Working Paper Series

Congressional Budget Office

Washington, DC

Early Announcement of a Public Pension Reform

in Italy

Maria I. Marika Santoro

Congressional Budget Office

Washington, DC

E-mail: marika.santoro@cbo.gov

January 2006

2006-1

Working papers in this series are preliminary and are circulated to stimulate discussion and critical comment. These papers are not subject to

CBO’s formal review and editing processes. The analysis and conclusions expressed in them are those of the authors and should not be

interpreted as those of the Congressional Budget Office. References in

publications should be cleared with the authors. Papers in this series

can be obtained at www.cbo.gov/publications/.

1
Abstract

There has been much discussion about the need for public pension reforms

in most of the Organization for Economic Cooperation and Development

(OECD) countries, but what is the macroeconomic impact of announcing reforms in advance? The Italian pension system reform in 1992 represents an

illustrative case to address this question. The Italian government announced

the pension system reform with the aim of slowing the growth of the system’s expenditures by raising the eligibility retirement age. The present

paper develops an overlapping generations (OLG) model, with endogenous

retirement, in order to analyze the impact of this pre-announced reform on

the agents’ retirement decision and pensions’ expenditure. We calibrate the

model to Italian data in 1992 and then we simulate the announcement of a

five-period increase in the eligibility age for retirement. The delay between

the announcement of the reform and its enactment creates the possibility for

eligible individuals to decide whether to retire immediately or keep working

under the new public pension system. The model shows that the transition to

the new pension system would be characterized by a drop in the employment

rate of workers ages 55 and older and explains 77 percent of the actual drop.

The model also predicts an 8.25 percent increase in pensions’ expenditure,

and explains 83 percent of the actual increase. Finally, the welfare analysis

highlights a loss for almost all the transitional generations because of the

specific structure of the Italian reform and its early announcement.

2
1 Introduction

This paper analyzes the macroeconomic effects of public pension reforms

when they are announced and then enacted with a delay. The illustrative

case for the study is Italy in 1992.

In the early 1990s, the pay-as-you-go (PAYG) public pension systems

in many European countries experienced significant financial distress due

to high dependency ratios (the ratio of workers entitled to social security

benefits to those paying payroll taxes). During the 1980s, the Italian public

pensions’ expenditure as a percentage of gross domestic product (GDP) grew

by almost 4 percentage points, from 7.4 percent in 1980 to 11.3 percent in

1991 (Fig. 1). Among other things, the growth in spending in the Italian

public pension system stemmed from amendments passed in the 1970s that

indexed pensions to nominal wages.1

In 1992 and 1993, Italy experienced an economic downturn,2 and not surprisingly the employment rate (total employment to total population ratio)

dropped sharply, by 2.6 percentage points, between 1991 and 1993.

However, a disproportionate part of the drop in the employment rate was

accounted for by workers ages 55 and older (Fig. 2). The total employment

rate of those 16 to 24, 25 to 40, and 41 to 54 years old declined by 2.8,

by 2.1, and by 1.5 percentage points, respectively, between 1991 and 1993.

The employment rates for those 55 years and older, instead, fell by 5.0 percentage points3 and accounted for 44 percent of the entire drop in the total

employment rate in those years.

Most of the decline for workers ages 16 to 54 was due to the economic

downturn, as had been true during other Italian recessions. However, in

earlier recessions there was no comparable drop in the employment rate of

1 Indexation to nominal wages was introduced in 1975 and this feature increased the

burden of the pension system through the 1980s due to the oil price shocks that occurred at

the beginning of that decade. Pension benefits increased at regular intervals with nominal

wages, i.e. consumer price growth plus real wages growth.

2The time frame in which the 1992 reform was announced is dense with negative economic events. The Italian GDP fell by almost 5 percentage points per capita with respect

to a 2 percent trend (from 107.0 percent to 102.1 percent). Italy was forced to abandon

the European Monetary System because of persistent pressure toward the devaluation of

the lira.

3 In particular, the largest drop in the employment rate for this age band intervened

between October 1992 and January 1993, as the labor market quarterly data show.

3
workers ages 55 and older. Furthermore, if we look at more disaggregated

data, the largest drop was among 60- to 65-year-old men (-7.8 percentage

points, Fig. 3) and 55- to 59-year-old women (-3.6 percentage points, Fig.

4).

This study suggests that a large part of this decline was due to the early

announcement of a major public pension system reform. The reform (known

as the “Amato reform” from the name of the prime minister then in charge)

was announced on September 5, 1992, but took effect only in February 1993.

The reform mainly changed two crucial features concerning the pension system: it raised the eligibility age for retirement (from 60 to 65 for men, and

from 55 to 60 for women) and the minimum number of years of contribution

by five (from 15 to 20).

The formal announcement focused on the increase in the eligibility age by

five years. This announcement affected the retirement decision of several cohorts of the working population, inducing them to retire earlier than planned.

In fact, eligible workers received a "time window" to decide whether to keep

working or retire at the time of the announcement. This paper shows that

announcing an increase in retirement ages may have induced a significant

number of older workers to retire early.

Existing analyses of the role of information within a policy reform process

can be mainly divided into two branches. In the first, agents receive announcements about the content and the timing of a policy change under

the assumption of perfect foresight. Auerbach and Kotlikoff (1987) use this

framework in a dynamic fiscal policy model with exogenous retirement to examine questions concerning the announcement’s effects on consumption and

savings of tax reforms within a social security system. They find that early

announcement can significantly alter economic behavior in periods before

new tax legislation is enacted, in most cases reversing the intended tax policy goals. In the same framework, Huang, Imrohoro  ̇ glu, and Sargent (1997)  ̆

analyze a pre-announced transition from an unfunded to a fully funded social security system, analyzing the implications of the announcement on consumption and saving in the short as well as in the medium run.

In the second branch of the literature, researchers focus on the anticipation effects of future possible policy shifts and deal with the uncertainty

about timing and measures adopted to reform the system, without the perfect foresight assumption. Drazen and Helpman (1990) analyze inflationary

effects of an anticipated expansionary monetary policy in the presence of a

clearly unsustainable fiscal deficit. Bütler (1999) pointed out how the two di4
mensions of uncertainty (the content and the timing of a reform) could affect

consumption and saving household behavior within a pay-as-you-go public

pension system, especially when the pension system is no longer financially

viable. Rossi and Visco (1995) provided an empirical study on 1991 crosssection data finding that younger cohorts clearly show an anticipation of a

possible pension reform in their saving decisions.

This paper aims to contribute to the first branch of literature, following

the perfect foresight approach. It focuses on retirement instead of consumption and saving behavior, and models the retirement decision, making it

endogenous. This feature allows the study of the impact of pension reforms

when they are enacted with a delay after the formal announcement, since

individuals can optimally choose a new retirement age at announcement. In

fact, the delay opens a window for a short time when workers are able to

change their retirement date planned under the existing system.

The paper extends Auerbach and Kotlikoff’s (1987) framework to an endogenous retirement decision and introduces uncertainty in agents’ life span.

Using an overlapping generations model, the paper analyzes the effects on

aggregate labor supply and on pensions’ expenditure of the delay between

the announcement and the enactment of the pension system reform of 1992

within the Italian PAYG social security system. Three sources of agents’

heterogeneity are introduced in order to capture empirical differences in retirement behaviors: gender, age efficiency profile, and health endowment.

The model is calibrated to Italian data and then simulated with the announcement of an increase in the eligibility age for normal retirement from

60 to 65 for men and from 55 to 60 for women.

The paper finds that announcing such a reform produces largely undesirable effects, in the short term, on key macroaggregates that contrast with

the reform’s intended objectives of decreasing pensions’ expenditure and increasing the average retirement age. The model predicts that some workers

who would otherwise have retired later decide to retire earlier, thus causing

employment to fall. It also shows that almost all the transitional generations

face a loss in welfare if the reform is announced early. Consistent with the

data, the paper shows that the Italian pension system reform of 1992 did not

produce the intended reduction in social security spending.

The paper is organized as follows. Section 2 introduces the macroeconomic model. Then, a brief review of the public pension system existing before the reform announcement is presented in Section 3, which also describes

the computation of pension benefits. Section 4 presents equilibrium defini5
tion for the economy and calibration of the model to Italian data, followed

by a description of the results of the announcement simulation and welfare

analysis in Section 5. Finally, concluding remarks are given in Section 6.

2 The model economy

Italy is modeled like a small open economy populated by overlapping generations à la Auerbach and Kotlikoff (1987) and an infinitely lived government.

The agents are rational, forward-looking, and face no liquidity constraints.

They are born at age a = 1, as 25-year-old people, and live at most until the

age a = T = 65, as 89-year-old people, facing an exogenous mortality profile.

One model period is equivalent to one year. For any variable, a subscript t

is for calendar time and superscript a is for age.

Individuals are considered as heterogeneous with respect to gender g ∈

{m, f}, namely male and female, and conditional on their gender are heterogeneous with respect to three dimensions. The first one is represented by

a gender-specific mortality profile ψa,g. As a second source of heterogeneity,

we introduce εa,g, which represents an age and gender-specific productivity

parameter. It is assumed to be constant over time and exogenously taken

from an age-efficiency profile computed as in Hansen (1993). Individuals are

endowed with one unit of time per period that can be transformed into one

unit of leisure or εa,g unit of labor l

a

t . Finally, individuals within the same

generation and gender are born as ex-ante heterogeneous with respect to their

attitude to work, represented by a fixed preference parameter θ, following a

known gender-specific distribution Θg, as it will be specified in the following.

In every period, supplying labor agents receive l

a

t εa,gwt income, where

wt is the real wage per efficiency unit of labor. They can also invest in two

types of assets: physical capital, ka

t , and government bonds, bat , which deliver

a capital income (ka

t +bat )rt in each period. Agents pay taxes τ t, proportional

to their labor income, l

a

t εa,gwt, to contribute to the pension system (payroll

taxes) and collect pension benefits when retired.

They live two stages in their life, labeled as “not eligible” (ne) and “eligible” (e) for retirement, that also depend on their gender g. During the

first stage of life (a = 1, ..., ag

e, where age is the eligibility age for normal

retirement depending on the gender g), the consumer chooses the time allocation between labor and leisure, and decides how much of her income to

6
allocate between consumption and saving. The second stage of the life (the

last T −(ag

e+1) years, a = age+1, ..., T) is characterized by the choice between

labor and retirement.

Agents with a different gender do not make joint retirement decisions, and

each agent belongs to a one-headed household, for simplicity. There exists a

strong empirical evidence by Blau (1998) and Blau and Gilleskie (2001) that

older married U.S. couples enjoy spending leisure time together, and thus,

jointly decide the optimal retirement age. We abstract from the possibility

of a joint retirement decision for two main reasons. First, consistent with the

goal of the paper, gender heterogeneity is mainly introduced in the model

in order to capture differences in pension rules for men and women within

the Italian PAYG system. Second, we do not observe the same U.S. empirical features for Italian households. Weak empirical evidence is provided

by Colombino et al. (2003): Italian males and females who are approaching

retirement show no strong similarities.

Retirement is considered an absorbing state and a complete withdrawal

from the labor market. We set the eligibility age for retirement to be am

e =

35 (60-year-old) and af

e = 30 (55-year-old) to match the features of the

existing Italian public pension system, as it will be specified in Section 3. A

reform that changes the eligibility age for retirement affects the length of the

two stages of the consumer’s life, and also, the total amount of the pension

benefits the individual can get from the eligibility age for retirement, ag

e, until

the end of the life, T.

The government provides a public pension system: it collects payroll taxes

from workers and pays pensions to eligible individuals. In order to maintain

the balanced budget the government also sets the eligibility age for retirement

ag

e, considered as not mandatory in the model. In the real world, governments

cannot determine directly workers’ retirement age by mandatory retirement

but they can only create incentives to drive the retirement timing decision.

2.1 Demographics

At each date t, a cohort of measure μN1

t of gender g = m and one of measure

(1−μ)N1

t of gender g = f individuals is born and lives at most during periods

t, t + 1, ..., t + T.

They face a certain mortality risk dependent on the age a and gender g,

1 − ψa,g, where ψa,g represents the gender-specific probability of being alive

7
at age a until age a + 1, conditional on having been alive at age a − 1, so

that Na+1,g

t+1 = ψa,gNa

t .

The unconditional stationary4 probability that a person born at t − a

survives to age a is given by Ψa,g = Ta

j=1

ψj,g such that the population of

m and f individuals moves according with the survival probabilities in the

following way:

Na,m

t = Ψa,mμN1

t−a

Na,f

t = Ψa,f (1 − μ)N1

t−a

(1)

The total population of age a at time t is defined by:

Na

t = Na,m

t + Na,ft (2)

Newborn individuals enter the labor market immediately after they are born;

hence, defining a population growth rate actually determines the growth rate

of potential workers. Assume that γt is the path of the population growth

rate and Gt = (1 + γt) is the growth factor, the law of motion of the birth of

potential workers is N1

t = Tt

h=1 Gh N1

0 .

The fraction of population of age a and gender g at time t is represented

by:

f a,g

t = Ψa,g Tt−a

h=1 Gh

ST

i=0 Ψi,g Tt−ih=1 Gh

(3)

While the total population alive of age a and gender g at time t is given by:

Na,g

t = Ψa,g \

t−a

h=1

GhN1

0 (4)

The total population at time t is a sum over all the live age generations:

Nt = [

f

g=m

[

T

a=1

Na,g

t (5)

where Na

t is the number of individuals of age a and gender g alive at time t,

according with (4).

4 I abstract from demographic transition by assuming a stationary survival probability

given that this is not relevant for the short-run focus of this paper.

8
2.1.1 Working population aggregates

Total employment5 Lt, as the total number of agents working at any time t,

is obtained aggregating over all the population of different ages a and genders

g that either are not eligible to retire (a ≤ ag

e) or, if eligible (a>age), have

chosen to keep working:

Lt = [

f

g=m

ag

[e

j=1

Nj,g

t + [

f

g=m

[

T

j=ag

e+1

(1 − φj,g

t )Nj,gt (6)

where φj,g

t accounts for the fraction of individuals of any age j>ag

e and gender g = m, f that are retired after the eligibility age ag

e and is endogenously

determined in the model once agents decide the optimal retirement age a∗

r.

Individuals are not allowed to retire earlier than this age, no matter how

many years they have worked.

The total employment rate et is derived as the total employment to the

total population ratio, et = Lt/Nt.

Other aggregates can be useful in order to study the dynamics of the oldage working population after the age a ≥ min(am

e , afe ). We define the total

employment of workers 55 and over at time t as the sum over the working

population of age a ≥ 30 = af

e :

L30

t =

am

[e

j=30

Nj,m

t + Naf

e ,m

t + [

f

g=m

[

T

j=ag

e+1

(1 − φj,g

t )Nj,gt (7)

The employment-to-population ratio or employment rate of 55-and-older

workers at any time t is then obtained as follows:

e30

t = L30t !N30t (8)

normalizing the working population of any age a ≥ 30 = af

e , L30, over the

total population of the same age:

N30

t = [

T

j=30

Nj

t (9)

5Total employment is computed under the assumption that labor factor is not mobile

and is a pure demographic variable abstracting from labor supply measure in efficiency

units.

9
2.2 Preferences

Time t preferences for an age a and gender g individual are given by the

following utility function:

Uθ(ca

t , lat ) = log cat + α log(1 − l

a

t ) − dθ (10)

where ca

t , (1 − l

a

t ) are the age a consumer’s consumption and leisure and α

is the leisure preference parameter. θ is the heterogeneity parameter, drawn

from a gender-specific known distribution Θg, and accounts for different attitudes with respect to work or different health conditions, as gender and

individual specific (see Phelan and Rust, 1997). This source of heterogeneity is able to capture the empirical fact that not all the agents within the

same cohort decide to retire at the same age. The d is an indicator function,

defined as follows:

d =

 1

0

if the individual works

if the individual doesn’t work

⇐⇒ l

a

t > 0

⇐⇒ l

a

t = 0

At any time t gender g newborn consumer maximizes her lifetime utility

function over the two stages, ne and e, and faces a discrete choice problem,

“retire” or “keep working”, after the eligibility age:

max

d,ar,cj

t ,ljt ,sj

t+1

[

j∈A

βj−1Ψj,g(log c

j

t+j−1 + α log(1 − l

j

t+j−1) − dθ) (11)

the parameter β ∈ (0, 1) is a discount factor capturing intertemporal preferences. The maximization is subject to two kinds of constraint.

1) The eligibility age constraint, depending on gender g ∈ {m, f}, that

is:

ar ≥ ag

e (12)

which means that retirement age cannot be less than the eligibility age and

at any age j ∈ A = 1, ..., T.

2) The budget constraint:

s1

t = 0 ∀t

s

j

t+1 = s

j−1

t Rt + d(1 − τ t)εj,gwtl

j

t + (1 − d)Pjt − c

j

t ∀t

sT

t = 0 ∀t

(13)

10
where s

j

t is the asset holding by an age j individual at the end of any time t

and R(·)=1+ r(·) is the gross return factor from the previous period asset

holding. Agents can either invest their savings in physical capital, kj

t , and

government bonds, b

j

t so, at any time t, s

j

t = kjt + b

j

t. Income from labor in

efficiency units is represented by εj,gwtl

j

t, net of payroll taxes τ t, while Pjt

stands for the pension benefits. The model abstracts from the possibility of

voluntary bequest, hence s1

t = sTt = 0.

Given their gender g, agents choose the optimal retirement age, a∗

r, and

the indicator function d, comparing different levels of utility associated with

the budget constraints, depending on different retirement ages such that the

consumption and leisure are the argmax of the utility function [11].

3 The pension system prior to the reform

The main features of the existing public pension system in the early 1990s

were established in 1969. The system’s resources come mainly from the

employers’ and employees’ contributions (payroll taxes) distributed in an

uneven way between the two entities.

In 1992, an employee was paying the 30.7 percent of the total payroll

taxes and a further 7.4 percent to a severance pay fund ("Trattamento di

Fine Rapporto" or TFR). These contributions were retained by the employer

and built up in a fund offering a legal rate of return (1.5 percent plus 75

percent of the annual inflation rate) and providing a lump-sum benefit upon

employee retirement. The employer paid the remaining 69.3 percent of the

total contributions to the system. The system was set as a pay-as-yougo mainly characterized by two kinds of eligibility requirements in order to

receive pension benefits:

1. eligibility requirements for normal retirement (old-age pension retirement): being 60 years old for men and 55 years old for women and having

worked for at least 15 years.

2. eligibility requirements for early retirement (seniority pension retirement): having worked for at least 35 years as a private employee or 20 years

as a public employee. The age requirement is irrelevant in this case, and this

option clearly represents an incentive to retire earlier than the minimum age

set for the old-age retirement.

11
When eligible, the individual is entitled to pension benefits calculated as

a percentage of the last five years (moving) average labor earnings, as will

be shown in detail in the following.

3.1 Modeling pension benefits

We model the pension rules for normal (old-age) retirement ones as gender

dependent, reflecting the law. However, we do not account for TFR contributions and the relative lump-sum benefit when retired since Brugiavini

(1999) finds that this kind of benefit does not alter dynamic incentives for

the retirement decision. Pension benefits are computed as they were drawn

in the Italian public pension system prior to the announcement of the reform

in 1992.

The government designs those benefits through a set of policy rules {b,

ag

e, ν}. The benefits are represented by a fixed percentage of the average

labor earnings over an averaging period ν at any time t for each individual

of age a. The consumer plans to retire after reaching the eligibility age ag

e,

choosing an optimal retirement age a∗

r and, in doing so, decides the level of

pension benefits Pa

t , which is related to the earnings by a replacement rate b

in the following way:

Pa

t =

 0

b Aa

t

if a<a∗

r

if a ≥ a∗

r

(14)

where t represents the calendar date t, at which the individual plans to retire

(such that a = a∗

r), and Aa

t is the average labor earning at time t = t, over

an averaging period ν:

Aa

t = 1

ν

a

[r−1

j=ar−1−ν

εj,gwt l

j

t+j−ar (15)

At any time t > t and age a>a∗

r the individual faces the same pension benefits Pa

t as a function of her choice variable a∗r, the optimal retirement age,

and of government policy parameters {ag

e, ν}, through the average earning

function Aa

t (a∗

r ≥ age, ν). These benefits are not updated through an indexation rule to a growth rate of wages. Stationary wages are fixed and given in a

partial-equilibrium approach, and this feature makes indexation useless. As

12
for the economy’s transition after the reform, we are interested in analyzing

the impact of the 1992 reform announcement in the short run thus indexation

becomes less appealing.

The parameter b is the policy rule through which the government decides

the replacement rate and is defined as b = f ixrate ∗ a∗

r, where f ixrate was

set at 2 percent in Italy, in 1992, and a∗

r here accounts for the number of

years worked.

3.2 The government

As mentioned above, the infinitely lived government in this economy only

provides a public pension system, in a PAYG form, facing a public pension

system’s budget at each time t. The government collects payroll taxes from

workers, pays pensions to eligible individuals who have decided to retire,

and provides a full confiscation of (involuntary) bequests, i.e. collects a 100

percent tax on bequests. The resulting public pension system debt, Bt, in

period t is determined by:

Bt = Rt−1Bt−1 + Pt − Tt (16)

where Pt represents the total pensions’ expenditure, at time t:

Pt = [

f

g=m

[

T

j=ae+1

φj,g

t Pjt Nj,gt (17)

that accounts for the fraction φj,g

t of the population of each gender alive of any

age j who decide to retire after the eligibility age ag

e and the corresponding

population at those ages. Conversely, Tt represents the total amount of

contributions to the system, collected at time t, as a proportion τt of labor

earnings from live individuals that are not eligible for retirement (a ≤ ag

e),

and from the fraction (1−φj,g

t ) of those who keep working after the eligibility

age (a∗

r > age). Accidental bequests are collected from individuals whose

assets available at the beginning of time t are s

j−1

t , and who do not survive

13
at time t.

Tt = τ t

[

f

g=m

[ae

j=1

εj,gwt l

j

tNj,gt + τ t

[

f

g=m

[

T

j=ae+1

(1 − φj,g

t )εj,gwt l

j

tNj,gt

+Rt

[

f

g=m

[

T

j=1

(1 − ψj,g)s

j−1

t Nj−1,g

t−1 (18)

Given an initial level of the pension system debt, the level of the tax

rate τ t is endogenously determined in the model (in order to maintain the

budget in balance) given the population structure as a function of the survival

probability distribution and the fraction of individuals who decide to retire,

after solving the maximization problem (11). The boundary constraint that

government debt cannot grow faster than the interest rate, in the long run,

is imposed as follows:

[∞

t=0 %

\

t

s=0

R−1

t

&

Tt = [∞

t=0 %

\

t

s=0

R−1

t

&

Pt + B0 (19)

where B0 represents the pension system as initial level of debt.

4 Equilibrium definition

A competitive equilibrium for this economy is: a set of allocations {c

a,g

t , l

a,g

t ,

s

a,g

t+1}, a retirement age ag

r, a decision rule d, and a set of government policies

{f ixrate, ag

e, ν, τ t,Bt} s.t.,

for each a ∈ A, g ∈ {m, f}, and θ is distributed according to Θg :

1. Given an exogenous path for the population growth γt and an exogenous profile for the mortality ψj,g, endogenous population dynamics are

generated by (5);

2. Given the prices rt and wt and the government policy and the initial

debt B1, the allocations, the decision rule, and ag

r solve the household’s

maximization problem (11);

14
3. Allocations and government policy satisfy the government budget constraint as in (16), at each date t;

The steady state is considered as a particular case of the equilibrium path

defined in the previous points, where the population grows at a constant rate

and aggregate variables grow at a fixed rate.

4.1 Calibration and initial steady state

In order to solve numerically for an initial steady state, we calibrate the model

to Italian data before the 1992 announcement of public pension reform, at

the beginning of 1992. We pick the set of government policy parameters

{f ixrate, ag

e, v} from the set of rules defined for the normal retirement

(old-age retirement), as described in Section 3. Then, given an exogenous

mortality and age-efficiency profile, we calibrate the remaining parameters

to match the following main Italian facts:

i) The demographic structure, in accordance with a given dependency ratio

(the ratio of workers entitled to public pension benefits to those paying

payroll taxes);

ii) The key retirement ages and retirement behaviors;

iii) The capital/output ratio;

iv) Hours worked.

Facts i) and ii) are crucial for the focus of the paper and they determine

how household retirement behavior is affected by the particular pension system. All parameters’ values are summarized in the following Table 1a and

1b.

15
Table 1a: Exogenous parameters

Param. Values Definition

μ 0.495 male population measure (25-year-old) in 1992

ψa,g gender-specific mortality profile (1991)

f ixrate 2% rate to transform years worked into replacement rate in 1992

v 5 averaging period for pensionable income in 1992

τ 0.247 payroll taxes in 1992

am

e 35 eligibility age for men in 1992

af

e 30 eligibility age for women in 1992

T 65 life span

r 0.062 gross interest rate in 1992 (Hviding and Mérette, 1998)

a,g Italian SHIW 1980-91 following Hansen (1993) algorithm

Table 1b: Parameters calibrated to pre-reform data

Param. Values Facts to match

β 0.984 average age-consumption profile

α 1.69 average (men and women) weekly hours worked (32.1)

γ 0.0056 dependency ratio (36.4%)

θ different retirement ages

Θg gender-specific hazard function (SHIW 1980-1991)

Note: SHIW=Survey on Household Income and Wealth.

16
4.1.1 Demographic structure

The demographic structure is the result of three leading parameters:

• γt, which determines the growth path of the population as a mixed

combination of fertility and immigration profiles. The model doesn’t distinguish between these two components because the impact of net immigration

flows on announcement effects of public pension system changes is weak. The

great majority of immigrants are between 20 and 40 years old in many OECD

countries. We pick this parameter in order to match, in the initial steady

state, the old dependency ratio as it was at the beginning of 1992 (0.364);

• μ, which defines the fraction of the population of gender g = m at

the birth. We pick it to match the average gender distribution of 25-year-old

individuals within the Italian population prior to 1992;

• ψa,g, which states the age-dependent gender-specific conditional survival probability. We take it according with the mortality profiles issued by

ISTAT (Italian National Institute of Statistics) as the population scenarios

for the 1990s.

4.1.2 Preference parameters and factor prices

The coefficient α that accounts for the individual’s preference for leisure is

picked in order to match the observed average weekly hours worked for male

population at the beginning of 1992. This drives the parameter to a value of

1.69 to account for 32.1 average hours worked per week.

We get a value of 0.984 for the rate of time preference β used to discount

utility over time, taking in consideration the average age consumption profile

over the 20 years prior to the announcement and the mortality profile, for a

given empirically plausible capital-to-output ratio (3.01).

Finally, we set the exogenous real gross interest rate r to be 0.062 and the

real wage rate w per efficiency unit to be 4.5 in the stationary equilibrium

of the economy. The stationary age-efficiency profile represented by ε is

computed using the Hansen (1993) algorithm on an Italian 10-year sample,

1983-1992, provided by the Bank of Italy’s Survey on Household Income and

Wealth (SHIW).

17
4.1.3 The parameter θ

The parameter θ accounts for gender- and individual-specific conditions (e.g.:

health conditions) that make the labor supply decision differently costly for

agents within the same cohort. Individuals born at the same time t but with

different θ choose different optimal retirement ages ag∗

r , as observed in the

data.

We first deal with the calibration of θ endowment that makes it optimal

for individuals to retire at the different ages observed in Italy during the prereform period. Hence, we assign a value to θ ∈ ?+ such that men (g = m)

within the same cohort decide to retire at different ages: am∗ r ∈ {35, ..., 45}

and so do women (g = f), af∗

r ∈ {30, ..., 45}6. The model deals with 27

types of agents so θ is indexed to the gender g = m, f and to the different

retirement ages ag∗

r .

Secondly, we distribute these 27 types of agent among the model population according with a distribution Θg that matches the model’s stationary

fraction of the retired workers at each age of both genders, hg,a, to actual

hazard functions for men (g = m) and women (g = f). The actual and the

model stationary hazard functions are displayed in Fig. 5, for both genders.

These functions are computed as the ratio between the number of eligible

individuals of a certain age who retire and the number of workers of the

same age. The actual hazard function is computed using the 10-year sample

(1983-92) provided by the Bank of Italy’s SHIW. The men’s hazard appears

to be more regular and well represented by the four-peak calibrated one,

while the females’ hazard shows a less regular behavior.

4.1.4 Pension benefits

In order to define the public pension system described in Section 3 we pick

some parameters {f ixrate, ag

e, ν,τ t} as the government policy rules and we

set the initial level of the public pension system debt B1 in order to match

the one in 1992.

6We assume that all the population is retired when 70 years old (a = 45 in the model),

according to the empirical cumulative distribution function by Brugiavini and Peracchi

(2000).

18
The eligibility age for old-age pension retirement am

e is chosen to be 35

(as a 60-year-old individual, given the assumption of agents born as a 25-

year-old) and af

e is chosen to be 30 (as a 55-year-old individual).

The averaging period ν that transforms the cumulative income into pensionable income is set to five so the pensionable income is obtained from a

five-year (moving) average labor earning.

Finally, the coefficient applied to the number of years worked in order to

get the final replacement rate, f ixrate, takes the value of 2 percent.

4.2 Computational insights

To solve the model and conduct our experiment, we adopt the following procedure. First, we compute the decision rules in the presence of a stationary

unfunded public pension system, as described in Section 3. For given r and

w, the algorithm solves for the equilibrium conditions such that consumers

maximize their expected utility, choose an optimal retirement age a∗

r, and

the stationary government budget equation is satisfied at each time t.

Second, using the resulting decision rules, we analyze the impact of the

experiment of announcing a future raise of the eligibility age by five years.

On the basis of those decision rules, agents have a certain amount of assets

at any point t in the calendar time and at any age a, consistent with an

optimal retirement age a∗

r, chosen facing the existing eligibility age (age ∈

{35, 30}). The announcement of a future raise in the eligibility age in a

perfect foresight environment induces agents to solve again the maximization

problem over their remaining life with new eligibility age constraints and

given a certain asset accumulation. Furthermore, the fraction (1 − φj,g

t ) of

workers matching the current pension system eligibility age at time t can

decide whether to retire immediately, after the announcement (i.e. changing

their optimal retirement age), or to continue to work undergoing the new

retirement rules.

19
5 Experiment: simulation of the reform announcement

Before a certain point in time t =0= tR, the economy is assumed to be in

the initial stationary equilibrium described in Section 4. In September 1992,

that is the t = 0, the Italian government announced the intention to pass,

for (September) 1993, that is t + 1, a pension reform that will change the

eligibility age for normal retirement ag

e, raising it by five periods (years) for

both genders m and f.

Let aR,g

e define the new eligibility age announced at time t =0= tR, such

that now aR,m

e = 40 and aR,fe = 35.

The change will occur after t + 1, and the eligibility age will remain

constant at aR,g

e through a transition period and forever. For simplicity,

we assume that the reform will interest all agents, ignoring the fact that

the eligibility age does not affect the retirement decision of those who have

already worked for 35 periods (years) or more, and could strike the early

retirement option, as the model mainly considers the pension system rules

for normal (old-age) retirement.7 As in Bütler (1999), we abstract from

dealing with any sort of grandfathering rights for the aged workers. This

choice is mainly related to the difficulty to model different expectations of

the elderly with respect to the announcement8, and is equivalent to set those

expectations to the worst possible scenario: the sudden five-period raise in

the eligibility age. The perspective of a future reform that does not account

for some degree of preserving benefits claims for the elderly actually implies

a transition that shifts the burden from the current young generation to the

current old one.

The transition is characterized by the fact that consumers born between

−T +t and 0 (and still alive at t = 0) were surprised by the announcement at

that date, and they planned the future on the basis of a different constraint

set, represented by the government policy parameter{ag

e}. Now they solve

their maximization problem starting in t = 0, taking their level of assets,

sa−1

t=0 , and cumulative income, Aa

t=0, as given from the past. Two main issues

are interesting to analyze: the reaction of "surprised" people, born between

7Furthermore, the Italian government suspended the possibility to apply for early retirement from September 1992 until December 1993.

8The Septemeber 1992 announcement did not specify the treatment of the different

cohorts within the Italian working population.

20
−T + t and 0, at time t = 0 to the announcement (what we defined as the

"announcement effect") and the transition of the economy in the short run.

The analysis mainly focuses on the short-term effect because, during 1995,

the Italian pension system was amended with a new reform. The number of

surprised individuals at t = 0 is given by those born between −T + t and 0:

Nt=0 = [

f

g=m

−

[

T +t

j=1

N0,g

t−j (20)

The announcement influences live agents whose optimal age of retirement a∗

r,

based on the previous system’s eligibility age constraint, lies in the interval

{ag

e, ..., aR,ge }.

Those agents can be divided into three sets, represented by the three

regions in Fig. 3, depending on their age a and on their optimal age of

retirement ag∗

r . When the announcement is given, each agent, belonging to

each of those sets, solves a maximization problem characterizing the discrete

choice to "retire immediately" or "keep working" (or, i.e., retire under the

old system or under the new system). We discuss the details of the problem

in the appendix.

5.1 Results

The simulation of the 1992 announcement produces large effects in the economy affecting the individuals’ retirement decisions. Fig. 6 and Table 2 show

the short-term impact of the simulation on the employment and pension system aggregates. The announcement generates an increase in the fraction of

total workers retired (h) between time t and time t+1. This fraction increases

from 0.344 to 0.361, between time t = 0 (1992) and t +1=1 (1993).

In the model, agents can move from the employed state to the unemployed

one only if they retire. A predicted increase in the retirement rate leads to a

predicted drop in the total employment rate, ∆e, as shown in Table 2.

Tables 3a and 3b show how the increase in the fraction of retired workers is

distributed among the male (g = m) and female (g = f) populations and the

age groups that changed their retirement behavior through the model hazard

functions or fractions of retired workers (hg,a). To simplify the presentation,

21
we refer to the calendar age9 instead of model age a when describing the

agents’ retirement behavior after the announcement.

Those males surprised by the announcement who choose a different retirement age are those 60 years old at the time of the announcement in 1992

(61 years old in 1993), whose optimal retirement age is either 61, 62, or 63

years old. If they do not retire at age 60 at the time of the announcement

they will not be allowed to retire at 61, 62, 63 under the new system, but

only after age 65.

A similar problem is faced by individuals age 61 at the time of the announcement (62 years old in 1993), whose optimal retirement age is either 62

or 63, and those 62 years old at the time of the announcement (63 years old in

1993), whose optimal retirement age is 63. Individuals age 60 at the time of

the announcement, planning to retire at 64, do not retire immediately since

the result of the optimization problem still makes them better off retiring at

65 instead of 60.

A comparable mechanism can explain the retirement behavior of the females.

Because of the increase in the retired population, the model predicts a

transition characterized by a drop in total employment of workers ages 55

and older and an increase in the pensions’ expenditure. The drop in the

number of 55-and-older workers, ∆L30, between time t and time t + 1 10, is

able to explain roughly 75 percent of the actual drop in the number of 55-

and-older workers in 1992-93. Because of it, the model predicts a drop in the

employment rate of 55-and-older workers, ∆e30, of 3.88 percentage points11,

able to explain 77 percent of the observed one. The model also generates

predictions that almost replicate the observed dynamics for the employment

9That is the age counting from the birth rather than from the entry in the model.

Agents enter in the model only when they are 25 years old.

10The reform’s timing and its effect on aggregate employment data overlap two years,

1992 and 1993, so I compare model predictions between t and t + 1 with these two years’

data.

11We conduct a sensitivity analysis of the simulation results to different levels of individuals preference for leisure. The range of the parameter values considered in the analysis is

[1.69, 1.3]. We find that if α falls to 1.3, the drop in employment for workers 55 and older,

∆e30, falls by 27.5 percent, from 3.88 percentage points to 2.81 percentage points, still

explaining 56 percent of the actual drop. A value of α equal to 1.3 implies an unrealistic

measure for the average number of hours worked per week: 48. For this reason we do not

try for values less than 1.3. Even with a very low preference parameter for leisure the

model still predicts a relevant effect of the reform’s early announcement.

22
rate for men and women ages 55 and older (Fig. 7).

Employment dynamics, though, were highly affected by the negative economic downturn that characterized the Italian economy in 1992. The downturn probably hit all the employment age bands but, as we mentioned, the

observed drop was concentrated on 55-and-older workers. The model’s goal

is to explain how the announcement of a future increase in the eligibility age

for retirement can account for the difference between the drop in employment

of those 55 and older and the other age bands’ drops, shown in Fig. 2. It

ends up, instead, explaining the great majority of the employment dynamics

for the elderly.

Consequently, the predicted increase in pensions’ expenditure (∆P/P)

in 1992-1993, determined by the increased fraction φ of individuals retired

after the eligibility age, results very high. The increase accounts for about

83 percent of the actual one, while the business cycle and inflation were

among the main factors responsible for such an increase.12 Many workers,

for example, were forced by their employers to retire early because of the

recession, not because of the reform announcement.

The main reason why the simulated announcement can create a larger effect on employment comes from the model’s public pension rules. As already

mentioned, the model’s public pension rules do not account for the possibility

of retiring early with a seniority pension. The announcement didn’t actually

affect the retirement decision of individuals who had already worked for more

than 35 years (seniority pension requirements), no matter their age. Those

individuals were not affected by a possible five-year increase in the eligibility

age for old-age retirement but could have been among the ones forced to

retire early because of the business cycle.

12The model does not account either for inflation or for the business cycle.

23
Table 2: Simulation of the announcement of a five-year increase in the

eligibility age for normal retirement: macroeconomic effects

Variable change Data (1992-1993) Model [1992-1993]

h (total fraction of retired workers) 0.344 0.361

∆L30 (number of workers, in thousands) -361.83 -270.52

∆e30 (empl. rate 55 and older) -5.04 -3.88

∆e30,m(empl. rate 55 and older, males) -6.72 -4.98

∆e30,f (empl. rate 55 and older, females) -2.22 -1.63

∆e (total empl. rate) -2.55 -0.90

∆P!P (%) (pensions’ expenditure) 9.87 8.25

24
Table 3: Change fraction of retired workers by age group and gender

(ha,g) in the model: announcement effect

g = m (males)

1992 1993

h35(60 year old) 0.61 0.61

h36(61 year old) 0.40 0.56

h37(62 year old) 0.39 0.56

h38(63 year old) 0.20 0.29

h39(64 year old) 0.21 0.21

h40(65 year old) 0.45 0.45

h41(66 year old) 0.37 0.37

h42(67 year old) 0.41 0.41

h43(68 year old) 0.32 0.32

h44(69 year old) 0.41 0.41

h45(70 year old) 1 1

g = f (females)

1992 1993

h30(55 year old) 0.29 0.29

h31(56 year old) 0.28 0.48

h32(57 year old) 0.19 0.29

h33(58 year old) 0.18 0.31

h34(59 year old) 0.16 0.16

h35(60 year old) 0.43 0.43

h36(61 year old) 0.20 0.20

h37(62 year old) 0.16 0.16

h38(63 year old) 0.21 0.21

h39(64 year old) 0.16 0.16

h40(65 year old) 0.32 0.32

h41(66 year old) 0.15 0.15

h42(67 year old) 0.14 0.14

h43(68 year old) 0.28 0.28

h44(69 year old) 0.3 0.3

h45(70 year old) 1 1

25
5.1.1 Welfare analysis

In this section we discuss the implications of an early announcement of the

Italian reform for the intergenerational redistribution of welfare during the

transition. The reform per se alters the utility level of each cohort, alive at

the time of the announcement, since they made retirement plans conditional

on the previous pension system.

We compare welfare gains and losses for transitional generations when the

reform is immediately enacted (benchmark case) with the ones that appear

when the reform is announced in advance (preannounced case). In order to

make this comparison, we measure welfare gains and losses as the fraction

ζ of the full lifetime resources needed under the original pension system to

generate the same level of lifetime utility achieved with the new system (i.e.

new eligibility age). Under the hypothesis of a homothetic utility function,

ζ is defined as follows:

[

T

j=a

βj−1Ψj,gu(ζc

j

t+j−1, ζ(1 − l

j

t+j−1)) = ue (21)

ζ =

ue

u

 (22)

where u and ue are, respectively, the level of lifetime utility under the current

system and the new system.

We take two interesting types of agents to analyze welfare effects during

the transition: agents whose θ type makes them choose as optimal retirement

age ag∗

r = {35, 40} and whose gender is g = m13. The mechanics driving the

welfare outcomes of these two agent types can be easily extended to others

whose optimal retirement age is:

am∗

r ∈ {am∗r : am∗r = 36, ..., 39} ∪ {am∗r : am∗r = 41, ..., 50} (23)

Fig. 8 and Fig. 9 report the findings of the analysis for agents whose optimal

retirement age is am∗ r = {35, 40} (60 and 65 years old). They display, on the

vertical axis, the measure of the welfare gains and losses, comparing the

13Symmetrically we can consider the cases of a gender g = f agent whose optimal

retirement age on the basis of the θ type is af∗

r = {30, 35}.

26
benchmark case of an immediate reform that raises the eligibility age by five

years (dashed line) with the case of the same reform (five-year increase in the

eligibility age) but preannounced and enacted with a one-year delay (solid

line).

Firstly, with a few exceptions, the announcement (dashed line) makes the

transitional generations worse off. Agents whose age allows them to retire

immediately are the only ones made better off by the early announcement.

They can benefit, in fact, from a “time window” in which to decide whether

to enter into the new system or not.

Fig. 8 displays this mechanism for the agent type planning to retire at

am∗ r = 35 (60 years old) under the existing system. This agent type is hit

the most by the reform with respect to others whose optimal retirement age

is am∗ r ∈ {36, ..., 39}, and is made even worse off if the reform is announced

early. As we said, all the generations are then made worse off by the announcement, except for the agents whose age allows them to retire at the

time of the announcement: a = 35 (60 years old) in t = 0 (1992). This

cohort is indifferent when the reform is announced early (solid line), while it

would be worse off in the case of an immediate and non-preannounced reform

(dashed line). In the latter case, in fact, they cannot retire at age a = 35

(60 years old) in t = 0 (1992), as planned, since an immediate enactment of

a new retirement age would not allow them to retire earlier than a = 40 (65

years old).

For the other generations, which cannot retire at the time of the announcement but whose optimal retirement age was am∗ r = 35 (60 years old),

Fig. 8 displays two driving forces, affecting the welfare outcomes:

1. As mentioned in the previous section, after the announcement, some

cohorts decided to retire earlier than the planned age. This drop in

employment boosts payroll taxes for the working generations during

the transition, due to the increase in pensions’ expenditure.

2. The second force that directly reduces the agents’ welfare is the disutility of working five years more than the optimal decided under the

previous system. Based on that optimal retirement age, in fact, workers

decided (depending on the generation) their asset accumulation.

While the first effect on the life-time utility of the reform reduces welfare

only if the reform is preannounced, this second effect reduces welfare in both

the benchmark (immediate) case and the preannounced case.

27
The five-year increase in the eligibility age boosts the welfare of agents

whose optimal retirement age am∗ r was already 40 (65 years old) in case the

reform is immediately enacted (dashed line, Fig. 9). The reason is the

dampening effect on payroll taxes. On the contrary, if the reform is enacted

with a delay (preannounced, solid line in Fig. 9), the same agents face a

welfare loss due to the increase in payroll taxes. As already mentioned, the

latter effect is caused by the fact that many of those aged a = 35 (60 years

old) in t = 0 (1992), whose optimal retirement age under the previous system

was am∗ r ∈ {36, ..., 39} , retire earlier, at the time of the announcement.

6 Concluding remarks

We develop an overlapping generations model à la Auerbach and Kotlikoff

(1987) with endogenous retirement to analyze the macroeconomic effects of a

preannounced public pension reform of the Italian pay-as-you-go public pension system in 1992. Three sources of ex-ante heterogeneity are introduced

to model the system of incentives designed by the existing public pension

regime: gender, age efficiency profile, and health endowment. These features

capture different retirement behaviors of individuals belonging to the same

cohort but characterized by different gender and individual characteristics,

such as health conditions.

We calibrate the model to Italian data to set the economy at the initial

steady state in 1992 (t = 0). Then, we simulate the announcement in 1992

(t = 0) of a five-period increase in the eligibility age for retirement enacted

with a one-year delay, in 1993 (t = 1).

The delay between the announcement of the reform and its enactment enables eligible individuals to assess how the reform will affect them and choose

an earlier retirement date than they had planned. They need to decide between retiring immediately or keeping working under the new public pension

system, which implies a new eligibility age. Some workers who planned to

retire before this new eligibility age will not be able to do so if they decide

to keep working. After solving their maximization problem with the new

rules, we find that many eligible workers in the model decide to retire at

announcement.

For this reason, the transition to the new pension system is characterized

in the short term by a drop in the employment rate of 55-and-older workers

28
that explains 77 percent of the actual one. The model also predicts a 8.25

percent increase in pensions’ expenditure, which explains 83 percent of the

actual one. Finally, the welfare analysis highlights a loss for almost all the

transitional generations when the reform is announced early.

The main economic message of the paper is that preannounced pension

reforms can deeply affect economic behavior prior to the implementation of

the new policy in the short run as well as in the medium run, because of

the absorbing state of retirement. A given reform announcement can induce

behavioral changes that affect some of the economic gains of the reform itself.

As we showed in the Italian case, the time between the announcement and

the enactment of the new legislation allowed individuals to change their retirement choices. This reduced the intended effect of mitigating the pensions’

expenditure because it increased the number of retired individuals collecting benefits and increased the length of time that participants drew those

benefits.

29
References

[1] Auerbach, A.J., Kotlikoff L.J. (1987), Dynamic Fiscal Policy, Cambridge (MA) Cambridge University Press.

[2] Blau D. (1998), "Labor Force Dynamics of Older Married Couples,"

Journal of Labor Economics, 16 (3), 595-629.

[3] Blau D., and Gilleskie D. B. (2001), Health Insurance and Retirement of

Married Couples, manuscript, University of North Carolina at Chapel

Hill.

[4] Brugiavini A.(1999), "Social Security and Retirement in Italy," in: Gruber J., and D. A. Wise (eds.) Social Security and Retirement around the

World, Chicago University Press, 181-237.

[5] Brugiavini A., and Peracchi F. (2000), Micro Modelling of Retirement

Behavior in Italy, mimeo, NBER International Project on Social Security and Retirement.

[6] Bütler M. (1999), "Anticipation Effects of Looming Public-Pension Reforms," Carnegie-Rochester Conference Series on Public Policy, 50, 119-

159.

[7] Colombino U., Hernæs E., Jia Z., and Strøm S. (2003), Retirement in

Italy and Norway, Memorandum no 10/2003, Department of Economics,

University of Oslo.

[8] Drazen A., and Helpman E. (1990), "Inflationary Consequences of Anticipated Macroeconomics Policies," Review of Economic Studies, 57 (1),

147-164.

[9] Hansen, G. D. (1993), "The Cyclical and Secular Behavior of Labor

Input: Comparing Efficiency Units and Hours Worked," Journal of Applied Econometrics, 8, 71-80.

[10] Huang H., Imrohoroglu S., and Sargent, T. J. (1997), "Two Computations to Fund Social Security," Macroeconomic Dynamics, 1, 7—44.

[11] Hviding K., and Mérette M. (1998), "Macroeconomic Effects of Pension

Reforms in the Context of Aging Populations: Overlapping Generation

30
Model - Simulation for seven Countries," OECD Working Papers no.

201.

[12] Phelan C., and Rust J. (1997), "How Social Security and Medicare Affect

Retirement Behavior in a World with Incomplete Markets," Econometrica 65 (4), 781-831.

[13] Rossi N., and Visco I. (1995), "National Saving and Social Security in

Italy," Ricerche Economiche, 49 (4), 329-357.

31
7 Appendix

7.1 Agents’ maximization problem after the announcement

Model individuals can be divided into three sets in order to analyze the

announcement effect of the 1992 reform on their retirement behavior.

Agents not eligible for retirement at time t = 0 belong to a first set, N1 ≡

{Na,g

t=0 : a<ag

e ∈ {35, 30}, a∗,gr ∈ AR,g}, where a∗,gr and AR,g = {age, ..., aR,ge }.

They optimize over their remaining expected life, conditioned to be alive at

age a, facing a new eligibility age constraint aR,g

e and taking the initial assets

sa−1

t=0 > 0 as given in (13).

max

d,ar,cj

t ,ljt ,sj

t+1

E{

[

T

j=a

βj−1Uθ(c

j

t+j−1, ljt+j−1)} (24)

The maximization is subject to the new eligibility age constraint:

ar ≥ aR,g

e (25)

(retirement age cannot be less than the new announced eligibility age aR,g

e )

and, at any age j ∈ {a, ..., T} with a<ag

e ∈ {35, 30}, to the budget constraint:

s

j−1

t [a∗g

r (θ)] > 0 t = 0

s

j

t+1 = s

j−1

t Rt−1 + d(1 − τ t)εj,gwtl

j

t + (1 − d)Pjt − c

j

t ∀t

sT

t = 0 ∀t

(26)

The second set of the population consists of agents that at time t = 0 are

eligible according to the previous eligibility age, hence N2 ≡ {Na,g

t=0 : ag

e ∈

{35, 30} ≤ a<aR,g

e ∈ {40, 35}, a∗,gr ∈ AR,g}. Those individuals have the

possibility to choose between retiring immediately or keep working. If they

decide to keep working, retirement must be postponed after the new eligibility age aR,g

e . This sort of indivisibility mainly affects the decision of eligible

32
agents (a ≥ ag

e ∈ {35, 30}) in t = 0 whose optimal retirement age, conditional

on their type θ, is a∗,m

r = {36, 37, 38, 39} and a∗,fr = {31, 32, 33, 34}.

14 Those

consumers at age a in t = 0 compare the optimal value functions delivered

by the two options: retire immediately or keep working. Thus, defining preferences recursively, the Bellman equation for the household’s optimization

problem is given by:

Wa(sa−1

t , Aat ) = max{War (sa−1t , Aat=0), Wal (sa−1t , Aat )} (27)

where Aa

t is the cumulative income function used to compute pension benefits,

described in Section 3, and Wa

r represents the value function associated to

the retirement at age a in t = 0. It represents the value function associated to

(aR,g

r )∗ = a if (aR,gr )∗ is defined as the new optimal retirement age (immediate

retirement). Hence:

Wa

r (sa−1t , Aat=0) = max c

j

t ,sj

t+1

{Uθ(c

a

t ) + βE[Wa+1r (sat+1)]} (28)

subject to:

sa−1

t [ag∗

r (θ)] > 0 t = 0

sa

t+1 = sa−1

t Rt−1 + Pa

t − cat ∀t

sT

t = 0 ∀t

(29)

where sa−1

t=0 [ag∗

r (θ)] is the level of the consumer’s asset holding at the end of

age a − 1, taken as given in the maximization problem at the beginning of

age a and time t = 0. This level is conditional on the retirement age ag∗

r (θ),

as a function of the agent type θ, chosen to be optimal under the previous

steady-state pension system.

Wa

l in (27) is the value function associated at time t = 0 to the choice

of keep working and to the new eligibility age constraint aR,g

e ∈ {40, 35}.

If the individual keeps working then the possibility to retire is shifted by

14 In fact, m individuals whose optimal retirement age is a∗

r = 35 are actually not affected

by the announced raise of the eligibility age. If their age is a = ae at t = 0 they retire

immediately as they already planned to do. If, conversely, their age is ae = 35 <a<

aR

e = 40 at t = 0 they are already retired. The same reasoning could be extended to f

individuals.

33
five periods, given the new eligibility age constraint associated to the future

reform. The following value function accounts for this:

Wa

l (sa−1t , Aat ) = max aR

r ≥aR,g

e ,cj

t ,ljt ,sj

t+1

{Uθ(ca

t ) + βE[Wa+1(sat+1, Aa+1t+1 )]} (30)

subject to:

[s

j−1

t !a∗

r(θ)] > 0 t = 0

s

j

t+1 = s

j−1

t Rt−1 + d(1 − τ t)εj,gwtl

j

t + (1 − d)Pjt − c

j

t ∀t

sT

t = 0 ∀t

(31)

where Aa

t , the cumulative income function used to compute the pension benefits, represents a state variable for the consumer optimization problem.

The discrete choice problem characterized by (27) determines the new

fraction φR,g of individuals retired after the eligibility age, or i.e. the retirement rate.

Finally agents belonging to the third set N3 ≡ {Na,g

t=0 : a ≥ aR,g

e ∈

{40, 35}} were not affected by the announcement because either they are

already retired or their optimal retirement age is a∗,g

r ≥ aR,ge .

34
Fig. 1: Pensions’ Expenditure (PE) (% of GDP) - Italy 1980-98.

Source: OECD Social Expenditure Database.

35
Fig. 2: Employment rate broken down in four age bands. Italy 1977-96.

Source: ISTAT.

36
Fig. 3: Employment rate broken down in four age bands (men). Italy 1977-

96.

Source: ISTAT.

37
Fig. 4: Employment rate broken down in four age bands (women). Italy

1977-96.

Source: ISTAT.

38
Fig. 5: Raw hazard function, Italy 1983—92 (men and women).

39
Fig. 6: Total employment of 55-and-older workers (thousand persons): model

prediction and data. Italy 1977-1996.

Source: ISTAT.

40
Fig. 7: Male and female employment rates of 55-and-older workers: model

prediction and data. Italy 1977-1996.

Source: ISTAT.

41
Fig. 8: Welfare effects of immediate and preannouced five-year raise of retirement eligibility age (g = m type agent whose optimal retirement age is

am∗ r = 35).

42
Fig. 9: Welfare effects of immediate and preannouced five-year raise of retirement eligibility age (g = m type agent whose optimal retirement age is

am∗ r = 40).

43