Certainty-equivalent Discounting And Time-consistent Decisions

The discount rate is the basis of the value analysis,and also is one of the most critical problems in all of intertemporal decision makings,since it can eliminate the influence of time.By assuming that the discount rate is influenced by the dual uncertainty of future macroeconomic conditions and project 's productivity,this paper studies the problem of certainty-equivalent discounting,and based on this,discusses time-consistent decisions.Chapter 2 establishes a generalized discount rate model for the risk project.To distinguish the generalized discount rate from the risk-free discount rate and the riskadjusted discount rate,this paper divides the factors that affect the term structure of the generalized discount rate into two effects.One is the “growth expectation difference effect”,which is the expectation difference between the risk-adjusted consumption growth rate and productivity rate.The other is the “correlated risk trend effect”,which reflects the joint uncertainty of the consumption growth rate and productivity rate.The specific form of the generalized discount rate is determined by the joint distribution of the consumption growth rate and the productivity rate.Based on the model proposed in chapter 2,by assuming the joint growth process of the comsumption growth rate and the project's productivity rate follows a mean regression process,the chapter 3 discusses the analytical expression and term structure of the generalized discount rate.The research shows that,on the one hand,if the parameter of the project's productivity is larger than the decision maker 's relative risk aversion coefficient,then the growth expectation difference effect makes the generalized discount rate increase.On the contrary,if the parameter of the project's productivity is less than the relative risk aversion coefficient of the decision-maker,then the growth expectation difference effect makes the generalized discount rate decrease.On the other hand,the “correlated risk trend effect” generates the negative effect on the generalized discount rate.The combined effect determines the term structure of the generalized discount rate.By assuming the joint growth process of the comsumption growth rate and the project's productivity rate follows a Markov process,the chapter 4 discusses the specific performance of the generalized discount rate and its term structure.The research shows that both the macroeconomic initial state and the “growth expectation difference effect” influence the term structure of the generalized discount rate,here the intensity of the “growth expectation difference effect” is determined by the relative risk aversion coefficient,the project's productivity rate and the consumption growth rate in different economic states,and the transition probability.The specific performance is that if the relative risk aversion coefficient of the decision-maker is greater than the mean difference ratio between the project's productivity rate and the consumption growth rate in different economic states,the generalized discount rate based on the initial condition of the good macroeconomic state decreases from a larger initial value to an unconditional limit value.Meanwhile,the gener alized discount rate based on the initial condition of bad economic state increases from a small initial value to an unconditional limit value.Chapter 5 discusses the term structure of the risk-adjusted discount rate,starting with a dispute that originates from two classical risk-adjusted discount rate models.The solution is obtained from two paths,one is the relationship between the project's productivity mode and the risk premium coefficient,the other is the relationship between the parameter of the project's productivity and the risk premium coefficient.It is found that the different term structure conclusions of the two risk-adjusted discount rates appear to be contradictory,but the internal essence is the same.The reason for the two different term structures is that two different risk premium coefficient ranges are set.The research of this chapter shows that,the systemic and unsystematic risk of project benefit determine the coefficient of risk premium at different levels,and further determine the term structure of the risk-adjusted discount rate.Chapter 6 discusses the problem of time-consistent investment decision based on the conclusions of the previous five chapters.The research shows that,to derive timeconsistent decision,the necessary condition is that the declining discount rate satisfies superadditive discounting,and the certainty-equivalent discount methods in the existing literatures lead to subadditive discounting,which derive to time inconsistency decisions.In particular,a specific example shows that when the future consumption growth process meets some certain conditions,the declining discount rate can also lead to a time-consistent decision.