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Because utility/profits, state transitions and discount rates are confounded in dynamic models, discount rates are typically fixed to estimate the other two factors. Yet these rate choices, if mis-specified, generate poor forecasts and policy prescriptions. Using a field study wherein cellphone users transitioned from a linear to three-part-tariff pricing plan, we estimate a dynamic structural model of minute usage and obtain discount factors that would normally be unidentifiable. The identification rests upon imputing the utility using decisions made in a context where the future is inconsequential; then using these utilities to identify discount rates when consumers were switched to a three-part tariff where dynamics became material.
We find that the estimated weekly discount factor (0.90) is much 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 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%. |