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Modeling dynamic effects of promotion on interpurchase times. (English) Zbl 1254.91585
Summary: Dynamic effects of marketing-mix variables on interpurchase times can be analyzed in the context of a duration model. Specifically, this can be done by extending the accelerated failure-time model with an autoregressive structure. An important feature of the model is that it allows for different long-run and short-run effects of marketing-mix variables on interpurchase times. The error-correction specification of the model contains parameters which measure the direct effect of a temporary change in a marketing-mix variable on interpurchase times and parameters which measure the long-run (cumulative) effect of a temporary change in a marketing-mix variable on current and future interpurchase times. As marketing efforts usually change during the spells, time-varying covariates are explicitly dealt with. Heterogeneity of individual behavior is allowed for through a mixture approach. An empirical analysis of purchases in three different categories reveals, for some segments of households, that the short-run effects of marketing-mix variables are significantly different from the long-run effects. The decay in the effect of changes in marketing-mix variables over time is larger in categories with large interpurchase times, and price has the largest long-run effect for the perishable product. Finally, ignoring dynamic effects leads to erroneous results about the effectiveness of marketing instruments.

##### MSC:
 91B82 Statistical methods; economic indices and measures 90B60 Marketing, advertising
Ox
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##### References:
 [1] Ailawadi, K.L.; Neslin, S.A., The effect of promotion on consumption: buying more and consuming it faster, Journal of marketing research, 35, 3, 390-398, (1998) [2] Allenby, G.M.; Leone, R.P.; Jen, L., A dynamic model of purchase timing with application to direct marketing, Journal of the American statistical association, 94, 446, 365-374, (1999) [3] Allenby, G.M.; Rossi, P.E., Marketing models of consumer heterogeneity, Journal of econometrics, 89, 57-78, (1999) · Zbl 0959.62116 [4] Bauwens, L.; Galli, F., Efficient importance sampling for ML estimation of SCD models, Computational statistics and data analysis, 53, 1974-1992, (2009) · Zbl 1453.62040 [5] Bauwens, L.; Veredas, D., The stochastic conditional duration model: a latent variable model for the analysis of financial durations, Journal of econometrics, 119, 381-412, (2004) · Zbl 1282.91236 [6] Blattberg, R.C.; Eppen, G.C.; Liebermann, J., A theoretical and empirical evaluation of price deals for consumer durables, Journal of marketing, 45, 116-129, (1981) [7] Böckenholt, U., Mixed INAR(1) Poisson regression models: analyzing heterogeneity and serial dependencies in longitudinal count data, Journal of econometrics, 89, 1-2, 317-338, (1999) · Zbl 0958.62110 [8] Bucklin, R.E.; Gupta, S.; Siddarth, S., Determining segmentation in sales response across consumer purchase behaviors, Journal of marketing research, 35, May, 189-197, (1998) [9] Chintagunta, P.K., Investigating purchase incidence, brand choice and purchase quantity decisions of households, Marketing science, 12, 2, 184-208, (1993) [10] Chintagunta, P.K.; Jain, D.C.; Vilcassim, N.J., Investigating heterogeneity in brand preferences in logit models for panel data, Journal of marketing research, 28, 417-428, (1991) [11] Chintagunta, P.K.; Prasad, A.R., An empirical investigation of the “dynamic mcfadden” model of purchase timing and brand choice: implications for market structure, Journal of business & economic statistics, 16, 1, 2-12, (1998) [12] Davies, R.B., Hypothesis testing when a nuisance parameter is present only under the alternative, Biometrika, 64, 2, 247-254, (1977) · Zbl 0362.62026 [13] Dekimpe, M.G.; Hanssens, D.M.; Silva-Risso, J.M., Long-run effects of price promotions in scanner markets, Journal of econometrics, 89, 269-291, (1999) · Zbl 0962.62116 [14] Dempster, A.P.; Laird, N.M.; Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm (with discussion), Journal of the royal statistical society, series B, 39, 1-38, (1977) · Zbl 0364.62022 [15] Doornik, J.A., Object-oriented matrix programming using ox, (1999), Timberlake Consultants Press and Oxford London [16] Engle, R.F.; Russell, J.R., Autoregressive conditional duration: a new model for irregularly spaced transaction data, Econometrica, 66, 5, 1127-1162, (1998) · Zbl 1055.62571 [17] Fok, D.; Horváth, C.; Paap, R.; Franses, P.H., A hierarchical Bayes error correction model to explain dynamic effects of price changes, Journal of marketing research, 43, 3, 443-461, (2006) [18] Fok, D.; Paap, R., Modeling category-level purchase timing with brand-level marketing variables, Journal of applied econometrics, 24, 469-489, (2009) [19] Gönül, F.; Srinivasan, K., Consumer purchase behavior in a frequently bought product category: estimation issues and managerial insights from a hazard function model with heterogeneity, Journal of the American statistical association, 88, 424, 1219-1227, (1993) [20] Gönül, F.; Srinivasan, K., Modeling multiple sources of heterogeneity in multinomial logit models: methodological and managerial issues, Marketing science, 12, 3, 213-229, (1993) [21] Gupta, S., Impact of sales promotions on when, what, and how much to buy, Journal of marketing research, 25, 342-355, (1988) [22] Gupta, S., Stochastic models of interpurchase time with time-dependent covariates, Journal of marketing research, 28, 1-15, (1991) [23] Helsen, K.; Schmittlein, D.C., How does a product market’s typical price-promotion pattern affect the timing of households’ purchases? an empirical study using upc scanner data, Journal of retailing, 68, 3, 316-338, (1992) [24] Helsen, K.; Schmittlein, D.C., Analyzing duration times in marketing: evidence for the effectiveness of hazard rate models, Marketing science, 11, 4, 395-414, (1993) [25] Hendry, D.F.; Pagan, A.R.; Sargan, J.D., Dynamic specification, (), 1023-1100, (Chapter 18) [26] Jain, D.C.; Vilcassim, N.J., Investigating household purchase timing decisions: a conditional hazard function approach, Marketing science, 10, 1, 1-23, (1991) [27] Jain, D.C.; Vilcassim, N.J.; Chintagunta, P.K., A random-coefficients logit brand-choice model applied to panel data, Journal of business & economic statistics, 12, 3, 317-328, (1994) [28] Jedidi, K.; Mela, C.F.; Gupta, S., Managing advertising and promotion for long-run profitability, Marketing science, 18, 1, 1-22, (1999) [29] Kalbfleisch, J.; Prentice, R., The statistical analysis of failure time data, (1980), John Wiley & Sons New York · Zbl 0504.62096 [30] Kamakura, W.A.; Russell, G.J., A probabilistic choice model for market segmentation and elasticity structure, Journal of marketing research, 26, 379-390, (1989) [31] Keane, M.P., Modeling heterogeneity and state dependence in consumer choice behavior, Journal of business & economic statistics, 15, 3, 310-327, (1997) [32] Kiefer, N.M., Economic duration data and hazard functions, Journal of economic literature, 26, 646-679, (1988) [33] Lancaster, T., Econometric methods for the duration of unemployment, Econometrica, 47, 939-956, (1979) · Zbl 0412.90018 [34] Lancaster, T., () [35] Mela, C.F.; Gupta, S.; Lehmann, D.R., The long-term impact of promotions and advertising on consumer brand choice, Journal of marketing research, 34, 2, 248-261, (1997) [36] Neslin, S.A.; Henderson, C.; Quelch, J., Consumer promotions and the acceleration of product purchases, Marketing science, 4, 2, 147-165, (1985) [37] Paap, R.; Franses, P.H., A dynamic multinomial probit model for brand choice with different long-run and short-run effects of marketing-mix variables, Journal of applied econometrics, 15, 717-744, (2000) [38] Ridder, G., The non-parametric identification of generalized accelerated failure-time models, Review of economic studies, 57, 167-182, (1990) · Zbl 0711.62087 [39] Seetharaman, The additive risk model for purchase timing, Marketing science, 23, 2, 234-242, (2004) [40] Strickland, C.M.; Forbes, C.S.; Martin, G.M., Bayesian analysis of the stochastic conditional duration model, Computational statistics and data analysis, 50, 2247-2267, (2006) · Zbl 1445.62241 [41] Vakratsas, D.; Bass, F.M., A segment-level hazard approach to studying household purchase timing decisions, Journal of applied econometrics, 17, 49-59, (2002) [42] Vermunt, J.K.; Magidson, J., Latent class models for classification, Computational statistics & data analysis, 41, 531-537, (2003) · Zbl 1429.62268 [43] Vilcassim, N.J.; Jain, D.C., Modeling purchase-timing and brand-switching behavior incorporating explanatory variables and unobserved heterogeneity, Journal of marketing research, 28, 29-41, (1991)
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