Estimating Discount Functions with Consumption Choices over the Lifecycle

Intertemporal preferences are di¢ cult to measure. We estimate time preferences using a structural bu¤er stock consumption model and the Method of Simulated Moments. The model includes stochastic labor income, liquidity constraints, child and adult dependents, liquid and illiquid assets, revolving credit, retirement, and discount functions that allow short-run and longrun discount rates to di¤er. Data on retirement wealth accumulation, credit card borrowing, and consumption-income comovement identify the model. Our benchmark estimates imply a 40% short-term annualized discount rate and a 4.3% long-term annualized discount rate. Almost all speci…cations reject the restriction to a constant discount rate. Our quantitative results are sensitive to assumptions about the return on illiquid assets and the coe¢ cient of relative risk aversion. When we jointly estimate the coe¢ cient of relative risk aversion and the discount function, the short-term discount rate is 15% and the long-term discount rate is 3.8%. We received helpful advice from Alberto Alesina, Orazio Attanasio, Felipe Balmaceda, Robert Barro, John Campbell, Christopher Carroll, Pierre-Olivier Gourinchas, Cristóbal Huneeus, Greg Mankiw, Jonathan Parker, Ariel Pakes, Raimundo Soto, Samuel Thompson, Nicholas Souleles, Motohiro Yogo, two referees and our editor Mark Gertler at the AER, and seminar audiences at the University of California-Berkeley, Central Bank of Chile, Harvard University, NBER, the University of Minnesota, Stanford University, and Princeton University. Laibson acknowledges …nancial support from the National Science Foundation (SBR-9510985), the National Institute on Aging (R01-AG-16605), and the Olin Foundation; Repetto, from DID-Universidad de Chile, FONDECYT (1990004), Fundación Andes and an institutional grant to CEA from the Hewlett Foundation; and Tobacman from a National Science Foundation Graduate Research Fellowship.