Population aging fertility and social security

Population Economics Akira Yakita Population Aging, Fertility and Social Security www.ebook3000.com Population Economics Editor-in-chief Klaus F Zimmermann Princeton University USA UNU-MERIT Maastricht, The Netherlands Managing Editor Alessio J.G Brown UNU-MERIT Maastricht, The Netherlands Series Editors Alessandro Cigno University of Florence Florence, Italy Erdal Tekin American University Washington D.C., USA Junsen Zhang The Chinese University of Hong Kong Shatin, Hong Kong More information about this series at http://www.springer.com/series/2190 www.ebook3000.com Akira Yakita Population Aging, Fertility and Social Security Akira Yakita School of Economics Nanzan University Nagoya, Japan ISSN 1431-6978 Population Economics ISBN 978-3-319-47643-8 ISBN 978-3-319-47644-5 DOI 10.1007/978-3-319-47644-5 (eBook) Library of Congress Control Number: 2016963232 © Springer International Publishing AG 2017 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland www.ebook3000.com Preface Population aging and fertility declines are commonly observed in developed countries and will be sooner or later in developing countries For example, in Japan, the speed of population aging is particularly high, involving rapid extensions in life expectancy and low fertility rate in the past several decades The demographic changes not only cause economic issues in economic societies but also affect the appropriateness of economic policies Individuals may prepare for longer retirement periods by saving more, although unfunded social security tends to induce individuals to save less than without social security Public pensions based on a pay-as-you-go finance system may face severe risks of bankruptcy Population aging even in one country will also affect other countries Differences in savings behaviors among countries with various demographic structures alter the directions of international capital mobility and thereby result in international inequality of income distribution among countries Indeed, consumption during longer lifetimes may affect the environmental quality globally In this book, I will address these issues caused by demographic changes, giving particular attention to fertility decisions of individuals facing expanding life expectancy The theoretical framework I employ in this book is an overlapping generations model, a model which is well known to be suited to exploring many aspects of economic behaviors of individuals and the economy as a whole This book builds in part on the research papers published in journals, some of which I coauthored with Makoto Hirazawa and/or Koji Kitaura While my master’s thesis was on life insurance and savings behaviors of individuals, a clue of my research on population aging was an article that appeared in the Journal of Population Economics in 2001 The motivation behind this book is to give an overview on research topics in population aging and fertility based on some of my existing research and giving insight into new findings Doing so allowed me to give a more comprehensive view of the demographic changes and achieve better understanding of the issues I have also benefited much from earlier joint works with Makoto v vi Preface Hirazawa and Koji Kitaura In particular, Chap is based on an unpublished work with Makoto Hirazawa, who also provided valuable comments and suggestions on an earlier draft of this book I am much indebted to all of them As for the past, I greatly thank Professors Kikuo Iwata and Kiyokazu Tanaka at Sophia University, who encouraged me to go on to a graduate school of Economics Professor Masaichi Mizuno, who was my supervisor at the Nagoya University Graduate School of Economics, guided me at various stages of life both formally and privately I am also indebted to Professor Nobuhiro Okuno, who showed me a way to formulate and shape ideas when I was a graduate student of Nagoya University, and Professor Michio Morishima gave me thoughtful advice on research activities during my stay at the London School of Economics and the University of Essex Without meeting these professors, I could not have published this book With regard to the specific topics in this book, I have been helped by many colleagues and friends My heartfelt thanks especially to Yuko Arayama, David de la Croix, Koichi Futagami, Toshihiro Ihori, Juni-ichi Itaya, Murray C Kemp, Yukio Ohtashiro-Karasawa, Ryuta Kato, Hideki Konishi, Noritaka Kudo, Tatsuaki Kuroda, Fabio Mariani, Lex Meijdam, Kazuo Mino, Kazutoshi Miyazawa, Miki Murata, Akira Momota, Hisahiro Naito, Tetsuya Nakajima, Ryoji Ohdoi, Hikaru Ogawa, Kazumasa Oguro, Tatsuya Omori, Yasuyuki Osumi, Tomoya Sakagami, Sawako Shirahase, Ken Tabata, Bas van Groezen, Tadashi Yagi, Shinji Yamashige, Masayoshi Yanagihara, Masaya Yasuoka, and Masatoshi Yoshida for their heartwarming comments and suggestions on my earlier works I also would like to thank my colleagues and friends at Fukuoka University, Mie University, Chukyo University, the University of Tsukuba, Nagoya City University, and Nanzan University for their help and support during my tenure of office The papers that the chapters are based on were presented at various conferences, seminars, and workshops Valuable comments that are gratefully acknowledged were provided by participants at seminars in Chukyo University, Hokkaido University, the Kansai Macroeconomics Workshop, the University of Tsukuba, the Chubu division of the Japan Society of Household Economics, Nagoya Macroeconomics Workshop, the Japan Association for Applied Economics, the Association for Public Economic Theory (PET), the Demographic Transition and Public Finance Workshop, the Japanese Economic Association, the Japanese Economic Policy Association, the European Economic Association, Doshisha University, the University of Hyogo, the Institute of Statistical Research (Tokyo), Osaka City University, and the Applied Regional Science Conference I am grateful to Professor Cigno, the editor of the book series Population Economics, for his support during the compilation of this volume I am also grateful to all at Springer for their generous collaborative effort in producing the final product Financial support from the Japan Security Scholarship Foundation (Nihon Shoken Shogaku Zaidan), the Postal Life Insurance Foundation, the Japan Society www.ebook3000.com Preface vii for the Promotion of Science (KAKENHI Grant Nos 18530127 and 25285091), and the Gakujutsushinkou Nomura Kikin is also gratefully acknowledged Finally, my greatest thanks go to my wife and children, Yuko Yakita, Sayaka Tsuchihashi, and Yutaka Yakita, who supported me at every stage of my life Yagoto Ishisaka, Japan August 2016 Akira Yakita Introduction and Overview Worldwide increases in longevity during the last few decades are well documented in numerous studies (e.g., World Bank 1993) Recent increases in longevity, especially in developed economies, are due to declines in the adult and elderly mortality rates rather than in infants (e.g., Lee and Tuljapurkar 1997) Bloom et al (2014) asserted that increases in life expectancy are associated with general health improvements in the form of reduction in morbidity, while Manton et al (2007) showed that the estimated life expectancy grew at about the same rate as active life expectancy from 1935 to 1982 for ages 65 and over in the USA The increased lifetime longevity is often associated with declines in the fertility rate, in particular, in the developed countries Both increases in the life expectancy and decreases in fertility cause population aging, which has shifted the age distribution toward older populations, and may have significant impacts on economic growth and intergenerational distribution of income In contrast, according to The World Population Prospects, The 2012 Revision, of the United Nations, currently the population of the less developed regions is still young, with children under the age of 15 accounting for 28 % of the population and young persons aged 15–24 accounting for a further 18 % in these countries, whereas children and youth account for 16 % and 12 % of the population, respectively, in the more developed regions The number of people in the main working ages, from 25 to 59 years, is expected to decline even for the next 40 years in the more developed regions, whereas it will continue rising in the less developed regions The young population in the less developed countries poses a major challenge for their countries, which are faced with the necessity of providing education and employment to large cohorts of children and youth The situation in the least developed countries is even more pressing The demographic changes also affect the policy decisions of the current government The aim of this book is to examine the effects of population aging on not only the domestic but also global economy as well as their economic policies from various aspects In the following chapters, we use an overlapping generations model, which has been introduced by Samuelson (1958) and Diamond (1965) and then developed by ix www.ebook3000.com x Introduction and Overview many authors; a model is considered to be appropriate for considering intergenerational income distribution as well as intertemporal resource allocation The model is appropriately varied so as to be suitable for topics in each chapter Part I is concerned with the effects of population aging on fertility, inflation, and retirement decisions of individuals Chapter examines the effects of an increase in life expectancy on the fertility rate and the lifecycle savings rate in a simple endogenous growth model When changes in life expectancy affect fertility decisions of individuals, population aging is accelerated in the sense that the fraction of retirees in the total population will be enlarged In Chap 2, assuming two assets of money and the claims on physical capital, we examine the effect of an increase in life expectancy on portfolio choices of individuals between these two assets Money is introduced based on the money-in-the-utility-function approach With capital externalities as an engine of growth, changes in portfolios of individuals affect the economic growth rate Chapter examines the effect of increases in life expectancy on fertility decisions of individuals if they can work in their old age by using the extended lifecycle model a la Feldstein (1976, 1977) and Hu (1979) If individuals can complement consumption with the elderly labor supply in old age, they can appropriate more time for child-rearing in young age rather than earning and saving wage income for consumption during retirement Part II focuses on the pay-as-you-go (PAYG) social security First, Chap examines the long-term effects of PAYG social security on fertility and the welfare of individuals, assuming that childcare services are available in the market The availability of market childcare services exerts positive effects on fertility decisions of parents, and a greater number of younger generations work in the market and contribute more to the social security system On the other hand, a PAYG social security will negatively affect capital accumulation of the economy through consumption-savings behaviors of individuals Chapter examines the effects of changes in the eligibility age on balanced growth and inflation rates through the adjustments of portfolio choices of individuals, assuming that individuals have to hold money for consumption during the earlier years of retirement before the eligibility age for public pensions [i.e., the cash-in-advance (CIA) constraint] There are still countries which have institutional or compulsory retirement age, although some Anglo-Saxon countries have recently abandoned it In such countries, there can be an estrangement between these ages Then, in Chap 6, incorporating heterogeneity in preference to having children in a small open economy model, we examine the effects of changes in the size of PAYG social security on fertility choices of individuals and population growth of the economy In this chapter, we focus on the differences in fertility rates under two benefit schemes of proportional-to-contribution or uniform benefits Chapter analyzes the effect of the benefit scheme reform from flat-rate benefits to proportional-to-contribution benefits of PAYG social security on the elderly labor supply The elderly labor supply is expected to mitigate the financial pressure on the social security budget in population aging economies Chapter investigates the effects of an unanticipated expansion in the length of retirement period on planned bequests to their offspring in an overlapping generations model with bequest motives and uncertain lifetime 14.3 Effects of Increased Life Expectancy 223   (i) > dl ð12Þ > dl ð11Þ dx dx (ii) dl  dl  ð12Þ > > ð11Þ dx dx (iii) dl  dl  ð12Þ > ð11Þ > dx dx   gl gx gglx ỵịgx dl  dl  where dx are the slopes of (14.11) and 11ị ẳ ỵỵ1ịg ị2 gg and dx 12ị ẳ g l l ll (14.12) in the neighborhood of the steady state These cases are depicted in Fig 14.1 Making use of (14.13), we can show that both loci shift upward when life expectancy increases.9 Since the sign of (14.14) is negative, we always have dl=dp > in cases (i) and (ii), that is, individuals with longer life expectancy input more labor in regeneration activities involving renewable resources, while dl/dp may be positive or negative in case (iii).10 The result can be interpreted as follows: When the life expectancy increases, individuals increase labor inputs in regeneration activities and, if the stock of renewable resources is greater, decrease labor supply in producing consumption-goods The greater resource stock enables them to sell more harvest to insurance companies (i.e., goods producers) for consumption during their longer retirement, while reducing bequests to their children Even in case (iii), if the upward shift of (14.11) is greater than that of (14.12), the same qualitative effects of an expansion of life expectancy will be obtained [see Fig 14.1 case (iiib)] In these cases the regeneration level of renewable resources g(x, l) may increase, remain constant, or decrease, depending on the relative effects of changes in labor inputs and the inherited stock of renewable resources The reallocation of labor to regeneration activities reduces labor inputs in goods production, lowering the returns to harvest inputs However, in case (iii) in which both loci have positive slopes, if the upward shift of locus (14.12) is sufficiently greater than that of (14.11), we have dl=dp < 0, that is, the expanded life expectancy reduces labor inputs in regeneration activities of renewable resources [see Fig 14.1 case (iiia)] In this case, together with dx=dp < 0, the regeneration level of the renewable resources will decrease with population aging, a possibility that cannot be ruled out a priori When gx is positive and sufficiently small, and when glx > is sufficiently great, the slopes of loci (14.11) and (14.12) will be positive.11 In addition, if ỵ ỵ ịgl ị2 ggll >> 1,  e =ỵị dl  We have dp 11ị ẳ 1ỵỵịg ị2 gg l ll g gl  eρ g dl  > and dp 12ị ẳ ỵ g > 0: l We also have case (iiic) in which dl=dp ¼ 0, which is not shown 11 It is said that there are forest areas that have not been tended properly in Japan Therefore, the marginal productivity of labor in tending the forest may be great 10 www.ebook3000.com 224 14 Does Aging Reduce Sustained Stock of Renewable Resources? case (i) case (ii) l l (12) (12) (11) (11) x l (12) (12) (11) (11) x case (iiib) case (iiia) l x x Fig 14.1 Effect of increased life expectancy on the steady state we will have dl=dp < That is, if the inherited stock of renewable resources is great, if the degree of technological complementarity between labor and resources in regeneration activities is sufficiently high, and if the degree of decreasing marginal returns to labor in the regeneration is great (in the sense that the absolute value of the second-order differentiation is great), population aging may decrease labor inputs in regeneration activities In this case, individuals reallocate the labor supply from regeneration to the consumption goods production, which ceteris paribus lowers the wage rate and raises the returns from the harvests The higher return will make the demand of goods producers for the harvest greater On the other hand, individuals may sell much more harvest for their long retirement, which results in smaller bequests and hence smaller sustained stock of renewable resources, than those in the case of dl=dp > 14.4 Discussions 225 ρ With our specification of the utility function, we have h ẳ ỵ gx; lị, from which the effect of aging on the harvest inputs in consumption goods production can be obtained as   dh e dx dl ẳ g ỵ gl gỵ : dp ỵ ị2 ỵ x dp dp An increase in life expectancy directly increases the harvest inputs in goods production, while the indirect effect through changes in regeneration is ambiguous If both resources and labor inputs decrease with population aging [as in case (iiia)], the indirect effect is negative, reducing ceteris paribus the harvest inputs in goods production The total effect is ambiguous, but we cannot rule out the possibility that population aging increases the harvest inputs in goods production If the harvest inputs increase, the steady-state output level of consumption goods (i.e., the total value of market goods in this model) increases in case (iiia) On the other hand, in cases (i) and (ii), in which labor inputs in consumption goods production are reduced, both steady-state output level of consumption goods and the sustained stock of renewable resources may decrease with population aging unless the increase in harvest inputs is sufficiently great.12 14.4 Discussions 14.4.1 Relevance to Environmental Issues So far we have not considered the environmental aspect of renewable resources explicitly With identical individuals, assuming that the stock of renewable resources exerts positive environmental externalities on the economy in the oneto-one manner, our analysis leads to the trade-off between environment and income (i.e., output of consumption goods) In this case, xtỵ1 in the utility function can be interpreted as the environmental quality in per capita term.13 We have two points First, population aging always harms the environmental quality by reducing the renewable resources in our model with a log linear utility function, i.e., with the elasticity of the marginal utility equal to one This result contrasts to that in Ono and Maeda (2001, Proposition 4.1) who asserted that greater longevity leads to higher per capita environmental quality if the relative risk aversion of the utility function 12 The assumption of constant size of population should be recalled here We can conjecture that if the fertility rate decreases with aging, whether per capita stock of renewable resources decreases depends on the relative magnitudes of the welfare weights on having children and the bequeathed stock of resources per child 13 Ono and Maeda (2001) proceeded with their analysis using per capita environmental quality and this is essentially the case in John and Pecchenino (1994) www.ebook3000.com 226 14 Does Aging Reduce Sustained Stock of Renewable Resources? with respect to the second-period consumption is equal to or smaller than one The difference in the results comes from the fact that in Ono and Maeda (2001) government chooses an intragenerationally efficient level of environmental quality, while in the present setting individuals choose the level as imperfectly altruistic bequests to their offspring, i.e., only in taking care of their own utility from leaving bequests Thus, if individuals are concerned only with asset values of renewable resources, population aging may be harmful to environmental quality Second, we may alternatively have a case in which greater longevity not only harms environmental quality but also decreases the output level of consumption goods at the same time, that is, the trade-off between environment and income disappears [as in case (iiia) in the previous section] When life expectancy expands, whether or not there is a trade-off between environment and income depends on the shape of the regeneration function with labor inputs In this sense, our result seems to extend the analysis in Ono and Maeda (2001) by incorporating the regeneration function The second case cannot be ruled out a priori, depending on the role of labor inputs in regeneration activities 14.4.2 Effects of Tax-Subsidy Policies14 Next, we provide a brief sketch about tax-subsidy policies within the present setting Focusing on the tax-subsidy effects, we assume that individuals live for two periods certainly (i.e., p ¼ ) It can be readily shown that taxes on wage income and/or sales of the harvest increase the steady-state stock of renewable resources bequeathed if the tax revenues are rebated to the respective taxpayers in a lump-sum fashion, despite their effects on labor inputs in regeneration of renewable resources and consumption goods production Subsidies (taxes) on the bequests increase (decrease) the renewable resource stock if they are financed (rebated) by lump-sum taxes (transfers) on the subsidy-receivers (tax-payers, respectively) The effects of intergenerational income redistribution policies on the resource stock are ambiguous Since the effects of the tax/subsidy policies on consumption are also ambiguous, the welfare effects of these policies are ambiguous in general even though they may retain the sustained level of natural renewable resources 14 For the analyses, see Appendix Appendix 1: Tax-Subsidy Policies 14.5 227 Concluding Remarks Focusing on the aspect of renewable resources as the means of intergenerationaltransfers and incorporating labor inputs in regeneration of renewable resources, we have examined the effects of population aging on the sustained steady-state stock of renewable resources, labor allocation between goods production and regeneration of resources, and output level of consumption goods Although population aging reduces sustained steady-state stock of renewable resources, the economy may also suffer from decreases in consumption when the sustained stock of renewable resources is reduced largely by population aging This can be the case when the degree of decreasing marginal product of labor in regeneration activities is sufficiently high In order to see whether it is the case or not, the characterization of the regeneration function should be subject to empirical examinations The stock of renewable resources can be interpreted as the environmental quality, which exerts positive external effects on individuals When population is aging, the environmental quality will inevitably deteriorate if the renewable resources are used in goods production However, we assumed away any innovation in goods production and resource regeneration Appendix 1: Tax-Subsidy Policies 1.1 Wage Taxes and Lump-Sum Rebates Denoting the wage tax rate as τ and the tax revenue as T t ẳ wt lt ị, the budget constraints of an individual of generation t are ịwt lt ị ỵ T t ẳ c1t e htỵ1 qtỵ1 ẳ c2tỵ1 : 14:16ị 14:17ị The optimal plans of the individual are lt ¼ þ Tt gðxt ; lt Þ À ð1 À ịwt ỵ gl xt ; lt ị xtỵ1 ẳ gxt ; lt ị: ỵ 14:18ị 14:19ị Taking into account the government’s budget constraint, we have in the steady state www.ebook3000.com 228 14 Does Aging Reduce Sustained Stock of Renewable Resources? lẳ1 xẳ gx; lị ỵ gl x; lị 14:20ị gx; lị: ỵ 14:21ị Assuming the stability of the steady state, we obtain g B ỵ x B " # B B À τ g g gg l x lx @ ỵ gl ị ¼ @ g A; ρ þ β gl 1 C dx CB dτ C CB C @ A À τ ðgl ị ggll C A dl 1ỵ d ỵ gl ị g ỵ l 14:22ị from which we obtain dx ẳ g>0 d Diị ỵ ị2   dl g ẳ gx d Diị ỵ ỵ gl ð14:23Þ ð14:24Þ where D(i) is the determinant of the coefficient matrix on the left-hand side of (14.22) and is positive by stability We always have dx=dτ > 0, while if ỵ ị= > gx , dl=d > When both x and l increase with the tax rate, the harvest input in consumption goods production increases However, when dð1 À lÞ=dτ < and dx=dτ > 0, output of consumption goods f ðh, À lÞ may increase, be constant, or decrease 1.2 Taxes on Returns from Harvests and Lump-Sum Rebates e Denoting the tax rate as α and the tax revenue as Btỵ1 ẳ qtỵ1 htỵ1 , the budget constraints of an individual of generation t are wt lt ị ẳ c1t e htỵ1 ịqtỵ1 The optimal plans of the individual are ỵ Btỵ1 ẳ 14:25ị c2tỵ1 : 14:26ị Appendix 1: Tax-Subsidy Policies 229 1 Btỵ1 gxt ; lt ị ỵ lt ẳ e ỵ gl xt ; lt ị ịqtỵ1 ! Btỵ1 g x t ; l t ị ỵ : xtỵ1 ẳ e ỵ ịqtỵ1 ! 14:27ị 14:28ị Taking into account the government’s budget constraint, we have in the steady state l¼1À xẳ gx; lị ị ỵ gl x; lị 14:29ị gx; lị: ị ỵ β ð14:30Þ Assuming the stability of the steady state, we obtain B B B B @ 1À β g ị ỵ x gl gx gglx ị ỵ gl ị2 ! 1 C dx CB dα C CB C @ A ðgl Þ À ggll C A dl 1ỵ d ị ỵ gl ị g B ẵ1 ị ỵ C C ẳB @ g A; ẵ1 ị ỵ gl g ị ỵ l 14:31ị from which we have " # dx g gl ị2 ggll ẳ ị ỵ >0 d Diiị ẵ1 ị ỵ βŠ3 ð gl Þ & ' dl ρg gg ẳ ẵ1 ị ỵ ỵ ịgx lx d Diiị ẵ1 ị ỵ gl gl ð14:32Þ ð14:33Þ where D(ii) is the determinant of the coefficient matrix on the left-hand side of (14.31) and is positive by stability If gx < fgglx =gl À ½ð1 ị ỵ g=ẵ1 ị, we have dl=d > 0; and vice versa 1.3 Subsidies to Bequests of Renewable Resources e Denoting the subsidy rate as s and the tax revenue as H tỵ1 ẳ sqtỵ1 xtỵ1 , the budget constraints of an individual of generation t are www.ebook3000.com 230 14 Does Aging Reduce Sustained Stock of Renewable Resources? wt lt ị ẳ c1t 14:34ị e e htỵ1 ỵ sqtỵ1 xtỵ1 H tỵ1 ẳ c2tỵ1 : qtỵ1 14:35ị The optimal plans of the individual may be stated as: ! H tỵ1 g x t ; l t ị e ỵ ịgl xt ; lt ị qtỵ1 ! H tỵ1 gxt ; lt ị e : ẳ sị ỵ ị qtỵ1 lt ẳ xtỵ1 14:36ị 14:37ị Assuming the existence of a stable steady state and taking into account the government’s budget constraint, we have in the steady state lẳ1 xẳ 1s gx; lị sị ỵ gl ðx; lÞ ð14:38Þ β gðx; lÞ: ð1 À sÞρ þ β ð14:39Þ Assuming the stability of the steady state, we obtain B B B @ 1À β g sị ỵ x 1s gl gx gglx sị ỵ gl ị2 10 dx CB C CB ds C C 1Às ðgl Þ2 ggll A@ dl A 1ỵ ds sị þ β ð gl Þ ρβ B ẵ1 sị ỵ g C C B ẳB C; @ gA ẵ1 sị ỵ gl g sị ỵ l 14:40ị from which we have dx g ẳ ds Diiiị ẵ1 sị ỵ ( " ) # 1s gl ị2 ggll ỵ >0 ỵ sị ỵ sị ỵ ð gi Þ ! dl β ð1 À sị gglx g ẳ gx ỵ ds Diiiị ẵ1 sị ỵ sị ỵ β gl gl ð14:41Þ ð14:42Þ where D(iii) is the determinant of the coefficient matrix on the left-hand side of (14.40) and is positive by stability We always have dx=ds > 0, while if 1sị gglx ỵ 1s ịỵ g > gx , we have dl=ds > When both x and l increase with the l Appendix 1: Tax-Subsidy Policies 231 subsidy rate, the harvest input in consumption goods production increases However, when dð1 À lÞ=ds < and dx=ds > 0, the output of consumption goods f ðh, À lÞ may increase, be constant, or decrease 1.4 Introduction of Intergenerational Transfers We consider the introduction of intergenerational transfers If they are already positive, the dynamics of the model will be different from that in the text Denoting the transfer from the working generation to the old by I, we assume that I ¼ initially The budget constraints are wt lt ị I ẳ c1t 14:43ị c2tỵ1 : 14:44ị e htỵ1 qtỵ1 ỵI ẳ The optimal plans of the generation t are & ' ! 1 I gxt ; lt ị ỵ e ỵ gl xt ; lt ịI lt ẳ À g l ðx t ; l t Þ ρ þ β qtþ1 wt ! β I gðxt ; lt ị ỵ e : xtỵ1 ẳ ỵ qtỵ1 14:45ị 14:46ị In the steady state with I ¼ 0, we have B B @ g ỵ x gl gx gglx 1 ỵ gl ị 10 dx gl CB dI C ỵ CB C ðgl Þ2 À ggll A@ dl A 1ỵ ỵ gl ị dI C B ỵ q  C ẳB @ 1 A; ỵ ỵ ịgl q w 14:47ị where q ẳ f h gx; lị x, lị and w ẳ f 1l gx; lị x, À lÞ All variables are evaluated in the steady state with I ¼ From (14.47) we have "  # dx β ggll β gl ẳ ỵ dI Divị q ỵ ị2 gl ị2 ỵ q w www.ebook3000.com 14:48ị 232 14 Does Aging Reduce Sustained Stock of Renewable Resources?    ! dl 1 β β gglx ¼ g ỵ : dI Divị w ỵ x ỵ ịgl q ỵ gl ð14:49Þ The signs of (14.48) and (14.49) are ambiguous The stock of renewable resources and labor inputs in regeneration activities may increase, be constant, or decrease when intergenerational transfers are introduced When I > 0, the dynamic system is characterized by two non-linear difference equations of xt and ht In this case we may have multiple steady-state equilibria the analysis of which goes beyond the scope of the present study References Food and Agriculture Organization of United Nations (FAO) (2005) Global forest resource assessment 2005 John, A., & Pecchenino, R (1994) An overlapping generations model of growth and the environment Economic Journal, 104(427), 1393–1410 John, A., Pecchenino, R., Schimmelpfennig, D., & Schreft, S (1995) Short-lived agents and the long-lived environment Journal of Public Economics, 58(1), 127–141 Kemp, M C., & van Long, N (1979) The under-exploitation of natural resources: A model with overlapping generations Economic Record, 55(3), 214–221 Koskela, E., Ollikainen, M., & Puhakka, M (2002) Renewable resources in an overlapping generations economy without capital Journal of Environmental Economics and Management, 43(3), 497–517 Li, C.-W., & Lofgren, K (2000) Renewable resources and economic sustainability: A dynamic analysis with heterogeneous time preferences Journal of Environmental Economics and Management, 40(3), 236–249 Mirman, L J., & To, T (2005) Strategic resource extraction, capital accumulation and overlapping generations Journal of Environmental Economics and Management, 50(2), 378–386 Mourmouras, A (1993) Conservationist government policies and intergenerational equity in an overlapping generations model with renewable resources Journal of Public Economics, 51(2), 249–268 Okuno, N., & Kurita, T (2010) Atarashii Kokyo wo Ninau Hitobito (People supporting the new public) Tokyo: Iwanami Shoten (in Japanese) Ono, T., & Maeda, Y (2001) Is aging harmful to the environment? Environmental and Resource Economics, 20(2), 113–127 Tahvonen, O., & Kuuluvainen, J (1993) Economic growth, pollution and renewable resources Journal of Environmental Economics and Management, 31(2), 160–177 Tahvonen, O., & Withagen, C (1996) Optimality of irreversible pollution accumulation Journal of Economic Dynamics and Control, 20(9–10), 1775–1795 Yakita, A (2001) Uncertain lifetime, fertility and social security Journal of Population Economics, 14(4), 635–640 Zhang, J., Zhang, J., & Lee, R (2001) Mortality decline and long-run economic growth Journal of Public Economics, 80(3), 485–507 Chapter 15 Conclusions We have been concerned with longevity and fertility decisions of individuals As shown in Chap 1, the population is now aging in developed countries and even developing countries are expected to follow in the not-too-distant future Although the global population has increased for a long time, the world is now facing a downward trend of population growth since the 1970s.1 Such a demographic change will inevitably affect not only economic development but also optimal economic policies In this book we analyzed these effects of population aging in overlapping generations models populated by two-period-lived (or three-periodlived) generations An increase in life expectancy lowers the fertility rate and raises life-cycle savings in order for individuals to prepare for longer retirement Therefore, if capital accumulation is an engine of economic growth, population aging boosts economic growth on the one hand On the other, when expansions in life expectancy are associated with declines in fertility, population aging will be accelerated.2 Then, introducing money as an asset substitutable for capital claims into a model based on the money-in-the-utility approach, we showed in Chap that an increase in longevity raises the balanced-growth rate and lowers the inflation rate, offsetting the Tobin effect, if spillovers from accumulated capital to labor productivity sufficiently raise wage income and real savings; and, if not, it may retard economic growth and aggravate inflation Under plausible conditions, the former will be the case As life expectancy expands, individuals may want to remain longer in the labor market and supply labor even in old age, i.e., the elderly labor supply If the retirement decision is endogenized in this sense, individuals with higher ability However, the population growth rate in the less developed is still high (UN, The World Population Prospects: The 2015 Revision http://esa.un.org/unpd/WPP/Download/Standard/Popu lation/ cited on March 2016) The idea of demographic transition, the so-called rule of thumb based on experiences in France and England, shows that declines in (crude) fertility follow those in (crude) death rate © Springer International Publishing AG 2017 A Yakita, Population Aging, Fertility and Social Security, Population Economics, DOI 10.1007/978-3-319-47644-5_15 www.ebook3000.com 233 234 15 Conclusions will supply labor in old age, although those with lower ability will not As population ages in the sense that life expectancy increases, individuals with lower earning ability will also remain in the labor market on the one hand, though the aggregate labor supply may not necessarily increase On the other hand, with longer life expectancy, individuals who retire in old age will reduce the number of their children, while those who work in old age may increase them Therefore, if individuals are allowed to choose the timing of leaving the labor market, the fertility rate of the economy may not necessarily decline; it may even rise This result in Chap is in contrast to the conventional result which has been obtained by assuming that the retirement age is fixed The fertility and retirement decisions of individuals may also be affected by intergenerational policies, in particular, social security policies This issue was discussed in Chap As is well known, pay-as-you-go (PAYG) social security has been introduced in most developed countries Although the reform of social security from the unfunded PAYG system to a fully-funded system has been asserted for several decades, the reform is known to involve a great burden for the current working generations during the transition Therefore, it seems plausible to consider a change in the size of social security or a reform of benefits schemes, given that social security is unfunded, rather than considering a reform from unfunded to fully funded In this book we assume a defined-contribution type of social security pensions Assuming that child-care services are available to the working generation in the market, we show that the impact of rises in the contribution rate of social security on fertility depends on the relative magnitudes of the standard intergenerational redistribution effect through the social security system, the (implicit) subsidy effect through tax-exemption of child rearing at home, and the price effect through changes in the relative price of market child care; and that if parental child-rearing time is sufficiently inelastic with respect to the wage rate, a tax cut could bring about a Pareto-improving allocation In some countries, for example, in Japan, the institutional retirement age and the eligibility age of social security may differ In such a situation, assuming that individuals have to hold money for consumption during the earlier years of retirement before the eligibility age for public pensions (i.e., the CIA constraint), we examined the effects of changes in the eligibility age on balanced growth and inflation through the adjustments of portfolio choices of individuals in Chap When the rate of inflation is sufficiently high, a postponement of the eligibility age lowers the economic growth rate and raises the rate of inflation, since it increases the demand for money and decreases real savings If the government increases the payroll tax rate in addition to the postponement of the eligibility age simultaneously, the fall in the growth rate and the rise in the rate of inflation will be greater However, when the inflation rate is sufficiently low, the inflation rate may conversely become lower, making the real return on real savings higher, and individuals may increase real savings, resulting in higher growth Part II focused on social security reforms In this book, we consider two alternative benefit schemes, i.e., flat-rate and proportional-to-contribution types The former is called the Beveridgean scheme and the latter the Bismarckian 15 Conclusions 235 scheme Incorporating heterogeneity in the preference of individuals to have children in an overlapping generations model of a small open economy, we examined the effects of changes in the size of PAYG social security on fertility choices of individuals and population growth of the economy in Chap For a given social security contribution rate, the number of individuals who have children is greater when the benefit level is not linked to the contribution, i.e., under the Beveridgean benefit scheme, than when the benefit level is proportional to the contribution, i.e., under the Bismarckian benefit scheme Second, it is shown that a rise in the contribution rate increases the fertility rate through increases in the number of individuals who have children and the number of children they have under the Beveridgean scheme In this case, therefore, it enhances the sustainability of the social security system in the sense that the supporters of both will increase in the future In contrast, under the Bismarckian benefit scheme without intragenerational redistribution, an increase in the contribution rate will not affect the population growth rate, i.e., the rate of return to PAYG social security contributions In Chap 7, we examined the effect of the reform of the social security benefit scheme on the elderly labor supply in a model similar to that in Chap 3, although we assume that life expectancy remains certainly constant The reform of the unfunded social security benefit scheme from the flat-rate to contributionproportional benefits reduces income redistribution from higher-ability to lowerability individuals If a smaller number of old workers with higher-ability supply market labor under a flat-rate benefit scheme, then the reform increases benefits of higher-ability old individuals Thus, those working under the flat-rate scheme will reduce their labor supply and even leave the labor market Although the old individuals not working under the flat-rate scheme will suffer from reductions in benefits owing to the regime change, the marginal utility from leisure during old age is still greater than the marginal utility of wage income from the elderly labor supply In this case, the total elderly labor will be smaller after the change to the contribution-proportional benefit scheme If otherwise a large number of old workers supply labor under the flat-rate benefit scheme, individuals who suffer from reductions of benefits under the new scheme will supply more labor, when working before the reform and those with increased benefits under the new scheme will reduce their labor supply and may even leave the labor market In this case, the effect of the reform on the total elderly labor supply is ambiguous Unexpectedly realized increases in life expectancy may cause individuals to re-schedule consumption-bequest plans The effect of rescheduling on government finance was examined in Chap The unexpectedly extended retirement period will induce individuals to decrease both the number of children and bequests to their offspring from those expected ex ante Individuals may choose to leave no bequests in re-optimizing if the revealed length of retirement is longer than expected In that case, they prefer government debt finance in order to prevent the welfare of their children from deteriorating with tax increases since the number of children has been already determined in the previous period The unexpected expansion in lifetime increases the number of such retired individuals, while the www.ebook3000.com 236 15 Conclusions next generation may have longer life expectation ex ante, reducing the number of their children The decrease in the number of the young population brings about heavier government spending per head, i.e., a higher social security contribution, inducing the young to prefer debt financing still more Part III was concerned with economic development In Chap we first distinguished between human capital obtained through schooling before entering the labor force and the stock of common knowledge of workers about productivity improvements Assuming an indirect effect of education on economic growth, we showed that the greater the educational expense, the higher the wage income, and that the greater the savings and capital accumulation, the higher the economic growth attained through knowledge spillovers among workers Longer retirement induces individuals to save more for retirement and to invest more in human capital in order to earn a higher wage income Increases in schooling years may be subject to diminishing returns to scale, while the greater borrowing of the youngest (i.e., childhood) generation for education tends to reduce income net of its repayments and hence savings, thus both depressing physical capital accumulation and thereby economic growth Therefore, a longer retirement raises both the growth rate of the educational expenditure of individuals and the balanced-growth rate of the economy In explaining the differences in educational performance, parental supports for their offspring may play an important role in raising the children’s educational performance In Chap 10, if the educational support stimulates their children’s cumulative learning process, we showed that if children are highly sensitive to the aspirations and activities of their parents to perform well in school, higher parental aspirations and educational activities will lead to a higher steady-state level of human capital, income, and consumption; and that even if the aspirations of parents are very strong, a smaller contribution of parental education to human capital production may result in a lower level of human capital stock In Chap 11, we show an alternative mechanism of economic development to those in the existing literature: income increases trigger parental human capital investment in due time, which in turn accelerates R&D innovations; and then the economy will experience modern economic growth with declining fertility Then, in Chap 12, we examined the effects of aging on the balanced-growth-maximizing public investment policy in an overlapping generations model with a growth engine of public capital accumulation Extended life expectancy tends to increase individual savings, while the increased old-age dependency requires more resources to be allocated to consumption in the economy Declining working population makes for a severe trade-off between private and public capital accumulation We showed that as aging proceeds, not only the income tax rate must be raised to accelerate public capital formation but the expenditure share of maintenance should be increased in order to maximize the balanced-growth rate In Chap 13 we examined the short- and long-term effects of capital taxation on international capital movements between countries and welfare of nations through changes in demographic dynamics If the tax revenue from capital taxation increases the income of the working and child-rearing generation, the capital tax 15 Conclusions 237 induces workers to have greater lifecycle savings for their retirement and a greater number of children Assuming that the initial steady-state population growth rates of both economies are the same, per worker savings is higher in the home economy with higher capital taxation Then, if the tax rate is reduced in the home economy, the home workers decrease the number of their children due to the reduced income brought about by lower government expenditures Although the tax cut tends to internationally attract capital to the home country and accelerate domestic capital accumulation through capital inflows in the short term, the capital labor ratios of both countries decline in the long term since the world economy approximately approaches the autarkic economy of higher population growth and hence greater population with a still smaller lifecycle savings Thereby, the long-term economic welfare will also be lower not only in the other economy but also at home This result is in contrast to that in conventional models with common and fixed fertility Our final analysis in Chap 14 is concerned with natural resources or stock Focusing on renewable resources as a means of intergenerational transfers and incorporating labor inputs in regeneration of the resources into a model, the effects of population aging on steady-state sustained renewable resources and GDP are examined An increase in life expectancy always reduces the sustained level of renewable resource stock However, the labor inputs in regenerating activities and sales of the harvest to consumption-goods producers may increase, remain constant or decrease, depending on the relative magnitude of the marginal product of labor in goods production and the degree of substitutability between labor and resource inputs in the renewable resource regeneration In considering renewable natural resources such as forests, we should realize not only that the resources can be used in goods production but also that the resources benefit us as a stock providing flows of public goods/services www.ebook3000.com ... Publishing AG 2017 A Yakita, Population Aging, Fertility and Social Security, Population Economics, DOI 10.1007/978-3-319-47644-5_1 www.ebook3000.com Longevity and Fertility income level, life... (2009) Fertility, child care outside the home, and pay-as-you-go social security Journal of Population Economics, 22(3), 565–583 Hirazawa, M., Kitaura, K., & Yakita, A (2010) Aging, fertility, social. .. (2001) Uncertain lifetime, fertility and social security Journal of Population Economics, 14(4), 635–640 Zhang, J., & Zhang, J (1998) Social security, international transfers, and endogenous growth