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

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  • Horváth, Csilla
  • Wieringa, Jaap E.

    (Groningen University)

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    Abstract

    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.

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    File URL: http://irs.ub.rug.nl/ppn/248290940
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    Bibliographic Info

    Paper provided by University of Groningen, Research Institute SOM (Systems, Organisations and Management) in its series Research Report with number 03F13.

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    Date of creation: 2003
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    Handle: RePEc:dgr:rugsom:03f13

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    References

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    1. Nathaniel Beck, Jonathan N. Katz, 2004. "Random Coefficient models for time-series-cross-section data," Working Papers 1205, California Institute of Technology, Division of the Humanities and Social Sciences.
    2. Horváth, Csilla & Kornelis, Marcel & Leeflang, Peter S.H., 2002. "What marketing scholars should know about time series analysis : time series applications in marketing," Research Report 02F17, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    3. Canova, Fabio & Ciccarelli, Matteo, 2004. "Forecasting and turning point predictions in a Bayesian panel VAR model," Journal of Econometrics, Elsevier, vol. 120(2), pages 327-359, June.
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    6. Carol Scotese Lehr, 1999. "Banking on fewer children: Financial intermediation, fertility and economic development," Journal of Population Economics, Springer, vol. 12(4), pages 567-590.
    7. Franses,Philip Hans, 1998. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521586412, Fall.
    8. International Monetary Fund, 1999. "Neglected Heterogeneity and Dynamics in Cross-Country Savings Regressions," IMF Working Papers 99/128, International Monetary Fund.
    9. repec:wop:humbsf:1999-29 is not listed on IDEAS
    10. Douglas Holtz-Eakin & Whitney K. Newey & Harvey S. Rosen, 1987. "The Revenues-Expenditures Nexus: Evidence from Local Government Data," NBER Working Papers 2180, National Bureau of Economic Research, Inc.
    11. Baltagi, Badi H. & Hidalgo, Javier & Li, Qi, 1996. "A nonparametric test for poolability using panel data," Journal of Econometrics, Elsevier, vol. 75(2), pages 345-367, December.
    12. Peter L. Rousseau & Paul Wachtel, 1998. "Equity Markets and Growth: Cross-Country Evidence on Timing and Outcomes, 1980-1995," Working Papers 98-09, New York University, Leonard N. Stern School of Business, Department of Economics.
    13. G. Dekimpe, Marnik & Hanssens, Dominique M. & Silva-Risso, Jorge M., 1998. "Long-run effects of price promotions in scanner markets," Journal of Econometrics, Elsevier, vol. 89(1-2), pages 269-291, November.
    14. Leeflang, P.S.H. & Wittink, Dick R., 2000. "Building models for marketing decisions: past, present and future," Research Report 00F20, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    15. Donald Robertson & James Symons, 1991. "Some Strange Properties of Panel Data Estimators," CEP Discussion Papers dp0044, Centre for Economic Performance, LSE.
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    Cited by:
    1. Wieringa, Jaap E. & Horvath, Csilla, 2005. "Computing level-impulse responses of log-specified VAR systems," International Journal of Forecasting, Elsevier, vol. 21(2), pages 279-289.
    2. Koen Pauwels & Imran Currim & Marnik Dekimpe & Dominique Hanssens & Natalie Mizik & Eric Ghysels & Prasad Naik, 2004. "Modeling Marketing Dynamics by Time Series Econometrics," Marketing Letters, Springer, vol. 15(4), pages 167-183, December.

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