MCMC Estimation of Extended Hodrick-Prescott (HP) Filtering Models

The Hodrick-Prescott (HP) method was originally developed to smooth time series, i.e. to get a smooth (long-term) component. We show that the HP smoother can be viewed as a Bayesian linear model with a strong prior for the smoothness component. Extending this Bayesian approach in a linear model set-up is possible by a conjugate and a non-conjugate model using MCMC. The Bayesian HP smoothing model is also extended to a spatial smoothing model. We have to define spatial neighbors for each observation and we can use in a similar way a smoothness prior as for the HP filter in time series. The new smoothing approaches are applied to the (textbook) airline passenger data for time series and to the problem of smoothing spatial regional data. This new approach can be used for a new class of model-based smoothers for time series and spatial models.Hodrick-Prescott (HP) smoothers, Spatial econometrics, MCMC estimation, Airline passenger time series, Spatial smoothing of regional data, NUTS: nomenclature of territorial units for statistics

The Extended Hodrick-Prescott (HP) Filter for Spatial Regression Smoothing

The Hodrick-Prescott (HP) method is a popular smoothing method for economic time series to get a longterm component of stationary series like growth rates. The new extended HP smoothing model is applied to data-sets with an underlying metric and requires a Bayesian linear regression model with a strong prior based on differencing matrices for the smoothness parameter and a weak prior for the regression part. We define a Bayesian spatial smoothing model with neighbors for each observation and we define a smoothness prior similar to the HP filter in time series. This opens a new approach to model-based smoothers for time series and spatial models based on MCMC. We apply it to the NUTS-2 regions of the European Union for regional GDP and GDP per capita, where the fixed effects are removed by an extended HP smoothing model.Hodrick-Prescott (HP) smoothers, smoothed square loss function, spatial smoothing, smoothness prior, Bayesian econometrics

Dating and Exploration of the Business Cycle in Iceland

The paper explores the quarterly sequence of business cycles in Iceland for 40 years between 1970 and 2009 using the business cycle technique of Leamer (2009). We apply first a turning point (TP) dating identification procedure based on the Hendrick- Prescott (HP) filter of the quarterly growth rates of GDP and then we use different candidates for leading indicators for turning points. We find that the Iceland economy has a rather short business cycle of about 3 years and most macroeconomic indicators are in accordance with the business cycles. Only a few indicators have a predictive potential, some variables like consumption show a one quarter lag. Furthermore, we apply the concept of abnormal contributions to growth for candidates as a leading indicator of turning points. We find that over the last decade there is some evidence that abnormal growth contributions are better indicators for troughs than for peaks.Business Cycle dating, HP filtering, exploratory turning point analysis, lead and lag indicators, abnormal growth contributions, gross domestic product (GDP) growth

Marketing Response Models for Shrinking Beer Sales in Germany

Beer sales in Germany are confronted for several years with a shrinking market share in the market of alcoholic beverages. I use the approach of sales response function (SRF) models as in Polasek and Baier (2010) and adapt it to time series observation of beer sales for simultaneous estimation. I propose a new class of growth sales (gSRF) models having endogenous and exogenous variables as in Polasek (2011) together with marketing efforts that follow a sustained growth allocation principle. This approach allows to model growth rates in markets that are exposed to fierce competition and where marketing efforts cannot be evaluated directly. The class of gSRF models has the property that it models supply (i.e. marketing efforts) and demand factors jointly in a log-linear regression model that are correlated over time. The estimated model can explain the relative success of marketing expenditures for the shrinking beer market in the period 1999-2010.Sales response functions (SRF), marketing budget models, MCMC estimation, beer consumption, optimal budget allocation

The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model

The Hodrick-Prescott (HP) method is a popular smoothing method for economic time series to get a smooth or long-term component of stationary series like growth rates. We show that the HP smoother can be viewed as a Bayesian linear model with a strong prior using differencing matrices for the smoothness component. The HP smoothing approach requires a linear regression model with a Bayesian conjugate multi-normalgamma distribution. The Bayesian approach also allows to make predictions of the HP smoother on both ends of the time series. Furthermore, we show how Bayes tests can determine the order of smoothness in the HP smoothing model. The extended HP smoothing approach is demonstrated for the non-stationary (textbook) airline passenger time series. Thus, the Bayesian extension of the HP model defines a new class of model-based smoothers for (non-stationary) time series and spatial models.Hodrick-Prescott (HP) smoothers, model selection by marginal likelihoods, multi-normal-gamma distribution, Spatial sales growth data, Bayesian econometrics

Multivariate Regression and ANOVA Models with Outliers: A Comparative Approach

Assuming a normal-Wishart modelling framework we compare two methods for finding outliers in a multivariate regression (MR) system. One method is the add-1-dummy approach which needs fewer parameters and a model choice criterion while the other method estimates the outlier probability for each observation by a Bernoulli mixing outlier location shift model. For the simple add-1-dummy model the Bayes factors and the posterior probabilities can be calculated explicitly. In the probabilistic mixing model we show how the posterior distribution can be obtained by a Gibbs sampling algorithm. The number of outliers is determined using the marginal likelihood criterion. The methods are compared for test scores of language examination data of Fuller (1987): The results are similar but differ in their strength of their empirical evidence.Multivariate regression, Multivariate one-way ANOVA, Outliers, Gibbs sampling, Marginal likelihoods, Sensitivity analysis

Endogeneity and Exogeneity in Sales Response Functions

Endogeneity and exogeneity are topics that are mainly discussed in macroeconomics. We show that sales response functions (SRF) are exposed to the same problem if we assume that the control variables in a SRF refl ect behavioral reactions of the supply side. The supply side actions are covering a flexible marketing component which could interact with the sales responses if sales managers decide to react fast according to new market situations. A recent article of Kao et al. (2005) suggested to use a class of production functions under constraints to estimate the sales responses that are subject to marketing strategies. In this paper we demonstrate this approach with a simple SRF(1) model that contains one endogenous variable. Such models can be extended by further exogenous variables leading to SRF-X models. The new modeling approach leads to a multivariate equation system and will be demonstrated using data from a pharma-marketing survey in German regions.Sales response functions, stochastic derivative constraints, simultaneous estimation, MCMC, pharma-marketing, model choice

Traffic Accessibility and the Effect on Firms and Population in 99 Austrian Regions

In this paper we describe the EAR (regional economic accessibility) model to investigate the impact of the improvement of railroad infrastructure on regional GDP, population and firms growth in 99 Austrian regions. We evaluate the impact of four potential railroad infrastructure investment projects on the accessibility of Austrian regions, which is used to forecast future growth of these regions. Regional performance is measured by four variables, gross regional product, number of firms, population size, and employment. Eventually a ranking of these four projects is carried out for the first ten years of operation of the four potential investment projects. We show that the improvement of train accessibility has different impacts on regions with high and low overall performance.Evaluation of infrastructure projects, Long-term regional forecasts, Accessibility and traffic analysis, Ranking

Aggregate and Regional Economic Effects of New Railway Infrastructure

Economists expect positive returns to investments in infrastructure. However a project with higher national returns might have less favorable effects on a regional level than the alternative. Therefore new infrastructure should also be assessed on a regional level, but econom(etr)ic evalua tion models are scarce, especially in regional science. This paper proposes new approaches to evaluate infrastructure by a dynamic spatial economet ric model that allows long-term predictions. We investigate the regional effects for 2 Austrian railway projects and show that infrastructure returns are positive on an aggregate and at a regional level but spatial variation can be large.Regional growth convergence, traffic accessibility, infrastructure evaluation, spatial econometrics

Long term regional forecasting with spatial equation systems

Long-term predictions with a system of dynamic panel models can have tricky properties since the time dimension in regional (cross) sectional models is usually short. This paper describes the possible approaches to make long-term-ahead forecast based on a dynamic panel set, where the dependent variable is a cross-sectional vector of growth rates. Since the variance of the forecasts will depend on number of updating steps, we compare the forecasts behavior of a aggregated and a disaggregated updating procedure. The cross section of the panel data can be modeled by a spatial AR (SAR) or Durbin model, including heteroscedasticity. Since the forecasts are non-linear functions of the model parameters we show what MCMC based approach will produce the best results. We demonstrate the approach by a example where we have to predict 20 years ahead of regional growth in 99 Austrian regions in a space-time dependent system of equations.