Modeling the underreporting bias in panel survey data

Panel survey data have been gaining importance in marketing. However, one challenge of estimating econometric models based on panel survey data is how to account for underreporting; that is, respondents do not report behavioral incidences that actually occur. Underreporting is especially likely to occur in a panel survey because the data-recording mechanism is often tedious, complex, and effortful. The probability of underreporting is likely to vary across respondents and also over the duration of the survey period. In this paper, we propose a model to simultaneously study reported behavioral incidences and partially observed actual behavioral incidences. We propose a Bayesian approach for estimating the proposed model. We treat those unobserved actual behavioral incidences as latent variables, and the Gibbs sampler makes it convenient to impute the nonreported consumption incidences along with making inferences on other model parameters. Our proposed method has two advantages. First, it offers a model-based approach to remove the underreporting bias in panel survey data and therefore allows marketing researchers to make accurate inferences about consumers' actual behavior. Second, the method also offers a natural way to study factors that influence respondents' propensity to underreport. Because we treat those underreported behavioral incidences as nonmissing at random, this underreporting propensity varies across respondents and over time. This understanding can help marketing researchers design the right strategy to intervene and incentivize respondents to authentically report and hence improve the quality of survey data. The proposed model and estimation approach are tested on both synthetic data and actual panel survey data on consumer-reported beverage-drinking behavior. Our analysis suggests that underreporting can significantly mask respondents' true behavior.