We study the contribution of rising longevity to the rise of wealth inequality in the U.S. over the last seventy years. We construct an OLG model with multiple sources of inequality, closely calibrated to the data. Our main finding is that improvements in old-age longevity explain about 30% of the observed rise in wealth inequality. This magnitude is similar to previously emphasized channels associated with income inequality and the tax system. The contribution of demographics is bound to raise wealth inequality further in the decades to come.

1. What shapes the U.S. wealth distribution?
Longevity vs income inequality
Krzysztof Makarski (FAME|GRAPE and Warsaw School of Economics)
Joanna Tyrowicz (FAME|GRAPE, University of Regensburg, and IZA)
Piotr Zoch (FAME|GRAPE, University of Warsaw)
EPCS, Vienna, 2024
1 / 25

2. Motivation

3. Unprecedented rise in wealth inequality in the US
2 / 25

4. The existing explanations
Explanation 1 | Rising income inequality
Gabaix et al. (2016), Chetty et al. (2017), Guvenen et al. (2021, 2022)
which leads to a rise in wealth inequality
Saez i Zucman (2016), Piketty et al. (2018), Gibson-Davis i Hill (2021), Black et al (2022)
3 / 25

5. The existing explanations
Explanation 1 | Rising income inequality
Gabaix et al. (2016), Chetty et al. (2017), Guvenen et al. (2021, 2022)
which leads to a rise in wealth inequality
Saez i Zucman (2016), Piketty et al. (2018), Gibson-Davis i Hill (2021), Black et al (2022)
Explanation 2 | Insufficient redistributon
Krussell, Smith and Hubmer (2020)
3 / 25

6. The existing explanations
Explanation 1 | Rising income inequality
Gabaix et al. (2016), Chetty et al. (2017), Guvenen et al. (2021, 2022)
which leads to a rise in wealth inequality
Saez i Zucman (2016), Piketty et al. (2018), Gibson-Davis i Hill (2021), Black et al (2022)
Explanation 2 | Insufficient redistributon
Krussell, Smith and Hubmer (2020)
Observation | Longevity rises
3 / 25

7. The existing explanations
Explanation 1 | Rising income inequality
Gabaix et al. (2016), Chetty et al. (2017), Guvenen et al. (2021, 2022)
which leads to a rise in wealth inequality
Saez i Zucman (2016), Piketty et al. (2018), Gibson-Davis i Hill (2021), Black et al (2022)
Explanation 2 | Insufficient redistributon
Krussel, Smith and Hubmer (2020)
Observation | Longevity rises having important economic implications:
1. incentives for old-age saving ↑
2. discrepancy between young and around-retirement ↑
3. share of population near retirement ↑
4 / 25

8. The existing explanations
Explanation 1 | Rising income inequality
Gabaix et al. (2016), Chetty et al. (2017), Guvenen et al. (2021, 2022)
which leads to a rise in wealth inequality
Saez i Zucman (2016), Piketty et al. (2018), Gibson-Davis i Hill (2021), Black et al (2022)
Explanation 2 | Insufficient redistributon
Krussel, Smith and Hubmer (2020)
Observation | Longevity rises having important economic implications:
1. incentives for old-age saving ↑
2. discrepancy between young and around-retirement ↑
3. share of population near retirement ↑
Our aim: study the role of longevity rise for wealth inequality in the US (1960-2020)
4 / 25

9. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
5 / 25

10. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
5 / 25

11. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
5 / 25

12. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
5 / 25

13. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
5 / 25

14. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
5 / 25

15. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
• tax policies:
5 / 25

16. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
• tax policies:
• tax rates & progression
5 / 25

17. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
• tax policies:
• tax rates & progression
• government expenditure & debt/GDP ratio
5 / 25

18. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
• tax policies:
• tax rates & progression
• government expenditure & debt/GDP ratio
3. We put that all into play in general equilibrium
5 / 25

19. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
• tax policies:
• tax rates & progression
• government expenditure & debt/GDP ratio
3. We put that all into play in general equilibrium
5 / 25

20. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
2. Drivers of change in the economy
• income inequality:
• labor share
• college premium & share of college-educated
• income shocks vary across birth cohorts
• tax policies:
• tax rates & progression
• government expenditure & debt/GDP ratio
3. We put that all into play in general equilibrium
In simulations we “switch off” specific channels of change
5 / 25

21. The Model

22. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
6 / 25

23. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
6 / 25

24. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
6 / 25

25. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
6 / 25

26. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
6 / 25

27. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
• idiosyncratic returns: a common aggregate component ˜
rt determined by the marginal product of
capital and taxes, and an i.i.d. component ϵs,r,t with mean zero (Hubmer et al, 2021)
6 / 25

28. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
• idiosyncratic returns: a common aggregate component ˜
rt determined by the marginal product of
capital and taxes, and an i.i.d. component ϵs,r,t with mean zero (Hubmer et al, 2021)
6 / 25

29. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
• idiosyncratic returns: a common aggregate component ˜
rt determined by the marginal product of
capital and taxes, and an i.i.d. component ϵs,r,t with mean zero (Hubmer et al, 2021)
6 / 25

30. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
• idiosyncratic returns: a common aggregate component ˜
rt determined by the marginal product of
capital and taxes, and an i.i.d. component ϵs,r,t with mean zero (Hubmer et al, 2021)
• pays taxes (capital income, consumption, and progressive on labor) & contributes to social security
6 / 25

31. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
• idiosyncratic returns: a common aggregate component ˜
rt determined by the marginal product of
capital and taxes, and an i.i.d. component ϵs,r,t with mean zero (Hubmer et al, 2021)
• pays taxes (capital income, consumption, and progressive on labor) & contributes to social security
6 / 25

32. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• ex ante heterogeneity (shares s(t): college and less than college)
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 (specific to education) & no annuity
• idiosyncratic income shocks: wi,j,s,t = wt · ηs,t · ωi,j,s,t.
with ωi,j,s,t given by AR(1) and approximated by Markov chains
• idiosyncratic returns: a common aggregate component ˜
rt determined by the marginal product of
capital and taxes, and an i.i.d. component ϵs,r,t with mean zero (Hubmer et al, 2021)
• pays taxes (capital income, consumption, and progressive on labor) & contributes to social security
+ firms use Cobb-Douglas production function with depreciation d
6 / 25

33. Redistribution by the government
The government:
• finances Gt expenditure
7 / 25

34. Redistribution by the government
The government:
• finances Gt expenditure
• balances progressive social security (PAYG DB): subsidyt
7 / 25

35. Redistribution by the government
The government:
• finances Gt expenditure
• balances progressive social security (PAYG DB): subsidyt
• services debt: ∆Dt + rt Dt = Dt − Dt−1 + rt Dt
7 / 25

36. Redistribution by the government
The government:
• finances Gt expenditure
• balances progressive social security (PAYG DB): subsidyt
• services debt: ∆Dt + rt Dt = Dt − Dt−1 + rt Dt
• collects taxes on capital income, consumption, and labor
Gt + subsidyt + ∆Dt + rt Dt = τk,t rt At + τc,t Ct + Taxℓ,t
7 / 25

37. Redistribution by the government
The government:
• finances Gt expenditure
• balances progressive social security (PAYG DB): subsidyt
• services debt: ∆Dt + rt Dt = Dt − Dt−1 + rt Dt
• collects taxes on capital income, consumption, and labor
Gt + subsidyt + ∆Dt + rt Dt = τk,t rt At + τc,t Ct + Taxℓ,t
• Progressive labor taxation (Benabou, 2002)
T (yj,t ) = yj,t − (1 − τℓ)y1−λ
j,t
7 / 25

38. Redistribution by the government - continued
Current US social security
ρ ¯
J,t · f B
¯
J,t = 0.9 · min{f ¯
J,t , F1,t } + 0.32 · min{f ¯
J,t − F1,t , F2,t } + 0.15 · (f ¯
J,t − F2,t )
8 / 25

39. Redistribution by the government - continued
Current US social security
ρ ¯
J,t · f B
¯
J,t = 0.9 · min{f ¯
J,t , F1,t } + 0.32 · min{f ¯
J,t − F1,t , F2,t } + 0.15 · (f ¯
J,t − F2,t )
The consumer choice: effects through the budget constraint and inter-temporal choice
ai,j+1,s,t+1 + (1 + τc,t )ci,j,s,t = (1 + (1 − τk,t )rt )ai,j,s,t + yj,t − T (yi,j,s,t ) + Γi,j,s,t + bi,j,s,t
8 / 25

40. Redistribution by the government - continued
Current US social security
ρ ¯
J,t · f B
¯
J,t = 0.9 · min{f ¯
J,t , F1,t } + 0.32 · min{f ¯
J,t − F1,t , F2,t } + 0.15 · (f ¯
J,t − F2,t )
The consumer choice: effects through the budget constraint and inter-temporal choice
ai,j+1,s,t+1 + (1 + τc,t )ci,j,s,t = (1 + (1 − τk,t )rt )ai,j,s,t + yj,t − T (yi,j,s,t ) + Γi,j,s,t + bi,j,s,t
u′
(c)i,j,s,t
u′(c)i,j,s,t+1
= πj,t · δj,s,t · (1 + (1 − τk,t )rt )
8 / 25

41. Redistribution by the government - continued
Current US social security
ρ ¯
J,t · f B
¯
J,t = 0.9 · min{f ¯
J,t , F1,t } + 0.32 · min{f ¯
J,t − F1,t , F2,t } + 0.15 · (f ¯
J,t − F2,t )
The consumer choice: effects through the budget constraint and inter-temporal choice
ai,j+1,s,t+1 + (1 + τc,t )ci,j,s,t = (1 + (1 − τk,t )rt )ai,j,s,t + yj,t − T (yi,j,s,t ) + Γi,j,s,t + bi,j,s,t
u′
(c)i,j,s,t
u′(c)i,j,s,t+1
= πj,t · δj,s,t · (1 + (1 − τk,t )rt )
+ obvious intra-temporal choice tradeoffs dued to τc,t and T (yi,j,s,t )
8 / 25

42. Calibration

43. Replicating the US economy
CRRA preferences with risk aversion θ = 2:
• Discounting:
aggregate δ matches the capital to output ratio of 3 in 2015
variance of shocks to δ matches Gini on wealth inequality in 1960
9 / 25

44. Replicating the US economy
CRRA preferences with risk aversion θ = 2:
• Discounting:
aggregate δ matches the capital to output ratio of 3 in 2015
variance of shocks to δ matches Gini on wealth inequality in 1960
Income inequality:
• College premium: Goldin andi Katz (2009) and share of college graduates: Bailey and Dynarski (2011)
• Income uncertainty: [PSID] persistence: 0.964 (college) and 0.980 (no college) and innovations vary by
birth cohort
9 / 25

45. Replicating the US economy
CRRA preferences with risk aversion θ = 2:
• Discounting:
aggregate δ matches the capital to output ratio of 3 in 2015
variance of shocks to δ matches Gini on wealth inequality in 1960
Income inequality:
• College premium: Goldin andi Katz (2009) and share of college graduates: Bailey and Dynarski (2011)
• Income uncertainty: [PSID] persistence: 0.964 (college) and 0.980 (no college) and innovations vary by
birth cohort
Social security: we replicate the balance, contribution rate and benefits
9 / 25

46. Replicating the US economy
CRRA preferences with risk aversion θ = 2:
• Discounting:
aggregate δ matches the capital to output ratio of 3 in 2015
variance of shocks to δ matches Gini on wealth inequality in 1960
Income inequality:
• College premium: Goldin andi Katz (2009) and share of college graduates: Bailey and Dynarski (2011)
• Income uncertainty: [PSID] persistence: 0.964 (college) and 0.980 (no college) and innovations vary by
birth cohort
Social security: we replicate the balance, contribution rate and benefits
Fiscal side takes the debt path from SNA
• τk , τc : McDaniel (2020), Bayer et. al (2020)
• τl , labor tax progression: Barro & Sahasakul (1983), Mertens & Montiel Olea (2018), Ferrere &
Navarro (2018)
9 / 25

47. Replicating the US economy
CRRA preferences with risk aversion θ = 2:
• Discounting:
aggregate δ matches the capital to output ratio of 3 in 2015
variance of shocks to δ matches Gini on wealth inequality in 1960
Income inequality:
• College premium: Goldin andi Katz (2009) and share of college graduates: Bailey and Dynarski (2011)
• Income uncertainty: [PSID] persistence: 0.964 (college) and 0.980 (no college) and innovations vary by
birth cohort
Social security: we replicate the balance, contribution rate and benefits
Fiscal side takes the debt path from SNA
• τk , τc : McDaniel (2020), Bayer et. al (2020)
• τl , labor tax progression: Barro & Sahasakul (1983), Mertens & Montiel Olea (2018), Ferrere &
Navarro (2018)
Depreciation rate d - matches the variation in data
9 / 25

48. Calibration: evolution of TFP, labor share & depreciation (GGDC)
10 / 25

49. Calibration: evolution of college share & college premium
11 / 25

50. Calibration: evolution of consumption taxation and capital taxation
12 / 25

51. Calibration: evolution of labor taxation
13 / 25

52. Calibration: evolution of social security contributions
14 / 25

53. Model vs data

54. Model vs data: evolution of social security benefits
15 / 25

55. Model vs data: evolution of the interest rate
16 / 25

56. Model vs data: income inequality
17 / 25

57. Model vs data: wealth inequality decomposition
18 / 25

58. Model vs data: wealth inequality change
19 / 25

59. Results

60. Demographics is actually a big thing
20 / 25

61. Three kinds of experiments
Disentangle the relative importance of the composition and behavioral effects
Γfm
a,t − Γcf
a,t
(Γfm
a,t − Γcf
a,t ) − (Γfm
a,1975 − Γcf
a,1975)
• the components of demographics
• the role of taxes
• the role of income inequality
21 / 25

62. Components of demographics: diffs and diffs-in-diffs
22 / 25

63. Demographics in context: diffs and diffs-in-diffs
23 / 25

64. Drivers of the income channel

65. Demographics in context: diffs and diffs-in-diffs
24 / 25

66. Conclusions

67. Summarizing
Still very much work in progress!
25 / 25

68. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
25 / 25

69. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
25 / 25

70. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
25 / 25

71. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
• Not so large role for taxes (earlier evidence stressed this channel)
25 / 25

72. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
• Not so large role for taxes (earlier evidence stressed this channel)
• Gradually rising and big role of longevity
25 / 25

73. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
• Not so large role for taxes (earlier evidence stressed this channel)
• Gradually rising and big role of longevity
• Way forward
25 / 25

74. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
• Not so large role for taxes (earlier evidence stressed this channel)
• Gradually rising and big role of longevity
• Way forward
• Think about evidence from other countries
25 / 25

75. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
• Not so large role for taxes (earlier evidence stressed this channel)
• Gradually rising and big role of longevity
• Way forward
• Think about evidence from other countries
• We learned a lot about what works and what does not → implications for our models
25 / 25

76. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
• We trace the drivers to:
• Pretty massive labor market (consistent with earlier evidence)
• Not so large role for taxes (earlier evidence stressed this channel)
• Gradually rising and big role of longevity
• Way forward
• Think about evidence from other countries
• We learned a lot about what works and what does not → implications for our models
• Fully internalizing the implications of demographics
25 / 25

77. Thank you for your attention!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
26 / 25