Efficiency of the pension reform: The welfare effects of various fiscal closures

Motivation Model Calibration Fiscal closures Results Summary

Efficiency of the pension reform:the welfare effects of various fiscal closures

Work in progress

Krzysztof Makarski 12 Joanna Tyrowicz234 Jan Hagemejer23

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

Labour Market and Demographic Change, September 13th, 2013

Welfare effects of pension reforms Makarski, Hagemejer & Tyrowicz


(One of many) Approaches to modeling of the pension reforms

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

BUT any such reform requires financing ⇒ additional welfare effectsWhat we cannot tell ex ante

which fiscal closure is better (debt today vs. in the future + criterion)?effect for savings, labor supply and productivity?

Comparing steady states (baseline and reform) is not enough ⇒ need toanalyze the whole path

We develop OLG model with pension reform & test the Pareto optimality

... for fiscal various closures: lump sum, labor and consumption taxes, debt

... with realistic demographics and productivity patterns

... to document welfare effects across different cohorts ⇒ implementability

... and to analyze the role of (potential) 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



What do we know already?

Nishiyama & Smetters (2007) - privatization of the pension system isefficient (US case)

a long discussion between Diamond, Feldstein, Grubber and White...Imrohoroglu, Imrohoroglu and Joines (2003) - time inconsistentpreferences for social security

Gustman and Steinmeier (2012) - individuals with hyperbolic preferencesvalue a real annuity more than individuals with exponential preferences whohave accumulated roughly equal amounts of assets (especially true forindividuals with relatively high time preference rates or who have low assetsfor whatever reason)

Boersch-Supan, Keuschnigg and coauthors (various years) - Germanpension system (carefully calibrated cases) and EU at large

raising retirement age counter-effective (lowered labour supply prior toretirement)some reforms raise efficiency, some not



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,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 effects 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 benefits 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 fixedamount of money on unproductive (but necessary) stuff + 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

wants to maintain long run debt/GDP ratio fixed

Gt + subsidyt + rGt Dt−1 = Tt + (Dt − Dt−1) + Υt

J∑j=1

πj,tNt−j (4)



Model setup

Reform scenarios

Always change from 60% replacement rate DB PAYG to a partially funded DC,but:

part of the system (as specified by law) stays PAYG

funded scheme is mandatory, while contribution rate stays constant

the SIF gap needs to be financed ⇒ five closures: lump sum, labor tax,consumption tax, debt + labor tax, debt + consumption tax

Does the government pay market interest rate on debt? ⇒ two interest rates

market interest rate on investment

risk-less interest rate for government bonds

household demand for government bonds is inelastic

private savings (voluntary and mandatory) yield a linear combination ofrisky and risk-less, that satisfies above



Model setup

System reform

Prior to the reform, PAYG system

b1,j,t = ρj,twt and b2,j,t = 0 (5)

After the reform, it is a NDC + FF system

b1,j,t =

∑J̄−1s=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−1s=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) =

∑Jj=1 Nt−jwj,t lj,t∑J

j=1 πj,t−1Nt−1−jwj,t−1lj,t−1(6)

and rt = αKα−1t (ztLt)1−α − d (7)

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 effect positive ⇒ reform efficient

5 Run reform again, with the compensation, to observe GE effects

What is “baseline”?

Change in the no of births

Change in the mortality rates

Change in aggregate productivity

Change in (effective) 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”? Benefits as % of GDP



Basic parameters

Macroeconomic indicators

Table: General calibration parameters

Parameter Valueα capital share 0.33β time inconsistency 1, 0.9, 0.8r 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 benefits/GDP ratio of 6%

Contributions rate (τ) chosen to match SIF deficit/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 - flat 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 0.538 0.576 0.535 0.5772 0.537 0.579δ 0.981 0.998 0.99 1.0033 0.994 1.009

depreciation rate 0.0415 0.055 0.053 0.055 0.055 0.06tl 0.11 0.11 0.11 0.11 0.11 0.11t1 0.063 0.0603 0.0608 0.0608 0.0606 0.0611rho 0.27 0.15 0.253 0.153 0.255 0.155

resulting∆kt/yt 21.1 21.2 21.2 21.2 21.1 21.1

r 7.5 7.5 7.5 7.5 7.5 7.5

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



Debt resulting from the reform ...

... is paid as a lump sum by all living generations

⇒ debt share in GDP and proportional taxes are held constant, Υ is adjustedamong all the living

... is paid as a labor tax or consumption tax by all living generations

⇒ debt share in GDP is held constant, so are taxes, but τl or τc is adjustedamong all the living

... is accumulated and then paid from a labor tax or a consumption tax

⇒ debt share in GDP grows to a threshold, with all taxes held constant, thendebt gets automatically reduced to 45% of GDP exponentially, τc or τl isadjusted for living then onwards



Baseline specification

Efficiency of the reforms

Table: LSRA net wealth after redistribution (as % of per capita permanent income)

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

Labor units of cons. 0.012 0.014 0.026 0.018 0.035 0.023tax % ∆ in cons. 0.029 0.055 0.062 0.076 0.088 0.101Debt with units of cons. 0.011 0.016 0.024 0.020 0.033 0.025τl % ∆ in cons. 0.025 0.062 0.058 0.083 0.083 0.106Cons in units of cons. 0.007 0.011 0.022 0.015 0.031 0.020tax % ∆ in cons. 0.007 0.011 0.022 0.015 0.031 0.020Debt with in units of cons. 0.007 0.012 0.022 0.017 0.030 0.021τC % ∆ in cons. 0.007 0.012 0.022 0.017 0.030 0.021Lump sum in units of cons. 0.007 0.013 0.022 0.017 0.031 0.022tax % ∆ in cons. 0.017 0.050 0.052 0.070 0.075 0.094

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




Extent of fiscal adjustment - lump sum tax




Extent of fiscal adjustment - labor tax




Extent of fiscal adjustment - consumption tax




Extent of fiscal adjustment - debt with consumption tax




Extent of fiscal adjustment - debt with labor tax




Overall effects - baseline results

Table: Baseline results - no time inconsistency (β = 1)

Closure GDP Labor supply CapitalPeriod D97 ω flat ω D97 ω flat ω D97 ω flat ω10 1.005 1.007 1.000 1.000 1.016 1.023

Labor tax 50 1.025 1.029 1.002 1.012 1.083 1.092∞ 1.026 1.031 1.000 1.005 1.088 1.09610 1.008 1.010 1.000 1.004 1.025 1.030

Consumption 50 1.034 1.039 1.005 1.013 1.113 1.124tax ∞ 1.026 1.030 1.001 1.005 1.085 1.093

10 1.000 1.002 1.004 1.007 1.000 1.006Debt with 50 1.023 1.028 1.003 1.014 1.076 1.088τl ∞ 1.026 1.031 1.000 1.004 1.088 1.096

10 0.999 1.001 1.003 1.005 0.998 1.004Debt with 50 1.034 1.040 1.005 1.013 1.114 1.127τl ∞ 1.026 1.030 1.001 1.005 1.085 1.093

10 1.006 1.007 1.005 1.009 1.018 1.023Lump sum 50 1.024 1.029 0.994 0.995 1.080 1.092tax ∞ 1.026 1.029 0.991 0.995 1.086 1.090



Consumption equivalents

Replacement rates




Replacement rates - relative to baseline




Consumption equivalent - all closures, no time inconsistency




Decomposition - lump sum tax




Decomposition - consumption tax




Decomposition - labor tax




Decomposition - debt with consumption tax




Decomposition - debt with labor tax



Time inconsistency

Time inconsistency - matters little for capital

Capital - consumption tax closure and debt closure with consumption tax



Time inconsistency

Time inconsistency - effect on utility of future generations

Welfare - consumption tax closure and debt with consumption tax closure



Where we are

The current stage model

Calibrated to 1999 Polish economy

Welfare effects on aggregate small, but some differences across closures

Fiscal closure matters for the composition effects!

DC with (partially) funded pillar is a perfect match with debt closure

This is in fact a “small” reform

Labor cannot adjust much in our framework

Retirement is exogenous too

Where we want to get

Indivisible labor

Endogenous retirement age

Sophisticated time inconsistency


Efficiency of the pension reform: The welfare effects of various fiscal closures

Economy & Finance

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