Determining Consumers' Discount Rates with Field Studies

Abstract

Because utility/profits, state transitions and discount rates are confounded in dynamic models, discount rates are typically fixed for the purpose of identification. We propose a strategy of identifying discount rates. The identification rests upon imputing the utility/profits using decisions made in a context where the future is inconsequential, the objective function is concave, and the decision space is continuous; and then using these utilities/profits to identify discount rates in contexts where dynamics become material. We exemplify this strategy using a field study wherein cellphone users transitioned from a linear to three-part-tariff pricing plan.

We find that the estimated discount rate corresponds to a weekly discount factor (0.90), lower than the value typically assumed in empirical research (0.995). When using a standard 0.995 discount factor, we find the price coefficient is underestimated by 16%. Moreover, the predicted inter-temporal substitution pattern and demand elasticities are biased, leading to a 29% deterioration in model fit; and suboptimal pricing recommendations that would lower potential revenue gains by 76%.

Keywords: dynamic structural model, identification, forward-looking consumers, pricing, three-part tariff, discount rate