Annuity market imperfection, retirement and economic growth
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1 Annuity market imperfection, retirement and economic growth Ben J. Heijdra 1 Jochen O. Mierau 2 1 University of Groningen; Institute for Advanced Studies (Vienna); Netspar; CESifo (Munich) 2 University of Groningen; Netspar NETSPAR Pension Workshop, 27 January 2010 B. J. Heijdra & J. O. Mierau Annuity market imperfection 1/38
2 Overview & Motivation I In the presence of mortality risk, annuities are welfare maximizing (Yaari, 1965) Annuity Market Puzzle (Cannon and Tonks, 2008) Annuity markets are surprisingly thin & annuities are overpriced (Friedman and Warshawsky, 1988) B. J. Heijdra & J. O. Mierau Annuity market imperfection 2/38
3 Overview & Motivation I In the presence of mortality risk, annuities are welfare maximizing (Yaari, 1965) Annuity Market Puzzle (Cannon and Tonks, 2008) Annuity markets are surprisingly thin & annuities are overpriced (Friedman and Warshawsky, 1988) B. J. Heijdra & J. O. Mierau Annuity market imperfection 2/38
4 Overview & Motivation I In the presence of mortality risk, annuities are welfare maximizing (Yaari, 1965) Annuity Market Puzzle (Cannon and Tonks, 2008) Annuity markets are surprisingly thin & annuities are overpriced (Friedman and Warshawsky, 1988) B. J. Heijdra & J. O. Mierau Annuity market imperfection 2/38
5 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
6 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
7 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
8 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
9 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
10 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
11 Overview & Motivation II Input: Overlapping generations model Endogenous labour supply Endogenous growth Load factor on annuities Output: Imperfect annuity markets reduce economic growth Imperfect annuity markets hardly affect the retirement age Properly modeled demography matters B. J. Heijdra & J. O. Mierau Annuity market imperfection 3/38
12 Outline Core Model 1 Core Model Households Firms General equilibrium 2 Calibration and visualisation Retirement & Growth Imperfect annuities 3 B. J. Heijdra & J. O. Mierau Annuity market imperfection 4/38
13 Outline Core Model 1 Core Model Households Firms General equilibrium 2 Calibration and visualisation Retirement & Growth Imperfect annuities 3 B. J. Heijdra & J. O. Mierau Annuity market imperfection 4/38
14 Outline Core Model 1 Core Model Households Firms General equilibrium 2 Calibration and visualisation Retirement & Growth Imperfect annuities 3 B. J. Heijdra & J. O. Mierau Annuity market imperfection 4/38
15 Outline Core Model Households Firms General equilibrium 1 Core Model Households Firms General equilibrium 2 Calibration and visualisation Retirement & Growth Imperfect annuities 3 B. J. Heijdra & J. O. Mierau Annuity market imperfection 5/38
16 Individual households Core Model Households Firms General equilibrium Individual agents maximise: EΛ(v,t)... subject to:... and: t [ εc lnc(v,τ)+(1 ε C )ln[1 L(v,τ)] ] e (ρ+µ)(t τ) dτ A(v,τ) = r A A(v,τ)+w(τ)L(v,τ) C(v,τ)+Π(v,τ) L(v,τ) 0 µ is the instantaneous probability of death (Blanchard, 1985) r A is the interest rate on annuities. B. J. Heijdra & J. O. Mierau Annuity market imperfection 6/38
![.. and: t [ εc lnc(v,τ)+(1 ε C )ln[1 L(v,τ)] ] e (ρ+µ)(t τ) dτ A(v,τ) = r A A(v,τ)+w(τ)L(v,τ)](/docs-images/52/12488105/images/page_16.jpg "C(v,τ)+Π(v,τ) L(v,τ) 0 µ is the instantaneous probability of death (Blanchard, 1985) r A is the")
17 Imperfect annuity market Households Firms General equilibrium Interest rate on annuities: r A = r +θµ; 0 θ 1 Different cases: Case PA: θ = 1, perfect annuity market, annuity firms break even (Yaari, 1965). Case IA: 0 < θ < 1, imperfect annuities; annuity firms make a profit of (1 θ) µa(τ). Profits are distributed through Π(v,τ) = z w(τ). Case NA: θ = 0, no annuities, no annuity market. Accidental bequests. Borrowing constraint. [ignored here] B. J. Heijdra & J. O. Mierau Annuity market imperfection 7/38
18 Households Firms General equilibrium Key features of the optimal plans, 1 Consumption Euler equation: Ċ(v,τ) C(v,τ) = r ρ (1 θ)µ > 0 During working life, 0 τ v R, labour supply is given by: (1 ε C )/(1 L(v,τ)) ε C /C(v,τ) = w(τ) B. J. Heijdra & J. O. Mierau Annuity market imperfection 8/38
19 Firms Core Model Households Firms General equilibrium Basic idea: strong external effects between firms keeps marginal product of capital positive. Aggregate production function and factor prices: Y (t) = Z 0 K(t) w(t)l(t) = (1 ε K )Y (t) r(t) = r = ε K Z 0 δ Constant interest rate: source of endogenous growth B. J. Heijdra & J. O. Mierau Annuity market imperfection 9/38
20 Households Firms General equilibrium The general equilibrium model: The micro part C(v,v) w(v) C(v,v) w(v) = = ε C (ρ+µ) ε C +(1 ε C ) [ 1 e (ρ+µ)r ] 1 e (r ˆγ+θµ)R +z r ˆγ +θµ (1) ε C e [r ˆγ ρ (1 θ)µ]r 1 ε C (2) B. J. Heijdra & J. O. Mierau Annuity market imperfection 10/38
![1 e (ρ+µ)r ] 1 e (r ˆγ+θµ)R +z r ˆγ +θµ (1) ε C e [r ˆγ ρ (1 θ)µ]r 1](/docs-images/52/12488105/images/page_20.jpg "ε C (2) B. J. Heijdra & J. O.")
21 Households Firms General equilibrium The general equilibrium model: The macro part w(t)l k(t) z = µ(1 θ) k(t) w(t) ˆγ k(t) k(t) = (r π)+ l [ l c(t) ] w(t) w(t) k(t) (3) (4) = (1 ε K )Z 0 (5) [1 e βr ] c(t) w(t) e[ˆγ+β+ρ+(1 θ)µ r]r 1 βe βr ˆγ +β +ρ+(1 θ)µ r β ˆγ +β +ρ+(1 θ)µ r C(v,v) w(v) (6) (7) B. J. Heijdra & J. O. Mierau Annuity market imperfection 11/38
22 Outline Core Model Calibration and visualisation Retirement & Growth Imperfect annuities 1 Core Model Households Firms General equilibrium 2 Calibration and visualisation Retirement & Growth Imperfect annuities 3 B. J. Heijdra & J. O. Mierau Annuity market imperfection 12/38
23 Calibration and visualisation Calibration and visualisation Retirement & Growth Imperfect annuities Study comparative static effects of imperfect annuities. Initial equilibrium: θ = 1, µ = (Dutch data), π = 0.01, β = , r = 0.06, ρ = 0.035, δ = ε C and ε K set such that R = 42 (years) and ˆγ = 0.02 in initial equilibrium. B. J. Heijdra & J. O. Mierau Annuity market imperfection 13/38
24 Calibration and visualisation Retirement & Growth Imperfect annuities Fig. 1: Life-cycle consumption, labour supply, and retirement C(u) w(0) BE 1 U 1 L / U C = w(r)! 0 U 0 E! E 0! BE E 1!!! E 2 U 2 U 1 U 1 L / U C = w(0) A BE BE 0! 1 1! L(u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 14/38
25 Calibration and visualisation Retirement & Growth Imperfect annuities Fig. 2: Optimal retirement age & growth Φ(R) E 0 PA scaled consumption at birth (C(v,v)/w(v) Ψ(R) retirement age (R) B. J. Heijdra & J. O. Mierau Annuity market imperfection 15/38
26 Calibration and visualisation Retirement & Growth Imperfect annuities Fig. 3: Imperfect annuities and the retirement age scaled consumption at birth (C(v,v)/w(v)) Φ(R) 1 Φ(R) 0 E IA E PA Ψ(R) 1 Ψ(R) retirement age (R) B. J. Heijdra & J. O. Mierau Annuity market imperfection 16/38
27 Calibration and visualisation Retirement & Growth Imperfect annuities Fig. 4(a): Scaled consumption of newborns (C(u)/w(0)) C(u)/w(0) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 17/38
28 Fig. 4(b): Labour supply (L(u)) Calibration and visualisation Retirement & Growth Imperfect annuities L(u) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 18/38
29 Calibration and visualisation Retirement & Growth Imperfect annuities Fig. 4(c): Scaled financial assets (A(u)/w(0)) A(u)/w(0) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 19/38
30 Calibration and visualisation Retirement & Growth Imperfect annuities Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 20/38
31 Calibration and visualisation Retirement & Growth Imperfect annuities Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 21/38
32 Outline Core Model 1 Core Model Households Firms General equilibrium 2 Calibration and visualisation Retirement & Growth Imperfect annuities 3 B. J. Heijdra & J. O. Mierau Annuity market imperfection 22/38
33 Fig. 5: Core Model e M(u), observed (solid) and fitted Blanchard BCL Data economic age B. J. Heijdra & J. O. Mierau Annuity market imperfection 23/38
34 Main features Core Model Euler equation: Ċ(u) C(u) Interest rate on annuities: r A = r +θµ(u) = r ρ (1 θ)µ(u), No life insurance available at age D so that A ( D) = 0 B. J. Heijdra & J. O. Mierau Annuity market imperfection 24/38
35 Fig. 6(a): Scaled consumption of newborns (C(u)/w(0)) ln (C(u)/w(0)) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 25/38
36 Fig. 6(b): Labour supply (L(u)) L(u) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 26/38
37 Fig. 6(c): Scaled financial assets (A(u)/w(0)) A(u)/w(0) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 27/38
38 Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 28/38
39 Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 29/38
40 Full model Core Model Take into account all model features: Age dependent mortality Age dependent productivity Imperfect annuities Lump-sum transfers B. J. Heijdra & J. O. Mierau Annuity market imperfection 30/38
41 Fig. 7: Productivity profile fitted E(u) 0.9 data economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 31/38
42 Fig. 8(a): Scaled consumption of newborns (C(u)/w(0)) ln (C(u)/w(0)) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 32/38
43 Fig. 8(b): Labour supply L(u) L(u) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 33/38
44 Fig. 8(c): Scaled financial assets A(u)/w(0) economic age (u) B. J. Heijdra & J. O. Mierau Annuity market imperfection 34/38
45 Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 35/38
46 Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 36/38
47 Table 2: Growth and retirement: Quantitative effects C(v,v) w(v) (a) Core case (b) Productivity (c) Mortality (d) Combined θ = 1.0 θ = (i) (ii) S R z γ (%) l (n) c(t) w(t) w(t) k(t) c(t) y(t) B. J. Heijdra & J. O. Mierau Annuity market imperfection 37/38
48 Concluding remarks Core Model In the theoretical part of the paper we have: Studied the implications for microeconomic decisions (retirement, consumption, labour supply) of imperfect annuities Studied the implications for macroeconomic outcomes (growth, capital accumulation) of imperfect annuities Identified some of the key mechanisms by which annuities affect the economy Conclusion from the quantitative exercise: Growth is lower if annuities are less than perfect Demographic factors play an important role for calibration results Transfers of annuity profits have important quantitative effects B. J. Heijdra & J. O. Mierau Annuity market imperfection 38/38
49 Concluding remarks Core Model In the theoretical part of the paper we have: Studied the implications for microeconomic decisions (retirement, consumption, labour supply) of imperfect annuities Studied the implications for macroeconomic outcomes (growth, capital accumulation) of imperfect annuities Identified some of the key mechanisms by which annuities affect the economy Conclusion from the quantitative exercise: Growth is lower if annuities are less than perfect Demographic factors play an important role for calibration results Transfers of annuity profits have important quantitative effects B. J. Heijdra & J. O. Mierau Annuity market imperfection 38/38
50 Concluding remarks Core Model In the theoretical part of the paper we have: Studied the implications for microeconomic decisions (retirement, consumption, labour supply) of imperfect annuities Studied the implications for macroeconomic outcomes (growth, capital accumulation) of imperfect annuities Identified some of the key mechanisms by which annuities affect the economy Conclusion from the quantitative exercise: Growth is lower if annuities are less than perfect Demographic factors play an important role for calibration results Transfers of annuity profits have important quantitative effects B. J. Heijdra & J. O. Mierau Annuity market imperfection 38/38
51 Concluding remarks Core Model In the theoretical part of the paper we have: Studied the implications for microeconomic decisions (retirement, consumption, labour supply) of imperfect annuities Studied the implications for macroeconomic outcomes (growth, capital accumulation) of imperfect annuities Identified some of the key mechanisms by which annuities affect the economy Conclusion from the quantitative exercise: Growth is lower if annuities are less than perfect Demographic factors play an important role for calibration results Transfers of annuity profits have important quantitative effects B. J. Heijdra & J. O. Mierau Annuity market imperfection 38/38
52 Concluding remarks Core Model In the theoretical part of the paper we have: Studied the implications for microeconomic decisions (retirement, consumption, labour supply) of imperfect annuities Studied the implications for macroeconomic outcomes (growth, capital accumulation) of imperfect annuities Identified some of the key mechanisms by which annuities affect the economy Conclusion from the quantitative exercise: Growth is lower if annuities are less than perfect Demographic factors play an important role for calibration results Transfers of annuity profits have important quantitative effects B. J. Heijdra & J. O. Mierau Annuity market imperfection 38/38
53 Concluding remarks Core Model In the theoretical part of the paper we have: Studied the implications for microeconomic decisions (retirement, consumption, labour supply) of imperfect annuities Studied the implications for macroeconomic outcomes (growth, capital accumulation) of imperfect annuities Identified some of the key mechanisms by which annuities affect the economy Conclusion from the quantitative exercise: Growth is lower if annuities are less than perfect Demographic factors play an important role for calibration results Transfers of annuity profits have important quantitative effects B. J. Heijdra & J. O. Mierau Annuity market imperfection 38/38
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