Probability Of Death And Permanent Income Hypothesis:a Theoretical Extension

In this paper,we introduce the death probability of constant value and the death probability of non-constant value respectively on the basis on of-the permanent income hypothesis(PIH)and the framework of Wang(2003).By optimizing,we obtained the closed-form function of the consumption function,savings functions and wealth accumulation function.On this basis.the existence conditions of general equilibrium are discussed.Friedman(1957)put forward the permanent income hypothesis,which was extended and supplemented in theory by many subsequent studies.Hall(1978)introduced the randomness of income,and individuals generated the motive of precautionary saving.Then he proved that the permanent income hypothesis was still valid.Based on Hall(1978),Caballero(1990)changed the utility function into the absolute risk aversion coefficient(CARA).The existence of individual's precautionary saving motivation made the permanent income hypothesis no longer valid Wang(2003)assumed that individual subjective discount rate and interest rate were different,and individuals had negative savings motivation caused by impatience.He also proved that under the general equilibrium condition,negative savings caused by impatience offset precautionary savings,and the permanent income hypothesis was still valid.The above articles on the permanent income hypothesis discuss the behavior of individuals with permanent lives.Under different assumptions,individuals have different motivation to save,so the hypothesis of consumption behavior and permanent income is not the same.However,none of the above articles considered the influence of the existence of death probability.Individuals'cognition of the finiteness of life and the suddenness of the end of life will have an impact on consumption behavior.Based on this,this paper introduces the probability of death and discusses its influence.In this paper,under the framework of Wang(2003),the fixed death probability and the death probability changing with age are respectively introduced to study individuals' consumption behavior,saving behavior and wealth accumulation behavior And we also consider whether individual consumption conforms to the permanent income hypothesis under general equilibrium.In the model,we assume that individuals face a certain probability of death each period and have no bequest motivation,and that individuals with uncertain life duration discount and optimize their expected utility of life.Under this model,the explicit solutions of-consumption,savings and wealth accumulation functions are obtained.After the introduction of normal death probability,individuals will generate a new savings--negative savings caused by the existence of death threat.In an economy where total precautionary saving is zero and the sum of precautionary saving and negative saving of individuals is zero,the permanent income hypothesis is still valid.Because of the death threat,the existence range of the equilibrium interest rate is larger than that when an individual has an infinite life.We use the Gomperty.s Law to describe the death probability of individuals of different ages.After the solution is obtained,we calibrate parameters,and found that when the death probability changes with age,the negative savings of individuals will increase with age.which correspondingly slows down the accumulation rate of wealth.