Longevity vs income inequality

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)
CEF, Dallas, 2022
1 / 27

2. Motivation

3. Unprecedented rise in wealth inequality in the US
2 / 27

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 / 27

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 / 27

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 / 27

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 which does have economic implications:
1. incentives for old-age saving ↑
2. discrepancy between young and around-retirement ↑
3. share of population near retirement ↑
4 / 27

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 which does have 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 / 27

9. Contribution
Our model has a lot of data driven moving parts:
1. OLG - accounting for rise in longevity
5 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

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 / 27

21. The Model

22. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
6 / 27

23. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
6 / 27

24. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
6 / 27

25. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
6 / 27

26. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
• ex ante heterogeneity (shares s(t): college and less than college
6 / 27

27. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
• ex ante heterogeneity (shares s(t): college and less than college
• 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 / 27

28. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
• ex ante heterogeneity (shares s(t): college and less than college
• 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 / 27

29. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
• ex ante heterogeneity (shares s(t): college and less than college
• 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
• pays taxes (capital income, consumption, and progressive on labor) & contributes to social security
6 / 27

30. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
• ex ante heterogeneity (shares s(t): college and less than college
• 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
• pays taxes (capital income, consumption, and progressive on labor) & contributes to social security
6 / 27

31. The model
The consumer
• CRRA utility, idiosyncratic shocks to discount rate δi,j,s,t
• lifetime uncertainty: lives for up to 16 periods with πj,t < 1 & no annuity
• ex ante heterogeneity (shares s(t): college and less than college
• 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
• pays taxes (capital income, consumption, and progressive on labor) & contributes to social security
+ firms use Cobb-Douglas production function with depreciation d
6 / 27

32. Redistribution by the government
The government:
• finances Gt expenditure
7 / 27

33. Redistribution by the government
The government:
• finances Gt expenditure
• balances progressive social security (PAYG DB): subsidyt
7 / 27

34. 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 / 27

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
• collects taxes on capital income, consumption, and labor
Gt + subsidyt + ∆Dt + rt Dt = τk,t rt At + τc,t Ct + Tax`,t
7 / 27

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 + Tax`,t
• Progressive labor taxation (Benabou, 2002)
T (yj,t ) = yj,t − (1 − τ`)y1−λ
j,t
7 / 27

37. 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 / 27

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 )
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 / 27

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
u0
(c)i,j,s,t
u0(c)i,j,s,t+1
= πj,t · δj,s,t · (1 + (1 − τk,t )rt )
8 / 27

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
u0
(c)i,j,s,t
u0(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 / 27

41. Calibration

42. 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 / 27

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
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 / 27

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
Social security is balanced in ∼2010 with retirement age of 65
9 / 27

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 is balanced in ∼2010 with retirement age of 65
Fiscal side takes the debt path from SNA
• τk , τl and labor tax progression: McDaniel (2020), Bayer et. al (2020)
• Γ calibrated in ∼1935 to balance the budget (conditional on τc )
• then τc adjusts to balance the budget constraint
9 / 27

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 is balanced in ∼2010 with retirement age of 65
Fiscal side takes the debt path from SNA
• τk , τl and labor tax progression: McDaniel (2020), Bayer et. al (2020)
• Γ calibrated in ∼1935 to balance the budget (conditional on τc )
• then τc adjusts to balance the budget constraint
Depreciation rate d - matches the investment rate of 21% in ∼ 2015.
9 / 27

47. Calibration: evolution of TFP & labor share
10 / 27

48. Calibration: evolution of college share & college premium
11 / 27

49. Calibration: evolution of cohort-specific innovations
12 / 27

50. Calibration: evolution of public debt and government expenditure
13 / 27

51. Calibration: evolution of capital taxation
14 / 27

52. Calibration: evolution of labor taxation
15 / 27

53. Implied income inequality: model vs. data
16 / 27

54. Results

55. Good match of the model to the data
17 / 27

56. The role of longevity

57. Recall the timing
18 / 27

58. Longevity ... seems like a little thing ...
19 / 27

59. Longevity ... seems like a little thing, but not really
20 / 27

60. Longevity ... seems like a little thing, but not really
21 / 27

61. If we fixed income inequality at 1960

62. Inequality would have ...?
This period means
• relatively high income uncertainty
=⇒ incentives to save more
• low share of college graduates
=⇒ more heterogeneous incomes
• low college premium
=⇒ less heterogeneous incomes
22 / 27

63. Inequality would have ... been much higher
23 / 27

64. If we fixed tax rates at 1967 ...

65. Inequality would have ... ?
(to compare with Krussell et al., 2020)
This period means
• historically high capital income gains taxation
=⇒ net return on assets is lower
• historically low labor tax
=⇒ net incomes are higher
• historically low labor tax progression
=⇒ less insurance/redistribution
=⇒ stronger incentives to save from more heterogeneous incomes
24 / 27

66. Inequality would have been much higher
25 / 27

67. Summarizing
Still very much work in progress!
26 / 27

68. Summarizing
Still very much work in progress!
• So far, our model does a good job in replicating rise in wealth inequality
26 / 27

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:
26 / 27

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)
26 / 27

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)
• Large role for taxes (consistent with earlier evidence)
26 / 27

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)
• Large role for taxes (consistent with earlier evidence)
• Gradually rising role of longevity
26 / 27

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)
• Large role for taxes (consistent with earlier evidence)
• Gradually rising role of longevity
• Way forward
26 / 27

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)
• Large role for taxes (consistent with earlier evidence)
• Gradually rising role of longevity
• Way forward
• Add correlation between education and δ shocks
26 / 27

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)
• Large role for taxes (consistent with earlier evidence)
• Gradually rising role of longevity
• Way forward
• Add correlation between education and δ shocks
• Differentiate πj,t by education (possible as of 1990s)
26 / 27

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)
• Large role for taxes (consistent with earlier evidence)
• Gradually rising role of longevity
• Way forward
• Add correlation between education and δ shocks
• Differentiate πj,t by education (possible as of 1990s)
• Add inheritance → challenges to make it work
26 / 27

77. Thank you for your attention!
w: grape.org.pl
t: grape org
f: grape.org
e: j.tyrowicz@grape.org.pl
27 / 27