Chapter 22 public and private DC pension schemes, termination indemnities, and optimal funding of pension system in italy

Public and Private DC Pension Schemes, Termination Indemnities, and Optimal Funding of Pension System in Italy Marco Micocci, Giovanni B.. Masala, and Giuseppina Cannas CONTENTS 22

Public and Private

DC Pension Schemes,

Termination

Indemnities, and

Optimal Funding of

Pension System in Italy

Marco Micocci, Giovanni B Masala,

and Giuseppina Cannas

CONTENTS

22.3 Optimal Portfolio Allocation in Occupational Pension Funds 588

22.4 Role of the Termination Indemnity Scheme 591

Soci a l s ecu r it y co nt r ibuti ons of Italian employees fi nance a two-pillar system: public and private pensions that are both calculated in a

DC scheme (funded for the private pension and unfunded for the public

one) In addition to this, a large number of workers have also termination indemnities at the end of their active service

In this chapter, we aim at giving an answer to the following questions Are the diff erent fl ows of contributions coherent with the aim of minimizing the pension risk of the workers? Given the actual percentages of contributions,

is the asset allocation of private pension funds optimal? Which percentages would optimize the pension risk management of the workers (considering public pension, private pension, and termination indemnities)?

Keywords: Pension f unds, p ublic a nd p rivate p ensions, ass et

allocation

22.1 INTRODUCTION

A literature that dates back to at least the contributions of Diamond (1965), Samuelson (1975), and Diamond (1977) points out the need for an unfunded pension system to avoid capital overaccumulation Th is situation could arise

in a social system in which only individualistic savings decisions are allowed, and so it is possible to accumulate capital to the extent that the return on cap-ital assets is lower than the growth rate in national income, and the economy becomes dynamically ineffi cient It is possible to make such a situation bet-ter if people save less and consume more As Blanchard and Fischer (1989) and Abel e t al (1989) remarked, it is improbable to sustain a dy namically ineffi cient economy in the long run, since the owners of the capital are likely

to t ransfer t heir c apital t o eco nomies off ering h igher r eturns D iamond (1965), Enders and Lapan (1982), and Merton (1983) highlighted t hat t he rationale for a public statutory pay-as-you-go pension program (henceforth paygo) depends on the potential for intergenerational risk sharing by means

of Pareto improving transfers from the young to the old

On the other hand, there is also a g rowing literature pointing out the case for funded pension system In their seminal papers, Aaron (1966) and Feldstein (1974, 1996) showed the condition under which, in the long run, funded pension schemes are superior to unfunded schemes It requires the real rate of return on the assets in funded schemes to exceed the real growth rate in the wage bill In this regard, it is well known that the implicit return

of t he pa ygo s ystem i s g iven b y t he g rowth o f a ggregate wa ge i ncome, refl ecting the combined eff ect of productivity and labor supply growth So, the real growth rate in the wage bill, in turn, equals the growth rate in the national income, if the share of wages in the national income is constant

Th e higher performance of the funded scheme has both an empirical and a theoretical reason Th e fi rst one lies in the experienced superior performance

of the capital market in terms of the rate of return on investment Th ese high real returns available make it more likely that funded pension schemes will be able to deliver the pension promise Th e theoretical reason for funded pension scheme is that, in the long-run equilibrium, saving via a high-yielding pen-sion fund helps the process of capital accumulation, which, in turn, improves the productivity of workers Th is has to do with the socalled dynamic effi -ciency of the economy Abel et al (1989) argued that the major Organization for Economic Cooperation and Development (OECD) economies were really dynamically e ffi cient, a nd Feldstein (1996) a sserted t hat t his i mplied t hat funded pensions were therefore superior to paygo transfer systems and that a paygo system could be regarded as a tax, with a distortive tax wedge

Th e general insight from the earlier literature dealing with pension scheme issues is b iased b y t he g eneral s ole det erministic en vironment t aken in to account Risk and uncertainty did not fi gure in those arguments Instead, since

a stochastic framework has been introduced, literature has later split the case

up into a deterministic and a stochastic one Th erefore, only in a deterministic dynamically effi cient world the steady state return from a fully funded pen-sion scheme is higher than the steady state return from a paygo scheme and, hence, the society does not want the unfunded component Not surprisingly, projections of deteriorating dependency ratios have led many economies to attempt to derive a politically feasible and maybe even Pareto-optimal transi-tion from a paygo program to a (partly) funded program Deterministic mod-els therefore predict that a funded program is superior to a paygo program in steady state, refl ecting that the benefi ts from a fully funded system depend on the return on fi nancial markets, while in a pay-as-you-go system the relevant variable is the growth of the contribution base, which depends on productiv-ity and labor supply growth In reference to this, see de Menil and Sheshinski (2004), Matsen and Th øgersen (2004), and Bilancini and D’Antoni (2008)

As we have a lready mentioned, t he situation cha nges if u ncertainty is introduced A s Merton (1983), Merton e t a l (1987), G ordon a nd Varian (1988), G ale ( 1990), a nd Bla ke ( 2000) ha ve em phasized, f unding i s n ot

a panacea Th e lifetime earnings of a co hort are subject to shocks; there-fore each cohort could ba lance its own earnings a nd d rawings w ith t hat

of its successor, through the intergenerational transfers entailed in a paygo pension scheme Following t his consideration, i n recent years, a n umber

of papers have emphasized the role of social security in providing inter-generational risk sharing with respect to several sources of risk, including return on fi nancial markets, and demographic and productivity shocks See

in this regard Marchand et al (1996), Belan and Pestieau (1999), Boldrin

et al (1999), Dutta et al (2000), Miles and Timmerman (1999), Demange and

Laroque (1999), (2000a), (2000b), Lindbeck (2000), Demange (2002), Bohn (2001), Bohn (2004), Wagener (2003), Matsen and Th øgersen (2004), Krueger and Kubler (2006), and Ball and Mankiw (2007) Th e general insight from this literature is that if you take into account that returns, on both paygo and funded systems, are stochastic, a funded program is not always superior to

a paygo program in steady state When returns are stochastic and they are not perfectly correlated, it is possible to diversify risk by optimally choos-ing a mix of unfunded and funded systems Contrary to what happens in a fully deterministic setting, the paygo asset is not necessarily banned from the rational worker’s portfolio: it depends on the covariances between stock returns and the growth of aggregate wage (or gross domestic product (GDP)) income Th us, the paygo system can be seen as a government-created asset that can be used as a hedge to reduce total portfolio risk, or rather it can be seen as a system that allows intergenerational risk sharing providing society with insurance against bad draws in lifetime income.*

Th e issue, as it has been set, can be dealt with a portfolio choice approach

to social security design Miles and Timmermann (1999), Dutta et al (2000), Persson (2002), Matsen and Th øgersen (2004), and de Menil, Murtin, and Sheshinski (2006) explicitly use a portfolio approach that treats the pay-as-you-go system and the funded system as fi nancial assets that can help diver-sify risk Th is kind of models highlights the optimal mix between a public paygo program and a private retirement saving

From a m ore t heoretical perspec tive, t here a re so me m odels ( Sinn, 1999; Von Weizsäcker, 2000; Miles, 2000; Castellino and Fornero, 2000; Menzio, 2000; Perrson, 2002; de Menil and Sheshinski, 2004; Bilancini and D’Antoni, 2008) that analyse, in diff erent contexts, specifi c circumstances and reasons why a mixed system is preferable to one that relies only on a sin-gle component, either paygo or funding For instance, in Von Weizsäcker (2000), the pension mix with a compulsory pay-as-you-go component and

a funded private one may be well suited for reducing pension risk due to demographic shocks, if contribution rates are politically determined as a function of the dependency ratio In this case, if you look, for instance, at

a sudden increase in population, the dependency ratio declines and so the contribution rate to the pension system also declines Th is counteracts the increased return to the pay-as-you-go system due to an increased national product Th e same stabilizing eff ect of the pay-as-you-go system works if the opposite holds De Menil and Sheshinski (2004) argued that the opti-mal size of the pension savings’ paygo part and the funded part depends

* See Merton (1983), Persson (2002), and Matsen and Th ø gersen (2004).

both on the stochastic characteristics of GDP growth and the return to market savings, and on the shape of the utility function of the represen-tative a gent B ilancini a nd D ’Antoni (2008) ha ndle t he o ptimal ch oice between funded and unfunded pension system, taking into account that people care about their consumption relative to others

All these models have almost two points in common:

A mixed paygo and funded system may be optimal due to the extent

•

that wages and the return on capital are negatively correlated

Th e role of paygo pension system is that of a provider of

intergenera-•

tional insurance

22.2 OPTIMAL PRIVATE/PUBLIC PENSION MIX

Th e Italian pension system is characterized by the fact that workers set aside about 43% (on average) of their income to pension savings Th is amount comprises 33% of unfunded (public) pension and 10% of the funded one

So, the actual split between public and private pension is 77% and 23% Basically, a two-pillar social security system exists Th e fi rst pillar is rep-resented by t he st atutory pay-as-you-go pension scheme (unfunded pen-sion) It is characterized by a contribution-based pension formula, following pension reforms introduced in Italy during the 1990s Th e formula incorpo-rates rough actuarial principles and thus represents a d rastic change from the previous system, based on a defi ned benefi t calculation rule

Alongside the public paygo system, a funded private second pillar has been provided by decree 124/1993 and, aft erwards, by t he state law no 335/1995 It consists of a voluntary occupational pension scheme

In addition, a pa rt of t he Italian employees get a ter mination indemnity

called trattamento di fi ne rapporto (henceforth TFR) Th e TFR is a lump sum

severance pay granted by the employer at the moment the active service ends

Th e indemnity due from the employer is calculated as follows Th e sum, for the entire period of employment, of 7.41% of the leaving indemnity reference salary for each year is diminished by 0.5% for the fi nancing of a leaving indemnity guarantee fund under the social security administration, Instituto Nationale Previdenza Sociale (INPS), which takes the place of insolvent employers Th e entitlement i s r evalued o n 31 De cember e ach y ear, e xcluding t he a mount accrued during the year, by 1.50% plus 75% of the infl ation rate measured by the national statistical institute (ISTAT) with respect to December of the previ-ous year More formally, the TFR revaluation yearly rate, called δt, is equal to

1.5% 4

where πt is infl ation rate at time t Th e recent pension reform (2007) stated

that f uture fl ows of T FR must automatically be pa id i nto occ upational pension funds, in a very conservative investment line.* Th is entails that, currently, the above-mentioned 10% pension saving set aside for funded pension scheme is composed by the TFR amount (about 6.91%) and by the employer and employee contribution for the remaining part

Our fi rst goal is to fi nd t he o ptimal pens ion s avings d istribution between public and private pension systems in Italy, from a representative worker’s point of v iew For t his purpose, we adopt a po rtfolio selection approach that allows us to fi nd the optimal split between the paygo part

of the pension savings and the funded part We use a simple static model with mean-variance preferences

Th e r epresentative I talian w orker i s defi ned a s ha ving t he f ollowing mean–variance utility function:

γ

[ ( )] ( ) 2 var( )

where

P is the employee’s total pension per u nit of money contributed P = 1 +

w ru + (1 − w) rf

γ is a risk-aversion parameter

We n ote t hat w is the unfunded pension share, and ru and rf are random variables representing, respectively, the return of the unfunded pension and

of the funded one

Let E(P) = 1 + w µu + (1 − w) µf and = 2⋅σ + −2 2⋅σ +2

var( )P w (1 w)

⋅ − ⋅σu,f

2 (1w w) stand for the mean and the variance of a two-asset portfolio, where µu and σ are, respectively, the mean and the variance of public pension 2u

returns, µf and 2

f

σ are the mean and the variance of private pension returns, and σu,f is the covariance between the two random variables ru and rf

To fi nd the optimal paygo pension share w*, we maximize the worker’s utility function:

γ

= + ⋅µ + − ⋅µ − ⋅

2

w

u

with 0 < w < 1.

* Single employees can always explicitly choose to divert their TFR individually to a personal pension plan or explicitly refuse to accept the transfer of TFR to pension funds and keep it with the employer.

To perform a n umerical analysis we utilized the Italian GDP growth

rate as a proxy for ru Th e return of the funded component rf is approxi-mated by a benchmark of the average Italian occupational pension fund

It consists of 74.2% bond and 25.8% equities Table 22.1 shows percentages

of t he va rious asset classes in t he average Italian pension f und a nd t he indexes used to approximate them

All the time series used in this chapter range over the period 1988–2007 and all nominal values have been defl ated by regular consumer price index (CPI) fi gures

Table 22.2 shows the empirical estimates of the mean, standard devia-tion, and covariance of the annualized 20 year real returns of unfunded and funded pension scheme in Italy

We specify that, for the public pension, we have made a co rrection of the GDP growth rate to refl ect the fact that the conversion factors, used to annuitize the amount accrued from the workers in their active lives, are more convenient than those used by the Insurance Companies to convert the amount accrued for the private pension

In other terms, the conversion factors applied by the State are more convenient than the conversion factors applied by the private pensions

Using these data, we can calculate the optimal paygo pension share w* As

Figure 22.1 illustrates, it varies with the degree of employee’s risk aversion,

TABLE 22.1 Th e Composition of the Average

Italian Private Pension Fund

Equity Italy MSCI Italy 2.20

Equity world MSCI World ex EMU 8.30

Bond Italia JP Morgan GBI Italy 26.90

Bond EU JP Morgan GBI EU 41.70

bond world JP Morgan GBI Global 5.60

TABLE 22.2 Financial Technical Bases GDP growth mean 2.50%

Pension fund return mean 4.08%

GDP growth volatility 2.68%

Pension fund return volatility 4.84%

which is here parameterized by γ As a st arting point, we use a va lue of γ which corresponds to the current split of the pension savings between pub-lic (77%) and private part*; other values are obtained varying γ

IN OCCUPATIONAL PENSION FUNDS

Furthermore, following the same approach used in Section 22.2, we investigate

if the average asset allocation between bond and equity in a domestic occupa-tional pension fund is optimal according to the selected utility function For this purpose, the model can be easily modifi ed:

= + ⋅µ + − ⋅ α⋅µ + − α ⋅µu e b

2

where

α is the fraction of the funded pension allocated to equity

µe and µb a re, respectively, t he returns on equities a nd t he returns on bonds, while 2

e

σ and 2

b

σ are the variances of equities and bond returns

σu,e, σu,b, and σe,b are the covariances

0,000%

10,000%

20,000%

30,000%

40,000%

50,000%

60,000%

70,000%

80,000%

90,000%

100,000%

γ ∞

FIGURE 22.1 Risk aversion and optimal public pension quota

* Th is value is about 180.

Given the fi xed value of w corresponding to

the current level, t he asset a llocation prob-lem is to choose the optimal level of α Our numerical analysis highlights that in Italy, the average yearly real yield on equity

in a private pension fund is 6.03%, over the period 1 988–2007 O ver t he sa me pe riod, the average yearly yield on bond asset class

is 3.41% Th e covariance matrix is g iven i n Table 22.3

First of all , w e investigate if t he c urrent asset allocation of the average pension fund

is optimal Currently, worker’s pension sav-ings consists 77% of a paygo system and 23%

of an occupational pension fund Th is 23%

is co mposed b y eq uities (6%) a nd b onds (17%)

Substituting t he val ue o f γ, f ound in the p revious s ection, w hich co rresponds

to t he c urrent situation, it turns out t hat the optimal level of equities in a n Italian pension fund α* should be equal to 4.86% This suggests that the current asset alloca-tion for the funded pension scheme is not the optimal one

Tables 22.4 and 22.5 show how the opti-mal split between bonds and equities var-ies with dif ferent le vels of employee’s r isk aversion

Until now, we have relied on historical means, variances, and correlations as inputs

to ou r c alculations a bove, but we c annot

TABLE 22.3 Th e Covariance Matrix

Paygo 0.072% −0.041% 0.037%

Equity −0.041% 1.944% 0.168%

Bond 0.037% 0.168% 0.134%

TABLE 22.4 Optimal

Quotas of Equities, Bonds,

and Risk Aversion within

Worker’s Total Pension

γ → ∞ 3.11 20.15

3γ 3.68 19.58

2γ 3.97 19.29

γ 4.86 a 18.40

γ/2 6.62 16.64

γ/3 8.39 14.87

γ/6 13.68 9.58

a Th e c urrent val ue o f eq uity

share co rresponding t o γ is

6%.

TABLE 22.5 Optimal

Quotas of Equities, Bonds,

and Risk Aversion within

the Asset Allocation of an

Italian Pension Fund

γ → ∞ 13.52 86.48

3γ 16.00 84.00

2γ 17.26 82.74

γ 21.12 a 78.88

γ/2 28.79 71.21

γ/3 36.47 63.53

γ/6 59.49 40.51

a Th e c urrent val ue o f eq uity

share co rresponding t o γ,

within the pension fund asset

allocation, is 25.8%.

neglect that all these conclusions are sensitive

not only to the specifi ed degree of

employ-ee’s risk aversion γ, but a lso to t he

correla-tion between the random variables involved

in our calculations As shown in the recent

dramatic crisis of the fi nancial markets,

cor-relations can change along the time

Th e following fi gures show the sensitivity

of t he r esults t o t he co rrelation coeffi cient

and to the risk aversion

22.3.1 Sensitivity Analysis

We su ppose n ow t hat t he co rrelation

between eq uity a nd bo nd is va riable a nd

we want to determine the sensitivity of the

equity weight with respect to correlation Th e covariance between equity and bond is 0.168% so that the actual correlation is about 33%

Th e results are given in the following Table 22.6 Th e risk-aversion

coef-fi cient takes the value γ = 180 as in the previous analysis

See Figure 22.2 for a graphical repre sentation

In a further analysis, we allow the risk-aversion coeffi cient to vary and

we consider the sensitivity of the equity weight with respect to both the correlation and the risk-aversion coeffi cient (Figure 22.3)

We can plot the results as a bidimensional surface

TABLE 22.6 Optimal Quotas

of Private Pension Fund and Risk Aversion

Correlation

0.01

0.02

0.03

0.04

0.05

0.06

0.07

FIGURE 22.2 Equity weight vs correlation between equity and bonds