Macroeconomic modeling of the pension reforms

Modeling the pension reforms

Macroeconomic modeling of the pension reforms1

Work in progressThe views expressed herein are those of the authors and not necessarily those of Narodowy Bank Polski

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

Narodowy Bank Polski, December, 20131 / 55

Motivation

The big(ger) picture

A (too) broad scienti�c project at the University of Warsaw

OLG modeling of the pension system reform in Poland

(Our intended) Contributions:

1 �scal closures have welfare e�ects (Pareto e�cient reform?)2 labor market e�ects when intensive and extensive margin is combined

with indivisibility of labor3 political stability of pension reforms

We have (almost) completed (1), still work on (2) and (3)

Today: the-best-of two papers written in stage (1)

1 Welfare e�ects of various �scal closures for 1999 reform2 Unprivatizing the pension system: welfare and macroeconomic e�ects of

2011 and 2013 reforms

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Motivation

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Motivation

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Motivation

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Motivation

Questions

How di�erent �scal closures of the pension system reform a�ectwelfare?

welfare e�ect of the reform (aggregate and across generations)?extent of �scal adjustment for di�erent �scal closurespensionsmacroeconomic variables

What are the e�ects of changes proposed/implemented recently?

additional welfare redistribution across cohortschanges to pensions and replacement rates�scal e�ect (debt/taxes) and capital

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Motivation

Questions

How di�erent �scal closures of the pension system reform a�ectwelfare?

welfare e�ect of the reform (aggregate and across generations)?extent of �scal adjustment for di�erent �scal closurespensionsmacroeconomic variables

What are the e�ects of changes proposed/implemented recently?

additional welfare redistribution across cohortschanges to pensions and replacement rates�scal e�ect (debt/taxes) and capital

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Roadmap

1 Motivation

2 Model

3 Calibration

4 Welfare e�ects of �scal closures

5 Unprivatizing the pension system

6 Summary

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Model overview

OLG model with endogenous labor and savings

Heterogeneity across cohorts (mortality and labor productivity)

No heterogeneity within cohorts

Agents have time inconsistent preferences

Exogenous retirement age and demographics

Competitive producers with CD production function

Pension system + pension system reform

Inter-generational transfers + utility to compare welfare across time withchanging demographics

Di�erent �scal closures (to do �scal rules)

Calibrated to the Polish economy

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What we do not know before modeling?

1999 reform: DB PAYG ⇒ NDC + FDC = partially funded DC

part of contributions stay in the PAYG system (SIF)part of contributions shifted away (OPFs) + �scal tension todaylower replacement rates + ease �scal tension in futurecomparing the steady states is not enough - transitory welfare e�ects

BUT SIF gap needs to be �nanced ⇒ possible �scal closures with ownwelfare e�ects

�ve closures: lump sum, labor tax, consumption tax, debt + labor tax,debt + consumption taxwe cannot tell ex ante

which �scal closure is better?e�ect for savings, labor supply and output?

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Consumers

Are free to choose how much to work, but only until J̄ (forced to retire)

Optimize 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+sπj,t

u (cj+s,t+s, lj+s,t+s) (1)

subject to

(1 + τc,t)cj,t + sj,t + τj + Υt = (1− τ ιj,t − τl,t)wj,tlj,t ← labor income

+ (1 + rt(1− τk,t))sj,t−1 ← capital income

+ (1− τl,t)pι,j,t + bj,t ← pensions + bequests

where u(c, l) = φ log(c) + (1− φ) log(1− l)

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Producers

maximize

Yt − wtLt − (rkt + d)Kt subject to Yt = Kαt (ztLt)

1−α

where the path of {z}∞t=0 is exogenous (calibrated to AWG, by EC)

Interest rate

interest rate on capital rkt = MPK − d, endogenous(riskless) interest rate on government debt to be rGt = 0.33 · rkthouseholds (and pension funds) by public debt inelastically

returns on savings yield a linear combination of risky and risk-less

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Producers

maximize

Yt − wtLt − (rkt + d)Kt subject to Yt = Kαt (ztLt)

1−α

where the path of {z}∞t=0 is exogenous (calibrated to AWG, by EC)

Interest rate

interest rate on capital rkt = MPK − d, endogenous(riskless) interest rate on government debt to be rGt = 0.33 · rkthouseholds (and pension funds) by public debt inelastically

returns on savings yield a linear combination of risky and risk-less

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Public �nances

SIF collects social security contributions and pays out pensions

subsidyt = τ ιt · wtLt −J∑j=J̄

bj,tπj,tNt−j (2)

any debt/surplus in SIF is government debt/surplus

Government

collects taxes on earnings, interest and consumption + Υ

spends �xed amount of GDP/money + services debt

long run debt/GDP ratio �xed

to �nance pension system can use taxes or debt ⇐ �scal closures

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Public �nances

SIF collects social security contributions and pays out pensions

subsidyt = τ ιt · wtLt −J∑j=J̄

bj,tπj,tNt−j (2)

any debt/surplus in SIF is government debt/surplus

Government

collects taxes on earnings, interest and consumption + Υ

spends �xed amount of GDP/money + services debt

long run debt/GDP ratio �xed

to �nance pension system can use taxes or debt ⇐ �scal closures

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Pension systems

initial steady state: PAYG De�ned Bene�t (DB), τ ιt = τDB

after the original reform: NDC + FDC (two pillars) τ = τ I + τ II

NDC = contributions indexed with growth of payroll + bene�tactuarially fair + post retirement indexation with 20% of payroll growthFDC = contributions earn interest + bene�t actuarially fair + postretirement also earn interest

JVR reform = �ve components:

(one o�) shift of bonds

(permanent) voluntary participation in FDC(permanent) FDC savings portfolio (mostly) has assets(permanent) reducing contribution rate to FDC

slider/zipper

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Pension systems

slider/zipper

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Pension systems

slider/zipper

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Solution method: Gauss-Seidel algorithm

Start from the initial steady state

Assume the economy eventually achieves the new steady state

Reform is unexpected

Algorithm

Guess k per worker (or path) and compute wt, rtt = 0T

Compute individual choices (may need value functions).Aggregate to get new k

′(or path)

If |k − k′ | < err �nishJust in case ... check feasibility

No contraction mapping theorem

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Algorithm

′(or path)

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Algorithm

′(or path)

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Algorithm

′(or path)

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How do we know what is "better"? LSRA!

Lump Sum Redistribution Authority as Nishiyama & Smetters (2007)

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?

Always the same: births, mortality, productivity and retirement age

1999 Reform: baseline = PAYG DB | reform = NCD + FDC

JVR: baseline = NDC+FDC | reform = changes to features

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What is baseline?

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What is baseline?

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What is baseline?

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Calibration

Roadmap

1 Motivation

2 Model

3 Calibration

6 Summary

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Calibration

Baseline: no of births (20 year olds):

Demographic projection (2060), constant afterwards (conservative)

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Calibration

Baseline: mortality rates

Demographic projection (2060), constant afterwards

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Calibration

Baseline: old age dependency ratio

Demographic projection (2060), constant afterwards

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Calibration

Baseline: labor augmenting technological progress

Historical data, projection from AWG, new steady state at 1.7%

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Calibration

Baseline: retirement age

Historical data, assumed (based on law) afterwards

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Calibration

Baseline (outcomes): pension bene�ts in GDP

Aging plus decreasing labor force

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Calibration

Calibration to replicate 1999 economy

Preference for leisure (φ) matches participation rate of 56.8%Replacement rate (ρ) matches bene�ts/GDP ratio of 5%Contributions rate (τ) matches SIF de�cit/GDP ratio of 0.8%Labor income tax (τl) set to 11% to match PIT/GDP ratioConsumption tax (τc) set to match VAT/GDP ratioCapital tax (τk) de iure = de facto

The initial capital

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Calibration

Life cycle productivity: �at or Deaton (1997)

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Calibration

Parameters for di�erent calibrations

Calibrated parameters

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 1.009d 0.0415 0.055 0.053 0.055 0.055 0.06tl 0.11 0.11 0.11 0.11 0.11 0.11τ 0.063 0.0603 0.0608 0.0608 0.0606 0.0611ρ 0.27 0.15 0.253 0.153 0.255 0.155

resultingxt/yt 21.1 21.2 21.2 21.2 21.1 21.1r 7.5 7.5 7.5 7.5 7.5 7.5

Note: D97: Deaton (1997) decomposition.

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Welfare e�ects of �scal closures

Roadmap

1 Motivation

2 Model

3 Calibration

6 Summary

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Results

SIF de�cit resulting from the reform is �nanced ...

... by labor tax or consumption tax

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

... by debt which is later repaid with labor or consumption tax

⇒ debt share in GDP grows to a threshold of 70%, with all taxes heldconstant, then debt gets automatically reduced to 45% of GDPexponentially, τc or τl is adjusted for living then onwards

... by lump sum taxes on all living generations

⇒ debt share in GDP and tax rates are held constant, Υ is adjusted amongall the living

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Results

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Results

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Results: Welfare

LSRA after redistribution (% of perm. cons.)

Fiscal β = 1 β = 0.9 β = 0.8closure �at D97 �at D97 �at D97

τl 1.2% 0.6% 0.8% 0.4% 0.5% 0.2%Debt/τl 1.3% 0.6% 0.8% 0.4% 0.5% 0.2%τC 1.2% 0.7% 0.8% 0.4% 0.5% 0.3%Debt/τC 1.2% 0.6% 0.8% 0.4% 0.5% 0.2%Υt 1.2% 0.7% 0.8% 0.4% 0.4% 0.2%

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

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Results: Fiscal adjustment

Extent of �scal adjustment - debt/consumption tax

Reform: Higher taxes initially, become lower after a while.

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Extent of �scal adjustment - debt/labor tax

Reform: Higher taxes initially, become lower after a while.

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Extent of �scal adjustment - labor tax

Higher taxes initially, become lower after a while.

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Extent of �scal adjustment - consumption tax

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Extent of �scal adjustment - lump sum tax

Note; lump sum taxes have real e�ects (redistribution)

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Results: Pensions

Replacement rates - relative to baseline

Pensions are substantially reduced by PAYG DB → DC

Fiscal closure matters little

Initial cohorts una�ected

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Results: Macroeconomic e�ects

Closure GDP Labor supply CapitalPeriod D97 ω �at ω D97 ω �at ω D97 ω �at ω

10 0.6% 0.7% -0.9% -0.5% 1.8% 2.3%Labor tax 50 2.2% 2.0% -1.3% 0.9% 7.2% 6.4%

∞ 2.5% 2.1% -1.2% 0.4% 8.3% 7.0%10 0.6% 0.7% -0.8% -0.2% 1.9% 2.4%

Consumption 50 2.9% 2.7% -0.6% 1.1% 9.8% 9.1%tax ∞ 2.4% 2.0% -0.9% 0.5% 7.8% 6.7%

10 0.2% 0.2% -0.3% 0.1% 0.6% 0.5%Debt with 50 2.0% 1.8% -1.1% 1.1% 6.7% 5.8%τl ∞ 2.5% 2.1% -1.2% 0.4% 8.3% 7.0%

10 0.2% 0.1% -0.4% 0.1% 0.6% 0.4%Debt with 50 3.0% 2.8% -0.5% 1.1% 10.0% 9.2%τl ∞ 2.3% 2.0% -0.9% 0.5% 7.8% 6.7%

10 0.5% 0.6% -0.2% 0.4% 1.7% 2.1%Lump sum 50 2.2% 2.0% -1.9% -0.5% 7.3% 6.7%tax ∞ 2.6% 2.0% -2.3% -0.5% 8.5% 6.6%

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Results: Distribution of welfare e�ects

Welfare: all closures, no time inconsistency

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Results: Decomposition of welfare e�ects

Decomposition - consumption tax (left) anddebt/consumption tax (right)

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Results: Decomposition of welfare e�ects

Decomposition - labor tax (left) and debt/labor tax (right)

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Results: Time inconsistency

Time inconsistency - matters little for capital

Capital - consumption tax closure and debt closure with consumption tax

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Results: Time inconsistency

Time inconsistency - preserves the general �ndings

Welfare - consumption tax closure and debt with consumption tax closure

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1999 reform - summary

Generally, 1999 reform is welfare enhancing

Our model calibrated to 1999 Polish economy

Shows that welfare overall e�ects positive, but �scal closure matters for(cohort) composition e�ects

Considerable redistribution across cohorts needed

Introduction of FDC makes debt desirable (redistributes)

Pensions fall

Log utility: taxes a�ect labor marginally (GHH preferences)

Endogenous retirement

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1999 reform - summary

Generally, 1999 reform is welfare enhancing

Our model calibrated to 1999 Polish economy

Shows that welfare overall e�ects positive, but �scal closure matters for(cohort) composition e�ects

Considerable redistribution across cohorts needed

Introduction of FDC makes debt desirable (redistributes)

Pensions fall

Log utility: taxes a�ect labor marginally (GHH preferences)

Endogenous retirement

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Unprivatizing the pension system

Roadmap

1 Motivation

2 Model

3 Calibration

6 Summary

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Introduced changes

JVR = changes to the pension system

2011 reform plus three policy options in 2013 reforms a�ectprivate savings and public debt (shift of bonds, przesuniecie obligacji)amount of savings in FDC

voluntary participation (voluntariness, doborowolnosc)split between τ1 and τ2 (shift of contributions, przesuniecie skladki)

portfolio structure of FDC (portfolio, portfel)the way pensions are paid out (slider, suwak)

these changes too a�ect di�erent cohorts di�erently

overall welfare e�ects undetermined

Objectives

with two �scal closures: VAT cut or debt reduction ...

... evaluation of these amendments vs. status quo of unchanged pensionsystem

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Introduced changes

Objectives

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Introduced changes

Objectives

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Introduced changes

Objectives

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Introduced changes

Objectives

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Introduced changes

Objectives

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Introduced changes

Objectives

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Introduced changes

Objectives

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Macroeconomic e�ects

Public debt in debt/tax closure (relative to baseline)

Fiscal situation improves (which translates into lower debt)

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Capital: debt reduction (left) and tax cut (right)

Fiscal situation improves: debt or taxes may fall

Long run: capital falls by up to 2%

Short run: increases or declines depending on behavior of debt.

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Return rates from pillars

Growth rate of GDP vs. interest rate (implied by the model)

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Replacement rates in relation to status quo

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Pensions in relation to status quo

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Welfare consequences

Zipper/slider (with tax closure)

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Shift of contributions (with tax closure)

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Voluntary participation (50%) (with tax closure)

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Change in portfolio structure (only assets) (with tax closure)

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All e�ects combined (with tax closure)

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All e�ects combined (both closures)

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Welfare (LSRA)

Welfare decline mainly due to

Lower pensions (due to lower replacement rates and unfavorablepost-retirement indexation)

Our model is veeeery merciful

no change in government expenditure (actual welfare gains materialize)no within-cohort heterogeneity (no minimum pension bene�t)�nal steady state population stationary

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Welfare (LSRA)

Welfare decline mainly due to

Lower pensions (due to lower replacement rates and unfavorablepost-retirement indexation)

Our model is veeeery merciful

no change in government expenditure (actual welfare gains materialize)no within-cohort heterogeneity (no minimum pension bene�t)�nal steady state population stationary

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Summary

Roadmap

1 Motivation

2 Model

3 Calibration

6 Summary

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Summary

Proposed reform scenarios - summary

Pensions decline (except in the 'portfolio' scenario)

Public and debt will be:

lower due to the �zipper/slider�, the shift of contributions and thevoluntary participation in OPFsthe shift of bonds - a one-o� e�ect

The change in GDP depends on the �scal closure (crowding out)

decrease in debt boosts capital accumulation and in turn GDP(transitory)in the long-run lower level of capital than in status-quo

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Summary

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Summary

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Summary

Welfare e�ects of �unprivatizing�?

The 2013 reform is a combination of �ve components:

Voluntary participation in OPFs (assumption of 50% participation)One-o� shift of bonds from OPFs back to governmentShift of contributionsA change in the portfolio structureThe �slider�

Overall welfare e�ect - negative (each component has negative e�ects)

SIF de�cit goes down - debt or taxes may fall

Welfare reduction mainly via lower pensions (some GE e�ects)

Capital stock declines in the long run, in the short run adjustmentdepends on �scal closure

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Summary

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Summary

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Summary

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Summary

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Macroeconomic modeling of the pension reforms

Technology

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