Working Paper: NBER ID: w26217
Authors: Andrey Simonov; Jean-Pierre H. Dubé; Günter J. Hitsch; Peter E. Rossi
Abstract: We analyze the initial conditions bias in the estimation of brand choice models with structural state dependence. Using a combination of Monte Carlo simulations and empirical case studies of shopping panels, we show that popular, simple solutions that mis-specify the initial conditions are likely to lead to bias even in relatively long panel datasets. The magnitude of the bias in the state dependence parameter can be as large as a factor of 2 to 2.5. We propose a solution to the initial conditions problem that samples the initial states as auxiliary variables in an MCMC procedure. The approach assumes that the joint distribution of prices and consumer choices, and hence the distribution of initial states, is in equilibrium. This assumption is plausible for the mature consumer packaged goods products used in this and the majority of prior empirical applications. In Monte Carlo simulations, we show that the approach recovers the true parameter values even in relatively short panels. Finally, we propose a diagnostic tool that uses common, biased approaches to bound the values of the state dependence and construct a computationally light test for state dependence.
Keywords: brand loyalty; state dependence; Bayesian estimation; initial conditions bias
JEL Codes: D12; L66; M3
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| initial conditions bias (C51) | overestimation of brand loyalty (M37) |
| independence of initial loyalty state from consumer preferences (D11) | specification errors (C20) |
| specification errors (C20) | inconsistent estimates of loyalty (L15) |
| naive treatment of initial loyalty state (C69) | upward bias in estimated degree of loyalty (C92) |
| initial state set to zero (Y20) | attenuation bias (D91) |
| magnitude of bias due to misspecified initial conditions (C51) | underestimation of true degree of loyalty (D80) |
| Bayesian estimator (C11) | accounts for dependence of initial conditions on unobserved consumer preferences (D11) |
| Bayesian estimator (C11) | generates estimates of state dependence (C51) |
| naive estimators (C51) | biases observed in estimates (C51) |
| proposed methods (C90) | provide more accurate assessment of state dependence (C32) |