the means of the two groups over the period 1960–1989 are the same. http://repub.eur.nl/res/pub/13156/ 2008-09-01T00:00:00Z Empirical analysis of individual response behavior is sometimes limited due to the lack of explanatory variables at the individual level. In this paper we put forward a new approach to estimate the effects of covariates on individual response, where the covariates are unknown at the individual level but observed at some aggregated level. This situation may, for example, occur when the response variable is available at the household level but covariates only at the zip-code level. We describe the missing individual covariates by a latent variable model which matches the sample information at the aggregate level. Parameter estimates can be obtained using maximum likelihood or a Bayesian analysis. We illustrate the approach estimating the effects of household characteristics on donating behavior to a Dutch charity. Donating behavior is observed at the household level, while the covariates are only observed at the zip-code level. http://repub.eur.nl/res/pub/14044/ 2008-08-29T00:00:00Z This paper addresses heterogeneity in determinants of economic growth in a data-driven way. Instead of defining groups of countries with different growth characteristics a priori, based on, for example, geographical location, we use a finite mixture panel model and endogenous clustering to examine cross-country differences and similarities in the effects of growth determinants. Applying this approach to an annual unbalanced panel of 59 countries in Asia, Latin and Middle America and Africa for the period 1971-2000, we can identify two groups of countries in terms of distinct growth structures. The structural differences between the country groups mainly stem from different effects of investment, openness measures and government share in the economy. Furthermore, the detected segmentation of countries does not match with conventional classifications in the literature. http://repub.eur.nl/res/pub/13051/ 2008-08-21T00:00:00Z We put forward a brand choice model with unobserved heterogeneity that concerns responsiveness to marketing efforts. We introduce two latent segments of households. The first segment is 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 the two responsiveness states over time. When comparing the performance of our model with alternative choice models that account for various forms of heterogeneity for tree different datasets, we find better face validity of our parameters. Our model also forecasts better. http://repub.eur.nl/res/pub/13212/ 2008-06-01T00:00:00Z GARCH models and Stochastic Volatility (SV) models can both be used to describe unobserved volatility in asset returns. We consider the issue of testing a GARCH model against an SV model. For that purpose, we propose a new and parsimonious GARCH-t model with an additional restricted moving average term, which can capture SV model properties. We discuss model representation, parameter estimation, and our simple test for model selection. Furthermore, we derive the theoretical moments and the autocorrelation function of our new model. We illustrate our model and test for nine daily stock-return series. http://repub.eur.nl/res/pub/12962/ 2008-03-01T00:00:00Z This paper considers the nature and the distribution of trade and FDI effects of a potential enlargement of the European Monetary Union (EMU) to the 10 countries that obtained EU membership in 2004. One-way and two-way error component gravity models are estimated using a data set of unbalanced panel data that combine bilateral trade flows among 29 countries and the distribution of outward FDI stocks among these countries. The results reveal a complementarity between trade and investment and a relationship between trade and exchange rate volatility that depend on the sign of bilateral trade balances. Using a simulation-based technique, we find that estimates of FDI effects of EMU range between 18.5% for Poland and 30% for Hungary. http://repub.eur.nl/res/pub/11723/ 2007-12-01T00:00:00Z We develop a parsimonious panel model for quarterly 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 (i) average growth rates of house prices, (ii) the propagation of shocks to house prices across regions, also known as the ripple effect, and (iii) the relationship of house prices with economic growth and other variables. Applying the model to quarterly data for the Netherlands, we find convincing evidence for the existence of two distinct clusters of regions, with pronounced differences in house price dynamics. http://repub.eur.nl/res/pub/10743/ 2007-09-23T00:00:00Z This paper considers the nature and the distribution of trade and FDI effects of a potential enlargement of the European Monetary Union (EMU) to the ten countries that obtained EU membership in 2004. Intuitively, the implementation of a single currency for these countries means replacing several fluctuating currencies by a common currency. This gives rise to both “level” and “risk” effects of reduced currency movements on trade and investment. Another factor is the nature of the link between trade and FDI. This is also important not only because cross-border factor flows are becoming increasingly important, but also the international trade literature has long recognized that cross-border factor flows and trade in goods and services can be substitutes or complements. Given this background, one-way and two-way error component gravity models are estimated to examine for these theoretical expectations within a dataset of unbalanced panel data that combines bilateral trade flows among 29 countries and the distribution of outward FDI stocks among these countries (including the 10 new EU members). The data generally cover the period from 1990 to 2004. Our empirical results convincingly support: (i) a complementarity between trade and investment, (ii) a relationship between trade and exchange rate volatility that depends on the sign of bilateral trade balances, (iii) a positive effect of EU on trade and investment, and (iv) a positive effect of EMU on foreign investment. Using a simulation-based technique, we find that estimates of FDI effects of EMU range between 18.5 percent for Poland and 30 percent for Hungary. http://repub.eur.nl/res/pub/11416/ 2007-05-01T00:00:00Z Scanner data for fast moving consumer goods typically amount to panels of time series where both N and T are large. To reduce the number of parameters and to shrink parameters towards plausible and interpretable values, Hierarchical Bayes models turn out to be useful. Such models contain in the second level a stochastic model to describe the parameters in the first level. In this paper we propose such a model for weekly scanner data where we explicitly address (i) weekly seasonality when not many years of data are available and (ii) non-linear price effects due to historic reference prices. We discuss representation and inference and we propose a Markov Chain Monte Carlo sampler to obtain posterior results. An illustration to a market-response model for 96 brands for about 8 years of weekly data shows the merits of our approach. http://repub.eur.nl/res/pub/11133/ 2007-04-01T00:00:00Z Editorial http://repub.eur.nl/res/pub/9230/ 2007-03-20T00:00:00Z We develop a formal statistical approach to investigate the possibility that leading indicator variables have different lead times at business cycle peaks and troughs. For this purpose, we propose a novel Markov switching vector autoregressive model, where economic growth and leading indicators share a common Markov process determining the state, but such that their cycles are non-synchronous with the non-synchronicity varying across the different regimes. An empirical application to monthly US industrial production (IP) and The Conference Board's Composite Index of Leading Indicators (CLI) for the period 1959-2004 shows that on average the CLI leads IP by more than seven months at peaks, but only by three and a half months at troughs. In terms of timeliness, the CLI is therefore most useful for signalling oncoming recessions. Furthermore, we find that allowing for asymmetric lead times leads to improved real-time dating of business cycle peaks and troughs and more accurate forecasts of turning points and IP growth. http://repub.eur.nl/res/pub/8533/ 2007-02-06T00:00:00Z In this paper we consider the situation where one wants to study the preferences of individuals over a discrete choice set through a survey. In the classical setup respondents are asked to select their most preferred option out of a (selected) set of alternatives. It is well known that, in theory, more information can be obtained if respondents are asked to rank the set of alternatives instead. In statistical terms, the preferences can then be estimated more efficiently. However, when individuals are unable to perform (part of) this ranking task, using the complete ranking may lead to a substantial bias in parameter estimates. In practice, one usually opts to only use a part of the reported ranking. In this paper we introduce a latent-class rank-ordered logit model in which we use latent segments to endogenously identify the ranking capabilities of individuals. Each segment corresponds to a different assumption on the ranking capability. Using simulations and an empirical application, we show that using this model for parameter estimation results in a clear efficiency gain over a multinomial logit model in case some individuals are able to rank. At the same time it does not suffer from biases due to ranking inabilities of some of the respondents. http://repub.eur.nl/res/pub/13297/ 2007-01-01T00:00:00Z http://repub.eur.nl/res/pub/13214/ 2006-10-01T00:00:00Z We put forward a statistical model for interpurchase times that incorporates all current and past information available for all purchases as time runs along the calendar time scale. It delivers forecasts for the number of purchases in the next period, as well as for the timing of subsequent and consecutive purchases. Purchase occasions are viewed as a counting process that counts the recurrent purchases for each house-hold as they evolve over time. We illustrate our model for yogurt purchases and highlight its managerial implications. http://repub.eur.nl/res/pub/7904/ 2006-08-24T00:00:00Z This paper develops a return forecasting methodology that allows for instabil ity in the relationship between stock returns and predictor variables, for model uncertainty, and for parameter estimation uncertainty. The predictive regres sion speci¯cation that is put forward allows for occasional structural breaks of random magnitude in the regression parameters, and for uncertainty about the inclusion of forecasting variables, and about the parameter values by em ploying Bayesian Model Averaging. The implications of these three sources of uncertainty, and their relative importance, are investigated from an active investment management perspective. It is found that the economic value of incorporating all three sources of uncertainty is considerable. A typical in vestor would be willing to pay up to several hundreds of basis points annually to switch from a passive buy-and-hold strategy to an active strategy based on a return forecasting model that allows for model and parameter uncertainty as well as structural breaks in the regression parameters. http://repub.eur.nl/res/pub/11412/ 2006-08-01T00:00:00Z 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. http://repub.eur.nl/res/pub/11488/ 2006-07-01T00:00:00Z The selection of the most profitable customers in a customer database for targeted activities is often done based on observed behaviour in the past. Consequently, databases arising from the responses to, for example, direct mailings in the past are not random samples. When not all heterogeneity across customers is observed, target selection will be based on unobserved heterogeneity and hence it is endogenous. We develop a method to adjust the likelihood function of latent class models to correct for this endogenous sampling process. We apply this technique to the selection of mail targets for a Dutch charity. Based on a joint model for the response rate and the amount donated, we create a target selection rule that maximizes expected revenues. http://repub.eur.nl/res/pub/13216/ 2006-07-01T00:00:00Z We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson [Annals of Mathematical Statistics (1951), 22, 327–351] sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald [Journal of the American Statistical Association (1996), 91, 1301–1309] and Gill and Lewbel [Journal of the American Statistical Association (1992), 87, 766–776] a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith [Econometric Theory (2000), 16, 151–175] usage of numerical optimization for the objective function statistic of Cragg and Donald [Journal of Econometrics (1997), 76, 223–250] and ignoring the non-negativity restriction on the singular values in Ratsimalahelo [2002, Rank test based on matrix perturbation theory. Unpublished working paper, U.F.R. Science Economique, University de Franche-Comté]. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic. http://repub.eur.nl/res/pub/7453/ 2006-02-20T00:00:00Z Empirical analysis of individual response behavior is sometimes limited due to the lack of explanatory variables at the individual level. In this paper we put forward a new approach to estimate the effects of covariates on individual response, where the covariates are unknown at the individual level but observed at some aggregated level. This situation may, for example, occur if the response variable is available at the household level but covariates only at the zip-code level. We describe the missing individual covariates by a latent variable model which matches the sample information at the aggregate level. Parameter estimates can be obtained using maximum likelihood or a Bayesian approach. We illustrate the approach estimating the effects of household characteristics on donating behavior to a Dutch charity. Donating behavior is observed at the household level, while the covariates are only observed at the zip-code level. http://repub.eur.nl/res/pub/7040/ 2005-11-09T00:00:00Z We propose a new model to describe consideration, consisting of a multivariate probit model component for consideration and a multinomial probit model component for choice, given consideration. The approach allows one to analyze stated consideration set data, revealed consideration set (choice) data or both, while at the same time it allows for unobserved dependence in consideration among brands. In addition, the model accommodates different effects of the marketing mix on consideration and choice, an error process that is correlated over time, and unobserved consumer heterogeneity in both processes. We attempt to establish the validity of existing practice to infer consideration sets from observed choices in panel data. To this end, we collect data in an on-line choice experiment involving interactive supermarket shelves and post-choice questionnaires to measure the choice protocol and stated consideration levels. We show with these experimental data that underlying consideration sets can be reliably retrieved from choice data alone. Next, we estimate the model on IRI panel data. We have two main results. First, compared with the single-stage multinomial probit model, promotion effects are larger when they are included in the consideration stage of the two-stage model. Second, we find that consideration of brands does not covary greatly across brands once we account for observed effects. http://repub.eur.nl/res/pub/6917/ 2005-09-13T00:00:00Z In this chapter we use a simulation experiment to examine whether the seasonal adjustment methods Census X12-ARIMA and TRAMO/SEATS effectively remove seasonality properties from time series data, while preserving other features like the stochastic trend. As data generating processes we use a variety of processes that are actually found in practice. These processes include constant seasonality, changing seasonal patterns due to seasonal unit roots and processes with periodically varying parameters. To check for seasonality, we consider tests for seasonal unit roots, for deterministic seasonality, for seasonality in the variance, and for periodicity in the parameters. Our simulation results show that both adjustment methods are able to remove stochastic seasonal patterns from the data with the exception of changing seasonal patterns due to periodicity in the parameters. On average, the two methods perform equally well. http://repub.eur.nl/res/pub/6908/ 2005-09-08T00:00:00Z The authors put forward 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 rewritten in error-correction format which allows 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-run regular price elasticity are correlated with various brand-speciffic and category-speciffic characteristics. The model is applied to seven years of data on weekly sales of 100 different brands in 25 product categories. We 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 turn out to increase the immediate price sensitivity of customers. We also find significant effects for the cumulative elasticity. The immediate effect of a regular price change is often close to zero. The long-run effect of such a decrease usually amounts to an increase in sales. This is especially true in categories characterized by a large price dispersion, frequent price promotions and hedonic, non-perishable products. http://repub.eur.nl/res/pub/11142/ 2005-08-01T00:00:00Z We address the question whether sub-Saharan African countries have lower average growth rates in real GDP per capita than countries in Asia, Latin and Middle America and the Middle East. In contrast to previous studies, countries are no a priori assigned to clusters based on geographical location. Instead, we propose a latent-class panel time series model, which allows a data-based classification of countries into clusters such that within a cluster countries have the same average growth rate. Our empirical results suggest that three clusters are sufficient to describe the different growth paths. Twenty-six African countries belong to the low growth cluster, but 8 African countries show growth rates comparable with many countries in Asia, Latin and Middle America and the Middle East. http://repub.eur.nl/res/pub/13217/ 2005-01-01T00:00:00Z We present a statistical model for voter choice that incorporates a consideration set stage and final vote intention stage. The first stage involves a multivariate probit (MVP) model to describe the probabilities that a candidate or a party gets considered. The second stage of the model is a multinomial probit (MNP) model for the actual choice. In both stages, we use as explanatory variables data on voter choice at the previous election, as well as sociodemographic respondent characteristics. Importantly, our model explicitly accounts for the three types of “missing data” encountered in polling. First, we include a no-vote option in the final vote intention stage. Second, the “do not know” (DNK) response is assumed to arise from too little difference in the utility between the two most preferred options in the consideration set, or is considered to be a missing observation. Third, the “do not want to say” (DNWTS) response is modeled as a missing observation on the most preferred alternative in the consideration set. Thus, we consider the missing data generating mechanism to be nonignorable and build a model based on utility maximization to describe the vote intentions of these respondents. We illustrate the merits of the model as we have information on a sample of about 5000 individuals from the Netherlands for who we know how they voted last time (if at all), which parties they would consider for the upcoming election, and what their vote intention is. A unique feature of the data set is that information is available on actual individual voting behavior, measured at the day of election. We find that the inclusion of the consideration set stage in the model enables the user to make a more precise inference on the competitive structure in the political domain and to obtain better out-of-sample forecasts. http://repub.eur.nl/res/pub/6941/ 2005-01-01T00:00:00Z We propose a new periodic autoregressive model for seasonally observed time series, where the number of seasons can potentially be very large. The main novelty is that we collect the periodic parameters in a second-level stochastic model. This leads to a random-coefficient periodic autoregression with a substantial reduction in the number of parameters to be estimated. We discuss representation, estimation, and inference. An illustration for monthly growth rates of US industrial production shows the merits of the new model specification. http://repub.eur.nl/res/pub/7028/ 2005-01-01T00:00:00Z The GARCH model and the Stochastic Volatility [SV] model are competing but non-nested models to describe unobserved volatility in asset returns. We propose a GARCH model with an additional error term, which can capture SV model properties, and which can be used to test GARCH against SV. We discuss model representation, parameter estimation and a simple test for model selection. Furthermore, we derive the theoretical moments and the autocorrelation function of our new model. We illustrate its merits for 9 daily stock return series. http://repub.eur.nl/res/pub/1515/ 2004-08-19T00:00:00Z We propose a new reference price framework for brand choice. In this framework, we employ a Markov-switching process with an absorbing state to model unobserved price recall of households. Reference prices result from the prices households are able to remember. Our model can be used to learn how many prices observed in the past are used for reference price formation. Furthermore, we learn to what extent households have sufficient price knowledge to form an internal reference price. For A.C. Nielsen scanner panel data on catsup purchases, we find that the prices observed at the previous purchase occasion have an average recall probability of about 20%. Furthermore, the average probability that a household has sufficient price knowledge to form a reference price is estimated at about 30%. Even though price recall is very limited the impact of reference price formation on brand choice is substantial, and it is stronger than two popular alternative models in the literature suggest. Moreover, contrary to the two alternative models, our model does not suggest asymmetry between price gains and losses. http://repub.eur.nl/res/pub/1476/ 2004-08-12T00:00:00Z For promotional planning and market segmentation it is important to understand the short-run and long-run effects of the marketing mix on category and brand sales. In this paper we put forward a sales response model to explain the differences in short-run and long-run effects of promotions on sales. The model consists of a vector autoregression rewritten in error-correction format which allows us to disentangle the long-run effects from the short-run effects. In a second level of the model, we correlate the short-run and long-run elasticities with various brand-specific and category-specific characteristics. The model is applied to weekly sales of 100 different brands in 25 product categories. Our empirical results allow us to make generalizing statements on the dynamic effects of promotions in a statistically coherent way. http://repub.eur.nl/res/pub/2168/ 2004-04-01T00:00:00Z Monthly observed unemployment typically displays explosive behavior in recessionary periods, while there seems to be stationary behavior in expansions. Allowing parameters in an autoregression to vary across regimes, and hence over time, can capture this feature. In this paper, we put forward a new autoregressive time series model with time-varying parameters, where this variation depends on a linear indicator variable. When the value of this variable exceeds a stochastic threshold level, the parameters change. We discuss representation, estimation and interpretation of the model. Also, we analyze its forecasting performance for unemployment series of three G-7 countries, and we compare it with various related models. http://repub.eur.nl/res/pub/2036/ 2004-01-01T00:00:00Z This book considers periodic time series models for seasonal data, characterized by parameters that differ across the seasons, and focuses on their usefulness for out-of-sample forecasting. Providing an up-to-date survey of the recent developments in periodic time series, the book presents a large number of empirical results. The first part of the book deals with model selection, diagnostic checking and forecasting of univariate periodic autoregressive models. Tests for periodic integration, are discussed, and an extensive discussion of the role of deterministic regressors in testing for periodic integration and in forecasting is provided. The second part discusses multivariate periodic autoregressive models. It provides an overview of periodic cointegration models, as these are the most relevant. This overview contains single-equation type tests and a full-system approach based on generalized method of moments. All methods are illustrated with extensive examples, and the book will be of interest to advanced graduate students and researchers in econometrics, as well as practitioners looking for an understanding of how to approach seasonal data. Provides an up-to-date survey of periodic time series models for seasonal data. Investigates such areas as seasonal time series; periodic time series models; periodic integration; and periodic cointegration. Contains many contemporary empirical examples and results. http://repub.eur.nl/res/pub/2041/ 2003-11-01T00:00:00Z Anytime an individual makes a cash payment, he or she needs to think about the amount to be paid, the coins and notes which are available, and the amount of change. For central banks and retail stores, it is of interest to understand how this individual choice process works. The literature of currency use concerns primarily theory, in the sense that, given certain assumptions, one can derive an optimal denomination range. There is no empirical study which deals with the actual use of coins and notes, given a specific denomination range. In this paper we present such a study, which is based on two rather unique data sets. We use descriptive statistics and a sophisticated model, which is designed for this specific purpose, to see whether two basic premises of the theories on optimal ranges are valid. In contrast to the widely accepted assumptions, we find that individuals appear not to pay efficiently and that they are also not indifferent to the use of coins and notes. In other words, some notes and coins are used less often than expected given the payment situation. http://repub.eur.nl/res/pub/11199/ 2003-10-01T00:00:00Z 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. http://repub.eur.nl/res/pub/336/ 2003-05-15T00:00:00Z To comprehend the competitive structure of a market, it is important to understand the short-run and long-run effects of the marketing mix on market shares. A useful model to link market shares with marketing-mix variables, like price and promotion, is the market share attraction model. In this paper we put forward a representation of the attraction model, which allows for explicitly disentangling long-run from short-run effects. Our model also contains a second level, in which these dynamic effects are correlated with various brand and product category characteristics. Based on the findings in for example Nijs et al. (2001), we postulate the expected signs of these correlations. We fit our resultant Hierarchical Bayes attraction model to data on seven categories in two geographical areas. This data set spans a total of 50 brands. Our main finding is that, in absolute sense, the short-run price elasticity usually exceeds the long-run effect. Moreover, we find that the longrun price effects are strongly correlated with relative price and coupon intensity of a brand. http://repub.eur.nl/res/pub/1715/ 2003-05-08T00:00:00Z Purchase timing of households is usually modeled at the category level. Marketing efforts are however only available at the brand level. Hence, to describe category-level interpurchase times using marketing efforts one has to construct a category-level measure of marketing efforts from the marketing mix of individual brands. In this paper we discuss two standard approaches suggested in the literature to solve this problem, that is, using individual choice shares as weights to average the marketing mix, and the inclusive value approach. Additionally, we propose three alternative novel solutions, which have less limitations than the two standard approaches. The new approaches use brand preferences following from a brand choice model to capture the relevance of the marketing mix of individual brands. One of these approaches integrates the purchase timing model with a brand preference model. To empirically compare the two standard and the three new approaches, we consider household scanner data in three product categories. One of the main conclusions is that the inclusive value approach performs worse than the other approaches. This holds in-sample as well as out-of-sample. The performance of the individual choice share approach is best unless one allows for unobserved heterogeneity in the brand choice models, in which case the three new approaches based on modeled brand preferences are superior. http://repub.eur.nl/res/pub/1681/ 2003-02-17T00:00:00Z We propose a novel statistic to test the rank of a matrix. The rank statistic overcomes deficiencies of existing rank statistics, like: necessity of a Kronecker covariance matrix for the canonical correlation rank statistic of Anderson (1951), sensitivity to the ordering of the variables for the LDU rank statistic of Cragg and Donald (1996) and Gill and Lewbel (1992), a limiting distribution that is not a standard chi-squared distribution for the rank statistic of Robin and Smith (2000) and usage of numerical optimization for the objective function statistic of Cragg and Donald (1997). The new rank statistic consists of a quadratic form of a (orthogonal) transformation of the smallest singular values of a unrestricted estimate of the matrix of interest. The quadratic form is taken with respect to the inverse of a unrestricted covariance matrix that can be estimated using a heteroscedasticity autocorrelation consistent estimator. The rank statistic has a standard chi squared limiting distribution. In case of a Kronecker covariance matrix, the rank statistic simplifies to the canonical correlation rank statistic. In the non-stationary cointegration case, the limiting distribution of the rank statistic is identical to that of the Johansen trace statistic. We apply the rank statistic to test for the rank of a matrix that governs the identification of the parameters in the stochastic discount factor model of Jagannathan and Wang (1996). The rank statistic shows that non-identification of the parameters can not be rejected. We further use the stochastic discount factor model to illustrate the validity of the limiting distribution and to conduct a power comparison. http://repub.eur.nl/res/pub/1077/ 2003-01-01T00:00:00Z We put forward a statistical model for interpurchase times that takes into account all the current and past information available for all purchases as time continues to run along the calendar timescale. It delivers forecasts for the number of purchases in the next period and for the timing of the first and consecutive purchases. Purchase occasions are modeled in terms of a counting process, which counts the recurrent purchases for each household as they evolve over time. We show that formulating the problem as a counting process has many advantages, both theoretically and empirically. We illustrate our model for yogurt purchases and we highlight its useful managerial implications. http://repub.eur.nl/res/pub/1695/ 2003-01-01T00:00:00Z In this paper we address the question whether countries on the African continent have lower average growth rates in real GDP per capita than countries in Asia and Latin America. In contrast to previous studies, we do not aggregate the data, nor do we a priori assign countries to clusters. Instead, we put forward a so-called latent class panel time series model, which allows a data-based classification of countries to clusters with growth levels that differ across the clusters. Our empirical results suggest that twenty-six African countries can be assigned to the low growth cluster, but that eleven African countries show growth levels which are comparable with many countries in Asia and Latin America. We also present results for sub-periods, which demonstrate that the relative performance of African countries has improved considerably over time. http://repub.eur.nl/res/pub/6791/ 2002-12-18T00:00:00Z We propose a consistent utility-based framework to jointly explain a household's decisions on purchase incidence, brand choice and purchase quantity. The approach differs from other approaches, currently available in the literature, as it is able to take into account consumption dynamics. In the model, households derive utility from consumption, and they relate their purchase behavior to consumption planning. We illustrate our model for yogurt purchases, and show that our model yields important additional insights. One such insight is that the reservation price of households is not fixed, but depends on the available inventory stock. Furthermore, we find that promotional activities increase sales through more purchases in the product category and brand switching, but the effect through larger purchase quantities is limited. http://repub.eur.nl/res/pub/538/ 2002-12-04T00:00:00Z 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. http://repub.eur.nl/res/pub/13232/ 2002-12-01T00:00:00Z 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). http://repub.eur.nl/res/pub/544/ 2002-10-09T00:00:00Z 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. http://repub.eur.nl/res/pub/6794/ 2002-10-07T00:00:00Z It is conceivable that the "whether to buy" and "how much to buy" decisions in the purchasing process of households are influenced by the inventory process. In this paper we therefore put forward a model for consumption, where we rely on established economic theory. We incorporate this model in a model for purchase behavior. Our consumption specification, which is derived from utility maximization principles, is more flexible than an ad hoc approach, which has recently been proposed in the literature. We illustrate our model for yogurt purchases, and show that our model yields important additional and useful insights. One such insight is that promotion anticipation behavior turns out not only to occur in the purchasing process, but also in the consumption process. http://repub.eur.nl/res/pub/11150/ 2002-10-01T00:00:00Z 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. http://repub.eur.nl/res/pub/13231/ 2002-09-01T00:00:00Z Due to high and low volatility periods, time series of absolute returns experience temporary level shifts which differ in length and size. In this paper we modify the basic Censored Latent Effects Autoregressive [CLEAR] model, such that it can describe and forecast the location and size of such level shifts. For our particular application, we assume that technical trading variables may have explanatory value for future level shifts, where these effects may differ across upward- or downward-tending markets. A natural competitor of the resultant switching regime CLEAR [SR-CLEAR] model is a long-memory model, which is known to pick up neglected level shifts. Hence, when we apply the SR-CLEAR model to nine stock markets and document its good fit and forecasting ability, we compare it with a long-memory model. http://repub.eur.nl/res/pub/6801/ 2002-07-09T00:00:00Z Anytime an individual makes a cash payment, s/he needs to think about the amount to be paid, the coins and notes which are available, and the amount of change. For central banks and retail stores, for example, it is of interest to un- derstand how this individual choice process works. The literature of currency use concerns primarily theory, in the sense that, given certain assumptions, one can de- rive an optimal denomination range. There is no empirical study which deals with the actual use of coins and notes, given a specific denomination range. In this paper we therefore present such a study, which is based on two rather unique data sets. We use descriptive statistics and a sophisticated model, which is designed for this specific purpose, to see whether two basic premises of the theories on optimal ranges are valid. In contrast to the widely accepted assumptions, we find that individuals appear not to pay efficiently and that they are also not indifferent to the use of coins and notes. In other words, some notes and coins are used less often than expected given the payment situation. http://repub.eur.nl/res/pub/13233/ 2002-07-01T00:00:00Z A model is proposed to describe observed asymmetries in postwar unemployment time series data. We assume that recession periods, when unemployment increases rapidly, correspond with unobserved positive shocks. The generating mechanism of these latent shocks is a censored regression model, where linear combinations of lagged explanatory variables lead to positive shocks, while otherwise shocks are equal to zero. We apply this censored latent effects autoregression to monthly US unemployment, where the positive shocks are found to be predictable using various leading indicators. The model fits the data well and its out-of-sample forecasts appear to improve on those from alternative models. http://repub.eur.nl/res/pub/2039/ 2002-02-01T00:00:00Z 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. http://repub.eur.nl/res/pub/2197/ 2002-01-01T00:00:00Z Het is voor sommige mensen nog even wennen, die euro. In het Duitse Erbach bleek een pompbediende nog niet helemaal op de hoogte van de nieuwe biljetten. Een klant rekende daar af met een biljet van 300 euro. Netjes kreeg hij vervolgens 250 euro terug. http://repub.eur.nl/res/pub/578/ 2002-01-01T00:00:00Z We propose a multivariate nonlinear econometric time series model, which can be used to examine if there is common nonlinearity across economic variables. The model is a multivariate censored latent effects autoregression. The key feature of this model is that nonlinearity appears as separate innovation-like variables. Common nonlinearity can then be easily defined as the presence of common innovations. We discuss representation, inference, estimation and diagnostics. We illustrate the model for US and Canadian unemployment and find that US innovation variables have an effect on Canadian unemployment, and not the other way around, and also that there is no common nonlinearity across the unemployment variables. http://repub.eur.nl/res/pub/1701/ 2001-11-13T00:00:00Z Due to high and low volatility periods, time series of absolute returns experience temporary level shifts (that is, periods with outliers) which differ in length and size. In this paper we put forward a new model which can describe and forecast the location and size of such level shifts. Our so called Switching Regime Censored Latent Effects Autoregression [SR-CLEAR] assumes that technical trading rules may have explanatory value for future volatility. It is assumed that these rules have a time-varying effect on absolute returns, and that this effect appears as an outlier or a level shift. We apply the SR-CLEAR model to nine stock markets and we document its excellent fit and competitive forecasting ability. http://repub.eur.nl/res/pub/110/ 2001-08-15T00:00:00Z 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. http://repub.eur.nl/res/pub/8092/ 2001-08-01T00:00:00Z Recent advances in data collection and data storage techniques enable marketing researchers to study the individual characteristics of a large range of transactions and purchases, in particular the effects of household-specific characteristics. This book presents the most important and practically relevant quantitative models for marketing research. Each model is presented in detail with a self-contained discussion, which includes: a demonstration of the mechanics of the model, empirical analysis, real world examples, and interpretation of results and findings. http://repub.eur.nl/res/pub/89/ 2001-05-02T00:00:00Z Market share attraction models are useful tools for analyzing competitive structures. The models can be used to infer cross-effects of marketing-mix variables, but also the own effects can be adequately estimated while conditioning on competitive reactions. Important features of attraction models are that they incorporate that market shares sum to unity and that the market shares of individual brands are in between 0 and 1. Next to analyzing competitive structures, attraction models are also often considered for forecasting market shares. The econometric analysis of the market share attraction model has not received much attention. Topics as specification, diagnostics, estimation and forecasting have not been thoroughly discussed in the academic marketing literature. In this chapter we go through a range of these topics, and, along the lines, we indicate that there are ample opportunities to improve upon present-day practice. http://repub.eur.nl/res/pub/70/ 2001-01-30T00:00:00Z A commonly applied modeling tool for the analysis of promotional effects on weekly sales data is a linear regression model. Usually, such a model includes 0/1 dummy variables for promotions, where weeks with a promotion get a value of 1. When these variables are included in a model with parameters which are constant over time, the market researcher implicitly makes two important but rather restrictive assumptions. The first is that anytime a dummy variable takes a value of 1 and the relevant parameter is significant, there is a non-zero effect of promotion on sales. The second is that this effect is constant across all weeks. In many practical cases however, one may conjecture that the effects of promo- tion are not constant over time. Therefore, we propose a new and rather parsimo- nious econometric model for the purpose of measuring the effects of promotions, while allowing for time-variation in these effects. The main idea is that promotions can (but not necessarily) lead to positive and suddenly large values of sales in the same week, and that they can perhaps lead to large negative values in the week there-after, if there is a, what is called, post-promotion dip. We discuss representation and interpretation of the model, and we outline the maximum likelihood parameter estimation method. Simulation results suggest that the estimation method is quite reliable and that the distribution of the estimator is approximately normal. We illustrate the model in substantial detail on two sets of empirical data in order to indicate its practical usefulness http://repub.eur.nl/res/pub/132/ 2001-01-01T00:00:00Z One of the aims of direct marketing in practice is to target the most profitable customers in the database at hand. This selection is often done based on observed behavior in the past. As a consequence, databases arising from the responses to direct mailings are not a random sample from all potential respondents. When not all heterogeneity is observed, part of the target selection rule will be based on the unobserved heterogeneity, so selection is endogenous. Treating an endogenously selected sample as a random sample results in inconsistent parameter estimates, which in general also harms the predictive performance of the model. We develop an adjustment to the likelihood of the model that corrects for the endogenous sample selection. We apply this technique to the selection of mail targets for a charitable organization. In the application we also show that, based on a model for the response rate and the amount donated simultaneously, we can create a target selection rule that maximizes expected revenues. Such a selection rule outperforms selection rules based on response rates or donated amount only. The traditional approach of maximizing response is therefore not the optimal approach to target selection. http://repub.eur.nl/res/pub/2035/ 2001-01-01T00:00:00Z http://repub.eur.nl/res/pub/2126/ 2001-01-01T00:00:00Z Recent advances in data collection and data storage techniques enable marketing researchers to study the individual characteristics of a large range of transactions and purchases, in particular the effects of household-specific characteristics. This book presents the most important and practically relevant quantitative models for marketing research. Each model is presented in detail with a self-contained discussion, which includes: a demonstration of the mechanics of the model, empirical analysis, real world examples, and interpretation of results and findings. The reader of the book will learn how to apply the techniques, as well as understand the latest methodological developments in the academic literature. Pathways are offered in the book for students and practitioners with differing numerical skill levels; a basic knowledge of elementary numerical techniques is assumed. http://repub.eur.nl/res/pub/1663/ 2000-12-15T00:00:00Z We present a statistical model for voter choice that incorporates a consideration set stage and final vote intention stage. The first stage involves a multivariate probit model for the vector of probabilities that a candidate or a party gets considered. The second stage of the model is a multinomial probit model for the actual choice. In both stages we use as explanatory variables data on voter choice at the previous election, as well as socio-demographic respondent characteristics. Importantly, our model explicitly accounts for the three types of "missing data" encountered in polling. First, we include a no-vote option in the final vote intention stage. Second, the "do not know" response is assumed to arise from too little difference in the utility between the two most preferred options in the consideration set. Third, the "do not want to say" response is modelled as a missing observation on the most preferred alternative in the consideration set. Thus, we consider the missing data generating mechanism to be non-ignorable and build a model based on utility maximization to describe the voting intentions of these respondents. We illustrate the merits of the model as we have information on a sample of about 5000 individuals from the Netherlands for who we know how they voted last time (if at all), which parties they would consider for the upcoming election, and what their voting intention is. A unique feature of the data set is that information is available on actual individual voting behavior, measured at the day of election. We find that the inclusion of the consideration set stage in the model enables the user to make more precise inferences on the competitive structure in the political domain and to get better out-of-sample forecasts. http://repub.eur.nl/res/pub/49/ 2000-10-13T00:00:00Z We propose a new method to model consumers' consideration and choice processes. We develop a parsimonious probit type model for consideration and a multinomial probit model for choice, given consideration. Unlike earlier models of consideration ours is not prone to the curse of dimensionality, while we allow for very general structures of unobserved dependence in consideration among brands. In addition, our model allows for state dependence and marketing mix effects on consideration. Unique to this study is that we attempt to establish the validity of existing practice to infer consideration sets from observed choices in panel data. To this end, we use data collected in an on-line choice experiment involving interactive supermarket shelves and post-choice questionnaires to measure the choice protocol and stated consideration levels. We show with these experimental data that underlying consideration sets can be successfully retrieved from choice data alone and that there is substantial convergent validity of the stated and inferred consideration sets. We further find that consideration is a function of point-of-purchase marketing actions such as display and shelf space, and of consumer memory for recent choices. Next, we estimate the model on IRI panel data. We have three main results. First, compared with the single-stage probit model, promotion effects are larger and are inferred with smaller variances when they are included in the consideration stage of the two-stage model. Promotion effects are significant only in the two-stage model that includes consideration, whereas they are not in a single-stage choice model. Second, the price response curves of the two models are markedly diferent. The two-stage model offers a nice intuition for why promotional price response is different from regular price response. In addition and consistent with intuition, the two-stage model also implies that merchandizing has more effect on choice among those who did not buy the brand before than among those who already did. It is explained why a single-stage model does not harbor this feature. In fact, the single-stage model implies the opposite for smaller or more expensive brands. Third, we find that the consideration of brands does not covary greatly across brands once we take account of observed effects. Managerial implications and future research are also discussed. http://repub.eur.nl/res/pub/1660/ 2000-10-05T00:00:00Z Two important empirical features of monthly US unemployment are that shocks to the series seem rather persistent and that unemployment seems to rise faster in recessions than that it falls during expansions. To jointly capture these features of long memory and nonlinearity, respectively, 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. http://repub.eur.nl/res/pub/7691/ 2000-04-19T00:00:00Z 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. http://repub.eur.nl/res/pub/1640/ 2000-02-17T00:00:00Z Charitable organizations often consider direct mailings to raise donations. Obviously, it is important for a charity to make a profitable selection from available mailing lists, which can be its own list or a list obtained elsewhere. For this purpose, a charitable organization usually has to address the following four questions: 1. Who should we send a mailing? 2. Who is likely to respond to that mailing? 3. How much time will it take for such an individual to respond? 4. How much money will this individual donate? Several techniques for addressing one or more of these questions have been suggested in the literature. For example, Bult and Wansbeek (1995) develop a model that addresses question 2. Otter et al. (1997) develop a model that jointly considers questions 2 and 4. In practice one often relies on techniques such as RFM-based decision rules (Bauer 1988) in order to answer question 1. In this paper we develop a model which enables a charitable organization to make an optimal selection from its own mailing list, while simultaneously considering the four questions above. Hence, our model consists of four components with a possible non-zero correlation structure. The explanatory variables in each of these components are RFM-type variables, where these are allowed to have different effects on the various variables to be explained. In particular, we show that the first component is essential when a target selection model is applied on a database. Neglecting this component can generate a substantial bias in the results of subsequent analysis. The various model parameters are estimated by maximum likelihood. We illustrate our model using a random drawing of about 5,300 individuals from the database of a large Dutch charitable organization. Our empirical results indicate the relevance of the non-zero correlation across the model components, and the relevance of taking account of the target selection part. We find some RFM variables to have effects with opposite signs on the probability to respond, the time for response and the donation. It is found that the most profitable individuals are not the ones who have maximum scores on the RFM variables. We conclude with a discussion of various further research topics. http://repub.eur.nl/res/pub/18192/ 2000-01-01T00:00:00Z We propose a novel Bayesian test under a (noninformative) Jeffreys’ prior specifica- tion. 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 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 misspecification in linear and cointegration models. http://repub.eur.nl/res/pub/2176/ 2000-01-01T00:00:00Z 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. http://repub.eur.nl/res/pub/2183/ 2000-01-01T00:00:00Z In this paper we propose a dynamic multinomial probit model in order to estimate the long-run and short- run effects of marketing mix variables on brand choice. The latent variables, which contain the unobserved perceived utilities, follow a first-order vector error correction autoregressive process of order 1 with current and lagged explanatory variables. The unrestricted autoregressive parameter matrix concerns the intertemporal correlation in perceived utilities of households over purchase occasions and indicates the persistence in brand choice. As explanatory variables we consider relative prices and promotional activities like feature and display. An important and novel feature of our model is that it allows for different long-run and short-run effects of promotional activities, thereby extending the models that are currently available in the literature. Additionally, to account for different base preferences for brands across households, we allow for consumer heterogeneity. Our application concerns a panel of households choosing among several brands of a FMCG. Our estimated model turns out to be an improvement over a static model and over a model with only short-run effects, in terms of in-sample fit and out-of-sample forecasts. http://repub.eur.nl/res/pub/1562/ 1999-01-01T00:00:00Z To enable answering the question in the title, we introduce a bivariate censored latent effects autoregression, and discuss representation, parameter estimation, diagnostics and inference. We show that this bivariate nonlinear model is very useful for examining common nonlinearity. We apply the model to the monthly unemployment rate in the US and Canada to examine if these variables have common cyclical properties conditional on lagged explanatory variables such as industrial production, the oil price and interest spread. We find that US variables have explanatory value for Canadian unemployment, but that Canadian variables do not predict cyclical patterns in the US. Also, we find that recessionary shocks in Canada are more persistent than similar sized shocks in the US in the same period. Finally, we obtain some evidence for a common nonlinear business cycle. http://repub.eur.nl/res/pub/1598/ 1999-01-01T00:00:00Z This paper is concerned with forecasting univariate seasonal time series data using periodic autoregressive models. We show how one should account for unit roots and deterministic terms when generating out-of-sample forecasts. We illustrate the models for various quarterly UK consumption series. http://repub.eur.nl/res/pub/2140/ 1999-01-01T00:00:00Z Periodic autoregressions are characterised by autoregressive structures that vary with the season. If a time series is periodically integrated, one needs a seasonally varying differencing filter to remove the stochastic trend. When the periodic regression model contains constants and trends with unrestricted parameters, the data can show diverging seasonal deterministic trends. In this paper we derive explicit expressions for parameter restrictions that result in common deterministic trends under periodic trend stationarity and periodic integration. http://repub.eur.nl/res/pub/2152/ 1999-01-01T00:00:00Z 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. http://repub.eur.nl/res/pub/1551/ 1998-07-02T00:00:00Z Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank reduction of the long run multiplier is modelled using a decomposition resulting from its singular value decomposition. It specifies the long run multiplier matrix as the sum of a matrix that equals the product of the adjustment parameters and the cointegrating vectors, i.e. the cointegration specification, and a matrix that models the deviation from cointegration. Priors and posteriors for the parameters of the cointegration model are obtained by restricting the latter matrix to zero in the prior and posterior of the unrestricted long run multiplier. The special decomposition of the long run multiplier results in unique posterior densities. This theory 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 illustrate the analysis with several simulated series, the UK data of Hendry and Doornik (1994) and the Danish data of Johansen and Juselius (1990). http://repub.eur.nl/res/pub/2030/ 1998-07-01T00:00:00Z We estimate the empirical bimodal cross-sectional distribution of real Gross Domestic Product per capita of 120 countries over the period 1960–1989 by a mixture of a Weibull and a truncated normal density. The components of the mixture represent a group of poor and a group of rich countries, while the mixing proportion describes the distribution over poor and rich. This enables us to analyse the development of the mean and variance of both groups separately and the switches of countries between the two groups over time. Empirical evidence indicates that the means of the two groups are diverging in terms of levels, but that the growth rates of the means of the two groups over the period 1960–1989 are the same. http://repub.eur.nl/res/pub/1525/ 1998-01-01T00:00:00Z We address the issue of time varying persistence of shocks to macroeconomic time series variables by proposing a new and parsimonious time series model. Our model assumes that this time varying persistence depends on a linear combination of lagged explanatory variables, where this combination characterizes the business cycle regimes. The key feature of our model is that an autoregressive parameter takes larger values only when this indicator variable exceeds a stochastic threshold. The parameters and the (lags of the) variables that constitute the indicator variable have to be determined from the data. Other forms of censoring amount to straightforward extensions. Our application to US unemployment shows that the model fits very well. A linear combination of lagged (differenced) industrial production, oil price, interest spread and stock returns amounts to an adequate indicator of an upcoming recession, which corresponds with explosive behavior of unemployment. Also, the out-of-sample forecasts from our model oftentimes improve those from linear and other nonlinear models. http://repub.eur.nl/res/pub/1532/ 1998-01-01T00:00:00Z A new time series model is proposed to describe observed asymmetries in postwar unemployment data. We assume that recession periods, when unemployment increases rapidly, are caused by unobserved positive shocks. The generating mechanism of these latent shocks is a censored regression model, where linear combinations of lagged explanatory variables lead to positive shocks, while otherwise shocks are equal to zero. We apply our censored latent effects autoregression [CLEAR] to monthly US unemployment, where the positive shocks are found to depend on lagged oil prices, industrial production, the term structure of interest rates and a stock market index. The model fits the data well, and its out-of-sample forecasts appear to outperform those from alternative models. http://repub.eur.nl/res/pub/2043/ 1997-11-27T00:00:00Z Many macroeconomic time series are characterised by long periods of positive growth, expansion periods, and short periods of negative growth, recessions. A popular model to describe this phenomenon is the Markov trend, which is a stochastic segmented trend where the slope depends on the value of an unobserved two-state first-order Markov process. The two slopes of the Markov trend describe the growth rates in the two phases of the business cycle. This thesis deals with a Bayesian analysis of univariate and multivariate macroeconomic time series using Markov trend models. We consider Bayesian methods to analyse the presence of stochastic trends and the business cycle. http://repub.eur.nl/res/pub/13251/ 1997-01-01T00:00:00Z In this paper we propose a Bayesian analysis of seasonal unit roots in quarterly observed time series. Seasonal unit root processes are useful to describe economic series with changing seasonal fluctuations. A natural alternative model for similar purposes contains deterministic seasonal mean shifts instead of seasonal stochastic trends. This leads to analysing seasonal unit roots in the presence of mean shifts using Bayesian techniques. Our method is illustrated using several simulated and empirical data. http://repub.eur.nl/res/pub/2102/ 1997-01-01T00:00:00Z Examples of descriptive models for changing seasonal patterns in economic time series are autoregressive models with seasonal unit roots or with deterministic seasonal mean shifts. In this paper we show through a forecasting comparison for three macroeconomic time series (for which tests indicate the presence of seasonal unit roots) that allowing for possible seasonal mean shifts can improve forecast performance. Next, by means of simulation we demonstrate the impact of imposing an incorrect model on forecasting. We find that an inappropriate decision can deteriorate forecasting performance dramatically in both directions, and hence we recommend the practitioner to take account of seasonal mean shifts when testing for seasonal unit roots. http://repub.eur.nl/res/pub/1398/ 1996-01-01T00:00:00Z Using the standard linear model as a base, a unified theory of Bayesian Analyses of Cointegration Models is constructed. This is achieved by defining (natural conjugate) priors in the linear model and using the implied priors for the cointegration model. Using these priors, posterior results for the cointegration model are obtained using a Metropolis-Hasting sampler. To compare the cointegration models mutually and with the vector autoregressive model under stationarity, we use two strategies. The first strategy uses the Bayesian interpretation of a Lagrange Multiplier statistic. The second strategy compares the models using prior and posterior odds ratios. The latter enables us to compute prior and posterior distributions over the cointegration rank and shows close resemblance with the posterior information criterium from Phillips and Ploberger (1996). To show the applicability of the derived theory, the constructed procedures are applied to data from Johansen and Juselius (1990) and a few simulated data sets. http://repub.eur.nl/res/pub/2046/ 1996-01-01T00:00:00Z This paper considers model selection and forecasting issues in two closely related models for nonstationary periodic autoregressive time series [PAR]. Periodically integrated seasonal time series [PIAR] need a periodic differencing filter to remove the stochastic trend. On the other hand, when the nonperiodic first order differencing filter can be applied, one can have a periodic model with a nonseasonal unit root [PARI]. In this paper, we discuss and evaluate two testing strategies to select between these two models. Furthermore, we compare the relative forecasting performance of each model using Monte Carlo simulations and some U.K. macroeconomic seasonal time series. One result is that forecasting with PARI models while the data generating process is a PIAR process seems to be worse thanvice versa. http://repub.eur.nl/res/pub/2088/ 1995-03-01T00:00:00Z The quarterly time series of German consumption and income are analyzed with respect to seasonality and stochastic trends. It emerges that both variables can be appropriately described by a periodically integrated autoregression. An implication is that the stochastic trend and the seasonal fluctuations are not independent for each of the univariate series. In order to test for cointegration across the two series, we propose several methods which take account of the relationship between seasons and trends in the univariate series. Some of these methods boil down to extracting the stochastic trend from the univariate series in a first step and to relating these trends using cointegration techniques in a second step. Another method is an extension of the Johansen cointegration testing approach to periodic vector autoregressions. Monte Carlo simulations are used to evaluate the empirical performance of the various methods. The main empirical result is that only in the first quarter there seems to be cointegration between German consumption and income. http://repub.eur.nl/res/pub/1354/ 1995-01-01T00:00:00Z In this paper we propose a Bayesian analysis of seasonal unit roots in quarterly observed time series. Seasonal unit root processes are useful to describe economic series with changing seasonal fluctuations. A natural alternative model for similar purposes contains deterministic seasonal mean shifts instead of seasonal stochastic trends. This leads to analysing seasonal unit roots in the presence of mean shifts using Bayesian techniques. Our method is illustrated using several simulated and empirical data. http://repub.eur.nl/res/pub/2044/ 1995-01-01T00:00:00Z http://repub.eur.nl/res/pub/2087/ 1995-01-01T00:00:00Z http://repub.eur.nl/res/pub/2082/ 1994-01-01T00:00:00Z This paper focuses on the issue of period autoagressive time series models (PAR) selection in practice. One aspect of model selection is the choice for the appropriate PAR order. This can be of interest for the valuation of economic models. Further, the appropriate PAR order is important for an adequate empirical application of tests for unit roots since too many parameters affect the performance of such tests. In fact, another aspect of PAR model selection is the decision on the number of unit roots. Finally, in case of unit roots, model choice involves a decision on the most suitable differencing filter to ensure stationarity of the transformed series.