Demographics, Wealth, and Global Imbalances in the Twenty ...web.stanford.edu/~aauclert/aging_slides_vmacs.pdf · Demographics and wealth[Auerback Kotliko˙ 1987, De Nardi-İmrohoroğlu-Sargent

Demographics, Wealth, and Global Imbalancesin the Twenty-First Century

Adrien Auclert, Hannes Malmberg, Frédéric Martenet and Matthew Rognlie

Virtual Macro Seminar, May 2020

1

The world population is aging... 65+ World

Source: 2019 United Nations World Population Prospects 2

...wealth-to-GDP ratios are increasing... National Wealth SCF vs WID

*IND: National rather than Private Wealth. Source: World Inequality Database (WID) 3

...real interest rates are falling... Feenberg-Teeper-Welch

Source: Laubach and Williams (2003), FRED, King and Low (2014) 4

...and “global imbalances” are rising

Source: International Monetary Fund (IMF), Penn World Table (PWT) 9.1 5

This paper

Q: How does population aging a�ect wealth-output ratios, realinterest rates, and capital �ows?

Given population projections, how will these macro trendslikely evolve over the rest of the 21st century?

• Our contribution: discipline this exercise with a shift-share(WtYt

)comp=

∑j πjtaj0∑j πjthj0

t ≥ 0

• aj0, hj0 are today’s asset and labor income pro�les by age j• πjt are projections of the population share of age j in year t

Captures the compositional e�ect of aging on W/Y

We show how to use this for counterfactuals in general eqbm:

1. Exactly, when there is “balanced growth by age” (special SOE case)2. Approximately, after demeaning, to forecast NFAs (general case)

6

What we �nd

∆compt ≡

∑j πjtaj0∑j πjthj0

− W0Y0

1. Measurement:• ∆comp is positive, large and heterogeneous across countries[in 2100: 85pp in Germany vs 305pp in India]

a) Older individuals hold more wealth and earn less incomeb) Timing of aging transition uneven across countries

2. Quantitative GE OLG model: across range of calibrations• ∆comp closely approximatesW/Y transition of small open econ.• In integrated world, matching ∆comp in each country implieslarge global imbalances by the end of the 21st century[2016-2100: ∆NFA/Y of -50pp in Germany vs 150pp in India]

• E�ects on interest rates and wealth-GDP ratiosmore uncertain

7

Related literature

Quantitative GE overlapping generations models:• Demographics and wealth [Auerback Kotliko� 1987, De Nardi-İmrohoroğlu-Sargent 2001,

Abel 2003, Geanakoplos-Magill-Quinzii 2004, Gottfries-Teulings 2015...]• Demographics and interest rates [Carvalho-Ferrero-Necchio 2016,

Gagnon-Johannsen-Lopez Salido 2016, Eggertsson-Mehrotra-Robbins 2019,Lisack-Sajedi-Thwaites 2017, Jones 2018, Papetti 2019, Summers-Rachel 2019...]

• Demographics and capital �ows [Domeij-Flodén 2006, Krueger-Ludwig 2007,Backus-Cooley-Henriksen 2014, Bárány-Coeurdacier-Guibaud 2019...]

We highlight an important moment that drives counterfactuals and can be measured in data

Shift share approaches to demographics:• Labor supply, productivity, participation [Shimer 2001, Hall-Jones 1999, Aaronson-Sullivan

2002, Bloom-Canning-Sevilla 2003, Aaronson et al 2006, Kwok-Daly-Hobijn 2010...]• Savings [Cutler-Poterba-Sheiner-Summers 1990, Poterba 2001, Lee-Mason 2011, Lee 2016...]

We exhibit a shift-share that can be used for general equilibrium counterfactuals

Macroeconomic trends:• Real interest rates [Eggertsson-Robbins-Wold 18, Farhi-Gourio 18, Gourinchas-Rey 18,

Gomme-Ravikumar-Rupert 16, Marx-Mojon-Velde 19...]• Income and wealth [Piketty-Zucman 2014, Piketty-Saez-Zucman 2018, Lagakos et al 2017...]• Global imbalances [Caballero-Farhi-Gourinchas 2008, Mendoza-Quadrini-Rios Rull 2009,...]

We isolate the role of demographics for these trends8

Outline

1. An age shift-share for W/Y

2. Model

3. Small open economy

4. Global imbalances

9

1. An age shift-share for W/Y

Environment

• Economy with output Yt experiencing demographic change

• Population of age j Njt, total population Nt ≡∑

j Njt

• WealthWt =

∑j

NjtAjt (1)

• E�ective labor supply

Lt =∑j

Njthjt (2)

• Suppose there is growth in labor productivity Yt/Lt• We expect Ajt to scale with Yt/Lt• Let ajt ≡

AjtYt/Lt

denote productivity-normalized assets by age

10

Wealth-to-GDP ratio

• Rewrite wealth (1)Wt =

YtLt

∑j

Njtajt

• Wealth-to-GDP ratio using (2)

WtYt

=

∑j πjtajt∑j πjthjt

where πjt ≡NjtNt is share of population age j

• Three reasons for changing Wt/Yt:1. Changing population shares: πjt2. Changing age pro�les of productivity-normalized assets: ajt3. Changing age pro�les of labor e�ciency: hjt

11

Age shift-share

• For any base year 0, de�ne

∆compt ≡

∑j πjtaj0∑j πjthj0

− W0Y0

• Can calculate ∆comp directly in from data and pop. projections

• Why is this a natural starting point for projections?

1. It can be a su�cient statistic in a demographic transition• Small open economy special case: ajt and hjt are constant• We say the economy ages without “behavioral e�ects”

2. It is always a component of the total change in W/Y:WtYt−W0

Y0︸ ︷︷ ︸≡∆t

= ∆compt +

∑j πjtajt∑j πjthjt

−∑

j πjtaj0∑j πjthj0︸ ︷︷ ︸

∆beht

→ Benchmark to evaluate transition dynamics in any GE model

12

Measuring ∆comp

• Calculate shift-share ∆compt for US and 24 other countries

• Implementation:• Normalize labor supply so that

∑πj0hj0 = 1

• Then aj0 is average wealth by age normalized by GDP per capita• Can measure relative hj0 from relative labor income

• Data• πjt : demographic projections by age

2019 UN World Population Prospects, SSA and Gagnon et al. (2016)

• aj0,hj0 : age-wealth and labor income pro�les in base yearLuxembourg Wealth/Income Study (LWS/LIS), European HouseholdFinance and Consumption Survey (HFCS), China Household FinanceSurvey (CHFS), Indian National Sample Survey (NSS), National Surveyof Family Income and Expenditure (JPN), Statistics Denmark

13

∆comp in the United States: 1950-2100 Base year Historical

14

Decomposing ∆comp

• Large e�ects. Where do they come from?

• Study separately e�ect on W and e�ect on Y

• Separate into respective contributions using:

∆compt '

∑j

(πjt − πj0)× aj0︸ ︷︷ ︸∆comp,at

+

−W0Y0

∑j

(πjt − πj0)× hj0

︸ ︷︷ ︸

∆comp,ht

[recall∑

j πj0hj0 = 1 ]

15

Contribution of W to ∆comp Alternative base years

16

Contribution of W to ∆comp Alternative base years

16

Contribution of W to ∆comp Alternative base years

16

Summary contribution of W to W/Y: ∆comp,at

17

Contribution of Y to ∆comp Alternative base years

18

Contribution of Y to ∆comp Alternative base years

18

Contribution of Y to ∆comp Alternative base years

18

Summary contribution of Y to W/Y: ∆comp,ht

19

Global trends in ∆comp for the 21st century Details Historical

20

∆comp around the world in 2100 Scenarios Level Pct US pro�les US demog.

21

2. Model

Environment: overview Demographics

• Standard multi-country GE OLG model featuring idiosyncraticincome risk, intergenerational transmission of skills, bequests,and a social security system [eg Krueger-Ludwig 2007]

• Final output is produced out of capital and e�ective labor

Yt = F (Kt, ZtLt)

where Zt is exogenous labor augmenting technology

• Perfect competition and free capital adjustment:

rt + δ = FL(KtZtLt

, 1), wt = ZtFL

(KtZtLt

, 1)

• Labor market clearing

Lt =∑j

Njthjt

where hjt is average labor supply per person at age j22

Asset demand: household problem 1/2 Retirement

• Heterogeneous households with ages j = 0 . . . T

0

Born

Tw

Start workHave children

Trt

Retire

T

Die for certain

• Income at age j in time t:

yjt = wtρjthjt`(sj)

where

• wt is the wage per unit of e�ective labor supply• ρjt ∈ [0, 1] is fraction of agents still working at age j (others retire)• hjt is exogenous age-e�ciency pro�le• `(sj) is a stochastic labor supply shifter

23

Asset demand: household problem 2/2 De�neψ Government

• A household born at time k solves

maxc,a

E

T∑j=Tw

βjΦkj

(ψj,k+ju

(cj,k+j

)+ Υ(1− φkj )vt

(aj+1,k+j+1

))• Φk

j = φkj Φkj−1: survival rate for cohort k

• ψj: utility modi�er due to children (can microfound func. form)• vt captures nonhomotheticies in bequests

• Constraints: aj+1,t+1 ≥ −aZt and

cjt + aj+1,t+1 ≤(1− τ yt

)yjt(sj) + (1+ rat )ajt + trjt(sj) + brjt(s

j)

• Government adjusts{ρjt, τ

yt , trjt(·),Gt,Bt

}, follows a �scal rule

24

Asset market clearing

At + Amig,nett = Kt + Bt + NFAt

At + Amig,nett︸ ︷︷ ︸≡Wt

= Kt + Bt︸ ︷︷ ︸≡Ast

+NFAt

where

• At is household wealth• Amig,nett is net wealth coming from migrants• Kt is the capital stock• Bt is domestic government bonds• NFAt is net foreign asset position• Small open economy has exogenous rt• World economy has

∑c NFAc,t = 0 (endogenous rt)

25

Steady state asset market equilibrium

• Divide by Y and consider a steady state for a given country• Let Θ index demographic parameters:

NFAY (r,Θ) =

WY (r,Θ)− As

Y (r)

• As/Y independent of demographics! (at unchanged B/Y)• Hence, change between two steady states

∆

(NFAY

)' ∆comp + ∆beh|r + εd∆r + εs∆r

where εd, εs are interest sensitivities of W/Y and As/Y• If bars denote averages across countries

∆r ' −∆comp + ∆beh|r

εd + εs

⇒ SOE e�ect ∆comp + ∆beh|r quanti�es net asset demand shiftKey determinant of equilibrium ∆r, so ∆NFA

Y and ∆WY

26

3. Small open economy

Balanced growth by age in population transitions

Proposition

Consider small open economy with constant r and assume:

1. Constant e�ciency-pro�le hj and TFP growth γ2. Constant mortality pro�les φj3. Constant valuation of children’s consumption ψj4. Constant tax and retirement policies: τ y , ρj and trj(sj) + brj (sj)

Then there exists an equilibrium with ajt(sj) = (1 + γ)t aj(sj), ∀t.In this equilibrium, the wealth-to-GDP ratio is

Wt

Yt=

∑j πjtaj0∑j πjthj0

, ∀t

where hj0 = ρjhj and aj0 =Ej0[Aij0]Y0/N0 are age pro�les in a base year 0.

• Su�cient statistic: aj0 is all we need to know about savings motives• Irrelevant: time vs cohort e�ects, type of savings motives,timing of G adjustment, ...

27

Behavioral responses

• Special case above has ∆beh|rt = 0, all t

• Full model has 5 forces for non-zero behavioral e�ects:

1. Labor supply e�ect (changing hjt or retirement policy ρjt)

2. Declining mortality e�ect (Φkj : allowed to vary by cohort k)

3. Cost of children e�ect (ψj: utility modi�er due to children)

4. Bequest dilution e�ect (changing ratio of givers to receivers)

5. Social security balance e�ect (adjust τ yt , trjt, ρjt rather than Gt)

• Next: evaluate quant. magnitude of ∆beh|r when relaxing 1–5

28

US calibration and counterfactual

• U.S. as laboratory. External calibration of• Elasticity of intertemporal substitution σ−1

• Income process, production side• Social security• Demographics: start from observed 2016 age distribution

• Estimated parameters:• Discount factor β• Bequest preferences: Υ and ν• Weight and exponent on altruism towards children: λ and ϕ

• Targets:• Shift-share 2016-2100: ∆comp = 1.27 [from Section 1]• Age-consumption pro�le [CEX]• Lorenz curve for bequests [Hurd-Smith 2002]• Bequest-to-GDP: 5% [Hendricks 2001, Alvaredo-Garbinti-Piketty 2017]

29

Calibration Survival Pop. growth Pop. shares Children Beq. dist.

Parameter Description Value SourceTw, Tr, T Age structure 20, 65, 100 Standard valuesnt, πjt, φjt Demographics Data Gagnon et al. (2016)

WY Household wealth 504% 2016 US value (SCF)BY Government debt 42% 2016 US value (FoF)GY Government expenditures 17.6% 2016 US value (BEA)IY Investment 17% 2016 US value (BEA)γ TFP growth rate 0.73% Average 2010-17 (Fernald)sL Labor share 62% 2016 US Value (NIPA)δ Depreciation rate 2.5% K

Yr Real interest rate 6.1% I

Y ,KY = W

Y −BY , s

L

d Bene�ts 47% 2016 bene�ts over GDPτ ss Social security tax 7.6% Balance SS systemτ Total income tax 31% Balance budget

(σε, ρε) Idiosyncratic risk (0.92,0.91) Auclert and Rognlie (2018)(σθ, ρθ) Intergenerational transmission (0.61,0.677) De Nardi (2014)

σ Inverse EIS 1 Standard valueβ Subjective discount factor 0.96 Calibrated value

(ν,Υ) Preference for bequests (0.81, 2.7) Calibrated values(λ, ϕ) Preference for children (0.07, 1.8) Calibrated values 30

Fitted age pro�les C, Beq

31

Evaluating behavioral responses: change in W/Y in the U.S.

32

Evaluating behavioral responses: transitions of W/Y Alternatives H

33

4. Global imbalances

World economy counterfactual Demog. Calibration Wealth pro�les KJZZ

• Solve for integrated world equilibrium

• 12 countries that are at least 1% of GDP among our 25

• Parameters remain the same, except:

• Demographics nct , πcjt• Social security system parameters τ ss,ct , τ ct , dct• Discount and bequests factors βc,Υc to hit empirical W

c

Yc ,∆comp,c

• Technology sL,c to hit empirical NFAcYc

• We vary, within range from literature:• Elasticity of intertemporal substitution σ−1• Elasticity of capital-labor substitution η

34

World change in r for alternative σ and η

35

World change in W/Y for alternative σ and η

36

Change in NFA/Y for fast aging countries for alternative σ and η

37

Role of interest rate sensitivities for ∆NFA εc by country

• Recall∆

(NFAcYc

)= ∆comp

c + ∆beh|rc + εdc∆r + εsc∆r

• Since average NFA is 0:

∆

(NFAcYc

)= ∆comp

c + ∆beh|rc −

(∆comp + ∆beh|r

)+[εdc + εsc −

(εd + εs

)]∆r

1. ∆compc is large and heterogeneous across countries [Section 1]

2. ∆beh|rc is small in comparison [Section 3]

3. σ and η a�ect level of εdc and εsc, not di�erences across countries

• This suggests

∆

(NFAcYc

)' ∆comp

c − ∆comp

⇒ Can approximately forecast GE NFAs with demeaned ∆compc 38

Change in NFA vs shift share in our model: 2016-2100

39

Change in NFA vs shift share historically: 1970-2011 data

40

Predicted global imbalances using ∆compc − ∆comp

41

Conclusion

• How does population aging a�ect wealth-output ratios, realinterest rates, and capital �ows?

• Use compositional e�ect ∆comp as starting point for forecasts

• ∆comp are large and heterogeneous in the data

• Going forward, our approach suggests demographics will cause:

1. real interest rates to fall, with uncertain magnitude (40-120 bp)2. wealth-GDP ratios to rise, with e�ects attenuated relative to ∆comp

3. global imbalances to substantially increase from today’s levels

• Global savings glut has just begun!

42

Thank you!

43

Additional slides

US Wealth-to-GDP from SCF vs World Inequality Database Back

Source: World Inequality Database (WID), Survey of Consumer Finances (SCF) 44

Share of the population aged 65+ Back

Source: 2019 United Nations World Population Prospects 45

Countries by income group Back

Source: 2019 United Nations World Population Prospects 46

National Wealth over GDP Back

Source: World Inequality Database (WID) 47

National Wealth over GDP Back

Source: World Inequality Database (WID) 48

Feenberg, Tepper and Welch (2018) Back

49

Age-wealth pro�les Back

50

Age-labor income pro�les Back

51

Contribution of fertility to aging in the 21st century Back

52

Measuring income and wealth pro�les Back

• Measuring age-labor income pro�les hjt• Data from the Luxembourg Income Study (LIS)• hjt is proportional to total labor income per person• In 2016: normalize aggregate e�ective labor per person

1 = L2016 =∑j

πj,2016hj,2016

• In t: Lt grows as aggregate labor input from the BLS LBLStLBLS2016

• Measuring age-wealth pro�les ajt =AjtYt/Lt

• Data from the Survey of Consumer Finances (SCF)• Provide net worth by age at the household level• Ajt is aggregate household net worth over total individuals• Divide by Yt/LBLSt to obtain ajt

53

Retrospective U.S. exercise Back

• To �rst order:WtYt−W0

Y0︸ ︷︷ ︸≡∆t

=

∑i πitai0∑πithi0

−∑

i πi0ai0∑πi0hi0︸ ︷︷ ︸

∆πt

+∑iπi0 (ait − ai0)

︸ ︷︷ ︸∆at

−∑iπi0

W0

Y0(hit − hi0)

︸ ︷︷ ︸∆ht

+∆ert

54

Robustness to baseline year for age pro�les (past) Back

55

Robustness to baseline year for age pro�les (future) Back

56

Low and high fertility scenarios Back

57

W/Y from shift-share in 2016 and in 2100 Back

58

Percentage change in W/Y from shift-share Back

59

Shift-share at common age pro�les (rescaled) Back

60

Shift-share at common demographic change Back

61

Environment: demographics Back

• Population evolves as

Njt =(Nj−1,t−1 +Mj−1,t−1

)φj−1,t−1

where

• Njt denotes the numbers of individuals aged j in year t• Mj,t is migration• φj,t are survival probabilities

• Total population isNt =

∑j

Njt

• Population converges to a stationary distribution in the longrun

62

Weight on children Back

• Let c = cP + ncC be the total cons. of parent and children• Assume �ow utility function of a parent is

U(cP, cC

)= u

(cP)

+ λnϕu(cC)

• Utility maximization implies:

u′(cP)

= λnϕ−1u′(cC)

⇒ total value of having children

W (c) = u(cP)

+ λnϕu(cC)

=(1+ λ

1σ n

σ+ϕ−1σ

)σu (c)

• Hence ψi =(1+ λ

1σ n

σ+ϕ−1σ

i

)σ• Children raise the m.u.c. if λ > 0 and ϕ > 1− σ• ni comes from empirical distribution of children for parent aged i

63

Retirement policy Back

• Retirement is phased at age Trt

• At age Trt , agents still work a fraction ρt ∈ [0, 1] of total hours

• Retirement policy is therefore

ρjt = 1j<Trt + ρt1j=Trt

• E�ective labor supply is

Lt ≡∑j<Trt

πjthjt + ρtπTrt thTrt t

• E�ective share of retirees is

µrett ≡ (1− ρt)πTrt t +∑j≥Trt

πjt

64

Government policy Back

• Flow budget constraint

Bt + Tt = (1+ rt−1)Bt−1 + Gt

where Bt is debt, Gt are expenditures, Tt are net taxes

Tt = wtNt(

(τ sst + τt (1− τ sst )) Lt − (1− τt) dtµrett)

• Government sets retirement policy{ρjt}and follows �scal rules

τ sst = τ ss + ϕss(Bt/Yt − b)

τt = τ + ϕτ (Bt/Yt − b)

GtYt

=GY − ϕ

G(Bt/Yt − b)

dt = d− ϕd(Bt/Yt − b)

where b is the 2016 debt-to-GDP ratio• Coe�cients ϕ’s regulate the aggressiveness of the adjustment

65

Extension 1: other sources of asset supply

• In simple cases, alternative assets just add to supply

• Allow for• Markups µ, capitalized monopoly pro�ts• Government bonds with long-run rule B

Y = b (r)

• Thena (r, θ)

y (r) =k (r)y (r) + b (r) +

(1− 1

µ

)1

r − (n+ γ)

• θ directly a�ects both W and market cap. through discounting

• Extra terms on RHS a�ect elasticity of asset supply εs

• Similar formula still determines dr

66

Extension 2: Housing Back

• Model housing by introducing Cobb-Douglas utility

11− σ

(c1−αhhαh

)1−σ• All households rent to a REIT who owns

• �xed supply of land L, equilibrium price PL

• stock of dwellings H, depreciating at δH, investment price = 1• β = PLL

PLL+H is s.s. share of land

• Households invest in mutual fund that owns the REIT

• Housing supply in steady state adjusts so that

a (r, θ)

y (r) =k (r)y (r) +

αh

1− αh

(β

r − (n+ γ)+1− βr + δH

) ∑i πi (θ) ci(r,θ)

y(r)∑i πi (θ)hi

67

Projected survival functions Back

68

Projected population growth rate Back

69

Projected population shares Back

70

Distribution of children Back

71

Distribution of bequests received Back

72

Bequests distribution and consumption pro�le Back

73

Robustness Back

74

Historical exercise: inputs Back

75

Historical exercise Back

76

Historical trends in wealth

• We’ll use our model primarily for prospective counterfactuals

• But: can the model account for trends in wealth since 1960?

• Concurrent developments to demographics over the period:• Falling real rates• Falling productivity growth

• We feed the model with observed trends in r, γ, B and G

77

Historical trends in wealth Fert./Mort. Inputs Inputs

78

Demographics: population distributions Back

79

Demographics: population growth rates Back

80

World economy calibration Back

Parameters WY ∆π

Country β Υ Model Data Model Data

AUS 0.98 0.00 5.66 5.66 1.64 1.55CAN 0.96 1.97 4.84 4.84 1.19 1.19CHN 0.94 5.51 4.20 4.20 2.81 2.81DEU 0.92 6.28 3.64 3.64 0.89 0.89ESP 0.98 0.00 5.46 5.46 2.15 1.81FRA 0.96 2.69 4.94 4.94 1.35 1.35GBR 0.95 2.77 5.03 5.03 1.41 1.41IND 0.95 3.73 3.44 3.44 3.07 3.07ITA 0.97 0.42 5.69 5.69 1.72 1.72JPN 0.94 1.98 4.98 4.98 0.85 0.85NLD 0.95 3.74 4.58 4.58 1.38 1.38USA 0.97 0.81 5.04 5.04 1.27 1.27

81

World economy calibration Back

82

Predicted NFA/Y from demographics Back

83

Elasticities by country Back

84

Jakobsen et al. (2020) validation Back

Note: Response of wealth to a reduction in the wealth tax. We replicate the model experiments of Jakobsen et al. (2020). The �rst(Couples DD) analyzes a reduction of the wealth tax from 2.2% to 1.2% on the top 1%. The second (Ceiling DD) analyzes the a reductionof 1.56 percentage points on the top 0.3%. 85