Hyperbolic Discounting And Time-consistent Investment Decisions

Time discounting is a frontier topic in areas of behavioral economics. It is critical to predetermine an appropriate discount rate for projects’cost-benefit analysis, especially if projects cross generations since a petty variation in discount rate could have dramatic impact. Since1980’s, experimental economists have proved that individuals’discounting behavior does not satisfy exponential discounting, which has long been the common assumption of neoclassical economics. Moreover, exponential discounting is gradually being replaced by hyperbolic discounting in various research areas. However, the discussion whether hyperbolic discounting is a plausible account of time preference is never ceased. On the other hand, if individuals with hyperbolic perferences follow the maximal principle, the plan is inconsistent and cannot be impleted in practice. Furthermore, it is very difficult to get analytical solutions in continuous time case for non-exponential discounting. Therefore, the researchs about the rationality of hyperbolic discounting and the corresponding time-consistency policy would be significant. In the light of the two questions mentioned above, this paper takes indiviudals as the main research object. Detailed research on rationality of hyperbolic discounting are present in Chapter2,3and4, and on time-consistent portfolio problems with non-exponential discounting are present in Chapter5.One of the anomalies in exponential discounting theory is known as preference reversals, such anomaly has often been used to prove the rationality of hyperbolic discounting. In chapter2, I answer whether preference reversals always prove the rationality of hyperbolic discounting. I first point out the difference between synchronic and diachronic preference reversals, and they are equivalent when exponential discounting satisfy the stationary assumption. After that, I prove that hyperbolic discounting is able to appropriately explain these two types of preference reversals when it satisfies the stationary assumption. Moreover, I construct a discount function with the consideration of uncertain lifetime and bequest utility in decision making process. Under some particular circumstances, this discount function, which is non-hyperbolic and non-stationary, is able to appropriately explain diachronic preference reversals, but fail to explain synchronic preference reversals. I conclude that diachronic preference reversals cannot prove the rationality of hyperbolic discounting in some cases. Current literatures deem that hyperbolic discounting does not predict the phenomenon of sub-additive discounting and question whether hyperbolic discounting is a plausible account of time preference. Chaper3responds to the question. This chaper firstly point out that, when making inter-temporal choices, an individual with hyperbolic time preference is aware that his/her preference will change over time, and would rather choose the future decision date than the current date as the reference point. Consequently, an individual’s attitude to the reference point is clearly going to affect his/her decision. Some individuals, namely partially sophisticated individuals, tend to underestimate their expectations of future preference changes, in which case this systematic misprediction is labelled as the projection bias. Secondly, this chaper point out that such bias is interpreted as a distortion of estimates of time preference, and could be one possible theoretical explanation of the evidence of sub-additive discounting. This chpter points out that individual choices of the reference point and projection bias were undeservedly neglected by previous studies that questioned hyperbolic discounting and sub-additive discounting cannot deny hyperbolic discounting. Lastly, when taking the discount function proposed by chaper2and dividing the individuals into three types, namely, sophisiticated, partially sophisticated and completely naive, the individuals also show the phenomenon of sub-additive discounting. The sophistication and the choices of the reference point may result in the phenomenon of sub-additive discounting.Chapter4analyzes the structure of the instantaneous certainty-equivalent discount rate by using a Ramsey optimal growth model, combined with uncertainty about future productivity. This chapter firstly obtains that the instantaneous certainty-equivalent discount rate is equal to the expected discount rate with a risk-adjusted PDF. The PDF of the productivity of capital, coefficient of relative risk aversion and the delay time have impact on the risk-adjusted PDF. Secondly, this chapter point out that the instantaneous certainty-equivalent discount rate decreases as the delay time increases. The declining of the instantaneous certainty-equivalent discount rate indicates that the uncertainty of the capital productivity rationalizes hyperbolic discounting. Lastly, this paper gives a numercal example.Chapter5studies the time-consistent consumption and portfolio problems of time-inconsistent individuals by incorporating the stochastic hyperbolic preferences into the classical model of Merton (1969,1971) with finite horizon. This chapter firstly gives the model setup and the time preference of the inividuals. Secondly, this chapter analyzes the HJB equation of the sophisticated individuals for finite planning horizon and further derives the HJB equation of the sophisticated indiviudals for infinite planning horizon. Thirdly, this chapter analyzes the time-consistent consumption and portfolio rules for log and power utility function. Lastly, this paper gives the comparative dynamic behavior and numerical results.