Tricked by Truncation: Spurious Duration Dependence and Social Contagion in Hazard Models

Authors:
Christophe Van den Bulte;Raghuram Iyengar
Affiliations:
The Wharton School of the University of Pennsylvania, Philadelphia, Pennsylvania 19104;The Wharton School of the University of Pennsylvania, Philadelphia, Pennsylvania 19104
Venue:
Marketing Science
Year:
2011

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Abstract

We show both analytically and through Monte Carlo simulations that applying standard hazard models to right-truncated data, i.e., data from which all right-censored observations are omitted, induces spurious positive duration dependence and hence can trick researchers into believing to have found evidence of social contagion when there is none. Truncation also tends to deflate the effect of time-invariant covariates. These results imply that not accounting for right truncation can lead managers to rely too much on word of mouth in generating new product adoption and to poorly identify the customers most likely to adopt early. Not accounting for right truncation can also lead to suboptimal pricing decisions and to erroneous assessments of variations in customer lifetime value. We assess the effectiveness of four possible solutions to the problem and find that only using an analytically corrected likelihood function protects one against truncation artifacts inflating coefficients of contagion and attenuating coefficients of time-invariant covariates.