Essays on Quantitative Marketing Models and Monte Carlo Integration Methods

The last few decades have led to an enormous increase in the availability of large detailed data sets and in the computing power needed to analyze such data. Furthermore, new models and new computing techniques have been developed to exploit both sources. All of this has allowed for addressing research questions via analyses which were infeasible to carry out previously. This thesis builds on both the modeling and the computing developments. The first part contains three quantitative marketing models. These models can be applied to scanner data to get a better understanding of purchase behavior of households and to infer the effectiveness of promotions on brand performance. The second part of the thesis provides an overview of several Monte Carlo techniques which can be used in Bayesian analyses to get insight into the posterior density of model parameters. Additionally, it describes a new methodology which extends current methods

Analyzing the effects of past prices on reference price formation

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

Which brands gain share from which brands? Inference from store-level scanner data

Market share models for weekly store-level data are useful to understand competitive structures by delivering own and cross price elasticities. These models can however not be used to examine which brands lose share to which brands during a specific period of time. It is for this purpose that we propose a new model, which does allow for such an examination. We illustrate the model for two product categories in two markets, and we show that our model has validity in terms of both in-sample fit and out-of-sample forecasting. We also demonstrate how our model can be used to decompose own and cross price elasticities to get additional insights into the competitive structure

The Davies Problem: A New Test for Random Slope in the Hierarchical Linear Model

__Abstract__ Crucial inference for the hierarchical linear model concerns the null hypothesis of no random slope. We argue that the usually applied statistical test suffers from the so-called Davies problem, that is, a nuisance parameter is only identified under the alternative. We propose an easy-to-implement methodology that exploits this property. We provide the relevant critical values and demonstrate through simulations that our new methodology has better power properties

On the econometrics of the Koyck model

The geometric distributed lag model, after application of the so-called Koyck transformation, is often used to establish the dynamic link between

Explaining Adaptive Radial-Based Direction Sampling

In this short paper we summarize the computational steps of Adaptive Radial-Based Direction Sampling (ARDS), which can be used for Bayesian analysis of ill behaved target densities. We consider one simulation experiment in order to illustrate the good performance of ARDS relative to the independence chain MH algorithm and importance sampling

Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods

Adaptive Polar Sampling (APS) algorithms are proposed for Bayesian analysis of models with nonelliptical, possibly, multimodal posterior distributions. A location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to sample directions and, conditionally on these, distances are generated by inverting the cumulative distribution function. A sequential procedure is applied to update the initial location and scaling matrix in order to sample directions in an efficient way. Tested on a set of canonical mixture models that feature multimodality, strong correlation, and skewness, the APS algorithms compare favourably with the standard Metropolis-Hastings and importance samplers in terms of flexibility and robustness. APS is applied to several econometric and statistical examples. The empirical results for a regression model with scale contamination, an ARMA-GARCH-Student t model with near cancellation of roots and heavy tails, a mixture model for economic growth, and a nonlinear threshold model for industrial production growth confirm the practical flexibility and robustness of APS