Should Public Retirement Pensions Be Means-tested?�

Cagri Seda Kumruy

University of New South WalesJohn Piggottz

University of New South Wales

13th February 2010

Abstract

The complex matrix of retirement policy trade-o¤s �encompassing elements of pater-

nalism, market failure, and overlaying incentives in a life-cycle context �have received much

attention in the literature. But the issue of whether publicly-funded retirement provision

should be means-tested, and if so how, has received limited attention, although it has been

highlighted from time to time. This paper examines the economic welfare e¤ects of means

testing using a stochastic overlapping generations model calibrated to the UK economy. A

labor-leisure choice is incorporated, with multiple individuals di¤erentiated by endowments

of e¤ective labor. Our results indicate that a change in the taper rate has implications for

both welfare and economic aggregates. In particular, with a second tier pension in place,

it is welfare improving to strictly means-test the �rst pillar. In contrast to much received

wisdom, higher taper rates increase social welfare.

JEL Classi�cation: E21, H55Keywords: Means-tested Pensions, Welfare, Social Security

�We would like to thank Pedro Gomis Porqueras, James Sefton, Alan Woodland, and participants of the2009 Southern Workshop in Macroeconomics at the University of Auckland, the 17th Australian Colloquium ofSuperannuation Researchers, the 2009 Far East and South Asia Meeting of the Econometric Society, and the2009 Singapore Economic Review Conference for their comments. We are grateful to the Australian ResearchCouncil for generous �nancial support.

ySchool of Economics, University of New South Wales, Sydney, 2052, Australia. E-mail:cs.kumru@unsw.edu.au

zSchool of Economics, University of New South Wales, Sydney, 2052, Australia. E-mail:j.piggott@unsw.edu.au

1

1 Introduction

Many countries run social insurance programs that provide protection to their citizens for

possible income �uctuations that they may face when they are old, unemployed, or disabled.

Costs of social insurance programs in the developed countries, in particular costs of age pension

programs, are rapidly increasing as populations age. Although age pension programs vary in

terms of their bene�t, �nancing, and coverage structures, they all provide longevity insurance

and can be welfare improving when private annuities markets are missing or when individuals

do not save enough for retirement because of myopia.1 On the other hand, they negatively

a¤ect individuals�labor supply and savings decisions.

This paper studies a stylized UK-type means-tested pension program, to quantify the e¤ects

of means testing on economic aggregates and social welfare. We develop a closed economy

overlapping generations (OLG) model and calibrate our model economy to that of the UK.

The UK is of special interest in this context because its retirement policies embrace both a

signi�cant means-tested pension and earnings-dependent pay-as-you-go (PAYG) social security,

providing a test-bed for a range of policy variations relevant to many countries. Our model

consists of 65-period-lived individuals who possess di¤erent skills. Individuals face mortality

and idiosyncratic income risks and make decisions on their consumption, saving, and labor

supply. We represent the institutional features of the UK�s social security system in the model.

In PAYG-�nanced pension programs, current retirees� bene�ts are paid by taxes borne

by current workers, impacting on both saving and labor supply choices. Using a large scale

deterministic overlapping generation (OLG) model and calibrating it to the US data, Auerbach

& Kotliko¤ (1987) show that the US social security reduces welfare substantially. Imrohoroglu

et al. (1995) and Hugget & Ventura (1999) extend the Auerbach and Kotliko¤ model by

assuming that individuals face idiosyncratic income shocks and stochastic life-spans. In their

environments, in contrast to the model of Auerbach and Kotliko¤, social security provides

insurance against income �uctuations and longevity risk. They show that social security�s

negative welfare e¤ects are largely mitigated because of its insurance bene�ts.

Although the e¤ects of PAYG-�nanced and earnings-dependent age pensions on individuals�

labor supply and savings decisions have been extensively analyzed, analysis of means tested

programs has been very limited. Nonetheless there are a few empirical and computational

studies that try to assess their behavioral implications. Neumark & Powers (1998) and Neumark

& Powers (2000) empirically analyze the e¤ects of the means-tested pension program of the

US, the Supplemental Security Income (SSI) program, on individuals�labor supply and savings

decisions. They show that an increase in SSI bene�ts results in a reduction in aggregate labor

supply and savings because potential participants of the program, in particular those who are

close to retirement age, reduce their savings and labor supply. In a similar vein, Disney &

Smith (2002) analyze the behavioral implications of the UK�s pension program. They show

that abolition of the earnings test raises working hours of older male workers by around 4 hours

1Although private annuities markets exist they are thin [see Diamond et al. (2005)]. For further discussionof the consequences of myopia in relation to an individual�s lifetime savings, refer to Fuster et al. (2005).

2

a week, with a lesser impact on women�s behavior.

In a recent paper, Sefton et al. (2008) assess the quantitative implications of the UK�s

means-tested pension program and evaluate alternatives. In particular, they consider the e¤ects

of a recent policy reform applied in the UK that reduced the marginal tax rate on private

income of means-tested retirement bene�ts from 100% to 40%. They conclude that the policy

reform encourages poor people to save more and delay retirement but has the opposite e¤ect

on richer households. The results clearly show that means-tested pension programs in�uence

individuals�labor supply and savings decisions. In a similar vein, Kudrna & Woodland (2008)

analyze the welfare e¤ects of a means-tested pension system using a deterministic small open

economy OLG model of the Australian economy. They show that the existing means-tested

age pension program represents a disincentive for older Australians to work and the removal

of labor earnings from the income test increases the labor supply of older Australians.

In this paper, similar to Sefton et al. (2008) we analyze the consequences of reforming the

UK�s pension program. To isolate the e¤ects of the taper rate on economic aggregates we �rst

assume that a PAYG-�nanced means-tested program (the MP) - representing a combination of

the UK�s basic state pension (BSP) and the means-tested program - is the only public pension

program in the economy and vary taper rates across a wide range. We show that higher taper

rates lead individuals to save more by reducing their payroll tax burden. But draw down of

non-pension assets is more rapid, especially among lower-income individuals, to increase their

public pension entitlements in old age.

We then add an earnings-dependent PAYG pension program [similar to the UK�s State

Second Pension (S2P)] to the model and precisely calibrate it to the UK data. Here we compare

the aggregate and welfare e¤ects of the six di¤erent pension arrangements. In the benchmark,

we model the UK�s pension program in 2003, which consists of the MP with a 100% taper rate

and the S2P. Because the S2P already provides some pension bene�t, we do not observe that

individuals decumulate their assets faster in middle and old age. Hence, a higher taper rate has

a more positive impact on economic aggregates. We also show that, in contrast to Sefton et al.

(2008), lowering the taper rate from 100% to 40% reduces savings of all individuals including

those of lower incomes. Having only the S2P or a universal pension system does not generate

much improvement compared with the benchmark case. In line with the previous literature

[see Imrohoroglu et al. (1995) and Hugget & Ventura (1999)], we �nd that the elimination

of both the MP and the S2P creates the largest welfare gain. With a second tier pension in

place, it is welfare improving to strictly means-test the �rst pillar. In our model speci�cation,

con�ned to a single taper rate, we �nd that a 100% taper rate yields the highest welfare. But

non-linear taper rates may in fact be optimal �the question of an optimal means test remains

for further investigation.

Our study di¤ers from those of Sefton et al. (2008) and Sefton & van de Ven (2009) in

three major directions. First, we incorporate the S2P into our analysis. Note that in the UK all

employees are required to either participate to the S2P or contract out for employer sponsored

or private pension programs, while most staying in the S2P [Disney et al. (2008)].Second,

3

individuals�labor supply decisions are elastic and hence, we can precisely capture labor supply

responses to the changes in pension programs. Third, since our model incorporates the S2P,

we can evaluate more pension policies that are often considered as alternatives. By doing so,

we can also contribute to the reform discussions of earnings-dependent PAYG social security

programs. In this respect, our paper can also be considered an extension of Hugget & Ventura

(1999) who study various social security reform proposals in the US context.

This paper is organized as follows. Section 2 provides an overview of the UK�s pension

systems. We present our model economy in section 3. Parameter values and the solution

method of the model are described in section 4 and section 5 respectively. Section 6 discusses

and interprets our results, while section 7 concludes. The remaining �gures appear in the

appendices.

2 Overview of the UK�s Pension System

In this section we summarize the main features of the UK�s pension and income tax systems.

Further details can be found in Sefton et al. (2008), The Pension Service (2008), and Disney

et al. (2008). Because our model calibration is based on 2003 data, we describe the structure

as it existed then. In broad terms the structure has not changed.

The UK�s pension system consists of three components: the Basic State Pension (BSP),

the earnings-dependent State Second Pension (S2P), and a means tested bene�t.

� Basic State Pension: The basic state pension is paid to individuals who have reached thestate pension age (SPA) [currently 60 for women and 65 for men]. It is based on the

National Insurance contributions (NICs) an individual has paid or been credited with

during his/her working life. The basic state pension is a �at rate bene�t but the amount

of bene�t depends on the number of qualifying years. If an individual earns annual income

that exceeds the Lower Earnings Limit (LEL) in a particular year, that year is considered

as a qualifying year for the individual. In order to receive the full bene�t an individual�s

qualifying years should be equal to 90% of his/her working life (between 16 and the SPA).

� State Second Pension: Participation in the state second pension scheme is mandatoryunless an individual opts out and participates in a private pension scheme. In contrast to

the �rst tier, a state second pension bene�t is based on an individual�s earning history.

An individual�s S2P entitlement is calculated as follows: Individuals who earn at, or

above, the LEL, but below the Lower Earnings Threshold (LET) are treated as if their

earnings were at the LET. Earnings above the LEL are called surplus earnings. Surplus

earnings up to the LET are multiplied by 46%; surplus earnings between the LET and

the Upper Earnings Threshold (UET) are multiplied by 11:5%; surplus earnings between

the UET and the Upper Earnings Limit (UEL) are multiplied by 23:5%.2 Any individual

2Note that the percentage rates are equal to the rates used for an individual who reaches state pension agein the 2003=2004 tax year. The LEL is $4004; the LET is $11200; the UET is $25600; and the UEL is $30900in the same tax year.

4

who earns above the LEL in a given year is credited with the amount calculated using

the procedure above. At retirement, each year�s credit is re-scaled by average earnings

growth and averaged over the working lifetime. An individual�s state second pension is

equal to the sum of the average values.

� Means-Tested Bene�t: The Government supports low income pensioners through the

means-tested program. Anyone aged 60 or over is guaranteed a minimum income (in-

cluding the BSP and the S2P). Bene�ts received between ages 60 and 64 years old are

subject to a 100% taper rate. Prior to the reform of the system in October 2003, bene�ts

received from the age of 65 were also subject to a 100% taper rate. This was reduced to

40% post reform. The means-tested program was called the Minimum Income Guarantee

(MIG) program prior to the reform; now it is called as the Pension Credit (PC) program.3

The UK pension system is administered by HM Revenue and Customs (HMRC) and is

self-�nancing. More precisely, the pension system is a part of the larger National Insurance

(NI) scheme that is �nanced through the NICs (taxes paid by employers and employees on

earnings). NIC liability commences when an employee�s total earnings exceed the LEL. If an

employee earns between the LEL and the Earnings Threshold (ET) then both employee and

employers�contributions are 0% of earnings; if an employee earns above the ET but less than

or equal to the UEL then the employee�s contribution is 11% and the employer�s contribution

is 12:8%; if an employee earns more than the UEL then the employee�s contribution is 1% and

the employer�s contribution is 12:8%.4 If an employee opts out in favor of a private pension

scheme his/her tax rate on earnings is reduced by 1:6% (contracting-out rebate).

3 The Model Economy

We use a general equilibrium OLG model economy that consists of heterogenous individuals,

a public sector, and a private sector.

3.1 Technology

Output Y at time t is produced by an aggregate technology that uses labor (L) and capital

(K) inputs. The technology is represented by a Cobb-Douglas constant returns production

function,

Yt = AtK�t L

1��t : (1)

3 In the 2003=2004 tax year the Government provided a minimum income of at least $102:10 per week for asingle person and $155:80 for a couple (including the state pension bene�ts).

4Note that these rates were in use in the 2003=2004 tax year. The annual ET was equal to $4615 in thesame tax year.

5

Output shares of capital and labor are given by � and 1�� respectively. The exogenouslygiven technology level A grows at a constant rate g and capital depreciates at a constant rate

� 2 (0; 1). Firms maximize their pro�ts by setting wage and rental rates equal to the marginalproducts of labor and capital respectively:

wt = (1� �)At�KtLt

��; (2)

rt = �At

�KtLt

���1: (3)

3.2 Demographics and Endowments

We consider an economy populated by overlapping generations. Every period t a generation

of individuals is born.5 Individuals face random lives, live up to a maximum of J periods; and

retire at age j�. The population grows at a constant rate n. An individual�s probability of

surviving up to age j conditional on surviving up to age j � 1; is denoted by �j . Demographicpatterns are stable and the constant cohort share of the generation j can be written as follows:

�j =�j�j�11 + n

for j = 2; 3; :::; J; (4)

wherePJj=1 �j = 1.

An individual�s productivity in a given period depends on his age j and an idiosyncratic

period shock sj to his productivity. In particular, we use the following functional form: �j :sj ,

where �j 2 �, the set of age-dependent mean e¢ ciency pro�les. We analyze both the case inwhich an individual experiences a shock at birth and lives with that shock forever (permanent

shock case) and the case in which an individual experiences a new shock during each period

of his lifetime (temporary shock case). Since the shocks are independently distributed there

is no aggregate uncertainty in the model. Following Huggett & Parra (2006), we assume that

shocks are log-normally distributed i.e. log(sj)~N(�; �2) and the log-normal distribution is

approximated by 5 evenly-spaced discrete values in logs on the interval [��2

2 � 3�; ��22 + 3�].

In both cases, probabilities are found by calculating the area under the normal distribution

conditional on the value of sj .

3.3 Preferences

All individuals have identical preferences over consumption and leisure denoted by the following

lifetime utility function:

5Because we are only interested in steady state values, time subscripts will be dropped from the equationsduring the rest of the analysis.

6

E

24 JXj=1

�j(

jYi=1

vi)u(cj;1� lj)

35 ; (5)

where E is the expectation operator and � is the time-discounting factor.6

Each individual is endowed with 1 unit of labor for each period. The amounts of labor and

leisure chosen at age j are given by lj and (1 � lj) respectively. The following is the periodutility function:

u(c; 1� l) = c1��

1� � + �(1� l)1�'1� ' ; (6)

where �; ' 2 [0;+1). The coe¢ cient of relative risk aversion is given by �. While the inter-temporal elasticity of substitution for consumption is 1� , the Frisch elasticity of leisure is �

1' .

The parameter � measures the dislike for work relative to the enjoyment of consumption.

King et al. (2002) show that the utility function is compatible with the balanced growth

path if � = 1 i.e. u(c; 1� l) = log(c) + � (1�l)1�'

1�' . Hence, we use the log period utility function

in our analysis. Without loss of generality, the value of the parameter � is normalized to unity.

3.4 The Public Sector

The government runs a public pension system that consists of an earnings-dependent and a

means-tested program and makes consumption expenditures. The public pension system�s

expenses are �nanced by taxes collected from labor earnings in a self-�nanced manner. In

other words, the system is �nanced in a PAYG fashion and it is treated as independent from

the general budget. The government collects income and consumption taxes and con�scates

accidental bequests to �nance its consumption expenditures.7

3.4.1 The Pension System

The pension program of our benchmark model is similar to that of the UK. All individuals are

required to participate in the program by paying tax on their gross labor earnings (similar to

NICs). The government provides earnings-dependent pension bene�ts to all individuals when

they retire.8 In addition, the government guarantees at least a minimum pension income to

6See Sommacal (2006) for the importance of endogenizing labor supply decisions in evaluations of pensionsystems.

7Note that all the �scal policy variables are necessary to generate the target moments of the calibratedeconomy. In addition, all forms of taxes a¤ect individuals� labor supply and saving behaviors. Ignoring thosee¤ects might hamper our policy analysis regarded with the pension program.Since individuals have stochastic life-spans, they leave "accidental" bequests when they die. We assume that

the inheritance tax rate is 100%. There are two ways to deal with the con�scated bequests in the literature.First, the government uses them to �nance its consumption expenditures. Second, the government transfersthem to the remaining individuals in a lump-sum manner. We choose the �rst option. This assumption is notimportant at all to deliver our results because the both options change the remaining individuals�net incomesat the same direction.

8The UK�s pension program allows individuals to contract out of the earnings-dependent pension programfor a private or employer-sponsored pension program. If individuals choose to contract out they pay less NI.

7

each individual through a means-tested program. Both programs are �nanced by tax payments

on gross labor earnings. The pension system in our model economy mimics the actual pension

system of the UK. The only di¤erence is that our model combines the BSP and the means-tested

program. The reason is that in the UK, if employees earn less than the LEL in a given year, they

do not contribute to the NIC scheme in that year. Individuals with insu¢ cient NICs receive

the basic state pension at a reduced rate or do not receive it at all. Many factors, for example

immigration, poor health, and child-care, can a¤ect individuals NICs. In our model, however,

all individuals participate in the system through compulsory payroll tax payments regardless

of their earnings levels. As a result every individual is entitled to a basic state pension. Since

there is no possibility of opting-out in the model, every individual receives the equivalent of

the UK�s state second pension bene�t too. This results in almost all individuals receiving more

pension income than the minimum pension income that is determined by the government. If

we incorporate the BSP to the model separately then the means-tested program might become

redundant.9 Hence, we choose to combine the BSP and the means-tested program. We call

our model economy�s earnings-dependent pension program the S2P and the combined program

the MP.

We calculate individuals�earnings-dependent pension bene�ts by using a formula similar to

the one used in the UK to calculate the actual S2Ps.10 First, we calculate individuals�average

growth-adjusted earnings over their working lifetime by using the following formula:

w =

Pj��1j=1 (1 + g)

(j��1)�jlj�jsjw

j� � 1 ;

where �jsjw is an individual�s e¤ective wage rate at age j. We represent the individual state

space by X, where x 2 X. Note that x denotes a state vector of the form (a; s; w), where a

stands for an individual�s asset holding. Then, we use threshold values and rates similar to the

ones used in the 2003/2004 tax year in the UK to calculate the S2P bene�ts.11 Hence, a j year

old individual whose state variable is denoted by x receives the following earnings-dependent

retirement bene�t after he reaches the exogenously determined retirement age, j�.

bj(x) =

8><>:0:46 � (LET � LEL) if w � LET;

0:46 � (LET � LEL) + 0:115 � (w � LET ) if LET < w � UET;0:46 � (LET � LEL) + 0:115 � (UET � LET ) + 0:235 � (w � UET ) if UET < w � UEL;

9>=>;(7)

where, LEL, LET, UET, and UEL stand for Lower Earnings Limit, Lower Earnings Threshold,

Upper Earnings Threshold, and Upper Earnings Limit respectively.

75% of the individuals�pension savings in those accounts should be annuitized at retirement. We would like tothank to an anonymous referee for this information.

9See Sefton et al. (2005) for a detailed explanation of this issue.10The details of the actual bene�t calculation are given in Section 2.11Note that in the actual calculations, each year�s earnings are used to calculate that year�s credit. At

retirement, each year�s credit is rescaled and averaged over the working lifetime. The sum of the average valuesdetermines an individual�s state second pension bene�ts.

8

Individuals who reach retirement age might be entitled to bene�ts that are subject to the

income test.12 Means-tested bene�ts are determined as follows:

b0j(x) = max(b� � �yj ; 0); (8)

where b0j(x) is the means-tested bene�t received by an j year old individual; b� is the minimum

pension income guaranteed by the government; � is the taper rate; and yj is the individual�s

gross taxable income. If we set the taper rate, � equal to 0 then the means-tested pension

program becomes a universal pension program that provides bene�ts to all retirees.

Both earnings-dependent and means-tested pension programs are �nanced through the

payroll taxes collected from labor earnings. In order to disentangle the tax burdens of earnings-

dependent pension and means-tested programs we assume that both programs are managed

separately and �nanced through separate payroll taxes. While the earnings-dependent pension

program is �nanced by taxes collected at the rate of � s, the means-tested program is �nanced

by taxes collected at the rate of �p. Both payroll tax rates are determined endogenously in the

model.

3.4.2 Income Taxation

The UK has a progressive income tax system. Individuals who are at or above the state

pension age are entitled to higher personal allowances than younger individuals. There are three

di¤erent taxable bands and rates.13 We use a quadratic function � i(yj) that passes through

the origin to approximate average income tax rates in the UK before and after retirement.

3.5 Budget Constraint

An individual�s gross income at period j is as follows:

yj =

(raj + lj�jsjw if j < j�;

raj + bj(x) if j � j�:

)Hence, the individual�s growth-adjusted budget constraint can be written as8><>:

cj + (1 + g)aj+1 � (1 + r)aj + (1� � s � �p)lj�jsjw � � i(yj) when j < j�;cj + (1 + g)aj+1 � (1 + r)aj + bj(x) + b0j(x)� � i(yj) when j � j�;

cJ = (1 + r)aj + bj(x) + b0j(x)� � i(yj) when j = J:

9>=>; (9)

12 In our model individuals can receive the means-tested bene�ts only after they reach the exogenously determ-ined retirement age (equivalent to the state pension age). However, in the UK, individuals might be entitled tomeans-tested bene�ts before they reach the state pension age.Means tested bene�ts are subject to both asset and income tests in the UK, but asset exemptions of various

kinds, most importantly of the owner-occupied home, mean that the income test is much more important. Wetherefore simplify our modelling of the means test to represent the income test only. In models of this kind, witha single homogeneous capital good, it is not possible to represent separate asset classes.13 In the 2003�2004 tax year individuals with taxable income (income after any personal allowances and relief

are deducted) below $1; 960 are taxed at the rate of 10%; between $1; 961 � $30; 500 are taxed at the rate of22%; and over $30; 500 are taxed at the rate of 40%.

9

We further assume that individuals cannot borrow against their future income at any age:

aj > 0;8j: (10)

3.6 An Individual�s Decision Problem

An individual�s decision problem in our model economy can be written as a dynamic program-

ming problem. Denoting the value function of the agent at age j by Vj , the decision problem

is represented by the following form:

Vj(x) = maxcj ;lj

fu(cj ; 1� lj) + ��j+1EVj+1(x0)g (11)

subject to equations 9 and 10. Note that x0 denotes the next period�state vector.

3.7 Equilibrium

Our equilibrium de�nition follows Auerbach & Kotliko¤ (1987), Imrohoroglu et al. (1995),

Imrohoroglu et al. (2003), and Hugget & Ventura (1999). We suppose that the pension system

is self-�nancing and the government runs a balanced budget. The pension programs�tax rates,

� s and �p and the consumption tax rate, � c are endogenously determined in order to satisfy

the balanced budget conditions.

Given a set of time-invariant government �scal policy instruments fLET;LEL;UET;UEL; b�; �; � i(:)g, a stationary equilibrium is de�ned as a set of value functions fVj(aj ; sj ; w)gJj=1, individuals�decision rules fcj(:); aj(:); lj(:)gJ;j=1, relative prices of labor and capital fw; rg, pension programtax rates � s and �p, consumption tax rate � c, and age dependent distributions of individuals

�j(x) that they must satisfy the following conditions:

1. Given �scal policy and prices, individuals�decision rules fcj(:); aj(:); lj(:)gJ;j=1 solve indi-viduals�decision problem 11 subject to the constraints 9 and 10.

2. Firms maximize pro�ts by choosing relative prices fw; rg according to the equations 2and 3.

3. The age dependent and time-invariant measure of individuals is computed as follows:

�j+1(x) =Ps�(sj+1; sj)

RX

d�j , where �(sj+1; sj) is the transition matrix for the shocks.

�1(x) is given.

4. Aggregate variables are derived from individuals�behaviors:

K =JPj=1

�jRX

aj(x)d�j ;

L =j��1Pj=1

�jRX

lj(x)d�j ;

10

C =JPj=1

�jRX

cj(x)d�j :

5. Age pension programs are self-�nancing:

JPj=j�

�jRX

bj(x)d�j = � sj��1Pj=1

�jRX

�jsjwlj(x)d�j :

JPj=j�

�jRX

b0j(x)d�j = �pj��1Pj=1

�jRX

�jsjwlj(x)d�j :

6. The sum of accidental bequests satisfy the following equation:

� =JPj=1

�jRX

(1� vj+1(z))aj(x)d�j :

7. The government�s income tax revenue is given by:

Ti =JPj=1

�jRX

� i(yj(x))d�j :

8. The government runs a balanced budget:

G = Ti + �CC + �:

6. The goods market clears:

C + (1 + g)(1 + n)K +G = Y + (1� �)K:

4 Calibration

This section de�nes the parameter values of our model. The limit and threshold values used

for the calculation of earnings-dependent pension bene�ts are set equal to their actual values

in the 2003=2004 tax year (LEL = $4004;LET = $11200;UET = $25600;UEL = $30940).

Similarly, we set the value of guaranteed minimum pension income, b� to its actual yearly value

for single individuals in the same tax year (b� = $5309). In our benchmark calibration we set

the value of taper rate, � to the pre-reform rate of 100%. Later, we set it to 0% (universal �at

rate) and 40% (post-reform rate).

We estimate pre- and post- retirement income tax rates by using a quadratic function that

passes through the origin. In particular we use the following functional form:

� j =

([2:698755

yj(x)10000 � 0:0423237(

yj(x)10000)

2]=100 if j < j�;

[1:508241yj(x)10000 � 0:0222008(

yj(x)10000)

2]=100 if j � j�:

)

Batini et al. (2000) report the values of labor�s share of income (1��) in the UK between1970 and 1995. The values �uctuate between 68% and 74% and their average is approximately

70%. Hence, we set the value of labor income share to 0:70. The growth rate of technological

11

progress is set to the average growth rate of the UK�s GDP per capita between 1999 and 2007

i.e. g = 2:8%:14 Weale (2004) estimates the capital depreciation rate in the UK in 2002 to be

4:82%. We use the same value for �. The technology level, A can be chosen freely and we set

it to 1:

Each model period corresponds to a year. Individuals are born at a real life age of 21

(model age of 1) and they can live up to a maximum real life age of 85 (model age of 65). The

population growth rate is assumed to be equal to the long-term average growth rate of the UK�s

population i.e. n = 0:5% [National Statistics (2009a)].15 The sequence of conditional survival

probabilities in the model, vj is set equal to the sequence of conditional survival probabilities of

men in the UK using 2002�2004 data [National Statistics (2009b)]. The mandatory retirementage is 65 (model age of 45), which is equal to the UK�s state pension age for men. The age

dependent e¢ ciency index, �j is set as follows: Robinson (2003) estimates age-earnings pro�les

for di¤erent educational levels by using various speci�cations. We take her estimates of weekly

earnings for di¤erent levels of experience, normalize the data by setting the value of weekly

earnings for a man with one year�experience to 1 and interpolate the normalized data by using

the spline method for missing values.16 Blundell & Etheridge (2008) calculate the variance

of permanent and temporary shocks to earnings in the UK as approximately 0:08 and 0:05

in 2003. We use the average of the two values as the variance of the shock in the model i.e.

�2 = 0:065.

Following Heathcote et al. (2008), without loss of generality, we set the value of � to 1.

There is no consensus on the values of the Frisch elasticities of labor supply and leisure. Domeij

& Flodén (2006) estimate the value of the Frisch elasticity of labor supply to be between 0:1

and 0:3. However, they show that these values are downward-biased and claim that unbiased

estimates are larger. Since elasticity estimates vary at a large margin, instead of using the

value of one of these estimates, we set the value of leisure parameter, ' to 2 so that we can

closely replicate the labor-supply pro�le across the working life-cycle. Although there is no

restriction for the value of the time discount factor (�) in the OLG models, it is generally

taken as smaller than one. For instance, Auerbach & Kotliko¤ (1987) and Hubbard & Judd

(1987) set � = 0:9852. Hurd (1989) estimates � as 1:011. Imrohoroglu et al. (1995), Hugget &

Ventura (1999), and Storesletten et al. (1999) use Hurd�s estimate. Since conditional survival

probabilities enter into their model, the e¤ective time discount factor (�vj) is smaller than one

during most of an individual�s lifetime. In our choice of � we follow Auerbach & Kotliko¤ (1987)

and Hubbard & Judd (1987) and set � < 1 in order to make sure that there is no arti�cial

welfare gain because of choice of the time discount factor. As in Auerbach and Kotliko¤ we

adjust the value of � to calibrate the model economy to the UK�s average capital-output ratio

14GDP per capita growth rates are taken from Eurostat (2009).15 It is the average annual population growth rate between 2001 and 2007.16Robinson (2003) estimates weekly earnings for both men and women according to whether they have attained

a low, medium, or high educational level. She uses quadratic, cubic, and quartic speci�cations. We use the valuesof her estimates for men in the group with the least amount of education which is calculated using a quadraticspeci�cation.

12

of 2:26.17

Public SectorLimit and threshold values 2003� 2004 tax year valuesMinimum guaranteed pension income b� 2003� 2004 tax year value for a single individualTaper rate � 100%Income tax rate � i Estimated by a quadratic functionGovernment expenditures G 0:227898

ProductionCapital share of the GDP � 0:30Annual depreciation of capital stock � 4:82%Annual per capita output growth rate g 2:8%

Demographics and EndowmentsMaximum possible life span J 65Obligatory retirement age j� 45Growth rate of population n 0:5%Conditional survival probabilities fvjgJj=1 UK 2002� 2004Age e¢ ciency pro�le f�jgt

��1t=1 Robinson (2003)

The variance of the employment shock �2 0:065

Markov transition matrix � for skills

2666640:012224 0:2144 0:54675 0:2144 0:0122240:012224 0:2144 0:54675 0:2144 0:0122240:012224 0:2144 0:54675 0:2144 0:0122240:012224 0:2144 0:54675 0:2144 0:0122240:012224 0:2144 0:54675 0:2144 0:012224

377775PreferencesAnnual discount factor of utility � 0:948Leisure parameter ' 2

Table 1: Parameter Values

17Weale (2004) states that the UK�s capital-output ratio in 2002 is 2:26.

13

5 Solution Method

Our solution procedure closely follows that of Hugget & Ventura (1999) and Imrohoroglu et al.

(2003). In particular, we use the following algorithm:

1. We guess values for capital (K), labor (L), and tax rates (� s; �p; and � c).

2. Calculate the corresponding factor prices.

3. Calculate the optimal decision rules: aj(x); lj(x); and cj(x):

� Create discrete sets A = f0; :::; amg for asset values, S = fs1; :::s5g for productivityshocks, and Wh = fwh1 ; :::; wh20g for average past earnings. Choose the upper boundam such that it never binds. Solve for the control variables y = (c; l) at each grid point

x = fa; s; whg by using the simplex method starting from the last period. Use linear

interpolation to calculate o¤-grid points decision rules and the value function.

4. Calculate new values ofK;L; and tax rates (� s; �p; and � c) implied by the optimal decision

rules and the balanced budget conditions.

� Simulate time paths of consumption, labor, asset holdings, means-tested and earningsdependent pension bene�ts for many individuals: Start with a newly born individual and

randomly draw the individual�s productivity shock and the survival outcome; use the

optimal policy functions to construct next period�s state variables; recursively follow this

process until the individual dies. Repeat the same process 10000 times. Compute the

aggregates as averages across the 10000 simulations.

5. If the guess values in the �rst step are close enough to the computed values in the fourth

step, this is a stationary recursive equilibrium. Otherwise iterations continue until the

convergence realizes.

6 Results

To isolate the e¤ects of the means-tested program on economic aggregates and welfare we �rst

shut down the earnings-dependent PAYG program (the S2P) and vary taper rates of the MP.

In this example, we do not worry about replicating the UK�s capital-output ratio and hence, we

call it the counter-factual example. The results of the counter-factual example are presented

in the section 6.1. We then add an earnings-dependent PAYG system that is very similar

to the S2P into the model and calibrate the model to 2003 UK data, setting the taper rate

equal to the pre-reform rate of 1. We call this case the benchmark. We try to be as precise

as possible in order to replicate the UK�s average capital-output ratio in the benchmark case.

Later we conduct policy analyses by assuming �rst that the taper rate is equal to the reform

rate of 0:4 and then that the taper rate is equal to 0. We also compare the cases in which the

14

means-tested pension program (the MP) is removed (leaving only the S2P exists); the earnings-

dependent PAYG program is removed (leaving only a universal pension program); and both

the means-tested and earnings-dependent PAYG pension programs are removed (privatization).

The results of the benchmark case and the relevant policy analyses are presented in the section

6.2.18

6.1 A Counter-factual Example

Table 2 reports equilibrium outcomes for a range of taper rates, where � is the taper rate; �p is

the MP tax rate; L is the amount of labor supply; K is the capital stock; C is consumption; Y

is output; � is the amount of the accidental bequests left; K=L is the capital-labor ratio; K=Y

is the capital-output ratio; and r is the interest rate.

� �p (%) L K C Y � K=L K=Y r(%)

0 24:28 100 100 100 100 100 100 2:2572 8:47070:1 22:56 100:0792 99:8705 101:2226 100:0156 95:6259 99:7738 2:2539 8:48380:2 20:85 100:0582 99:7607 102:4288 99:9949 91:5780 99:6512 2:2519 8:50580:3 19:23 100:0309 99:3827 103:5684 99:8584 86:9674 99:3143 2:2464 8:53520:4 17:70 100:0422 99:3859 104:7860 99:8585 83:2879 99:2771 2:2465 8:54070:5 16:18 100:6040 101:0009 106:6803 100:7639 84:7290 100:2765 2:2625 8:44150:6 15:23 100:9340 102:1594 107:8865 101:3629 85:9636 101:0723 2:2749 8:37240:7 14:59 101:0883 102:7742 108:6301 101:7032 86:5905 101:5083 2:2810 8:33030:8 13:89 101:3067 103:4474 109:4859 102:0482 87:7951 101:9321 2:2881 8:29250:9 13:32 101:4914 104:1359 110:2267 102:4199 88:7276 102:4320 2:2950 8:24631:0 12:80 101:6589 104:7504 110:8794 102:7107 89:9869 102:8599 2:3020 8:2071

Table 2: E¤ects of Taper Rates on Economic Aggregates

Not surprisingly, an increase in the taper rate decreases young individuals� payroll tax

burdens. As a result, they have larger net wage income from which to save for their future

consumption in each period. However, an additional saving in earlier years reduces the amount

of state pension bene�t received later. In other words, each $1 increase in savings creates

a � pence reduction in state pension bene�ts without taking interest earnings into account.

In addition, retired individuals prefer to accelerate their decumulation of assets in order to

maximize their state pension bene�ts during their remaining lifetime. Let�s take � = 0 as our

reference point. An increase from the reference point (up to 40%) do not generate a higher

capital stock. This is because the individual�s desire to maximize their state pension bene�ts

outweighs the income e¤ect of a higher taper rate (a lower payroll tax). Yet, because each

increase from the reference point results in a higher net wage earning, the amount of labor

supplied (see the third column) increases slightly. When the taper rate is increased from 0%

to 10%, L increases from 100 to 100:0792 and K decreases from 100 to 99:8705. Although K18 In the section 6.1 we conduct our analysis by assuming that the ability shocks are permanent. In the section

6.2 we �rst conduct our analysis by assuming that the ability shocks are permanent then we conduct the sameanalysis under the assumption that the shocks are temporary.

15

decreases slightly, the increase in L dominates, and hence Y increases. Yet, when the taper

rate is increased from 0% to 20%; L increases from 100 to 100:0582 (the increase is less than

that of the previous case) but K decreases from 100 to 99:7607 (the decrease is more than that

of the previous case). As a result, Y decreases slightly. Similarly in the cases in which the

taper rate increases from 0% to 30% and from 0% to 40%, the decreases in K dominate the

increases in L, and hence Y decreases. Yet, we still observe an increase in average consumption

levels.

The intuition is as follows. An increase in the taper rate up to 40% does not increase the

level of savings. Although young individuals increase their savings slightly, middle and old

age individuals decumulate their assets so fast that it causes a reduction in the overall level

of savings. As a result, both the capital stock and the level of accidental bequests decrease.

However, the sharp decrease in the accidental bequests creates a moderate increase in the

average consumption level although the output level has slightly decreased. Note that accidental

bequests are con�scated by the government to �nance its non-productive expenditures. Hence,

a decrease in accidental bequests translates into a higher average consumption level.19

Above 40%, we observe that an increase in the taper rate increases the capital stock in the

economy: the income e¤ect of higher taper rates outweighs individuals�desire to increase their

pension bene�ts. As expected, the output level increases as a consequence of increases in both

the capital stock and the labor supply. This in turn results in higher average consumption

levels. Over this range, an increase in the consumption level is generated by an increase in

the output level, not a decrease in the amount of accidental bequests (in fact, the amount of

accidental bequests starts to increase).20 Thus, in this range, a higher taper rate�s positive

income e¤ect outweighs its negative e¤ect on individuals�savings and labor supply decisions.

To demonstrate the e¤ects of taper rates on saving, labor supply and consumption levels at

each age we present the average life-cycle pro�les of asset holdings, labor supply and consump-

tion. Figure 1 depicts the average asset holdings across the life-cycle. An increase in the taper

rate (a decrease in the MP payroll tax rate) creates a moderate increase in younger individuals�

savings: Although individuals have larger net wage incomes to save, they also want to maxim-

19The exact mechanism is as follows. Since the ratio between the level of government consumption expendituresand the level of aggregate output is �xed whenever the level of aggregate output decreases, the level of governmentconsumption expenditures decreases. The government �nances its consumption expenditures by collecting taxeson consumption and income and con�scating accidental bequests. Note that in the model the consumptiontax rate is endogenously determined in order to balance the government�s budget. A decrease in the level ofaccidental bequests might require more tax revenues to balance the budget. In this calibration exercise thedecrease in the government expenditures is quite large and hence, the government�s revenue requirement hasdeclined. As a result, we observe that the level of consumption increases although the level of output slightlydecreases.Another way of dealing with accidental bequest is to assume that the government transfers them to the

remaining generations in a lump sum manner. If the government transfers the accidental bequests in a lumpsum manner, the individuals�income levels and tax liabilities increase at the same time. As a result, the �nale¤ect of a change in the accidental bequest won�t di¤er from what we observe.

20Higher levels of pension bene�ts and precautionary savings increase the amount of accidental bequests left.While higher taper rates reduce pension bene�ts, they generate more savings. Savings are large enough tosuppress the downward e¤ect of lower pension bene�ts on the amount of accidental bequests.

16

ize their publicly provided pension bene�ts and hence, they increase their savings moderately.

While a higher taper rate increases the savings before retirement, it causes an abrupt decrease

in retirees�asset holdings. Furthermore, an increase in the taper rate extends the duration of

the dependence on pension bene�ts as the only source of the retirement income. In other words,

retirees�desire to maximize their state pension bene�ts lead them to decumulate their assets

as fast as possible when the taper rate is high. On average, as can be seen in table 2, a higher

taper rate�s positive e¤ect on savings dominates its negative e¤ect on asset decumulations and

hence, the level of aggregate savings increases slightly.

Figure 1: Average asset holdings across the life-cycle

Figure 2 depicts average labor supply levels. While individuals� labor supply pro�les are

almost same in earlier ages, individuals supply slightly more labor when the taper rate is 100%

in middle ages. As a result, on average, individuals supply more labor when the taper rate

is high because of higher net wage earnings. From �gure 2, it may also be inferred that the

compulsory retirement age of 65 substantially impacts behavior. In the full model described in

the next section, this is far less important.

Figure 2: Average labor-supply pro�le across the life-cycle

Figure 3 depicts average consumption levels. Figures 1, 2, and 3 reveal together that most

of the increase in a young individual�s net income, which is generated by a higher taper rate,

17

is spent on consumption in the earlier years. Since old individuals decumulate their assets

rapidly when the taper rate is high, their consumption levels fall behind those in lower taper

rates sometime after retirement. This in turn increases the discrepancy between individuals�

consumption levels in early and late ages. Although this is the fact, the higher taper rates still

provide better consumption smoothing across the life-cycle.

Figure 3: Average consumption pro�le across the life-cycle

As we explained above, in our model, there are �ve types of individuals who di¤er in terms

of their skill levels. Higher skilled individuals are more productive and hence, their wage rates

are larger. This, in turn, leads them to hold more assets as protection against future income

�uctuations and longevity risk. To investigate the e¤ects of taper rates further we direct

our attention to the cross-sectional asset holdings and consumption pro�les of each type of

individual. By doing so we can analyze the reactions of di¤erent income groups to a change in

the taper rate. We report the �gures in appendix A.

Figures 7-11 show the cross-sectional asset holdings of di¤erent types of individuals. Not

surprisingly, the poorer individuals�asset holdings are lower than those of richer individuals

at every age. Poorer individuals� asset holdings peak far before the compulsory retirement

age but richer individuals�asset holdings peak at around retirement age. The poorest type

(type I) saves less and completely decumulates her assets by around real age of 73 when the

taper rate is 1 but she saves relatively more and decumulates her assets by real age 81 and

85 when the taper rate is 0:4 and 0 respectively (see �gure 7). Note that lowering the taper

rate positively a¤ects the poorest individuals�savings. In contrast, middle-income individuals

(types II and III) save more when the taper rate is higher. Yet, the decumulation pattern

does not change: assets are decumulated faster when the taper is high. It looks like richer

individuals�accumulation decisions are not a¤ected by changes in taper rates. Although richer

individuals (types IV and V ) decumulate their assets faster when the taper rate is higher, the

pace of decumulation is slower than that of the poorer income groups.

Figures 12-16 depict the cross-sectional labor supply pro�les of di¤erent types of individuals.

We �nd that higher taper rates have a positive impact on all middle age individuals�labor supply

18

decisions no matter what their types are. The reason is simple: higher taper rates correspond

to higher net wage earnings.

Figures 17-21 demonstrate the cross-sectional consumption pro�les of di¤erent types. We

�nd that while lower taper rates provide better consumption smoothing for poorer individuals,

higher taper rates provide better consumption smoothing for richer individuals. Higher taper

rates cause poorer individuals to save less before retirement and decumulate their asset holdings

abruptly after retirement. This, in turn causes big distortions in their consumption levels after

retirement. It is also evident from the �gures that higher taper rates result in poorer individuals

becoming completely dependent on pension bene�ts for most of the remainder of their lives.

We now turn to the welfare e¤ects of a decrease in the taper rate. The welfare criterion

we employ is ex-ante (before ability is realized) expected (with respect to idiosyncratic shocks)

lifetime utility of a newborn individual in a stationary equilibrium. To measure the welfare cost

of a decrease in the taper rate we use the percentage change in the expected utility by taking

the case with 100% taper rate as the reference point. Table 3 reveals that higher taper rates

increase social welfare in our example. For example, an individual�s expected utility decreases

5:82% if the taper rate is decreased from 100% to 0%. The reason is as follows. On average,

higher taper rates increase the overall levels of savings and labor supply. This in turn results in

a higher consumption level over life-cycle. Our result con�rms the �ndings of Feldstein (1987)

who shows that a means-tested program is generally superior.

Taper rate The MP tax rate (%) % change in EU1:0 12:80 00:9 13:32 �0:290:8 13:89 �0:620:7 14:59 �1:00:6 15:23 �1:330:5 16:18 �1:850:4 17:70 �2:700:3 19:23 �3:400:2 20:85 �4:140:1 22:56 �4:960:0 24:28 �5:82

Table 3: E¤ects of Taper Rates on Welfare

6.2 Full Policy Results

Next we compare aggregate and welfare e¤ects of six di¤erent social security arrangements

assuming that productivity shocks are permanent. In the benchmark case we mimic the UK�s

pre-reform social security system which comprises the means tested pension (MP) with a 100%

taper rate and the state second pension (S2P). Our benchmark calibration is able to generate

the UK�s capital-output ratio. Then we decrease the taper rate to 40% (reform rate), and

19

0% respectively. We also analyze the cases in which only the S2P exists; only the universal

pension program (MP with 0% taper rate) exists; and both the MP and the S2P are removed

(privatization).

The �rst three rows of Table 4 show that employees�MP payroll tax rates (�p) decrease

signi�cantly with an increase in the taper rate.21 This in turn increases individuals�net wage

incomes and hence, positively a¤ects their saving and labor supply decisions (income e¤ect

of a high taper rate). Because individuals�consumption in old age is also supported by the

S2P, the higher taper rates�negative e¤ects on saving decisions (substitution e¤ect of a high

taper rate) are not as strong as in the previous section. In particular, we make the following

two observations by comparing �gures 22-26 in appendix B to �gures 7-11 in appendix A.

First, older individuals do not decumulate their assets as fast as in the previous counter-factual

examples. Second, a 100% taper rate generates higher saving rates for almost all income groups.

In contrast to the results of Sefton et al. (2008), the reduction in the means-tested taper rate

does not create higher saving rates for the lowest-income individuals. Yet, our results regarding

middle and high income individuals are compatible with those of Sefton et al. (2008): while

reducing the taper rate from 100% to 40% reduces savings of middle-income individuals, it does

not a¤ect higher-income individuals.

The intuition is as follows. When the S2P is present individuals�means-tested bene�ts

depend not only on their asset holdings but also on their S2P bene�ts. This means that

individuals� bene�ts are subject to a tighter means-test on discretionary income. In other

words, individuals should have relatively low wealth to receive some means-tested pension

bene�ts. Therefore, even for the lowest income group, the positive income e¤ect of a higher

taper rate dominates its negative substitution e¤ect on savings. Furthermore, since the means-

test is tighter, the faster asset decumulation does not happen. Thus, we can conclude that

the negative substitution e¤ect is smaller for all income groups when the S2P is present. Note

that in contrast to the previous section, our full model incorporates the S2P, that also distorts

individuals� saving and labor supply decisions. Hence, an increase in the taper rate might

create more positive income e¤ect in our environment by reducing the compounded distortions

on young individuals�fundamental economic decisions. In sum, because of the smaller negative

substitution and possibly larger positive income e¤ects, low and middle income individuals�

savings increase relatively more when the taper rate is higher.

Note that lower taper rates result in much lower aggregate capital and aggregate labor

supply when the S2P exists (see tables 2 and 4). This in turn creates much lower aggregate

consumption. Hence, the negative e¤ects of reducing the taper rate on aggregate capital stock,

labor supply, and consumption are greater in our environment.

Removing the MP from the system creates a slight increase in aggregate variables because

of the reduction in individuals� tax burdens. The universal pension system�s tax burden is

almost the same as that of the benchmark case and hence we do not observe much change in

economic aggregates. Table 4 reveals that the largest gain occurs when both the MP and the

21Note that �s stands for the S2P payroll tax rate.

20

S2P are removed consistent with the previous literature [see for instance, Imrohoroglu et al.

(1995) and Hugget & Ventura (1999)].

� �p(%) � s(%) L K C Y K=L K=Y r(%)

MP&S2P 1:0 2:17 22:88 100 100 100 100 100 2:26 8:49MP&S2P 0:4 12:97 22:81 95:07 86:83 85:16 92:19 91:69 2:13 9:31MP&S2P 0:0 24:18 22:77 91:12 78:81 73:65 86:51 87:35 2:06 9:78S2P � 0:00 22:88 100:49 101:52 102:93 100:77 100:97 2:28 8:40Universal 0:0 24:29 0:00 99:28 99:33 100:91 99:23 100:16 2:27 8:47Privatization � 0:00 0:00 103:31 114:07 127:58 106:47 110:29 2:43 7:61

Table 4: E¤ects of Reforms on Economic Aggregates

Figure 4 shows average asset holdings across the life-cycle. Although individuals� asset

holdings are slightly lower at earlier ages under a 100% taper rate, they increase by real age

50. It is also interesting to see that individuals do not decumulate their assets faster when the

taper rate is 1:0. A comparison of �gures 1 and 4 reveals that the existence of the S2P prevents

faster decumulation.

Figure 4: Average asset holdings across the life-cycle

Figure 5 shows that, on average, individuals supply more labor when the taper rate is

high. In fact, all types supply more labor as can be seen in �gures 27-31. A quick comparison

of �gures 2 and 5 reveals that higher taper rates�positive e¤ects on labor supply are more

pronounced when the S2P exists. The reason is simple: Since the S2P has already created

a burden on individuals�wage income, an increase in the taper rate provides more relief by

decreasing the compounded distortions.

21

Figure 5: Average labor supply pro�le across the life-cycle

A higher taper rate improves consumption smoothing. This result is also in contrast to the

counter-factual example (compare �gures 3 and 6). In the absence of the S2P, although higher

taper rates boost savings at earlier ages, they hasten decumulations in middle and old age.

Hence, we observe relatively less consumption smoothing with higher taper rates. Yet, when

the S2P exists, although higher taper rates increase savings, they do not hasten decumulations

so that we observe more consumption smoothing. Moreover, when the S2P exists, higher taper

rates provide better consumption smoothing for all types as can be seen in �gures 32-36.

Figure 6: Average consumption pro�le across the life-cycle

The last three rows of table 5 demonstrate that reducing the taper rate causes an abrupt

decrease in welfare because of the compounded labor tax distortions. Although individuals�

expected utilities in the economy with the pre-reform UK pension system are 13:97% lower

compared to those of an economy without the MP and S2P (privatization), individuals�ex-

pected utilities in the economy with the post-reform UK pension system are 22:32% lower

compared to the same reference point. The welfare costs of the universal pension system and

the pre-reform UK pension system are almost the same. The second best alternative is remov-

ing the MP and having only the S2P. Our welfare results are in line with previous studies

which �nd that privatization of the social security system creates the highest welfare.

22

� �p(%) � s(%) % change in EUPrivatization � 0:00 0:00 0:00S2P � 0:00 22:88 �12:49Universal 0:0 24:29 0:00 �13:37MP&S2P 1 2:17 22:88 �13:97MP&S2P 0:4 12:97 22:81 �22:32MP&S2P 0:0 24:18 22:77 �31:59

Table 5: Welfare E¤ects of Reforms

Tables 6 and 7 present aggregate and welfare e¤ects of various social security arrangements

when productivity shocks are temporary. A comparison of tables 4 and 6 shows that the

direction and magnitude of the e¤ects of various programs on economic aggregates do not

change.

� �p(%) � s(%) L K C Y K=L K=Y r(%)

MP&S2P 1:0 5:84 22:76 100 100 100 100 100 2:26 8:50MP&S2P 0:4 14:62 22:66 96:06 87:80 87:38 92:97 92:34 2:14 9:29MP&S2P 0:0 24:24 22:52 93:42 81:17 77:60 88:38 88:45 2:08 9:60S2P � 0:00 22:79 101:49 103:96 108:21 102:63 102:26 2:29 8:29Universal 0:0 24:28 0:00 100:23 100:74 105:80 99:23 100:42 2:30 8:30Privatization � 0:00 0:00 104:39 117:98 134:70 108:85 112:36 2:45 7:48

Table 6: E¤ects of Reforms on Economic Aggregates (Transitionary)

Not surprisingly, the welfare implications of various programs do not change under the

temporary shock case either.22

� �p(%) � s(%) % change in EUPrivatization � 0:00 0:00 �0:00S2P � 0:00 22:79 �12:33Universal 0:0 24:28 0:00 �13:16MP&S2P 1 5:84 22:76 �16:29MP&S2P 0:4 14:62 22:66 �23:27MP&S2P 0:0 24:24 22:52 �31:03

Table 7: Welfare E¤ects of Reforms (Transitionary)

In our model economy, the retirement decision is not endogenous i.e. everybody must retire

by age 65. Since the state pension age is 65 too, our assumption is innocuous. When the

S2P is not present, low and middle income individuals supply almost the same amount of

labor under di¤erent taper rates (see �gures 12-14). If the retirement decision was endogenous,

individuals would supply less labor especially closer to retirement as a result of an increase in22Robustness tests of our results have been successfully performed and are available upon request.

23

the taper rate. When the S2P is present, we see that a higher taper rate increases labor supply

substantially more (see �gures 27-29). In other words, the higher taper rate�s positive income

e¤ect dominates its negative substitution e¤ect. The intuition is similar to the one provided

earlier. In an economy with the S2P, the means test is tighter on discretionary income. Hence,

a higher taper rate�s negative substitution e¤ect is weaker than that of the previous case.

Thus, with endogenous retirement, a higher taper rate would have some negative e¤ect on

labor supply towards the end of the working-life but the negative e¤ect would not be larger

than that of the previous case. Furthermore, if the means-test becomes tighter as a result of an

increase in the generosity of the S2P, we might see that the positive income e¤ect dominates

the negative substitution e¤ect.23

7 Conclusion

The issue of whether publicly-funded retirement provision should be means-tested, and if so

how, has received limited attention, although it has been highlighted from time to time [e.g.

Feldstein (1987)]. This paper examines the economic welfare e¤ects of means testing using a

stochastic overlapping generations model calibrated to the UK economy. A labor-leisure choice

is incorporated, with multiple individuals with di¤erent endowments of e¤ective labor.

To isolate the e¤ects of the taper rate on economic aggregates we �rst assume that the

MP is the only public pension program in the economy and vary taper rates. We show that

under this scenario higher taper rates lead individuals to save more by reducing their payroll

tax burden. Yet, individuals, especially in the lower income bracket, draw down their assets

faster to increase their public pension entitlements in old age. In other words, the higher the

taper rate the longer the individuals depend on the means-tested pension bene�ts as a means

of �nancing old age consumptions. We also show that when the S2P is not present, an increase

in the taper rate does not have a substantial impact on individuals�labor supply decisions.

We then add the S2P to the model and precisely calibrate it to the UK data. This dramatic-

ally changes our results. In the benchmark, we model the UK�s pension program in 2003, which

consists of the MP with a 100% taper rate and the S2P. Because the S2P already provides some

pension bene�ts, we do not observe that individuals decumulate their assets faster in middle

and old age. Hence, a higher taper rate has a more positive impact on economic aggregates.

We also show that, in contrast to the results of Sefton et al. (2008), lowering the taper rate

from 100% to 40% does not have a positive impact on individuals�saving decisions including

those of lower income individuals.

Since we explicitly modelled the S2P, we were able to compare aggregate and welfare e¤ects

of six di¤erent pension arrangements that are often considered as alternatives: Having only

the S2P or a universal pension system does not generate much improvement compared to

the benchmark case. Not surprisingly, as in the previous studies, our results show that the

23We thank to an anonymous referee for pointing out the possible importance of endogenous retirement decisionon labour supply.

24

elimination of both the MP and the S2P creates the largest welfare.

Like many other countries, the UK faces a rapidly ageing population. This in turn extends

the tax burden of the working age population assuming that pension bene�ts are �xed. Under

this demographic condition, loosening the taper rate of the means-tested program might create

more distortions on working individuals� saving and labor supply decisions than our model

demonstrates. In addition, loosening the taper rate might result in more retirees depending on

the means-tested pension bene�ts as a means of �nancing their old age consumption. Thus,

reducing the taper rate in an environment with ageing population might be more detrimental

to economic aggregates and social welfare.

In our model speci�cation, we �nd that a 100% taper rate is optimal. But non-linear

taper rates may in fact be optimal �the question of an optimal means-test remains for further

investigation.

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Appendix A: Figures of the Counter-Factual Example

Figure 7: Type I�s asset holdings

Figure 8: Type II�s asset holdings

27

Figure 9: Type III�s asset holdings

Figure 10: Type IV�s asset holdings

Figure 11: Type V�s asset holdings

Figure 12: Type I�s labor-supply pro�le

28

Figure 13: Type II�s labor supply pro�le

Figure 14: Type III�s labor supply pro�le

Figure 15: Type IV�s labor supply pro�le

Figure 16: Type V�s labor supply pro�le

29

Figure 17: Type I�s consumption pro�le

Figure 18: Type II�s consumption pro�le

Figure 19: Type III�s consumption pro�le

Figure 20: Type IV�s consumption pro�le

30

Figure 21: Type V�s consumption pro�le

Appendix B: Figures of the Full Policy Analysis

Figure 22: Type I�s asset holdings

Figure 23: Type II�s asset holdings

31

Figure 24: Type III�s asset holdings

Figure 25: Type IV�s asset holdings

Figure 26: Type V�s asset holdings

Figure 27: Type I�s labor supply pro�le

Figure 28: Type II�s labor supply pro�le

32

Figure 29: Type III�s labor supply pro�le

Figure 30: Type IV�s labor supply pro�le

Figure 31: Type V�s labor supply pro�le

Figure 32: Type I�s consumption pro�le

33

Figure 33: Type II�s consumption pro�le

Figure 34: Type III�s consumption pro�le

Type IV�s consumption pro�le

Figure 36: Type V�s consumption pro�le

34