Global demographic trends and social security reform Orazio Attanasio, University College London Sagiri Kitao, University of Southern California Gianluca Violante, New York University June 28, 2007 The University of Tokyo Tokyo, June 28, 2007 – p. 1
Introduction Demographic trends significant increase in longevity decline in fertility the retirement of the ‘baby boom’ generations Global demographic trends are not completely synchronized across countries Tokyo, June 28, 2007 – p. 2
Introduction Demographic Transition: total fertility rates Demographic Transition: median age 7 60 South: UN (data/projection) 6 50 South: model Total fertility rates North: UN (data/projection) 5 Median age North: model 40 4 30 North: UN (data/projection) 3 North: model 20 South: UN (data/projection) 2 South: model 1 10 1950 2000 2050 2100 2150 2200 1950 2000 2050 2100 2150 2200 Years Years Demographic Transition: old dependency ratio (60 or above) Demographic Transition: population growth 0.5 4 North: UN (data/projection) 0.4 3 North: model Population growth Dependency ratio South: UN (data/projection) 0.3 2 South: model 0.2 1 North: UN (data/projection) North: model South: UN (data/projection) 0.1 0 South: model 0 −1 1950 2000 2050 2100 2150 2200 1950 2000 2050 2100 2150 2200 Years Years Tokyo, June 28, 2007 – p. 3
Introduction Economic implications of the demographic trends large changes in factor prices and welfare sustainability of PAYG pension systems Question: when thinking about how to reform the social security system in the developed world , does the distinction open vs closed economy matter for factor prices welfare fiscal policy variables? Contribution: offer an alternative benchmark for policy evaluation. Tokyo, June 28, 2007 – p. 4
Introduction Social security in closed economy Conesa and Krueger (1999), De Nardi, Imrohoroglu and Sargent (1999), Huggett and Ventura (1999), Abel (2003), Bohn (2003), and many more small open economy: Huang, Imorohoroglu and Sargent (1997), Kotlikoff, Smetters and Walliser (1999) Global demographic trends and current account dynamics Brooks (2003), Domeij and Floden (2004), Attanasio, Kitao and Violante (2006), Krueger and Ludwig (2007) and many more Labor flow across regions Storesletten (2000), Fehr, Jokisch and Kotlikoff (2004) Tokyo, June 28, 2007 – p. 5
Overview OLG model calibrated on observed and projected demographic trends two regions: North and South Different ways to finance the social security system in the North PAYGO system is maintained The system is privatized to a fully-funded system Open and closed economy versions of the model Tokyo, June 28, 2007 – p. 6
MODEL Tokyo, June 28, 2007 – p. 7
Model Two regions: r = n, s Tokyo, June 28, 2007 – p. 8
Model Two regions: r = n, s Technology CRS production function F ( Z r t , K r t , L r t ) TFP Z r t grows exogenously at rate λ r t Tokyo, June 28, 2007 – p. 8
Model Two regions: r = n, s Technology CRS production function F ( Z r t , K r t , L r t ) TFP Z r t grows exogenously at rate λ r t Demographics OLG of pairs of individuals, indexed by age i = 1 , 2 , ...I dependent for I d periods, become adults and start working at I d + 1 , and retire from work at I R surviving probability s r i,t , S r i,t fertility rate φ r i,t i,t = � i number of dependent children d r k = i − I d +1 φ r k,t − ( i − k ) S r i − k +1 ,t Tokyo, June 28, 2007 – p. 8
Model: evolution of population At time t , population shares µ r t evolve according to the transition matrix φ r φ r φ r ... ... ¯ 1 ,t 2 ,t I,t s r 0 ... ... 0 2 ,t +1 s r Γ r 0 0 ... 0 = 3 ,t +1 t ... ... 0 0 0 s r 0 0 ... 0 ¯ I,t +1 µ r Γ r t µ r = t +1 t Tokyo, June 28, 2007 – p. 9
Model: preferences � 1 − θ � 1 − θ � � c a c d i,t i,t u r ( c a i,t , c d + d r d r � � i,t ) = i,t ω i,t 1 − θ 1 − θ Tokyo, June 28, 2007 – p. 10
Model: preferences � 1 − θ � 1 − θ � � c a c d i,t i,t u r ( c a i,t , c d + d r d r � � i,t ) = i,t ω i,t 1 − θ 1 − θ From F.O.C. � 1 c d i,t = c a d r � i,t ω θ i,t Tokyo, June 28, 2007 – p. 10
Model: preferences � 1 − θ � 1 − θ � � c a c d i,t i,t u r ( c a i,t , c d + d r d r � � i,t ) = i,t ω i,t 1 − θ 1 − θ From F.O.C. � 1 c d i,t = c a d r � i,t ω θ i,t Express utility as a function of household consumption c i,t = c a i,t + d i,t c d i,t 1 − θ c � θ � 1 � i,t θ d r u r ( c i,t ) = Ω r Ω r d r � 1 − θ, i,t = 1 + ω i,t i,t i,t Tokyo, June 28, 2007 – p. 10
Model: preferences � 1 − θ � 1 − θ � � c a c d i,t i,t u r ( c a i,t , c d + d r d r � � i,t ) = i,t ω i,t 1 − θ 1 − θ From F.O.C. � 1 c d i,t = c a d r � i,t ω θ i,t Express utility as a function of household consumption c i,t = c a i,t + d i,t c d i,t 1 − θ c � θ � 1 � i,t θ d r u r ( c i,t ) = Ω r Ω r d r � 1 − θ, i,t = 1 + ω i,t i,t i,t 1 − θ I c U r = i,t + i − 1 � β i − 1 S r i,t + i − 1 Ω r i,t + i − 1 1 − θ i =1 Tokyo, June 28, 2007 – p. 10
Model: budget constraint 1 + τ r c r i,t + s r i +1 ,t +1 a r i +1 ,t +1 = y r 1 − τ r a r � � � � � � i,t + 1 + r t c,t a,t i,t Tokyo, June 28, 2007 – p. 11
Model: budget constraint 1 + τ r c r i,t + s r i +1 ,t +1 a r i +1 ,t +1 = y r 1 − τ r a r � � � � � � i,t + 1 + r t c,t a,t i,t 1 − τ r w r t ε r i,t l r 1 − τ r y r if i < I R , � � � � i,t = ˜ w,t w,t i,t y r i,t = W r p r i,t = κ r if i ≥ I R i,t t I R − 1 Tokyo, June 28, 2007 – p. 11
Model: budget constraint 1 + τ r c r i,t + s r i +1 ,t +1 a r i +1 ,t +1 = y r 1 − τ r a r � � � � � � i,t + 1 + r t c,t a,t i,t 1 − τ r w r t ε r i,t l r 1 − τ r y r if i < I R , � � � � i,t = ˜ w,t w,t i,t y r i,t = W r p r i,t = κ r if i ≥ I R i,t t I R − 1 y r ˜ if i = 1 1 ,t W r y r i,t + W r if 1 < i < I R ˜ i,t = i − 1 ,t − 1 W r if i ≥ I R . i − 1 ,t − 1 Tokyo, June 28, 2007 – p. 11
Model: government t + � I G r t + (1 + r t ) B r i = I R p r i,t µ r i,t = � I R − 1 � � i,t + � I τ r w,t w r µ r i,t ε r i,t l r i =1 µ r τ r a,t r t a r i,t + τ r c,t c r + B r t i =1 i,t i,t t +1 Tokyo, June 28, 2007 – p. 12
Equilibrium A Competitive Equilibrium of the Two-Region Economy, for given sequences of demographic matrices { Γ r t =1 , TFP { Z r t } ∞ t } ∞ t =1 � ∞ G r t , κ r t , τ r a,t , τ r c,t , B r � and fiscal variables t =1 , is t —————————————————————————– 1. household allocations 2. wage tax rates 3. wage rates (in North and South) 4. world interest rate 5. aggregate variables 6. external wealth of the North such that: Tokyo, June 28, 2007 – p. 13
Equilibrium A Competitive Equilibrium of the Two-Region Economy, for given sequences of demographic matrices { Γ r t =1 , TFP { Z r t } ∞ t } ∞ t =1 � ∞ G r t , κ r t , τ r a,t , τ r c,t , B r � and fiscal variables t =1 , is t —————————————————————————– such that: 1. households and firm maximize 2. regional labor markets clear 3. regional bond markets and international capital market clear 4. government budget constraints are satisfied 5. allocations are feasible Tokyo, June 28, 2007 – p. 13
CALIBRATION Tokyo, June 28, 2007 – p. 14
Calibration Model period: five years Tokyo, June 28, 2007 – p. 15
Calibration Model period: five years Demographics demographic variables: UN projections (2005-2200) North “more developed regions" US, Canada, Europe, Japan, Australia and NZ South “less developed regions" Africa, Asia (ex-Japan), Latin America, and the rest I d = 3 , I = ¯ I − I d = 24 − 3 = 21 , I R = 11 , Tokyo, June 28, 2007 – p. 15
Calibration Model period: five years Demographics demographic variables: UN projections (2005-2200) North “more developed regions" US, Canada, Europe, Japan, Australia and NZ South “less developed regions" Africa, Asia (ex-Japan), Latin America, and the rest I d = 3 , I = ¯ I − I d = 24 − 3 = 21 , I R = 11 , Technology Cobb-Douglas with 0.3 share of capital growth of Z r t : match historical growth of income per capita and converge to the same rate in the long-run Z r 0 to match the North-South income per capita ratio of 7 in 2000 Tokyo, June 28, 2007 – p. 15
Calibration Preference risk-aversion coefficient σ = 2 preference weight for children ω ( d r i,t ) calibrated to match equivalence scale (Fernandez-Villaverde and Krueger, 2006) Tokyo, June 28, 2007 – p. 16
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