We study the evolution of wealth inequality in an economy undergoing structural change. Economic intuition hints that structural change should imply increased income inequality, at least transitory. Economic intuition is more ambiguous for the effects on wealth inequality. On the one hand, increased dispersion in incomes implies increased dispersion in the ability to accumulate wealth across individuals. On the other hand, workers experience greater uncertainty which may push them to more precautionary savings, which works towards equalizing wealth distribution. The net effect of these two opposing forces is essentially an empirical question. We build an overlapping generations model which features heterogeneous sectors and workers. Using this model, we quantify the role of demographics and the structural change in the evolution of wealth inequality in Poland as of 1990.

1. Structural change and inequality
in general equilibrium
Jan Lutynski (FAME|GRAPE and BGSE)
Krzysztof Makarski (FAME|GRAPE and Warsaw School of Economics)
Joanna Tyrowicz (FAME|GRAPE, University of Regensburg, and IZA)
ECEE, Tallinn, 2022
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2. Motivation

3. Motivation
Important fact | Income inequality rose during transition, more andegdotally wealth inequality as well
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4. Motivation
Important fact | Income inequality rose during transition, more andegdotally wealth inequality as well
Mechanisms | Labor market
• employment structure: ↑ income inequality
• unemployment: ↑ income inequality
• earnings uncertainty: ∼ income inequality
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5. Motivation
Important fact | Income inequality rose during transition, more andegdotally wealth inequality as well
Mechanisms | Labor market
• employment structure: ↑ income inequality
• unemployment: ↑ income inequality
• earnings uncertainty: ∼ income inequality
Mechanisms | Rise in longevity (demographics)
• ↑ old-age savings
• ↑ inequality between young and old
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6. Motivation
Important fact | Income inequality rose during transition, more andegdotally wealth inequality as well
Mechanisms | Labor market
• employment structure: ↑ income inequality
• unemployment: ↑ income inequality
• earnings uncertainty: ∼ income inequality
Mechanisms | Rise in longevity (demographics)
• ↑ old-age savings
• ↑ inequality between young and old
Aim: study wealth inequality during demographic and structural change
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7. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
3 / 18

8. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
3 / 18

9. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
3 / 18

10. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
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11. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
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12. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
3 / 18

13. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
3 / 18

14. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
2. OLG, to adequately tackle generational exchange
3 / 18

15. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
2. OLG, to adequately tackle generational exchange
• young workers have increasing educational attainment (data driven)
3 / 18

16. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
2. OLG, to adequately tackle generational exchange
• young workers have increasing educational attainment (data driven)
• young workers enter S more frequently than M (data driven)
3 / 18

17. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
2. OLG, to adequately tackle generational exchange
• young workers have increasing educational attainment (data driven)
• young workers enter S more frequently than M (data driven)
3. general equilibrium
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18. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
2. OLG, to adequately tackle generational exchange
• young workers have increasing educational attainment (data driven)
• young workers enter S more frequently than M (data driven)
3. general equilibrium
3 / 18

19. This study in the existing literature
• Most studies work with infinitely lived agents
Aghion & Blanchard 1994, Caballero & Hammour 1996, Castanheira & Roland 2000, Buera & Kaboski 2012, Rogerson et al. 2015
• Empirical challenge: demographic exchange rather than worker flows
Tyrowicz & van der Velde, 2018
Our model:
1. Structural change in the form of
• sectors: {M, S}
• educational attainment: {H, L}
• unemployment: data driven, heterogneous across {M, S} ⊗ {H, L}
2. OLG, to adequately tackle generational exchange
• young workers have increasing educational attainment (data driven)
• young workers enter S more frequently than M (data driven)
3. general equilibrium
We simulate this economy “switching on” specific channels of change
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20. Model

21. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
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22. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
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23. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
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24. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
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25. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires (& receives benefits) and non-negative assets constraint
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26. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires (& receives benefits) and non-negative assets constraint
4 / 18

27. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t < 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires (& receives benefits) and non-negative assets constraint
Firms have Cobb-Douglas production function with depreciation d, thus in the equilibrium:
• Lt =
P ¯
J
j=1
P
h∈H
R
Ωh
ξh,tηj,h,tdPj,h,t
χj,h,tNj,t and wt = MPLt
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28. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires ( receives benefits) and non-negative assets constraint
Firms have Cobb-Douglas production function with depreciation d, thus in the equilibrium:
• Lt =
P ¯
J
j=1
P
h∈H
R
Ωh
ξh,tηj,h,tdPj,h,t
χj,h,tNj,t and wt = MPLt
• At+1 =
PJ
j=1
P
h∈H
R
Ωh
aj+1,h,t+1(sj,h,t)dPj,h,t
χj,h,tNj,t
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29. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires ( receives benefits) and non-negative assets constraint
Firms have Cobb-Douglas production function with depreciation d, thus in the equilibrium:
• Lt =
P ¯
J
j=1
P
h∈H
R
Ωh
ξh,tηj,h,tdPj,h,t
χj,h,tNj,t and wt = MPLt
• At+1 =
PJ
j=1
P
h∈H
R
Ωh
aj+1,h,t+1(sj,h,t)dPj,h,t
χj,h,tNj,t
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30. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires ( receives benefits) and non-negative assets constraint
Firms have Cobb-Douglas production function with depreciation d, thus in the equilibrium:
• Lt =
P ¯
J
j=1
P
h∈H
R
Ωh
ξh,tηj,h,tdPj,h,t
χj,h,tNj,t and wt = MPLt
• At+1 =
PJ
j=1
P
h∈H
R
Ωh
aj+1,h,t+1(sj,h,t)dPj,h,t
χj,h,tNj,t and Kt+1 = At+1 − Dt+1
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31. The consumer and the firms
Consumer has CRRA utiilty
• lifetime uncertainty: live for up to 80 periods with πj,t 1
• exogeneous labr supply with wj,h,t = wtξh,tηj,h,t.
• idiosyncratic income shocks + unemployment shock
AR(1) process approximated by Markov chains
• pays taxes (on labor income, capital income and consumption)
• pays social security contributions, retires ( receives benefits) and non-negative assets constraint
Firms have Cobb-Douglas production function with depreciation d, thus in the equilibrium:
• Lt =
P ¯
J
j=1
P
h∈H
R
Ωh
ξh,tηj,h,tdPj,h,t
χj,h,tNj,t and wt = MPLt
• At+1 =
PJ
j=1
P
h∈H
R
Ωh
aj+1,h,t+1(sj,h,t)dPj,h,t
χj,h,tNj,t and Kt+1 = At+1 − Dt+1 and
rt = MPKt − d
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32. Social security
pj,h,t =



ρt(ρr + ρhξh,t)w̄t for j = ¯
J
pj−1,h,t−1 × (1 + ι∆w) for j ¯
J
Status quo is our baseline scenario
• replacement rate ρt declilnes in line with the data
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33. Social security
pj,h,t =



ρt(ρr + ρhξh,t)w̄t for j = ¯
J
pj−1,h,t−1 × (1 + ι∆w) for j ¯
J
Status quo is our baseline scenario
• replacement rate ρt declilnes in line with the data
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34. Social security
pj,h,t =



ρt(ρr + ρhξh,t)w̄t for j = ¯
J
pj−1,h,t−1 × (1 + ι∆w) for j ¯
J
Status quo is our baseline scenario
• replacement rate ρt declilnes in line with the data
Alternative scenario: benefits remain generous
• replacement rate ρt is the same as in ∼ 1990 roku
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35. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
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36. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
• Balances social security: subsidyt
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37. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
• Balances social security: subsidyt
• Services public debt: ∆Dt + rtDt = Dt − Dt−1 + rtDt
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38. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
• Balances social security: subsidyt
• Services public debt: ∆Dt + rtDt = Dt − Dt−1 + rtDt
• Collects taxes on capital, consumption, labor
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39. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
• Balances social security: subsidyt
• Services public debt: ∆Dt + rtDt = Dt − Dt−1 + rtDt
• Collects taxes on capital, consumption, labor
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40. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
• Balances social security: subsidyt
• Services public debt: ∆Dt + rtDt = Dt − Dt−1 + rtDt
• Collects taxes on capital, consumption, labor
Gt + subsidyt + ∆Dt + rtDt = τk,trtAt + τc,tCt + τl,tw̄tLt
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41. The government
• Spends expenditure Gt (cailbrated as a fixed share of GDP)
• Balances social security: subsidyt
• Services public debt: ∆Dt + rtDt = Dt − Dt−1 + rtDt
• Collects taxes on capital, consumption, labor
Gt + subsidyt + ∆Dt + rtDt = τk,trtAt + τc,tCt + τl,tw̄tLt
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42. Calibration

43. We replicate the economy of Poland ∼ 1990
Income uncertainty similar to Fehr et al (2013), based on SOEP:
• Persistence %h,η = {0.9548, 0.9016}
• Innovation σh,η = {0.0098, 0.0347}
Taxes {τc, τk, τl} match the revenues as % of GDP {16.1%, 12.2%, 15.8%}
Social security
• Contribution rate: matches benefits/GDP ∼1990
• Retirement age: 62
• Redistributive component: ρr = 0.24
• Individual component: ρh = 0.155 to balance social security ∼ 1990
• Replacement rate: ρt = 1 in 1990 and declines to match the social security deficit over the years
Depreciation rate d matches the investment rate of 20% across 1990-2020.
Preferences: CRRA
• Risk aversion 2 (or 4, for sensitivity analysis)
• Disount rate δ matches the (final steady state) interest rate of 3%
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44. Unemployment: model vs data
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45. Employment shares: model vs data
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46. The results

47. Change in wealth inequality
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48. Change in wealth inequality
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49. Change in wealth inequality
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50. Change in wealth inequality
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51. Capital (Kt/zt)
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52. Taxes
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53. Counterfactual: higher generosity of
social security

54. Inequality rises more
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55. Summary

56. Key take-aways
• We study wealth inequality during the change: structural and demographic
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57. Key take-aways
• We study wealth inequality during the change: structural and demographic
• Rising longevity proves to be the main driving force for the rise
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58. Key take-aways
• We study wealth inequality during the change: structural and demographic
• Rising longevity proves to be the main driving force for the rise
• Structural change reduces wealth inequality during the first decades.
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59. Thank you for your attention!
w: grape.org.pl
t: grape_org
f: grape.org
e: j.tyrowicz@grape.org.pl
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