Pensions and the role of the State Massimo DAntoni Dept of - - PowerPoint PPT Presentation

Pensions and the role of the State

Massimo D’Antoni

Dept of Economics and Statistics, University of Siena

Course of Public Economics

Academic Year 2013-2014

Some introductory concepts

The functions of a pension system

A pension system can be viewed as a transfer mechanism among groups/generations, as it transfers resources from the active to the inactive (old, survivors, poor, inable individuals) a financial instrument as it smooths income and provides insurance We can identify several functions of a pension system

◮ consumption smoothing ◮ insurance ◮ poverty relief ◮ redistribution

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Two families of pension systems

Fully funded (FF) future payments are secured by the cumulation of financial assets. The individual is entitled a share of the assets, which is converted to an annuity at retirement Pay-as-you-go (PAYG) a direct transfer of resources from the active to the inactive population. The individual relies on a "promise" of the State

• n future payments

Note that

◮ a PAYG system requires that an intergenerational pact is enforced,

hence an enduring public authority is needed, and its objectives are not usually limited to insurance/income smoothing

◮ in principle, the distinction funded/pay-as-you-go is not necessarily

• verlapped to the distinction private/public, as a public system may be

partially funded

◮ in a PAYG system, what each generation receives is not constrained by

the amount of previous savings/value of assets

◮ in a public system, the presence of a precautionary fund is superfluous

as solvibility is granted by the continuity of the state

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Public expenditure on pensions

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Historical evolution

◮ the old are supported by their families ◮ mutual help organization and other volutary associations ◮ involvement of the State is required by insolvency and insufficiency of

voluntary solutions; it implies at a minimum

◮ mandatory savings ◮ a guarantee of a minimum return

◮ Germany: in 1889 (Bismark) introduces a mandatory earning-related

pension system

◮ An alternative approach: means-tested system financed with general

taxes—Denmark (1891), New Zealand (1898), Australia and United Kingdom (1908), Canada (1927)

◮ USA: in 1920s means-tested systems in many states, in 1935 (New

Deal) the OASDI (Old Age Survivors & Disability Insurance), popularily known as social security, is started

◮ expansion of social security after the 2nd World War

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Defined contribution vs defined benefit schemes

Defined contribution (DC) each member pays into an account a fixed fraction of his or her earnings; benefits at retirement, given life expectancy and the rate of interest, are determined by the size of his or her lifetime pension accumulation, preserving the individual character

• f a person’s lifetime budget constraint

Defined benefit (DB) a worker’s pension is based on his/her wage history, possibly including length of service; pensions are usually based on a person’s wage in his/her final year, or few year (although it can be based on a person’s real or relative wages over an extended period), and is tipically wage-indexed until retirement. A recent innovation (Sweden, Italy): Notional Defined Contribution (NCD) it mimic funded DC schemes by paying an income stream whose present value over the person’s expected remaining lifetime equals his/ her accumulation at retirement, but with an interest rate set by government rules (typically linked to GDP growth), not market returns.

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Why is there a role of the State?

Public role in pensions

This includes

◮ Mandatory contribution to the pension system. Why?

◮ Myopia: individuals do not correctly perceive their future needs, they do

not discount correctly future income

◮ Free-riding counting on the fact that society will take care (Samaritan’s

dilemma). Two conditions

◮ other individuals are altruistic ◮ they cannot credibly commit not to intervene ex post to support the old who

have not saved enough

◮ Self-control (quasi-hyperbolic preferences)

◮ Mandatory annuitization. Why?

◮ Myopia (wrong perception of the fact that annuitization is always

beneficial)

◮ Adverse selection

◮ Guaranteed minimum return on pension savings and regulation of

private funds

◮ Macroeconomic instability, inflation etc. non insurable risks ◮ Difficult to ascertain long term solvibility of investors

◮ Direct provision of benefits

◮ Necessary in the case of a PAYG system Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Myopia

Individuals discount too much their future needs: their decisions are based

• n a discount rate higher than the "true" rate

U(C1) + δU(C2) s.v. C2 = (R − C1)(1 + r) First order conditions: U′

1(C1) = (1 + r)δU′(C2). The lower δ, the larger the

• ptimal value of C1.

E1 E2 C1 C2

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Quasi-hyperbolic preferences

◮ We usually assume exponential preferences, or

U(C1) + δU(C2) + δ2U(C3) + . . . in this case, the MRS between Ct and Cτ does not change as we get close to t: we have time consistency.

◮ Consider alternatively that the current period is given more weight than

future periods (see Laibson, 1997) U(C1) + β

• δU(C2) + δ2U(C3) + . . .
• 0 < β < 1

in this case we have time inconsistency, because in period 2 the utility is U(C2) + β

• δU(C3) + δ2U(C4) + . . .
• hence the MRS between C2 and C3 is different if it is calculated in

period 1 or in period 2

◮ Quasi-hyperbolic preferences imply procrastination. Today the

individual underestimate the cost of reducing consumption tomorrow to increase consumption later on.

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

An example of procrastination

Consider an action involving an immediate cost c and a flow of benefits x in future periods. The utility—calculated in period zero—from taking the action in t is V(t) =            βδt [−c + δx + δx + . . . ] = βδt

• δ

1 − δx − c

• with t > 0

−c + β

• δx + δ2x + . . .
• = β

δ 1 − δx − c with t = 0

◮ Assume that x > c(1 − δ)/δ, so that the present value of benefits exceed

the cost;

◮ we have that V(t) > V(t′) when t′ > t > 0, i.e. there is no benefit from

delaying the action with t > 0

◮ however, V(0) < V(1) as long as x < c(1 − βδ)/βδ, which may well be

compatible with the previous condition if β < 1; in this case, the best timing for the action is period 1 (tomorrow)

◮ for example, assume δ = .8 and β = .75; with 2 3c > x > .25c we have at

the same time V(1) > V(t) with t > 1 and $V(0)>V(1)

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

An example of procrastination /2

◮ Although the individual knows that it is optimal to carry out the action

in period 1, once in period 1 the individuals will find it optimal to delay the action to period 2, and so on: the action is never carried out!

◮ If the individual is sophisticated, he/she will find it optimal to commit

to carry out the action in period 1 by fixing a deadline (he/she will self impose a penalty for not respecting it)

◮ note that the possibility of procrastination is reduced if the action can

be carried out at longer intervals; for example, consider that the action is possible only after 5 intervals, so that the action is delayed if V(5) > V(0), but this requires x < (1 − δ)(1 − βδ5) βδ(1 − δ5) c = .37c so that procrastination is much less likely to occur On procrastination see also Akerlof (1991) "Procrastination and obedience"

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Comparison among pension systems

Assessment should be made with reference to all objectives:

◮ consumption smoothing ◮ insurance ◮ poverty relief ◮ redistribution

Usually, comparisons consider

◮ return of the pension investment ◮ the effect of the pension system on the economy

◮ savings ◮ labour market

◮ risk exposure ◮ administrative costs

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Return of a pension system

◮ In the case of a funded system, the return is given by the average

(across individuals, across assets) return on financial markets

◮ In the case of a PAYG system, the return for a representative individual

• f generation t is given by

Bt τWt − 1 where Bt is average future pension, τ is contribution rate, Wt is current average salary

◮ the future budget constraint of the pension system implies

τWt+1Nt+1 = NtBt or Bt τWt − 1 = Wt+1 Wt Nt+1 Nt − 1 = (1 + m)(1 + n) − 1 ≃ n + m where Nt is numerosity and n is the growth rate of the workforce in period t, while m is wage/productivity growth

◮ what about the risk?

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Dynamic inefficiency

◮ An economy is dynamically inefficient when g > r (g is GDP growth) ◮ when n + m = g > r it is possible to devise a Pareto improvement for all

generations by starting a PAYG system

◮ assume for simplicity that m = 0 so that g = n: one euro from the young

= (1 + n) euro to the old

◮ if the young reduce savings by one euro, their consumption when young

is unchanged, while their consumption when old increases by (n − r)

◮ the old generation when the system is started receives 1 + n ◮ =⇒ all generations are better off ◮ this is possible because there is no final generation

Starting in the 1960s, it has been debated whether advanced economies are dynamically efficient. A criterion is to compare profit and investment (profits must exceed investment as long as r > g). Abel et al. (1989) show that dynamic efficiency is verified for all largest capitalist countries.

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

The "golden rule"

◮ In an economy with overlapping generations it can be g > r, g < r or

g = r depending on the savings decision (intertemporal preferences) of each generation.

◮ When g = r (golden rule) the steady state aggregate consumption is

maximized

◮ A properly designed pension system with a PAYG component can move

an economy to the golden rule (Samuelson, 1975)

◮ However, note that when an economy is moved from a situation of

dynamic efficiency (g < r) to the golden rule (g = r) there is no Pareto improvement, because during the transition some generations can be made worse off

◮ In general, from the fact that a steady state A is better than a steady

state B cannot be concluded that moving from B to A is beneficial to all

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Demographic pressures and reforms

The nature of the demographic "crisis"

Pressures from demographics (see European Commission, The 2012 Ageing report)

◮ birth rate has fallen (only partially offset by immigration) ◮ increased length of life ◮ retirement age falling

These factors increased the old-age dependency ratio population aged 65+ population aged 20-64

◮ In a PAYG system, because the equilibrium of the system requires

τNt−1 = BtNt, an increase in Nt−1/Nt must be accompanied either by an increase in τ or by a decrease in Bt.

◮ Is the situation different for a funded system?

What matters is output, a funded system can avert the demographic crisis only if it can increase the output available for the population as a whole.

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Fertility rate

◮ Total fertility rate = children per woman (for each year, it is calculated

the sum of fertility rates by age)

1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 2050 2053 2056 2059 European Union Euro Area

Total fertility rates

Source: Eurostat, EUROPOP2010

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Migration flows

◮ Projection of cumulated net migration flows over the period 2010-2060,

as a percentage of the population in 2010

• 5.0%

0.0% 5.0% 10.0% 15.0% 20.0% 25.0% 30.0% 35.0% 40.0% LT BG EE LV PL RO NL MT DE FR SK FI DK HU EU27 CZ EA UK EL SI SE PT IE NO AT BE ES IT CY LU

Source: Eurostat, EUROPOP2010

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Life expectancy at birth (men)

◮ Projections of life expectancy at birth

60.0 64.0 68.0 72.0 76.0 80.0 84.0 88.0 92.0 LT LV EE BG RO HU SK PL CZ SI PT FI DK IE BE EU27 AT DE LU MT EL EA FR CY NL NO UK ES IT SE 2010 2010-2060

Source: Eurostat, EUROPOP2010

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Change in the population by age group

◮ Projection of changes in the structure of the population by main age

groups, EU27 (in %)

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 2010 2020 2030 2040 2050 2060 0-19 20-64 65-79 80+

Source: Eurostat, EUROPOP2010

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Old-age dependency ratio

Old-age dependency ratio (ratio of people aged 65 or above relative to the working-age population)

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 IE UK NO DK BE LU SE FR NL CY FI AT EU27 EA17 CZ MT EE ES IT EL PT LT HU SI DE BG SK RO PL LV

2010 2010-2030 2030-2060

Source: Eurostat, EUROPOP2010

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Not only the demographics...

◮ The burden of pensions is on working population. Labour market

participation rates (aged 20-64, in %) count

50 54 58 62 66 70 74 78 82 86 90 RO IT HU PL LU IE SK MT BE BG EL EU27 EA17 CZ LT SI AT UK FI FR NL NO PT EE DK ES LV DE CY SE 2010 2060

Source: Eurostat, EUROPOP2010

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

The Washington consensus on pension reform

In the 1990s, in the face of demographic trends, recommendations of the World Bank (Averting the Old Age crisis, 1994) dominate the wave of

• reforms. The blueprints are

◮ move from PAYG to funded systems ◮ move from defined benefit to defined contribution (a strict actuarial link

between contributions and benefits)

◮ privatization to enhance redditivity

The "ideal" pension system is based on three pillars:

• 1. a PAYG public pension covering a minimum uniform for all
• 2. a funded mandatory pension (with a State guarantee and encouraged by

tax breaks) provided by private pension funds

• 3. voluntary savings

Such recipe is criticized by economists as Stiglitz or Diamond

◮ The financial crisis has modified the consensus

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Can funding be the answer?

◮ With dynamic inefficiency (g > r) there is a strong case for the

introduction of a PAYG system

◮ Should we switch from a PAYG to a FF when r > g? ◮ Comparing the steady states is not enough. The transition counts.

Consider the following case:

◮ A stationary economy with g = 0 ◮ the interest rate r is 20% ◮ the representative worker has an income of 1000, of which 400 are paid

as contributions to finance the pension system

◮ in a PAYG system, contribution are transferred directly to pensioners ◮ in a FF system, contributions are invested Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

A comparisong of FF vs PAYG

PAYG 1 2 3 4 5 income of the young 1000 1000 1000 1000 1000 contributions 400 400 400 400 400 consumption of the young 600 600 600 600 600 pension/consumption of the old 400 400 400 400 400 FF 1 2 3 4 5 income of the young 1000 1000 1000 1000 1000 contributions 400 400 400 400 400 consumption of the young 600 600 600 600 600 pension/consumption of the old 480 480 480 480

Note that the gain for the first generation under a PAYG is equal to present value of the cost for future generations

∞

• t=1

80 (1 + r)t = 80 r = 400

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Transition from a PAYG to a FF

◮ As the FF requires that current contributions are invested in financial

assets, we need to finance the current pensions

◮ assume this is done by imposing the cost of transition on the first two

generations, as follows

PAYG to FF (burden on 1 and 2) 1 2 3 4 5 income of the young 1000 1000 1000 1000 1000 1000 contributions (PAYG) 400 400 200 contribution (FF) 200 400 400 400 400 consumption of the young 600 400 400 600 600 600 pension/consumption of the old 400 400 440 480 480 480

Consider the present value of lost consumption across generations −200 − 160 1.2 + 80 1.22 + 80 1.23 + · · · = 0

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Transition from a PAYG to a FF/2

◮ Consider the possibility to pay for current pensions by issuing public

debt, and design the tax system so that the debt is serviced by the old benefited by the system change

PAYG to FF (debt) 1 2 3 4 5 income of the young 1000 1000 1000 1000 1000 1000 contributions (PAYG) 400 contributions (FF) 400 400 400 400 400 consumption of the young 600 600 600 600 600 600 debt 400 400 400 400 400 pension before taxes 400 400 480 480 480 480 interest on debt / tax on pension 80 80 80 80 net pension/consumption of the old 400 400 400 400 400 400

◮ There is no benefit for anyone from the system change ◮ the implicit pension debt has been turned into explicit public debt

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Transition from PAYG to FF (general analysis)

◮ The budget constraint of the individual of generation t

C2

t =

• (1 − τ)Wt − C1

t

• (1 + r) + Bt

◮ because in a PAYG system Bt = τWt(1 + g), the constraint can be

written as C2

t =

• 1 − τ r − g

1 + r

• Wt − C1

t

• (1 + r);

a PAYG system amounts to imposing a "tax" of rate τ(r − g)/(1 + r), as the individual is forced to save to an asset (the PAYG pension system) whose return g is different (lower) than r

◮ in a system in equilibrium, it must be Bt−1Nt−1 = τWtNt ◮ in steady state, WtNt grows at a rate g, hence Wt+1Nt+1 = WtNt(1 + g)

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Transition from PAYG to FF (general analysis)/2

◮ The present value of the implicit tax imposed on generations from t

• nward:

∞

• s=t

τ r − g 1 + r WsNs (1 + r)s−t = τ r − g 1 + rWtNt

∞

• s=0

1 + g 1 + r s = τWtNt = Bt−1Nt−1

◮ Hence: pensions paid to generation t − 1 are equal, in present value, to

the implicit taxes paid by subsequent generations (from t onward) Some further results follow:

◮ the "gift" to the first generation (when the PAYG pension system is

started) is equal to the taxes paid by all future generations—it is a zero sum game (note however that this conclusion abstracts from informal transfers existing among generations when the system is started)

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Transition from PAYG to FF (general analysis)/3

◮ When a PAYG system is rolled back, future generations will save the

implicit tax

◮ however, we need to finance pension claims by the current generation

• f pensioners: Bt−1Nt−1

◮ if we finance such claims by issuing debt and we levy taxes

(at,at+1,at+1,. . . ) on all generations (t,t + 1,t + 2,. . . ) so that revenue from generation t is atNt and Bt−1Nt−1 = atNt + at+1Nt+1 1 + r + at+2Nt+2 (1 + r)2 + · · · =

∞

• s=t

asNs (1 + r)s−t .

◮ Because we roll back the PAYG system, each generation save the

implicit tax: Bt = Wt(1 + r) instead of Bt = Wt(1 + g)

◮ The implicit tax and the tax levied to repay the debt have the same

present value!

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Endogenous r and g

◮ In the analysis above the interest rate r and the growth rate g were

exogenous, they were not affected by the change of the pension system

◮ the assumption of exogenous r can be justified for an open economy

with integrated financial markets (provided the economy is small enough)

◮ if the economy is closed, an increase in funding can affect (increase) k

and future output: the change of the system is not anymore a zero sum game

◮ however, because r > n implies dynamic efficiency, it is not possible to

devise a Pareto improvement

◮ additionally, the benefit for future generation depends on a number of

assumptions

◮ the reform increases savings (it is not debt financed) and reduced

consumption of the current generation

◮ increase in savings increases output (what if we have a problem of

aggregate demand?)

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Averting the old age crisis by switching to a FF

◮ The idea is that with a FF, each generation saves for itself ◮ However, this idea is misleading: consumption goods and services are

not actually "stored" for old age. Financial asset (claims on capital goods) are bought and then sold in exchange for consumption goods and services.

◮ In the future, demographic pressure will decrease k and the price of

asset when they must be converted into consumption goods

◮ In the end, what counts is the available amount of goods and services in

the future—i.e. output

◮ In the neoclassical model, this is obtained by increasing savings today

(see discussion above). Switching to a FF system is a possible way to increase savings, although other ways (policies) are possible

◮ An alternative in open economies: import of goods and services from

abroad—however

◮ the age structure of the country where investment is made counts ◮ future import can affect the exchange rate ◮ immigration to provide services may be required Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Effect on savings (individual)

Effect on individual savings. In both cases (FF and PAYG) we expect some crowding out of voluntary savings:

W (1−τ) W C1 ˜ C1 B ˜ B C2 ˜ C2

Contributions are less than voluntary savings

W (1−τ) W C1 B ˜ B C2

Contributions exceed voluntary savings

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Effects on savings (aggregate)

◮ In an overlapping generation model, we must consider together savings

by the young and (negative) savings by the old

◮ Let σ propensity to save: aggregate savings are

σWtNt − σWt−1Nt−1 = σgWt−1Nt−1

◮ If we have a 1:1 reduction, aggregate savings are reduced to

(σ − τ)gWt−1Nt−1

◮ Note however that this analysis relies on the life-cycle hypothesis:

savings are aimed at funding consumption in old-age. Other explanations are possible:

◮ precautionary motif ◮ bequests Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Labour market

◮ The idea is that contributions to a PAYG of a defined benefit type are

taxes, while contributions to a FF of a defined contribution type are more like savings

◮ However: they are forced savings ◮ Individual may discount too much future consumption ◮ Notional defined contributions (sistema contributivo in Italy since

1995): a closer actuarial link between contributions and benefits—although the rate of capitalization is the growth rate g, not r

◮ Note that a key difference between DC and DB is how risks are shared

among generations and individuals

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Notional Defined Contributions

◮ Each worker pays a contribution which is credited to a notional

individual account (although no asset is actually comulated)

◮ contributions are cumulated with a notional interest rate (a moving

average of growth rates)

◮ at retirement, the value of the notional accumulation is converted into

an annuity in a way that mimics actuarial principles Consequences:

◮ less redistribution (although some redistribution takes place because of

a minimum pension guarantee, or the fact the same rate is used for males and females, etc)

◮ if there are no changes in contribution, the difference with respect to a

DB scheme is not so relevant

◮ what is relevant is the response to shocks: under a NDC system the

demographic risk is on pensioners, as pension are (should be) adjusted to life expectancy

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Notional Defined Contributions — Italy

The amount of the pension is Mθ where

◮ M are cumulated contributions, or

M =

L

• t=1

τWt

L

• s=t+1

(1 + rs) with rs is notional interest rate (moving average of GDP growth in the last 5 years), L is time of retirement, τ = 33% is a notional rate

◮ θ = 1/e(L) is a coefficient, with

e(L) =

T−L

• t=1

1 (1 + rs)t−1 +

T′−T

• t=1

ηλ (1 + rs)t−1 with η the probability of a survivor, and λ the ratio between the pension

• f the survivor and that of the pensioner.

◮ e(L) reflects demographic and macroeconomic variables, and is revised

periodically

◮ θ is the same for men and women, and is the same for married and

unmarried: this involves some redistribution

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Pension contracts and risk allocation

◮ From τtWtNt = Bt−1Nt−1 follows

τt = Bt Wt Nt−1 Nt = ρt Dt 1 + mt where ρt is the replacement rate and Dt the dependency rate, mt productivity growth.

◮ We can see how shocks affecting Dt or mt are reflected on ρt or τt.

We follow Musgrave (1981) and identify several possible "contracts"

◮ Period-by-period renegotiation ◮ Replacement rate is fixed: because ρt = ρ, changes in Dt or mt affect τt ◮ Contribution rate is fixed: we have τt = τ and shocks are absorbed by

changes in ρt

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Pension contracts and risk allocation/2

◮ Replacement rate is fixed and pensions is linked to productivity: the

ratio Bt/Wt = b is kept constant, so that st = b(1 + mt) (productivity risk is shared by workers and pensioners) while τt = bDt (demographic risk borne by workers)

◮ The ratio between pensions and net wage is constant: it is Bt (1−τt)Wt = b,

hence τt = bDt 1 + bDt ρt = b 1 + mt 1 + bDt

◮ Replacement rate is adjusted to demographics: it is $ρt=b/Dt, which

implies τt = b/(1 + mt); changes in the dependency ratio affect pensions, while workers bear the risk of productivity changes. (This is the worst solution from the point of view of pensioners)

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena

Pension contracts and risk allocation—summary

τt ρt, Bt (1 − τt)Wt

Bt (1−τt)Wt

ρ fixed ∆mt (productivity increases) – = + – ∆Dt (dependency increases) + = – + τ fixed ∆mt = + + = ∆Dt = – = – Bt linked to productivity ∆mt = + + = ∆Dt + = – + Constant pension/wage ratio ∆mt = + + = ∆Dt + – – = ρt linked to demographics ∆mt – = + – ∆Dt = – = –

Massimo D’Antoni Course of Public Economics, Academic Year 2013-2014 Dept of Economics and Statistics, University of Siena