On the econometrics of the Koyck model

The geometric distributed lag model, after applicationof the so-called Koyck transformation, is often used to establishthe dynamic link between sales and advertising. This year, theKoyck model celebrates its 50th anniversary.In this paper we focus on the econometrics of this popular model,and we show that this seemingly simple model is a little more complicated than we always tend to think. First, the Koyck transformation entails a parameter restriction, which should not be overlooked for efficiency reasons. Second, the t-statistic for the parameter for direct advertising effects has a non-standard distribution. We provide solutions to these two issues.For the monthly Lydia Pinkham data, it is shown that variouspractical decisions lead to very different conclusions.sales-advertising relationship;Koyck model

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 structuresby delivering own and cross price elasticities. These models can however not be used toexamine which brands lose share to which brands during a specific period of time. It is for thispurpose that we propose a new model, which does allow for such an examination. We illustratethe model for two product categories in two markets, and we show that our model has validity interms of both in-sample fit and out-of-sample forecasting. We also demonstrate how our modelcan be used to decompose own and cross price elasticities to get additional insights into thecompetitive structure.market shares;competitive structure;elasticity decomposition;share-switching;store-level scanner data

Analyzing the effects of past prices on reference price formation

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

Testing changes in consumer confidence indicators

The authors propose a statistical methodology to test changes in consumer confidence indicators. These indicators are surveyed monthly and each time concerndi®erent individuals. This complicates a straightforward interpretation of changesin the values of the index. The proposed methodology involves estimating the transition matrix which connects the fractions of positive, neutral and negative opinions.The elements of this matrix can be estimated and confidence bounds can be computed. A by-product of the method is a simple tool to correct for seasonality. Anillustration to about two decades of Dutch data shows that monthly changes inconsumer confidence are not often significantly different from zero.consumer confidence;Markov process

Simulation based bayesian econometric inference: principles and some recent computational advances.

In this paper we discuss several aspects of simulation basedBayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluatingintegrals by simulation methods is a crucial ingredientin Bayesian inference. Next, the most popular and well-knownsimulation techniques are discussed, the Metropolis-Hastingsalgorithm and Gibbs sampling (being the most popular Markovchain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed samplingmethods: adaptive radial based direction sampling [ARDS],which makes use of a transformation to radial coordinates,and neural network sampling, which makes use of a neural network approximation to the posterior distribution ofinterest. Both methods are especially useful in cases wherethe posterior distribution is not well-behaved, in the senseof having highly non-elliptical shapes. The simulationtechniques are illustrated in several example models, suchas a model for the real US GNP and models for binary data ofa US recession indicator.

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.importance sampling;Markov Chain Monte Carlo;radial coordinates

Adaptive radial-based direction sampling; Some flexible and robust Monte Carlo integration methods

Adaptive radial-based direction sampling (ARDS) algorithms are specified for Bayesian analysis of models with nonelliptical, possibly, multimodal target distributions.A key step is a radial-based transformation to directions and distances. After the transformations a Metropolis-Hastings method or, alternatively, an importance sampling method is applied to evaluate generated directions. Next, distances are generated from the exact target distribution by means of the numerical inverse transformation method. An adaptive procedure is applied to update the initial location and covariance 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 ARDS algorithms compare favourably with the standard Metropolis-Hastings and importance samplers in terms of flexibility and robustness. The empirical examples include a regression model with scale contamination and a mixture model for economic growth of the USA.Markov chain Monte Carlo;importance sampling;radial coordinates

Simulation based Bayesian econometric inference: principles and some recent computational advances

In this paper we discuss several aspects of simulation based Bayesian econometric inference. We start at an elementary level on basic concepts of Bayesian analysis; evaluating integrals by simulation methods is a crucial ingredient in Bayesian inference. Next, the most popular and well-known simulation techniques are discussed, the MetropolisHastings algorithm and Gibbs sampling (being the most popular Markov chain Monte Carlo methods) and importance sampling. After that, we discuss two recently developed sampling methods: adaptive radial based direction sampling [ARDS], which makes use of a transformation to radial coordinates, and neural network sampling, which makes use of a neural network approximation to the posterior distribution of interest. Both methods are especially useful in cases where the posterior distribution is not well-behaved, in the sense of having highly non-elliptical shapes. The simulation techniques are illustrated in several example models, such as a model for the real US GNP and models for binary data of a US recession indicator.

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