Influence of Omitted Variables in Consumer Choice Models on Engineering Design Optimization Solutions

This paper examines the impact of omitted variable bias (OVB) within consumer choice models on engineering design optimization solutions. Engineering products often have a multitude of attributes that influence consumers' purchasing decisions, many of which are difficult to include in revealed-preference models due to a lack of data. Correlations among these omitted variables and product attributes included in the model can bias demand parameter estimates. However, engineering design optimization studies typically do not account for this bias. We examine the influence consumer choice OVB can have on design optimization results. We first mathematically derive how OVB propagates into optimal design solutions and characterize properties of optimization problems that affect the magnitude of the resulting error in solutions. We then demonstrate the impact of OVB on optimal designs using a case study of automotive powertrain design optimization. In the case study, we estimate two sets of choice models: one using only "typically observed" vehicle attributes commonly found in the literature, and one with an additional set of "typically unobserved" attributes gathered from Edmunds.com. We find that the model with omitted variables leads to, in some scenarios, substantial bias in parameter estimates (5-143%), which propagates up to 21% error in the optimal engine size.