Effiency of the pension reform: the welfare effetcs of various fiscal closures

Motivation Model Calibration Fiscal closures Results Summary

E�ciency of the pension reform:the welfare e�ects of various �scal closures

Work in progress

Krzysztof Makarski 12 Jan Hagemejer23 Joanna Tyrowicz234

with the assistance of Agnieszka Borowska and Karolina Goraus

1Warsaw School of Economics2Faculty of Economics, University of Warsaw3Economic Institute, National Bank of Poland

4Rimini Center for Economic Analyses

National Bank of Poland seminar, July 5th, 2013

Welfare e�ects of pension reforms Makarski, Hagemejer & Tyrowicz


(One of many) Approaches to pension reforms modeling

Some well known factsChanging demography challenges �scal stability and political viability of thepension systemsReforms DB/PAYG ⇒ DC/FF lower replacement rates + ease �scal tension

BUT any such reform requires �nancing ⇒ additional welfare e�ects

What we cannot tell ex ante

which �scal closure is better (debt today vs. in the future)?e�ect 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 e�ects across di�erent cohorts ⇒ implementability

see the role of time inconsistency



In order to ask such questions, what do we do?

Things we really care forprivate and public savings (inter-temporal choice) + time inconsistencylabor supply decision (intra-temporal choice) + retirement agepension system + pension system reforminter-generational transfers + utility to compare welfare across time withchanging demographicscalibrating the model closely

Things we simplifyproduction sector (just standard CB production function with depreciation)labor market (elastic labor supply now, will become "indivisible" labor inextension)input data (demographics, life-cycle patterns, etc.)no heterogeneity within cohorts



This is REALLY preliminary :)



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

δsπj+s,t+s

πj,tuj (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 J̄ (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



Model setup

Model structure - producer

has a production function:

Yt = Kαt (ztLt)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 pathgoes up

Even with exogenous z , we get growth e�ects of pension system reforms

Parameter z is calibrated to AWG productivity growth by EC, but may beany other path

Value of z matters for determining the relative bene�ts of capital basedsystems compared to PAYG.



Model setup

Model structure - government

collects social security contributions and pays out pensions

subsidyt = (t1,t + t2,t) · wtLt −J∑

j=J̄

bj,tπj,tNt−j (3)

collects taxes on earnings, interest and consumption + spends GDP �xedamount of money on unproductive (but necessary) stu� + servicing debt

Tt = τl,t(wtLt +

J∑j=J̄

bj,tπj,tNt−j

)+(τc,tct + τk,trtsj,t−1

) J∑j=1

πj,tNt−j(4)

Γt = Gt + (1 + rt)Dt−1 − Dt + subsidyt (5)

wants to maintain long run debt/GDP ratio �xed

Gt +(1 + r̄t)BIt−1+St +rtDt−1 = Tt +(Dt−Dt−1)+BIt +Υt

J∑j=1

πj,tNt−j

(6)



Model setup

System reform

Prior to the reform, PAYG system

b1,j,t = ρj,twt and b2,j,t = 0 (7)

After the reform, it is a NDC + FF system

b1,j,t =

∑J̄−1

s=1

[Πsι=1(1 + rI ,t−j+ι−1)

]τ1,t−j+s−1wj,t−j+s−1lj,t−j+s−1∏J

s=J̄ πs,t

b2,j,t =

∑J̄−1

s=1

[Πsι=1(1 + rt−j+ι−1)

]τ2,t−j+s−1wj,t−j+s−1lj,t−j+s−1∏J

s=J̄ πs,t

where (1 + rt) =

∑J

j=1 Nt−jwj,t lj,t∑J

j=1 πj,t−1Nt−1−jwj,t−1lj,t−1

(8)

and rt = αKα−1t (ztLt)1−α − d (9)

We use actual participation rates in FF (for generations that had suchchoice) and initial capital (from ZUS data)



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 e�ect positive ⇒ reform e�cient

5 Run reform again, with the compensation, to observe GE e�ects

What is �baseline�?

Change in the no of births

Change in the mortality rates

Change in aggregate productivity

Change in (e�ective) retirement age



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%



Model setup

What is �baseline�? Newborns



Model setup

What is �baseline�? Mortality



Model setup

What is �baseline�? Old age dependency rate



Model setup

What is �baseline�? Productivity growth



Model setup

What is �baseline�? Retirement age



Model setup

What is �baseline�? Bene�ts as % of GDP



Model setup

What does the �reform� do? Bene�ts as % of GDP



Basic parameters

Macroeconomic indicators

Table: General calibration parameters

Parameter Value

α capital share 0.33β time inconsistency 1, 0.9, 0.8

r market interest rate 7.5%investment rate 20.8% - 24.1%



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 bene�ts/GDP ratio of 6%

Contributions rate (τ) chosen to match SIF de�cit/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



Life cycle productivity - �at or what?



Retirement age



Final parameters

Calibrated results

β = 1 β = 0.9 β = 0.8ω = 1 ω - D97 ω = 1 ω - D97 ω = 1 ω - D97

φ 0.53 0.57 0.532 0.573 0.533 0.57δ 0.982 0.999 0.986 1.005 0.9925 1.011d 0.048 0.055 0.055 0.055 0.055 0.055τl 0.11 0.11 0.11 0.11 0.11 0.11τ 0.065 0.065 0.065 0.065 0.065 0.065ρ 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 21.6r 7.5 7.5 7.5 7.4 7.5 7.4



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, thendebt gets automatically reduced to 50% exponentially, τc is adjusted for livingthen onwards



Baseline speci�cation

E�ciency of the reforms

Table: E�ciency of the reforms - LSRA net wealth after redistribution (as % ofpermanent income)

Fiscal β = 1 β = 0.9 β = 0.8closure ω = 1 ω - D97 ω = 1 ω - D97 ω = 1 ω - D97

Labor tax 0.0276 0.0237 0.0389 0.0280 0.0504 0.0315Lump sum tax 0.0192 0.0226 0.0303 0.0242 0.0416 0.0279Debt 0.0134 0.0211 0.0248 0.0204 0.0369 0.0243

Note: D97 denotes calibration according to Deaton (1997) decomposition.




Interest rate - a caveat




Extent of �scal adjustment - labor tax




Extent of �scal adjustment - labor tax




Extent of �scal adjustment - debt




Extent of �scal adjustment - debt




Extent of �scal adjustment - lump sum tax




Extent of �scal adjustment - lump sum tax




Overall e�ects - baseline results

Table: (β = 1), age-productivity pattern after Deaton (1997)

Closure GDP Labour supply CapitalYear With LSRA No LSRA With LSRA No LSRA With LSRA No LSRA

10 1.004 1.004 0.998 0.998 1.013 1.013Labor 30 1.016 1.017 0.996 0.996 1.055 1.056tax 50 1.026 1.026 1.005 1.004 1.089 1.091

∞ 1.032 1.032 1.002 1.002 1.110 1.11010 1.000 1.000 1.000 1.000 0.999 0.999

Debt 30 1.021 1.021 1.000 1.000 1.071 1.07150 1.039 1.039 1.009 1.009 1.135 1.136∞ 1.030 1.030 1.004 1.003 1.102 1.10310 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 1.052tax 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




Overall e�ects - 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 1.013Labor 30 1.016 0.996 1.055tax 50 1.026 1.005 1.089

∞ 1.032 1.002 1.110

10 1.000 1.000 0.999Debt 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 1.013Lump 30 1.015 1.003 1.051sum tax 50 1.025 0.993 1.085

∞ 1.030 0.988 1.103



Consumption equivalents

Replacement rates




Replacement rates - relative to baseline




Consumption equivalent - all closures




Decomposition - labor tax




Decomposition - debt




Decomposition - lump sum tax



Time inconsistency

Time inconsistency - matters a lot for capital

Capital - labor tax closure



Time inconsistency

Time inconsistency - matters a lot for capital

Capital - debt closure



Time inconsistency

Time inconsistency - e�ect on utility of future generations

Welfare - labor tax closure



Time inconsistency

Time inconsistency - real welfare e�ects of the reform

Welfare - debt closure



Where we are

The current stage model

Calibrated to 1999 Polish economy

Welfare e�ects on aggregate small, but some di�erences across closures

Fiscal closure matters for the composition e�ects!

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


Economy & Finance

Effiency of the pension reform: the welfare effetcs of various fiscal closures