This document describes a model developed to analyze the welfare effects of different fiscal closures (ways of financing) for pension reforms in Poland. The model is an overlapping generations model that considers household optimization of consumption and leisure over a lifetime, as well as a production sector. The document outlines the baseline scenario, pension reform scenario, and three fiscal closure options analyzed: labor tax increases, lump sum taxes, and debt accumulation. Preliminary results suggest that while all reforms increase long run GDP and capital, a labor tax increase leads to the smallest reduction in labor supply and is most efficient according to a lump sum redistribution analysis.

1. Motivation Model Calibration Fiscal closures Results Summary
Eciency of the pension reform:
the welfare eects of various scal closures
Work in progress
Krzysztof Makarski
12
Jan Hagemejer
23
Joanna Tyrowicz
234
with the assistance of Agnieszka Borowska and Karolina Goraus
1
Warsaw School of Economics
2
Faculty of Economics, University of Warsaw
3
Economic Institute, National Bank of Poland
4
Rimini Center for Economic Analyses
National Bank of Poland seminar, July 5th, 2013
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

2. Motivation Model Calibration Fiscal closures Results Summary
(One of many) Approaches to pension reforms modeling
Some well known facts
Changing demography challenges scal stability and political viability of the
pension systems
Reforms DB/PAYG ⇒ DC/FF lower replacement rates + ease scal tension
BUT any such reform requires nancing ⇒ additional welfare eects
What we cannot tell ex ante
which scal closure is better (debt today vs. in the future)?
eect for savings, labor supply and productivity?
What we do
develop OLG model with pension reform test the Pareto optimality
do that for three scal closures: lump sum, labor tax, debt
do this with realistic demographics and productivity patterns
document eects across dierent cohorts ⇒ implementability
see the role of time inconsistency
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

3. Motivation Model Calibration Fiscal closures Results Summary
In order to ask such questions, what do we do?
Things we really care for
private and public savings (inter-temporal choice) + time inconsistency
labor supply decision (intra-temporal choice) + retirement age
pension system + pension system reform
inter-generational transfers + utility to compare welfare across time with
changing demographics
calibrating the model closely
Things we simplify
production sector (just standard CB production function with depreciation)
labor market (elastic labor supply now, will become indivisible labor in
extension)
input data (demographics, life-cycle patterns, etc.)
no heterogeneity within cohorts
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

4. Motivation Model Calibration Fiscal closures Results Summary
This is REALLY preliminary :)
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

5. Motivation Model Calibration Fiscal closures Results Summary
Model setup
Model structure - consumer
optimizes lifetime utility derived from leisure and consumption
Uj (cj,t , lj,t ) = uj (cj,t , lj,t ) + β
J−j
s=1
δs πj+s,t+s
πj,t
uj (cj+s,t+s , lj+s,t+s ) (1)
is paid a market clearing wage for labour supplied
receives market clearing interest on private savings
is free to choose how much to work, but only untill ¯J (forced to retire)
dies with certitude at J, but has a non-zero probability of dying before -
then leaves accidental bequests equal to all cohorts
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

6. Motivation Model Calibration Fiscal closures Results Summary
Model setup
Model structure - producer
has a production function:
Yt = K
α
t (zt Lt )1−α
(2)
Thus, output per person grows with K /L, hours worked and z .
If a pension system favors faster capital accumulation, growth speeds up
If a pension system gives incentives to extend working hours, growth path
goes up
Even with exogenous z , we get growth eects of pension system reforms
Parameter z is calibrated to AWG productivity growth by EC, but may be
any other path
Value of z matters for determining the relative benets of capital based
systems compared to PAYG.
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

7. Motivation Model Calibration Fiscal closures Results Summary
Model setup
Model structure - government
collects social security contributions and pays out pensions
subsidyt = (t1,t + t2,t ) · wt Lt −
J
j=¯J
bj,t πj,t Nt−j (3)
collects taxes on earnings, interest and consumption + spends GDP xed
amount of money on unproductive (but necessary) stu + servicing debt
Tt = τl ,t wt Lt +
J
j=¯J
bj,t πj,t Nt−j + τc,t ct + τk,t rt sj,t−1
J
j=1
πj,t Nt−j(4)
Γt = Gt + (1 + rt )Dt−1 − Dt + subsidyt (5)
wants to maintain long run debt/GDP ratio xed
Gt +(1 + ¯rt ) BIt−1 +St +rt Dt−1 = Tt +(Dt −Dt−1)+BIt +Υt
J
j=1
πj,t Nt−j
(6)
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

8. Motivation Model Calibration Fiscal closures Results Summary
Model setup
System reform
Prior to the reform, PAYG system
b1,j,t = ρj,t wt and b2,j,t = 0 (7)
After the reform, it is a NDC + FF system
b1,j,t =
¯J−1
s=1
Πs
ι=1(1 + rI ,t−j+ι−1) τ1,t−j+s−1wj,t−j+s−1lj,t−j+s−1
J
s=¯J
πs,t
b2,j,t =
¯J−1
s=1
Πs
ι=1(1 + rt−j+ι−1) τ2,t−j+s−1wj,t−j+s−1lj,t−j+s−1
J
s=¯J
πs,t
where (1 + rt ) =
J
j=1
Nt−j wj,t lj,t
J
j=1
πj,t−1Nt−1−j wj,t−1lj,t−1
(8)
and rt = αK
α−1
t (zt Lt )1−α
− d (9)
We use actual participation rates in FF (for generations that had such
choice) and initial capital (from ZUS data)
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

9. Motivation Model Calibration Fiscal closures Results Summary
Model setup
Lump Sum Redistribution Authority - like Nishiyama Smetters (2007)
What does the model actually do?
1 Run the no policy change scenario ⇒ baseline
2 Run the policy change scenario ⇒ reform
3 For each cohort compare utility, compensate the losers from the winners
4 If net eect positive ⇒ reform ecient
5 Run reform again, with the compensation, to observe GE eects
What is baseline?
Change in the no of births
Change in the mortality rates
Change in aggregate productivity
Change in (eective) retirement age
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

10. Motivation Model Calibration Fiscal closures Results Summary
Model setup
Baseline - exogenous processes
Demographics
Demographic projection until 2060, after that 80 years, and after that
new steady state
No of births (j=20) - from the projection, constant afterwards
Mortality rates - from the projection, constant afterwards
Productivity growth
Labor augmenting productivity parameter
Data historically, projection from AWG, after that new steady state, 1.7%
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

11. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What is baseline? Newborns
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

12. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What is baseline? Mortality
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

13. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What is baseline? Old age dependency rate
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

14. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What is baseline? Productivity growth
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

15. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What is baseline? Retirement age
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

16. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What is baseline? Benets as % of GDP
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

17. Motivation Model Calibration Fiscal closures Results Summary
Model setup
What does the reform do? Benets as % of GDP
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

18. Motivation Model Calibration Fiscal closures Results Summary
Basic parameters
Macroeconomic indicators
Table: General calibration parameters
Parameter Value
α capital share 0.33
β time inconsistency 1, 0.9, 0.8
r market interest rate 7.5%
investment rate 20.8% - 24.1%
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

19. Motivation Model Calibration Fiscal closures Results Summary
Calibration to replicate 1999 economy
Preference for leisure (φ) chosen to match participation rate of 56.8%
Impatience (δ) chosen to match interest rate of 7.5%
Replacement rate (ρ) chosen to match benets/GDP ratio of 6%
Contributions rate (τ) chosen to match SIF decit/GDP ratio of 1.5%
Labor income tax (τl ) set to 11% to match PIT/GDP ratio
Consumption tax (τl ) set to match VAT/GDP ratio
Capital tax set de iure = de facto
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

20. Motivation Model Calibration Fiscal closures Results Summary
Life cycle productivity - at or what?
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

21. Motivation Model Calibration Fiscal closures Results Summary
Retirement age
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

22. Motivation Model Calibration Fiscal closures Results Summary
Final parameters
Calibrated results
β = 1 β = 0.9 β = 0.8
ω = 1 ω - D97 ω = 1 ω - D97 ω = 1 ω - D97
φ 0.53 0.57 0.532 0.573 0.533 0.57
δ 0.982 0.999 0.986 1.005 0.9925 1.011
d 0.048 0.055 0.055 0.055 0.055 0.055
τl 0.11 0.11 0.11 0.11 0.11 0.11
τ 0.065 0.065 0.065 0.065 0.065 0.065
ρ 0.307 0.1825 0.307 0.1825 0.31 0.1825
resulting
(kt+1 − kt )/yt 21.3 21 21.4 21.6 21.4 21.6
r 7.5 7.5 7.5 7.4 7.5 7.4
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

23. Motivation Model Calibration Fiscal closures Results Summary
Debt resulting from the reform ...
... is paid as a lump sum by all living generations
⇒ debt share in GDP is held constant, Υ is adjusted among all the living
... is paid as a labor tax by all living generations
⇒ debt share in GDP is held constant, τl is adjusted among all the living
... is accumulated and then paid from a consumption tax
⇒ debt share in GDP grows to a threshhold, with all taxes held constant, then
debt gets automatically reduced to 50% exponentially, τc is adjusted for living
then onwards
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

24. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Eciency of the reforms
Table: Eciency of the reforms - LSRA net wealth after redistribution (as % of
permanent income)
Fiscal β = 1 β = 0.9 β = 0.8
closure ω = 1 ω - D97 ω = 1 ω - D97 ω = 1 ω - D97
Labor tax 0.0276 0.0237 0.0389 0.0280 0.0504 0.0315
Lump sum tax 0.0192 0.0226 0.0303 0.0242 0.0416 0.0279
Debt 0.0134 0.0211 0.0248 0.0204 0.0369 0.0243
Note: D97 denotes calibration according to Deaton (1997) decomposition.
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

25. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Interest rate - a caveat
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

26. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Extent of scal adjustment - labor tax
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

27. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Extent of scal adjustment - labor tax
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

28. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Extent of scal adjustment - debt
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

29. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Extent of scal adjustment - debt
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

30. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Extent of scal adjustment - lump sum tax
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

31. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Extent of scal adjustment - lump sum tax
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

32. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Overall eects - baseline results
Table: (β = 1), age-productivity pattern after Deaton (1997)
Closure GDP Labour supply Capital
Year With LSRA No LSRA With LSRA No LSRA With LSRA No LSRA
10 1.004 1.004 0.998 0.998 1.013 1.013
Labor 30 1.016 1.017 0.996 0.996 1.055 1.056
tax 50 1.026 1.026 1.005 1.004 1.089 1.091
∞ 1.032 1.032 1.002 1.002 1.110 1.110
10 1.000 1.000 1.000 1.000 0.999 0.999
Debt 30 1.021 1.021 1.000 1.000 1.071 1.071
50 1.039 1.039 1.009 1.009 1.135 1.136
∞ 1.030 1.030 1.004 1.003 1.102 1.103
10 1.004 1.004 1.001 1.001 1.013 1.013
Lump sum 30 1.015 1.015 1.003 1.003 1.051 1.052
tax 50 1.025 1.025 0.993 0.993 1.085 1.086
∞ 1.030 1.030 0.988 0.988 1.103 1.104
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

33. Motivation Model Calibration Fiscal closures Results Summary
Baseline specication
Overall eects - baseline results - with LSRA
Table: No time inconsistency (β = 1), age-productivity pattern after Deaton (1997)
Closure Year GDP Labor supply Capital
10 1.004 0.998 1.013
Labor 30 1.016 0.996 1.055
tax 50 1.026 1.005 1.089
∞ 1.032 1.002 1.110
10 1.000 1.000 0.999
Debt 30 1.021 1.000 1.071
50 1.039 1.009 1.135
∞ 1.030 1.004 1.102
10 1.004 1.001 1.013
Lump 30 1.015 1.003 1.051
sum tax 50 1.025 0.993 1.085
∞ 1.030 0.988 1.103
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

34. Motivation Model Calibration Fiscal closures Results Summary
Consumption equivalents
Replacement rates
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

35. Motivation Model Calibration Fiscal closures Results Summary
Consumption equivalents
Replacement rates - relative to baseline
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

36. Motivation Model Calibration Fiscal closures Results Summary
Consumption equivalents
Consumption equivalent - all closures
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

37. Motivation Model Calibration Fiscal closures Results Summary
Consumption equivalents
Decomposition - labor tax
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

38. Motivation Model Calibration Fiscal closures Results Summary
Consumption equivalents
Decomposition - debt
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

39. Motivation Model Calibration Fiscal closures Results Summary
Consumption equivalents
Decomposition - lump sum tax
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

40. Motivation Model Calibration Fiscal closures Results Summary
Time inconsistency
Time inconsistency - matters a lot for capital
Capital - labor tax closure
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

41. Motivation Model Calibration Fiscal closures Results Summary
Time inconsistency
Time inconsistency - matters a lot for capital
Capital - debt closure
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

42. Motivation Model Calibration Fiscal closures Results Summary
Time inconsistency
Time inconsistency - eect on utility of future generations
Welfare - labor tax closure
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

43. Motivation Model Calibration Fiscal closures Results Summary
Time inconsistency
Time inconsistency - real welfare eects of the reform
Welfare - debt closure
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz

44. Motivation Model Calibration Fiscal closures Results Summary
Where we are
The current stage model
Calibrated to 1999 Polish economy
Welfare eects on aggregate small, but some dierences across closures
Fiscal closure matters for the composition eects!
This is in fact a small reform
Labor cannot adjust much in our framework
Problem with the interest rate
Where we want to get
Indivisible labour
Endogenous retirement age
Sophisticated time inconsistency
Welfare eects of pension reforms Makarski, Hagemejer Tyrowicz