Demographic Structure and Macroeconomic Trends

Transcription

1 Demographic Structure and Macroeconomic Trends Yunus Aksoy (Birkbeck, London) Ron Smith (Birkbeck, London) Henrique S. Basso (Banco de España) Tobias Grasl (Birkbeck, London) Demographics and the Macroeconomy: BoF/CEPR; October 217 October 12, 217

2 Motivation Medium-run outlook? Slow recovery after great recession and disappointedly low growth of productivity in the last decade Medium-long run stagnation may have started long before the onset of the financial crisis Production of ideas and demographic changes may be related (Kuznets (196)) ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

3 Motivation Proportion of Population in Age Group Year Figure: Demographic Structure in (sample) OECD countries Population aged 6+ 16% in 197 to 29% in 23. Working age group (2 59) 5% in 197, 56% in 23, 48% in 23 BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

4 Motivation Demographics, Labour Supply and Population Growth Demographics is generally linked to lower population growth and lower labour supply A more general view: demographic structure, defined as the proportion of the population in each age group, may have an impact on economic performance Both demand and supply side effects of demographic structure changes Different age groups: may have different savings behaviour, according to the life-cycle hypothesis; may have different contributions to productivity gains, following the age profile of wages; may contribute differently to the innovation process, with young and middle age workers contributing the most; may generate different investment opportunities, as firms target their different needs. ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

5 Motivation This paper proposes a framework to formally assess the impact of demographics in advanced economies both empirically and theoretically Empirically - Does demographic structure affect the trend of growth, investment, saving, real rates? How about innovation (R&D)? Yes. It follows life-cycle profile. Theoretically - What does the theory has to say about the links between demographic structure, demand/supply channels and macroeconomic trends? Ingredients: Demographic heterogeneity (Gertler-Blanchard-Yaari) with human capital accumulation; Endogenous productivity: (Comin and Gertler (26)) real business cycle model add invention of new varieties a la Romer (199). Link these two such that age profile of the population matters for innovation and adoption (i.a. Jones, Reedy, and Weinberg (214) ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

6 Empirical Analysis Empirics - Impact of Demographic Structure on Macroeconomy Estimate a Panel VAR with intercept heterogeneity but slope homogeneity given by (we additionally control for population growth and oil prices (2 lags) which as demographics are assumed exogenous) Y it = a i + A 1 Y i,t 1 + DW it + controls + u it, Benchmark - Y it = (g it, I it, S it, H it, rr it, π it ) - Extension - Y it = (g it, I it, S it, H it, rr it, R&D PA it, π it ) W it denote the matrix with population shares (-19, 2-59, 6+) - granular representation (most literature assumes single variable; Higgins (1998), Fair and Dominguez (1991) use low order polynomial function to describe age structure) Dataset: ; twenty countries; Australia, Austria, Belgium, Canada, Denmark, Finland, France, Greece, Iceland, Ireland, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Spain, Sweden, Switzerland, UK, US. Estimation Details BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

7 Empirical Analysis Methodology - Impact of Demographic Structure on Macroeconomy We are interested in the long run prediction of macro variables conditional on a particular vector of demographic shares after the completion of the endogenous adjustment of the economic variables Cross section variability crucial for short term identification. Some countries enter demographic transition earlier than others Much greater range variance of independent variables available in a panel. (two way effects for robustness) Concentrate on the demographic attractor Y D it = (I A 1 ) 1 DW it. (1) Exploit dynamic properties of macro variables to obtain estimates of the long-run effect Thus NOT ONLY demographics DIRECT impact on each variable but their effects transmitted through the whole system after the macroeconomic feedback effects are accounted for Important to distinguish between steady state effect and long-run effect. WeakExo BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

8 Empirical Analysis Estimation - Three generations of Life Cycle Matrix - (I A 1 ) 1 D β 1 β 2 β 3 g ** I.13*** ** S.24*** ** H -.54*** 1.8** -.54** rr * π.7*** -.75***.5 Note: = 1%, = 5%, = 1% levels of significance. Table: Long-Run Demographic Impact - D LR Short-Run Demographic Impact Robustness ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

9 Empirical Analysis Table: Average Predicted Impact on GDP Growth by Country Sample Average Projected at Projected at Change (197-21) ( ) Prob(Change ) Australia 3.33% 3.11% 2.6% -.51%.89 Austria 2.51% 2.37% 1.53% -.84%.8 Belgium 2.57% 2.45% 1.88% -.57%.87 Canada 3.5% 2.69% 1.81% -.88%.8 Denmark 2.18% 1.97% 1.5% -.46%.6 Finland 2.8% 2.44% 1.93% -.51%.84 France 2.57% 2.26% 1.72% -.54%.68 Germany 2.11% 1.91% 1.15% -.77%.81 Greece 3.77% 3.49% 2.82% -.67%.61 Iceland 3.46% 3.13% 2.39% -.74%.65 Ireland 5.% 4.59% 3.99% -.61%.68 Italy 2.91% 2.64% 1.84% -.79%.73 Japan 2.95% 2.56% 2.14% -.42%.69 Netherlands 3.1% 2.68% 1.9% -.78%.66 New Zealand 2.72% 2.47% 1.78% -.69%.66 Norway 3.63% 3.53% 3.1% -.43%.63 Portugal 3.69% 3.33% 2.58% -.75%.56 Spain 3.73% 3.41% 2.51% -.9%.73 Sweden 2.2% 2.17% 1.86% -.31%.119 Switzerland 2.22% 2.13% 1.4% -.74%.84 United Kingdom 2.6% 2.47% 1.96% -.51%.87 United States 2.85% 2.53% 1.87% -.65%.66 ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

10 Empirical Analysis.35.3 United States.35.3 Japan.25 Sweden.3.25 France Output Growth Output Growth Output Growth.2.15 Output Growth Interest Rate -.5 Interest Rate -.5 Interest Rate -.5 Interest Rate Years Years Years Years Figure: Impact of Predicted Future Demographic Structure on Long-term Growth and Real rates Additional Countries BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

11 Empirical Analysis.24 United States.32 Japan.26 Sweden.24 France Investment Investment Investment Investment Interest Rate -.5 Interest Rate -.5 Interest Rate -.5 Interest Rate Years Years Years Years Figure: Impact of Predicted Future Demographic Structure on Long-term Investment and Real rates ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

12 Empirical Analysis Link between demographics and innovation - Great EW OF ECONOMICS AND STATISTICS Inventions novators in the ns and locates I find substany demographic pward trend in e careers. The t minds of the ctive at age 23 at age 31 at the hile, there has y of innovators further underhow that PhD century. I next iments, testing nnovation and be made up ld, cross-time age typically Frequency FIGURE 1. AGE DISTRIBUTION OF GREAT INNOVATION Age Note: Data are pooled across time. Nobel Prize Winners Great Inventors Figure: Age Distribution of Great Inventions - Source Jones (21) this is simply the year in which the achievement is listed. For the Nobel Prize, the year of achievement was deter- ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

13 Empirical Analysis 9 A G E S T R U C T U R E A N D P R O D U C T I V I T Y Link between demographics and innovation - Patents FIGURE 4 Distribution by single years of age of US inventors granted patents, Age Age Age Age SOURCE: Jones (25) Age Figure: Distribution by single years of age of US inventors granted patents, Source Jones (25) Idea adoption While creative output is one potential channel through which age may affect productivity, it may not be the most relevant for cross-country comparisons. For most of the countries in the world, idea creation matters less than idea ABGS (Demographics and the Macroeconomy: adoption. BoF/CEPR; Organizations October (or countries) 217 ) that increase productivity by produc- October 12, / 48

14 Empirical Analysis Estimation - Results Matrix - (I A 1 ) 1 D β 1 β 2 β 3 g * I.15**.5 -.2* S.24*** *** H -.48**.95** -.47 rr * R&D -3.7*** 4.5*** -.8 π.72*** -.81***.8 Note: = 1%, = 5%, = 1% levels of significance. Table: Long-Run Demographic Impact - D LR BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

15 Empirical Analysis Output Growth United States Output Growth Japan Output Growth Sweden Output Growth France Interest Rate -.5 Interest Rate -.5 Interest Rate -.5 Interest Rate Years Years Years Years Figure: Impact of Predicted Future Demographic Structure with R&D on Long-term Growth and Real rates ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

16 Empirical Analysis Investment United States Investment Japan Investment Sweden Investment France Interest Rate -.5 Interest Rate -.5 Interest Rate -.5 Interest Rate Years Years Years Years Figure: Impact of Predicted Future Demographic Structure with R&D on Long-term Investment and Real rates ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

17 Empirical Analysis Robustness Robust w.r.t.: common trend: two ways effects per capita real GDP mortality and fertility trends (Lee-Carter) open economy effects (net foreign assets/gdp) long term rates more granular demographics: 6 Generations more granular demographics: 8 Generations ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

18 Empirical Analysis Summary - Empirical Results Long term effects of demographic structure change are larger than short term effects Long term: clear life cycle effects Long term: real rates are increasing with the share of workers and declining with the share of dependants Long term: life cycle effects on innovation Population predictions for the next 2 years: demographic changes are a strong force in reducing trend growth and real rates ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

19 Theoretical Model Theoretical Model-Overview A real model that combines two strands of literature: Demographic heterogeneity: via Gertler-Blanchard-Yaari model include young dependants introduce human capital accumulation. Endogenous productivity: (Comin and Gertler (26)) real business cycle model adds invention of new varieties a la Romer (199).Simplify to consider only a one sector economy. Link these two such that age profile of the population matters for innovation and adoption life-cycle consumption/saving decisions incentives alter human capital accumulation process young workers influence innovation process BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

20 Theoretical Model Economic Environment Educa on (ξ) Young Workers Retirees Assets Households F. Intermediary Consump on Γ yw Innovators Funding Final Good Production Prototypes (Z) K ξl Inputs Adopters Varie es (A) Input Production Innovation Sector yw Γ Production Sector Demographic Flows = Share of Workers contribu ng to Innova on ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

21 Theoretical Model Model - Key Features Model Detail be the stock of invented goods (prototypes) and Γ yw t that contribute to innovation. Thus, Z p t = share of workers Z p t+1 = ϕ ts p t + φz p t = (Γ yw t ) ρyw χ[( Ψ t ) ρ (S t ) 1 ρ ] 1 Z t St p + φzt p Aggregate consumption functions are: C w t = ς t [R t FA w t + H w t + D w t T w t ] C r t = ε t ς t [R t FA r t + D r t ] Population (N t ) grows at rate n t Young (N y t ) becomes worker with probability 1 ω y Workers (N w t ) retire with probability 1 ω r Once retired (N r t ) individual survives with probability γ Share of Retirees over Workers, ζ r t = N r t /N w t, and Share of young dependants over workers, ζ y t = N y t /N w t. BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

22 Theoretical Model Simulation Use the parameters of Gertler (1999) (for households and population dynamics) and Comin and Gertler (26) (firms and innovation) Parameters. Show results for different ρ yw (importance of workers for innovation) and λ y (persistency of stock of workers/age for innovation). Perform various simulation exercises (perfect foresight) baby-boomers analyses the effect of increasing fertility holding longevity constant. aging looks at the effects of increasing longevity by increasing γ permanently. prediction, attempt to match the change in the demographic structure predicted for a selected number of countries in our sample during the next two decades and measure their impact on growth and real interest rates. BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

23 Theoretical Model Three Channels through which Age Profiles Affect the Macroeconomy Changes in fertility and the implicit cost of taxing workers affect investment in human capital. Aging affects the saving decision of workers and thus real interest rates. The share of young workers impacts the innovation process positively and, as a result, a change in the demographic profile that skews the distribution of the population to the right, leads to a decline in innovation activity. BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

24 Theoretical Model Simulation - Aging Population ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

25 Conclusions Conclusions Robert Gordon (212) asks how much further could the frontier growth rate decline? A new empirical methodology to measure the life cycle effects of demographic structure Use properties of the dynamic system to obtain long-run impact and show age profile impacts macroeconomic trends. Build a model with demographic heterogeneity and endogenous productivity that matches well the empirical findings. three main channels by which demographics affects the macroeconomy: through life-cycle consumption decisions, through incentives that alter human capital accumulation process through the influence of young workers on the innovation process Population aging and reduced fertility expected in the next decades imply strong reduction on the trend of growth and real rates across most OECD economies, but particularly in Europe. ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

26 Conclusions References I Comin, D., and M. Gertler (26): Medium-Term Business Cycles, American Economic Review, 96(3), Gertler, M. (1999): Government Debt and Social Security in a Life-cycle Economy, Carnegie-Rochester Conference Series on Public Policy, 5(1), Jones, B., E. Reedy, and B. A. Weinberg (214): Age and Scientific Genius, NBER Working Papers 19866, National Bureau of Economic Research, Inc. Jones, B. F. (25): Age and Great Invention, NBER Working Paper 11359, NBER. (21): Age and Great Invention, The Review of Economics and Statistics, 92(1), Kuznets, S. (196): Population Change and Aggregate Output, in Demographic and Economic Change in Developed Countries, NBER Chapters, pp National Bureau of Economic Research, Inc. BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

27 Conclusions References II Park, C. (21): How does Changing Age Distribution Impact Stock Prices? A Nonparametric Approach, Journal of Applied Econometrics, 25(7), Romer, P. M. (199): Endogenous Technological Change, Journal of Political Economy, 98(5), S ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

28 Additional Material Spot Yields on 1 Year Bonds, G7 Exl. Italy, Quarterly: King&Low (214) Weighted Unweighted /1/1985 1/1/1988 1/1/1991 1/1/1994 1/1/1997 1/1/2 1/1/23 1/1/26 1/1/29 1/1/212 Back ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

29 Additional Material Methodology - Demographic Structure How granular should demographic structure be? Due to lack of data for all periods for some countries we use data by 1 yrs of cohorts and thus do not to restrict age shape effects (as in Park (21)) Denote the share of age group j = 1,..8 ( 9, 1 19,..., 7+) in total population by w jit. The effect on the variable of interest, say x it, where i denote country and t denotes year, takes the form x it = α + 8 δ j w ji,t + u it. j=1 8 j=1 w jit = 1 exact collinearity To deal with this, we restrict the coefficients to sum to, use (w ji,t w 8i,t ) as explanatory variables and recover the coefficient of the oldest age group. We denote the 7 element vector of (w ji,t w 8i,t ) as W it. Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

30 Additional Material Methodology - Dynamic System Endogenous variables Y it = (g it, I it, S it, H it, rr it, π it ) Ideal - Estimate an identified structural system allowing for expectations Φ (θ)y t = Φ 1 (θ)e t (Y t+1 ) + Φ 2 (θ)y t 1 + Γ(θ)W t + ε t. (2) We can only estimate reduced form, where A solves Φ 1 (θ)a 2 Φ (θ)a + Φ 2 (θ) =. Y t = AY t 1 + Φ 1 ΓW t + Φ 1 ε t. (3) Given we want to analyse impact of W t, we do not need to take a stand on link between A and Φ (θ), Φ 1 (θ), Φ 2 (θ). Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

31 Additional Material Weak Exogeneity Tests [ Yit W it ] [ A endo D = a i + endo B 1 B 2 ] [ ] Yi,t 1 + u W it (4) i,t 1 g I S H rr π β 1 β 2 g.22*** ** **.8*.2 I.1***.82***.81***. -.4* S *.87*** -.3* -.7** -.7**.8***.4 H.2***..8***.89*** -.7** **.9** rr ***.24* -.13*.25*** π..24* ***.23*** -.26*** β * -.2***.9*** -.8*. 1.***.1 β ** -..1**.1*.2*** 1.1*** Note: = 5% level of significance. Table: Exogeneity Test Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

32 Additional Material Estimation - Results II Y it = a i + A 1 Y i,t 1 + DW it + u it β 1 β 2 β 3 g.9* * I S.8* * H -.7*.11* -.3 rr -.14*.28* -.14* π.24* -.28*.4* Table: Short-Run Demographic Impact - Matrix D Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

33 Additional Material Canada Spain Greece Italy Output Growth Output Growth.3.2 Output Growth.3.2 Output Growth Interest Rate -.5 Interest Rate -.5 Interest Rate -.5 Interest Rate Years Years Years Years Figure: Impact of Predicted Future Demographic Structure - Additional Countries Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

34 π.7*** -.75***.5.66*** -.6*** -.5.5*** -.51***.1 Additional Material No Oil Prices GDP Per capita Long-run Rates Net Foreign Assets β1 β2 β3 β1 β2 β3 β1 β2 β3 β1 β2 β3.5*.1* -.15*** **.7**.4 -.1* g I.15*** ***.13*** **.14*** ***.14** * S.26*** ***.24*** ***.19** ***.21*** *** H -.45*** 1.35*** -.89*** -.54*** 1.8*** -.54** -.57*** 1.13*** -.55** -.52** 1.5** -.53 rr * π.74*** -.64*** -.9.7*** -.75***.5.59*** -.5*** -.9 g pc **.71*** -.8***.9 rr lr nfa Benchmark Lee-Carter 2ways Without Inflation β1 β2 β3 β1 β2 β3 β1 β2 β3 β1 β2 β3 g **.13* **.9*** **.4*.4 -.9* I.13*** ** *** *** S.24*** ***.85*** ***.69*** ***.26*** *** H -.54*** 1.8*** -.54**.18.61* -.79** ** -.65* -.45***.76*** -.31 rr * -.5.5* -.22* *** -.65*** π.7*** -.75***.5.66*** -.6*** -.5.5*** -.51***.1 No Oil Prices GDP Per capita Long-run Rates Net Foreign Assets β1 β2 β3 β1 β2 β3 β1 β2 β3 β1 β2 β3.5*.1* -.15*** **.7**.4 -.1* g I.15*** ***.13*** **.14*** ***.14** * S.26*** ***.24*** ***.19** ***.21*** *** H -.45*** 1.35*** -.89*** -.54*** 1.8*** -.54** -.57*** 1.13*** -.55** -.52** 1.5** -.53 rr * π.74*** -.64*** -.9.7*** -.75***.5.59*** -.5*** -.9 g pc **.71*** -.8***.9 rr lr nfa Table 2: Robustness Exercises Back ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

35 Additional Material Production Final Good Producers - Y c,t = [ N f t (Y j c,t) (1/µt) dj where Nt f is the number of firms in input sectors and µ t = µ(nt f ), µ ( ) <. So variable mark-up and fact that firms must pay operating costs control entry and exit. Production of input firm j Yc,t j = [(U tk j t j ) α (ξ t L j t) (1 α)] (1 γ I ) [ ] Mt j γi Intermediate composite good M j t = [ At (M ji t ) (1/ϑ) di where each producer i acquires the right to market the good via the creation and adoption process. Thus A t is determined by innovation sector. ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48 ] µt ] ϑ

36 Additional Material Innovation: R&D Let Zt p be the stock of invented goods (prototypes) at the beginning of time t. Inventor p spends St p to add new prototypes to her stock. Productivity of innovation spending is given by ϕ t. Z p t+1 = ϕ ts p t + φz p t = (Γ yw t ) ρyw χ[( Ψ t ) ρ (S t ) 1 ρ ] 1 Z t St p + φzt p φ = implied product survival rate ρ = elasticity of new technology creation Γ yw t = share of workers that contribute to innovation ρ yw = Importance of workers for innovation process. Innovators borrow St p from the household. Define J t as the value of an invented intermediary good. Then φe[j t+1 ] = R t+1 ϕ t ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

37 Additional Material Innovation: Adoption Let A q t Zt q denote the stock of converted goods marketed to firms. Adopter q invest (intensity) Ξ t to transform Zt q into A q t.( ) Conversion process is successful with probability λ t = λ A q t Ξ Ψ t t with λ > Flow of converted goods A q t+1 = λ tφ(z q t A q t ) + φa q t A converted good can be marketed at every period to firms, thus its value, denoted V t is given by V t = Π m,t + (R t+1 ) 1 φe t V t+1 where Π m,t is the profit from selling an intermediate good to input firms. The value of a unadopted product (J t ) is J t = max Ξ t Ξ t + (R t+1 ) 1 φe t [λ t V t+1 + (1 λ t )J t+1 ] ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

38 Additional Material Household Sector: Population Dynamics Population N t Young (N y t ) becomes worker with probability 1 ω y Workers (N w t ) retire with probability 1 ω r Once retired (N r t ) individual survives with probability γ. N y t+1 = ñ t,t+1 N y t + ω y N y t = (ñ t,t+1 + ω y )N y t = n t,t+1 N y t, N w t+1 = (1 ω y )N y t + ω r N w t, Nt+1 r = (1 ω r )Nt w + γ t,t+1 Nt r define ζt r = Nt r /Nt w and ζt y = Nt y /Nt w. Stock of workers that contribute to innovation Γ yw t (1 ω y ) Ny t N t + (1 λ y )Γ yw t 1 = (1 ωy ) 1 + ζt y + ζt r ζ y t + (1 λ y )Γ yw t 1, λ y < 1 augments the stock of young workers just entered work! Worker s age matters for innovation. BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

39 Additional Material Household Sector: Human Capital Let ξ t be the average effective units across workers at period t. Let It y = τt W tn be the total effective expenditure society makes on the t w education of the young, financed by transfer τ t from workers. Each young who becomes a worker at the end of period t will provide ξ y t+1 effective units. ξ y t+1 = ρ E ξ t + χ E 2 ( I y t The evolution of workers effective labour units ξ t+1 = ω r Nt w Nt+1 w ξ t ) 2 ξ t ξ t + (1 ω y ) Ny t Nt+1 w ξ y t+1 ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

40 Additional Material Household Sector: Consumption and Labour Retirees are assumed not to work. Two key assumptions to offset impact of risk of death (perfect annuity market) and retirement (risk neutrality) on households decision. Gertler (1999) Thus, for z = {w, r} we assume agent j selects consumption and asset holdings to maximise subject to { } Vt jz = (C jz ) ρ U + βt,t+1(e z t [V j t+1 1/ρU z]ρ U ) C jz t Aggregate consumption functions are: + FA jz t+1 = Rz t FA jz t + W t ξti j z + dt z τt jz I z C w t = ς t [R t FA w t + H w t + D w t T w t ] C r t = ε t ς t [R t FA r t + D r t ] Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

41 Additional Material Growth Three drivers of growth: a. exogenous growth of population, n t b. endogenous growth rate of effective labour force, ξ c. endogenous innovation/adoption of new intermediate goods, A t that affects K t, L t ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

42 Additional Material Parameters Standard β =.96 α =.33 δ =.8 U == 8% γ I =.5 µ = 1.1 (1/ (1 ρ U )) =.25 Innovation obsolescence: (1-φ)=.3 productivity in innovation:χ = elasticity of intermediate goods w.r.t R&D ρ =.9 ave. adoption time λ =.1 elasticity of adoption time to intensity ɛ λ =.9 Population N y (1 ω y ) =.5 w = 48% (1 ω r N r ) =.23 N w = 2% 1 yrs in retirement γ =.9 Population and Inovation ratio of workers influencing innovation (1 λ y ) = 2 3 importance of worker to innovation productivity ρ yw =.9 BGS (Demographics Back and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

43 Additional Material 5 5 x 1 3 g A x 1 3 g x 1 4 g ξ x 1 3 R.1 investment.4 MPC workers c w 15 x 1 3 c r Aging holding population growth constant ρ yw =.9 Aging holding population growth constant ρ yw = Aging holding population growth constant ρ yw =.5 Figure: Simulation: benchmark aging versus different ρ yw ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

44 Additional Material Simulation - Babyboomers 3.5 x 1 3 g n.4 ζ y x 1 3 ζ r 3 x 1 3 Γ yw x 1 3 g A 8 x 1 3 g x 1 3 g ξ 12 x 1 3 R investment 5 x 1 3 MPC workers.1 c w 1 x 1 3 c r Figure: Simulation: baby-boomers ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

45 Additional Material 1 x 1 3 g A x 1 3 g x 1 3 g ξ x 1 3 R.15 investment 5 x 1 3 MPC workers c w 1 x c r Baby boomers Benchamrk Baby boomers ρ yw =.5 Figure: Simulation: benchmark Baby-boomers versus ρ yw =.5 ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

46 Additional Material 5 5 x 1 3 g A x 1 3 g x 1 4 g ξ R.1 investment.4 MPC workers c w 15 x 1 3 c r Aging holding population growth constant λ y = 1/3 Aging holding population growth constant λ y =1/1 Figure: Simulation: benchmark aging versus different λ y = 1/1 ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

47 Additional Material Robustness Human capital and Innovation: Reinforce the second mechanism by assuming that not only the share of young workers affects innovation, but new workers higher level of human capital also boosts the productivity of innovation. The growth rate of new prototypes, or the rate of invention, is now given by Z t+1 Z t = (g ξ t ) κρyw (Γ yw t ) ρyw χ[( Ψ t ) ρ (S t ) 1 ρ ] 1 S t + φ. (5) κ = : our benchmark model and κ = 1, : both quantity and quality of labour force have the same effect on innovation; κ > 1 : increase in quality of labour force has a greater impact on innovation. Absence of aggregate supply channel: Eliminate the link between innovation and demographics by shutting down the third mechanism, i.e. setting ρ yw =. Pay-as-you-go Pensions and health expenditures: set the replacement ratio (ratio of pension payment to labour income) to 4% ; we increase the effect of aging on the aggregate demand but contrary to before, total savings are not directly impacted. Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

48 Additional Material Calibration of Demographics and Innovation Production of Ideas is a function of individuals participating in innovation - Γ yw t Z t+1 = ϕ t St p + φz t = (Γ yw t ) ρyw χ[( Ψ t ) ρ (S t ) 1 ρ ] 1 Z t S t + φz t Flow of individuals participating in innovations is give by Γ yw t (1 ω y ) κ y N y t N t + (1 λ y )Γ yw t 1 (6) κ y is share of young entering in the labour market who participate in R&D. Set such that we match the ratio of population working in R&D in the US (OECD data) λ y - Decaying factor - Set such that the average age of workers in R&D sector is 4 years old ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

49 Additional Material Calibration of Demographics and Innovation (Γ yw t ) ρyw denotes the contribution of workers to innovation. Let S Γ,j be the share of workers in R&D for each five year groups based on (6), where j = 1 to 7, for age groups 2-25 till Let Φ j be the relative productivity of innovation for each for these age groups according to Jones(25). Then we set ρ yw such that 7 j=1 S Γ,j Φ j = (Γ yw t ) ρyw ABGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48

50 Additional Material Robustness Figure: Simulation: benchmark aging Robustness Back BGS (Demographics and the Macroeconomy: BoF/CEPR; October 217 ) October 12, / 48