预期寿命、年金市场与经济行为
|
摘要
随着经济的发展,人口预期寿命持续增加,社会养老压力逐步加大;年金作为养老保障的重要支柱,其需求也在不断增大。文章在一个包含信贷约束和年金市场的三期生命周期模型框架下,从理论上分析了预期寿命增加和年金市场发展对典型消费者人力资本投资、储蓄行为、退休决策和预期终生劳动供给的影响。研究发现,随着预期寿命的增加,消费者会增加人力资本投资水平,增加储蓄率,但是退休行为和预期终生劳动供给的变化不确定,取决于年金市场的完善程度和外生的市场利率水平。如果年金市场不完善程度较高或市场利率水平较低,预期寿命增加会引起退休提前。但是即使进入劳动力市场的时间推迟,退出劳动力市场的时间提前,由于生存概率增加,预期终生劳动供给的变化并不确定。文章还发现,当预期寿命保持不变时,随着年金市场的不断完善,消费者会提前退休。
In the past century,life expectancy in most countries has increased. At the same time,there is an increasing demand for the development of annuity markets. In this paper,we construct a three-period lifecycle model with credit constraints and annuity markets,and investigate the effects of increasing life expectancy and the development of annuity markets on individuals' optimal choices of the length of schooling,saving behavior,retirement length and expected lifetime total labor supply. Within this framework,we find that as life expectancy increases,individuals choose to gain more education and increase savings,but how they are going to change the retirement decision and expected lifetime labor supply depends on the maturity of annuity markets and the interest rate in the economy. If there is no mature annuity market,or if the interest rate is low,as life expectancy increases,individuals will retire earlier.However,since the survival rate also increases,expected lifetime labor supply may not decline even when labor supply at the two end stages of life does. We also find that if life expectancy remains unchanged,as annuity markets develop,individuals will retire earlier. The robustness of the results has been checked with numerical examples. Our work is part of an important literature that tries to explain the"Ben-Porath puzzle"raised by Hazan(2009),who shows that a necessary condition for the Ben-Porath mechanism(Ben-Porath,1967)to hold is that increased life expectancy must also increase expected lifetime labor supply,which is not supported by empirical evidence. The main contributions of our paper are as follows:First,we introduce the annuity market,which is closely linked with life expectancy and retirement,to the model when revisiting the BenPorath mechanism. We emphasize the importance of annuity markets when analyzing the effects of increasing life expectancy on individuals' behaviors,and also show that the development of annuity markets will have an effect on individuals' optimal choice. Second,we not only analyze the effects of increasing life expectancy and the development of annuity markets on individuals' retirement decision,but also focus on the effects on individuals' expected lifetime labor supply,which is affected by both mortality rates and labor supply in each period. This makes our results comparable to the empirical findings by Hazan(2009).
In the past century,life expectancy in most countries has increased. At the same time,there is an increasing demand for the development of annuity markets. In this paper,we construct a three-period lifecycle model with credit constraints and annuity markets,and investigate the effects of increasing life expectancy and the development of annuity markets on individuals' optimal choices of the length of schooling,saving behavior,retirement length and expected lifetime total labor supply. Within this framework,we find that as life expectancy increases,individuals choose to gain more education and increase savings,but how they are going to change the retirement decision and expected lifetime labor supply depends on the maturity of annuity markets and the interest rate in the economy. If there is no mature annuity market,or if the interest rate is low,as life expectancy increases,individuals will retire earlier.However,since the survival rate also increases,expected lifetime labor supply may not decline even when labor supply at the two end stages of life does. We also find that if life expectancy remains unchanged,as annuity markets develop,individuals will retire earlier. The robustness of the results has been checked with numerical examples. Our work is part of an important literature that tries to explain the"Ben-Porath puzzle"raised by Hazan(2009),who shows that a necessary condition for the Ben-Porath mechanism(Ben-Porath,1967)to hold is that increased life expectancy must also increase expected lifetime labor supply,which is not supported by empirical evidence. The main contributions of our paper are as follows:First,we introduce the annuity market,which is closely linked with life expectancy and retirement,to the model when revisiting the BenPorath mechanism. We emphasize the importance of annuity markets when analyzing the effects of increasing life expectancy on individuals' behaviors,and also show that the development of annuity markets will have an effect on individuals' optimal choice. Second,we not only analyze the effects of increasing life expectancy and the development of annuity markets on individuals' retirement decision,but also focus on the effects on individuals' expected lifetime labor supply,which is affected by both mortality rates and labor supply in each period. This makes our results comparable to the empirical findings by Hazan(2009).
引文
[1]邵国栋,朱小玉,刘伟.基于生命周期理论的延迟退休年龄合理性研究[J].云南社会科学,2007,(5):53-56+88.
[2]孙祁祥,王国军,郑伟.中国养老年金市场未来发展战略与政策建议:2013-2023年[J].审计与经济研究,2013,28(5):3-13.
[3]张川川,赵耀辉.老年人就业和年轻人就业的关系:来自中国的经验证据[J].世界经济,2014,37(5):74-90.
[4]张熠.内生退休年龄研究前沿[J].经济学动态,2015,(3):90-103.
[5]Auerbach A J,Kotlikoff L J.Dynamic fiscal policy[M].Cambridge University Press,1987.
[6]Barro R J,Lee J W.A new data set of educational attainment in the world,1950-2010[J].Journal of Development Economics,2013,104:184-198.
[7]Barro R J,Sala-i-Martin X.Economic Growth.2nd Edition[M].The MIT Press,2003.
[8]Ben-Porath Y.The production of human capital and the life cycle of earnings[J].Journal of Political Economy,1967,75(4,Part 1):352-365.
[9]Bloom D E,Canning D,Moore M.Optimal retirement with increasing longevity[J].The Scandinavian journal of economics,2014,116(3):838-858.
[10]Cervellati M,Sunde U.Life expectancy,schooling,and lifetime labor supply:theory and evidence revisited[J].Econometrica,2013,81(5):2055-2086.
[11]Diamond P A.National debt in a neoclassical growth model[J].The American Economic Review,1965,55(5):1126-1150.
[12]Gruber J,Wise D.Social security and retirement:An international comparison[J].The American Economic Review,1998,88(2):158-163.
[13]Hazan M.Longevity and lifetime labor supply:Evidence and implications[J].Econometrica,2009,77(6):1829-1863.
[14]Hazan M,Zoabi H.Does longevity cause growth?A theoretical critique[J].Journal of Economic Growth,2006,11(4):363-376.
[15]Hansen C W,L?nstrup L.Can higher life expectancy induce more schooling and earlier retirement?[J].Journal of Population Economics,2012,25(4):1249-1264.
[16]Kalemli-Ozcan S,Weil D N.Mortality change,the uncertainty effect,and retirement[J].Journal of Economic Growth,2010,15(1):65-91.
[17]Liu P,Th?gersen J.Pay-as-you-go pensions and endogenous retirement[J].Macroeconomic Dynamics,forthcoming,2019.
[18]Strulik H,Werner K.Life expectancy,labor supply,and long-run growth:Reconciling theory and evidence,University of Goettingen[R].Cege Discussion Paper 140,2012.
[19]Tang K K,Zhang J.Health,education,and life cycle savings in the development process[J].Economic Inquiry,2007,45(3):615-630.
[20]Thimme J.Intertemporal substitution in consumption:A literature review[J].Journal of Economic Surveys,2017,31(1):226-257.
(1)这里没有限制消费者在青年期的存款,但是正如Hansen和L?nstrup(2012)指出,在生命周期模型中,消费者一般在青年期选择向未来借钱而不是储蓄。
(2)张熠(2015)指出,从各国的数据来看,死亡率下降存在“老龄化”趋势。对比中国第五次和第六次人口普查结果可发现,在我国主要的死亡率下降已经转移到退休后年龄段中。因此,本文模型中主要考察从中年期过渡到老年期的生存概率的提高,而没有考虑从青年期到中年期的生存概率的变化。
(3)这里的实际回报率是指年金市场中由于生存风险而产生的高于经济中其他资产回报率的利率水平,并不是指文献中常见的对名义利率和实际利率的区分。
(1)感谢审稿人指出本文的模型框架在刻画长寿风险影响退休行为作用机制方面的局限性。
(2)Kalemli-Ozcan和Weil(2010)指出,当生存概率较低时,偶发遗赠风险较高,消费者倾向于不储蓄而一直工作以满足消费需求;随着生存概率的上升,储蓄被浪费的概率减小,因而消费者会考虑通过储蓄的方式满足退休后的消费需求,并提前退休。
(1)假设1要求R>1-δ+δφφβ(1+θ)(1-δ+δφ)2δ+δβφ2+δθβφ2-1-1-δ+δφφβ(1+θ)=(1-δ+δφ)(1-δ)φβ(1+θ)+1(δ+δβφ2+δθβφ2-1)φβ(1+θ)?0δ<1(δ=1)R <1β(1+θ)R>1β(1+θ)。易证,因此只要,在假设1条件下,一定存在外生利率水平满足该条件。在完全年金市场条件下,预期寿命增加引起退休提前要求外生利率水平需满足,与假设1的条件相矛盾。因此在假设1条件下,如果存在完全年金市场,预期寿命增加一定引起消费者推迟退休。
(1)当存在不确定时,该效用函数又称为CRRA函数。当σ=1,函数为对数形式。
(1)由于生存概率不变,预期终生劳动供给的变化取决于消费者进入和退出劳动力市场的时间点。因此这里不讨论预期寿命不变时年金市场完善程度对消费者预期终生劳动供给的影响。
[2]孙祁祥,王国军,郑伟.中国养老年金市场未来发展战略与政策建议:2013-2023年[J].审计与经济研究,2013,28(5):3-13.
[3]张川川,赵耀辉.老年人就业和年轻人就业的关系:来自中国的经验证据[J].世界经济,2014,37(5):74-90.
[4]张熠.内生退休年龄研究前沿[J].经济学动态,2015,(3):90-103.
[5]Auerbach A J,Kotlikoff L J.Dynamic fiscal policy[M].Cambridge University Press,1987.
[6]Barro R J,Lee J W.A new data set of educational attainment in the world,1950-2010[J].Journal of Development Economics,2013,104:184-198.
[7]Barro R J,Sala-i-Martin X.Economic Growth.2nd Edition[M].The MIT Press,2003.
[8]Ben-Porath Y.The production of human capital and the life cycle of earnings[J].Journal of Political Economy,1967,75(4,Part 1):352-365.
[9]Bloom D E,Canning D,Moore M.Optimal retirement with increasing longevity[J].The Scandinavian journal of economics,2014,116(3):838-858.
[10]Cervellati M,Sunde U.Life expectancy,schooling,and lifetime labor supply:theory and evidence revisited[J].Econometrica,2013,81(5):2055-2086.
[11]Diamond P A.National debt in a neoclassical growth model[J].The American Economic Review,1965,55(5):1126-1150.
[12]Gruber J,Wise D.Social security and retirement:An international comparison[J].The American Economic Review,1998,88(2):158-163.
[13]Hazan M.Longevity and lifetime labor supply:Evidence and implications[J].Econometrica,2009,77(6):1829-1863.
[14]Hazan M,Zoabi H.Does longevity cause growth?A theoretical critique[J].Journal of Economic Growth,2006,11(4):363-376.
[15]Hansen C W,L?nstrup L.Can higher life expectancy induce more schooling and earlier retirement?[J].Journal of Population Economics,2012,25(4):1249-1264.
[16]Kalemli-Ozcan S,Weil D N.Mortality change,the uncertainty effect,and retirement[J].Journal of Economic Growth,2010,15(1):65-91.
[17]Liu P,Th?gersen J.Pay-as-you-go pensions and endogenous retirement[J].Macroeconomic Dynamics,forthcoming,2019.
[18]Strulik H,Werner K.Life expectancy,labor supply,and long-run growth:Reconciling theory and evidence,University of Goettingen[R].Cege Discussion Paper 140,2012.
[19]Tang K K,Zhang J.Health,education,and life cycle savings in the development process[J].Economic Inquiry,2007,45(3):615-630.
[20]Thimme J.Intertemporal substitution in consumption:A literature review[J].Journal of Economic Surveys,2017,31(1):226-257.
(1)这里没有限制消费者在青年期的存款,但是正如Hansen和L?nstrup(2012)指出,在生命周期模型中,消费者一般在青年期选择向未来借钱而不是储蓄。
(2)张熠(2015)指出,从各国的数据来看,死亡率下降存在“老龄化”趋势。对比中国第五次和第六次人口普查结果可发现,在我国主要的死亡率下降已经转移到退休后年龄段中。因此,本文模型中主要考察从中年期过渡到老年期的生存概率的提高,而没有考虑从青年期到中年期的生存概率的变化。
(3)这里的实际回报率是指年金市场中由于生存风险而产生的高于经济中其他资产回报率的利率水平,并不是指文献中常见的对名义利率和实际利率的区分。
(1)感谢审稿人指出本文的模型框架在刻画长寿风险影响退休行为作用机制方面的局限性。
(2)Kalemli-Ozcan和Weil(2010)指出,当生存概率较低时,偶发遗赠风险较高,消费者倾向于不储蓄而一直工作以满足消费需求;随着生存概率的上升,储蓄被浪费的概率减小,因而消费者会考虑通过储蓄的方式满足退休后的消费需求,并提前退休。
(1)假设1要求R>1-δ+δφφβ(1+θ)(1-δ+δφ)2δ+δβφ2+δθβφ2-1-1-δ+δφφβ(1+θ)=(1-δ+δφ)(1-δ)φβ(1+θ)+1(δ+δβφ2+δθβφ2-1)φβ(1+θ)?0δ<1(δ=1)R <1β(1+θ)R>1β(1+θ)。易证,因此只要,在假设1条件下,一定存在外生利率水平满足该条件。在完全年金市场条件下,预期寿命增加引起退休提前要求外生利率水平需满足,与假设1的条件相矛盾。因此在假设1条件下,如果存在完全年金市场,预期寿命增加一定引起消费者推迟退休。
(1)当存在不确定时,该效用函数又称为CRRA函数。当σ=1,函数为对数形式。
(1)由于生存概率不变,预期终生劳动供给的变化取决于消费者进入和退出劳动力市场的时间点。因此这里不讨论预期寿命不变时年金市场完善程度对消费者预期终生劳动供给的影响。