Contents
Abstract 3968
Keywords 3969
1. Introduction 3970
2. Investor preferences 3971
2.1. Risk adjustment 3972
2.1.1. A smooth adjustment 3972
2.1.2. A version without smoothness 3974
2.2. Robustness and uncertainty aversion 3974
2.3. Intertemporal complementarity and social externalities 3976
3. Stochastic discount factors 3976
3.1. One-period pricing 3977
3.2. CES benchmark 3979
4. Empirical observations from asset returns 3980
4.1. Log linear approximation and present values 3981
4.1.1. Moving-average models 3982
4.1.2. Decompositions 3984
4.1.3. Identifying shocks 3985
4.2. Test assets 3986
4.2.1. Vector autoregression 3987
5. Intertemporal substitution and pricing 3989
5.1. Discrete time 3990
5.1.1. Continuation values 3991
5.1.2. Wealth expansion 3992
5.1.3. Stochastic discount factor expansion 3992
5.1.4. Log-linear dynamics 3993
5.1.5. Example economies 3995
5.2. Wealth and asset price variation 4000
5.2.1. Wealth variation 4001
5.2.2. Measurement of wealth 4004
5.3. Continuous time 4007
5.3.1. Continuous time Bellman equation 4007
5.3.2. Value function when ρ = 1 4008
5.3.3. Derivative with respect to ρ 4009
5.3.4. Stochastic discount factor 4011
5.3.5. Risk prices 4011
5.3.6. Risk-free rate 4015
5.3.7. Cash flow returns 4016
6. Information about risk aversion from multiple returns 4020
7. GMM estimation of stochastic discount factor models 4025
7.1. Identification 4025
7.2. Conditioning information 4028
7.3. GMM estimation 4029
7.4. GMM system estimation 4031
7.5. Inference by simulation 4032
7.6. Estimation under misspecification 4033
7.7. Intertemporal elasticity estimation 4035
7.7.1. Treasury bills 4035
7.7.2. Market return 4038
7.8. CES Preferences and the wealth return 4039
7.9. Multiple assets and Markov chain Monte Carlo 4041
8. Conclusions 4045
Appendix A: Additional formulas for the Kreps–Porteus model 4048
A.1. Discrete time 4048
A.2. Continuous time 4049
Appendix B: Bayesian confidence intervals 4050
Appendix C: MCMC 4051
Appendix D: Data description 4052
References 4052

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