PASTA: A State-Space Representation for In-Line Estimation of Time-Varying Parameters of Market Response Models

Abstract

This article presents a state-space representation known as parameters as states (PASTA) for linear market response models with time-varying parameters. The PASTA representation enables (a) conversion of the problem of estimating the time-varying effectiveness of marketing interventions from a maximum likelihood–based, offline estimation to a Bayesian, update-based, in-line estimation; (b) development of a computationally efficient approach to estimating and tracking time-varying parameters; and (c) early estimates of the effectiveness of marketing interventions and changes in that effectiveness. These characteristics are important in today’s digital marketing world, in which data availability, the size of the marketer’s decision space, the computational complexity of the estimation problem, market dynamics, and significance of proactive marketing are factors of increased in importance. We also present a Kalman filter–based estimation approach that can be used in conjunction with PASTA and establish the stability, observability, and optimality of the estimator. Using computational studies to supplement theoretical results and compare parameter estimates obtained from PASTA with those using ordinary least squares and recursive least squares, we show that PASTA-based estimation reduces the impact of collinearity, autocorrelation, and measurement errors on the quality of the estimates.