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. The authors propose a strategy of identifying discount rates. The identification rests on imputing the utility/profits using decisions made in a context in which the future is inconsequential, the objective function is concave, and the decision space is continuous. They then use these utilities/profits to identify discount rates in contexts in which dynamics become material. The authors exemplify this strategy using a field study in which cell phone users transitioned from a linear to a three-part-tariff pricing plan. They find that the estimated discount rate corresponds to a weekly discount factor (.90), lower than the value typically assumed in empirical research (.995). When using a standard .995 discount factor, they find that the price coefficient is underestimated by 16%. Moreover, the predicted intertemporal 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%.

To Know and to Care: How Awareness and Valuation of the Future Jointly Shape Consumer Spending

“…More recently, research that tries to estimate discount factors from dynamic behavior has treated consumers as fully forward-looking either by assumption (Yao et al 2012) or by experimentally providing full information (Dube, Hitsch, and Jindal 2014). Our findings imply that time preference and planning horizon are not equivalent, and they highlight the importance of qualifying the interpretation of models that make strong assumptions about either factor.…”

“…More explicitly in line with this assumption, Adams and Nettle (2009) correlated measures of smoking with a measure of discounting and, separately, with the propensity to consider future consequences, without considering interactions. Similarly, quantitative models of consumer choice often either assume a fixed discount rate consistent with market interest and estimate aspects of the planning horizon (e.g., probability of taking future discounts into account ;Hartmann 2006) or fix the planning horizon and estimate the discount rate (Yao et al 2012). Empirically, if hypothesis 2 holds, manipulating either factor does not affect the influence of the other factor-the likelihood of purchase would reveal two simple effects with no interaction (see middle panel of fig.…”

Consumer learning and evolution of consumer brand preferences

“…We estimated the model with few different weekly discount factors but the results were not very sensitive to the exact value of the discount factor. Please note that the best way to identify the discount factor is either to find contexts where proper exclusion restrictions and practical identification exist (e.g., Chung et al (2014)) or use (experimental or field) data that has information on behavior both in static and dynamic contexts/regimes to pin down the discount factor (e.g., Yao et al (2012)) but we do not have such data. There are indeed very few cases where such data are available.…”

Moral Hazard in Health Insurance: Do Dynamic Incentives Matter?

“…Indeed, a large literature, going back at least to Hausman (1985), develops methods that address the difficulties that arise in modeling selection and utilization under non-linear budget sets, and applies these methods to other settings in which similar non-linearities are common, such as labor supply (Burtless and Hausman, 1978; Blundell and MaCurdy, 1999; Chetty et al, 2011), electricity utilization (Reiss and White, 2005), and cellular phones (Grubb and Osborne, forthcoming; Yao et al, 2012). …”