TY - UNPB

T1 - Combining time series and cross sectional data for the analysis of dynamic marketing systems

AU - Horváth, Csilla

AU - Wieringa, Jaap E.

N1 - Relation: http://som.rug.nl/
date_submitted:2003
Rights: Graduate School/Research Institute, Systems, Organisations and Management (SOM)

PY - 2003

Y1 - 2003

N2 - Vector AutoRegressive (VAR) models have become popular in analyzing the behavior of
competitive marketing systems. However, an important drawback of VAR models is that the
number of parameters to be estimated can become very large. This may cause estimation
problems, due to a lack of degrees of freedom. In this paper, we consider a solution to these
problems. Instead of using a single time series, we develop pooled models that combine time
series data for multiple units (e.g. stores). These approaches increase the number of available
observations to a great extent and thereby the efciency of the parameter estimates. We present a
small simulation study that demonstrates this gain in efficiency. An important issue in estimating
pooled dynamic models is the heterogeneity among cross sections, since the mean parameter
estimates that are obtained by pooling heterogenous cross sections may be biased. In order
to avoid these biases, the model should accommodate a sufficient degree of heterogeneity.
At the same time, a model that needlessly allows for heterogeneity requires the estimation
of extra parameters and hence, reduces efciency of the parameter estimates. So, a thorough
investigation of heterogeneity should precede the choice of the nal model. We discuss pooling
approaches that accommodate for parameter heterogeneity in different ways and we introduce
several tests for investigating cross-sectional heterogeneity that may facilitate this choice. We
provide an empirical application using data of the Chicago market of the three largest national
brands in the U.S. in the 6.5 oz. tuna sh product category. We determine the appropriate level
of pooling and calibrate the pooled VAR model using these data.

AB - Vector AutoRegressive (VAR) models have become popular in analyzing the behavior of
competitive marketing systems. However, an important drawback of VAR models is that the
number of parameters to be estimated can become very large. This may cause estimation
problems, due to a lack of degrees of freedom. In this paper, we consider a solution to these
problems. Instead of using a single time series, we develop pooled models that combine time
series data for multiple units (e.g. stores). These approaches increase the number of available
observations to a great extent and thereby the efciency of the parameter estimates. We present a
small simulation study that demonstrates this gain in efficiency. An important issue in estimating
pooled dynamic models is the heterogeneity among cross sections, since the mean parameter
estimates that are obtained by pooling heterogenous cross sections may be biased. In order
to avoid these biases, the model should accommodate a sufficient degree of heterogeneity.
At the same time, a model that needlessly allows for heterogeneity requires the estimation
of extra parameters and hence, reduces efciency of the parameter estimates. So, a thorough
investigation of heterogeneity should precede the choice of the nal model. We discuss pooling
approaches that accommodate for parameter heterogeneity in different ways and we introduce
several tests for investigating cross-sectional heterogeneity that may facilitate this choice. We
provide an empirical application using data of the Chicago market of the three largest national
brands in the U.S. in the 6.5 oz. tuna sh product category. We determine the appropriate level
of pooling and calibrate the pooled VAR model using these data.

M3 - Working paper

BT - Combining time series and cross sectional data for the analysis of dynamic marketing systems

PB - s.n.

ER -