Income Growth in the 21st Century: Forecasts with an Overlapping - PowerPoint PPT Presentation

Income Growth in the 21st Century: Forecasts with an Overlapping Generations Model David de la Croix Fr´ ed´ eric Docquier Philippe Li´ egeois FNRS, IRES and CORE CADRE ECARES 1

Main question Rise in life expectancy Drop in fertility rates ⇒ share of the elderly in population will increase Aging is forecasted by demographers: – inescapable – little can be done to modify its magnitude for the next 50 years – Strength varies across countries Effects of these demographic changes upon the economy ? –in theory, many effects whose weights are unknown a priori –need for a quantitative approach 2

Theoretical effects of aging Reduces the growth rate of the labor force (become negative in FR and CA) Stimulates savings → more capital per worker, lower interest rates Changes the characteristics of the labor force: experience vs education Public finance effects: sustainability of pension systems ? 3

What we do Take demographic forecast for France, Canada, USA. Build an overlapping generations model capturing some key fea- tures to study aging ⇒ growth. Calibrate the parameters over the period 1960-2000. Simulate the model to forecast GDP per capita over 2000-2050. Three scenarios: constant policies, rise in retirement age, drop in pensions Same methodology for the three countries → comparability. 4

Our model compared to existing studies Strong demographic block with life uncertainty and migrations (exogenous) Link the evolution of taxes and expenditures to demographic changes (use of generational accounting studies) Labor market: interactions between education and experience 5

The model – population (1) Model time is discrete and goes from 0 to + ∞ . At each date, some individuals die and a new generation appears. Households reaching age 15 at year t belong to generation t . Each household lives a maximum of 8 periods ( a = 0, ..., 7 ) 6

The model – population (2) The size of the young generation: N 0, t + 1 = N 0, t m t m t : exogenous demographic growth rate (fertility + migration) The size of each generation: N a , t + a = N 0, t β a , t + a + M a , t + a cumulative survival probability decreasing with age: β a , t + a . Total population at time t 7 ∑ N t = N a , t a = 0 7

The model – households – objective The expected utility: 7 ∑ E ( U t ) = β a , t + a ln ( c a , t + a ) (1) a = 0 The budget constraint: 7 � � c a , t + a ( 1 + τ c ∑ p a , t + a t + a ) − T a , t + a a = 0 7 � � ω L a , t + a + ω E a , t + a e a , t + a + ω H ∑ = ℓ a , t + a (2) a , t + a h a , t + a a = 0 Households choose their consumption spending and their invest- ment in education. 8

The model – households – labor supply Labor supply: ℓ t = ( q t ( 1 − u t ) , q t + 1 , q t + 2 , q t + 3 , q t + 4 ( 1 − α t + 4 ) , 0, 0, 0 ) (3) Experience: e t = ( 0, ( 1 − u t ) q t , ( 1 − u t ) q t + q t + 1 , ( 1 − u t ) q t + q t + 1 + q t + 2 , (4) ( 1 − u t ) q t + q t + 1 + q t + 2 + q t + 3 , 0, 0, 0 ) , Education capital: � � 0, ǫ u ψ t , ǫ u ψ t , ǫ u ψ t , ǫ u ψ h t = (5) t , 0, 0, 0 , 9

The model – households – transfers Public transfers: � v t q t u t ω L = 0, t + γ 0 g t , γ 1 g t + 1 , γ 2 g t + 2 , γ 3 g t + 3 , T t α t + 4 b t + 4 + γ 4 g t + 4 , b t + 5 + γ 5 g t + 5 , b t + 6 + γ 6 g t + 6 , b t + 7 + γ 7 g t + 7 ) , (6) v t : rate of subsidy on the cost of education b t : pension benefit γ a : share of total transfer g t in favor of age a . 10

The model – households – first-order-conditions The optimal education investment: 1   � � 1 − ψ ǫψ ∑ 4 ω H a , t + a q t + a ℓ a , t + a a = 1 u ∗   t = (7) � � � �   ω L 0, t + ω H + ∑ 4 ω E ( 1 − v t ) q t a , t + a q t + a ℓ a , t + a a = 1 0, t Optimal consumption: c a + 1, t + a + 1 = ( 1 + r t + 1 )( 1 + τ c t ) c a , t + a ∀ a = 0, ..., 6 (8) ( 1 + τ c t + 1 ) 11

The model – firms – technology Production function: Y t = A t K 1 − ϕ Q ϕ (9) t t total factor productivity: A t (10) ≡ G t = ( 1 − λ ) G + λ G t − 1 + ε t A t − 1 efficiency units of labor: Q t = L 1 − δ [ µ E t + ( 1 − µ ) H t ] δ (11) t 12

The model – firms – first-order-conditions firms maximize profits: Y t − ( r t + d ) K t − w L t L t − w H t H t − w E t E t (12) FOC: (13) r t = ( 1 − ϕ ) A t Y t / K t − d w L (14) = ϕ ( 1 − δ ) A t Y t / L t t ϕδµ A t K 1 − ϕ Q ϕ − 1 w E L 1 − δ [ µ E t + ( 1 − µ ) H t ] δ − 1 = (15) t t t t ϕδ ( 1 − µ ) A t K 1 − ϕ Q ϕ − 1 w H L 1 − δ [ µ E t + ( 1 − µ ) H t ] δ − 1 = (16) t t t t 13

The model – public sector Government budget constraint: τ w t ( w L t L t + w E t E t + w H t H t ) + τ c t C t + τ k t r t K t + D t + 1 − ( 1 + r t ) D t 7 N 0, t v t q t u t w L t ( 1 − τ w ∑ = t ) + N a , t γ a g t a = 0 7 ∑ (17) + ϑ t Y t + ( N 4, t α t + N a , t ) b t a = 5 D t : public debt at the beginning of period t 14

The model – equilibrium conditions (1) Definition of the net discount factor: t + a ( 1 + r s ( 1 − τ k s )) − 1 ∏ R a , t + a ≡ s = t + 1 Equilibrium prices: p a , t + a = R a , t + a β a , t + a p t + a = R a , t + a β a , t + a (18) ω L R a , t + a β a , t + a w L t + a ( 1 − τ w = t + a ) a , t + a ω E R a , t + a β a , t + a w E t + a ( 1 − τ w = t + a ) (19) a , t + a ω H R a , t + a β a , t + a w H t + a ( 1 − τ w = t + a ) a , t + a 15

The model – equilibrium conditions (2) Goods market: 7 Y t + K ⋆ ∑ (20) t = N a , t c a , t + K t + 1 − ( 1 − d ) K t + ϑ t Y t ���� � �� � a = 0 G t I t � �� � C t Labor market: 7 7 7 ∑ ∑ ∑ L t = N a , t ℓ a , t , E t = N a , t ℓ a , t e a , t , H t = N a , t ℓ a , t h a , t (21) a = 0 a = 0 a = 0 16

The quantitative experiment - method Get data for observed exogenous variables, Fix some parameters (same for the 3 countries), Choose paths for other unobserved exogenous variables and pa- rameters in order to match a series of characteristics (calibra- tion). Calibration not done at steady state but dynamically, over the period 1960-2000. The equilibrium is computed as a transition from one steady state in 1900 to one another in 2250. By starting in 1900, the stocks of education and experience around 1960 reflect the correct history of the population. 17

Observed exogenous variables Demography Education and participation rates Public finance 18

Population size (index 2000=100) 1.6 1.4 Usa France 1.2 Canada 1.0 0.8 0.6 0.4 0.2 0.0 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 19

Growth rate of the population aged 15-64 3.0% Usa 2.5% France 2.0% Canada 1.5% 1.0% 0.5% 0.0% 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 -0.5% -1.0% 20

Old Age Dependency (65+ / 15-64) 0.5 0.5 Usa France 0.4 Canada 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0.0 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 21

Parameters The labor share in output, ϕ , is set to 0.7 The depreciation rate of capital d equals 0.4. (5% annual) Share of raw labor in labor income ( 1 − δ ) is set to 0.4 ǫ is set to 2.1 to deliver an adequate wage profile ψ = 0.6 is in accordance with a return to an additional year of schooling of 11.5% 22

Identification of unobserved exogenous variables Four unobserved exogenous variables: – total factor productivity, A t – the rate of subsidy on education expenditures, v t – the level of pension benefit, b t – the scale of the age-specific transfer profile, g t . Chosen to match – the GDP growth rate, –the share of social security in GDP –the share of other transfers in GDP –the education investment of young cohorts. 23

Growth factor of TFP 1.9 1.8 Calibrated white noise White noise = 0 1.7 Canada 1.6 Usa 1.5 France 1.4 Longrun 1.3 1.2 1.1 1.0 0.9 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 2030 2040 2050 24

Wage and assets profile per age Important to have relatively correct wage and asset age-profiles. The shape of the wage profile per age is fully determined by the accumulation of experience; no exogenous trend. Good match for France, OK for the US. Good job also for the asset profile. No need to suppose a pure time preference parameter on top of the mortality rate. The annuity market is also helpful to avoid poverty in the old age. 25

Wage profile - USA 2000 0.800 30000 0.700 25000 0.600 20000 0.500 0.400 15000 0.300 10000 Simulations (left scale) 0.200 Observations (right scale) 5000 0.100 0.000 0 15-24 25-34 35-44 45-54 55-64 26

Wage profile - France 2000 0.700 180000 0.600 160000 0.500 140000 120000 0.400 100000 0.300 80000 Simulations (left scale) 0.200 Observations (right 60000 scale) 0.100 40000 0.000 20000 15-24 25-34 35-44 45-54 55-64 27

Wealth profile - USA 2000 0.600 3300 0.500 2800 0.400 2300 0.300 1800 0.200 1300 0.100 800 Simulations (left scale) Observations (right scale) 0.000 300 -0.100 -200 15-24 25-34 35-44 45-54 55-64 65-74 75-84 85-94 28