A comparison of alternative price specifications in conjoint analysis

This paper examines how alternative price specifications, budget constraints, and structural price restrictions affect inference about demand and willingness to pay (WTP) in dual-response conjoint analysis. Using a large-screen television study, we compare linear and dummy-coded price effects under three budget treatments: no budget constraint, a budget constraint imposed on the second response, and a cliffing rule that fixes each respondent’s budget at the highest purchased price. We also evaluate monotonicity constraints for dummy-coded price part-worths. We find that non-price part-worths are similar across models, but the implied demand curves and WTP estimates differ substantially. Incorporating a budget constraint improves model fit without materially reducing hold-out predictive performance, while producing more plausible high-price demand estimates and avoiding inflated price sensitivity that can distort counterfactual and equilibrium pricing analyses. Cliffing can perform well in fit and prediction, but its design-dependent cutoff generates mechanically sharp demand drops and non-smooth counterfactual behavior. Linear price effects provide a stable and interpretable foundation, whereas unconstrained dummy-coded price effects can yield unstable high-price demand and highly dispersed WTP estimates. Imposing monotonicity substantially mitigates these problems by enforcing economically coherent price ordering. Finally, hyperparameter-based inference reduces WTP uncertainty by pooling information across respondents, supporting more reliable economic conclusions.