Talk_boE_end_proyect2013

The automatic adjustment of pension expenditure in
Spain:
an evaluation of the 2013 proposals
Alfonso R. S´anchez Mart´ın
Seminario Banco de Espa˜na () Pension automatic adjustment September 19, 2013 1 / 56

Septiembre 2013: the government presents it proposal for the design of the
pension sustainability factor
Se garantiza la subida de las pensiones, que crecerán como
m´ınimo un 0,25% anual
Su compromiso es asegurar a todas las generaciones una
pensión garantizando un trato equitativo; de forma que los
esfuerzos similares de aportación obtengan retornos similares
de la prestación a lo largo del tiempo.
Nota de prensa MEYSS

Septiembre 2013: the government presents it proposal for the design of the
pension sustainability factor
Se garantiza la subida de las pensiones, que crecerán como
m´ınimo un 0,25% anual
Su compromiso es asegurar a todas las generaciones una
pensión garantizando un trato equitativo; de forma que los
esfuerzos similares de aportación obtengan retornos similares
de la prestación a lo largo del tiempo.
Nota de prensa MEYSS
La tarea de los economistas es convencer a los agentes
sociales y a los gobernantes de que los Reyes Magos no
existen
Luis Ángel Rojo

The underlying problem: a sketch
We are aging

We are aging
Less workers means less product, probably ...

We are aging
With the current laws (created under far better demographic
conditions), the elderly would take a bigger chunk of the cake than
now ...

We are aging
With the current laws (created under far better demographic
conditions), the elderly would take a bigger chunk of the cake than
now ...
We we’ll take that from the income of the young ... which means
bigger taxation ...

Gloomy perspectives

Restoring the balance
Political authorities have reacted by “reforming” the system:
Occasional parametric changes (1997, 2002, 2011);
Introducing ABM (Automatic Balancing Mechanisms)

Restoring the balance
Political authorities have reacted by “reforming” the system:
Occasional parametric changes (1997, 2002, 2011);
Introducing ABM (Automatic Balancing Mechanisms)
Germany, Sweden, Japan ...
Now Spain: Indexing to Life Expectancy and the Balance of the
pension system.

Targets of the paper
1 Explore the ﬁnancial condition of the pension system in the next few
decades
PPt
Y t
,
COTt
Y t
,
Ft
Y t
,
TAXt
Y t
, ... t ∈ T
Quantify the impact of the reform proposals
2 Intergenerational Balance:
Which cohorts gain with the reform and by how much.

Outline
1 Projection Methodology
2 The GE model
3 The Calibration
4 Simulation path
Status quo in the BASE ECO
Alternative ECOs
5 Reform proposals
Reforms in the BASE ECO
Reforms in the Alternative ECOs
6 Conclusions & future research

Projection Methodology
Three alternative methodologies
(i) Accounting projections
PPt
Y t = b
t
yt
Rt
Et = b
t
yt
Rt
Pt
+65
Pt
+65
Pt
20−64
Pt
20−64
Et
replacement · coverage · dependency · 1
emp

Three alternative methodologies
(i) Accounting projections
PPt
Y t = b
t
yt
Rt
Et = b
t
yt
Rt
Pt
+65
Pt
+65
Pt
20−64
Pt
20−64
Et
replacement · coverage · dependency · 1
emp
Idea:
- Adopt a macro scenario: demog, employment, prod.
- Conjecture impact on coverage and dynamics of replacement
(with/without reforms);
- Do sensitivity analysis.
Pros & cons: Good: range of possible ﬁnancial outcomes;
Problem: coherence of the diﬀerent pieces is not granted; Hard to do
intergenerational comparisons ;
Examples EC:AWG 2012 (2010:2060)

(ii) Partial equilibrium Microsimulation
Idea: (1) Create a representative sample; (2) estimate labor dynamics conditional
on macro; (3) given the macro scenario, create in sample simulated labor records;
(4) compute pension aggregates.

(ii) Partial equilibrium Microsimulation
Idea: (1) Create a representative sample; (2) estimate labor dynamics conditional
on macro; (3) given the macro scenario, create in sample simulated labor records;
(4) compute pension aggregates.
Pros & cons:
Good: Detailed reproduction of pension regulations; Intergenerational income
comparisons
Bad:
Imposes historical behavior under diﬀerent institutional settings
Lack of feedback between individual performance and macro
assumptions
Welfare analysis.
Examples : Conde & Gonzalez (2013), I.Moral IEF (2013)

(iii) General Equilibrium
Idea: Fundamentals: preferences; technology; institutions + Exogenous
demographics, & productivity growth
Solve individual behavior, aggregate to compute macro-variables.

(iii) General Equilibrium
Idea: Fundamentals: preferences; technology; institutions + Exogenous
demographics, & productivity growth
Solve individual behavior, aggregate to compute macro-variables.
Pros & cons:
Some endogenous behaviour; feedback behavior → macro.
Macro coherence: aggregates emerge from individual behavior
Standard Welfare analysis.
Bad: we can only solve stylized worlds. Otherwise, huge computation costs, specially
with uncertainty
Examples : (OLG) D´ıaz Gim´enez & D´ıaz Saavedra (2009), Izquierdo et al. (2010)

The artiﬁcial economy

The GE model
Model overview
OLG model in the Auerbach & Kotlikoﬀ (87): 1 year=1 period
Build-in demographic model (exogenous fertility, mortality and migration patterns)
Closed Economy with ﬂows of immigrants
No aggregate uncertainty. Life uncertainty at the individual level.
“Representative” Households pools LU
Heterogenous Households that take consumption/savings and retirement decisions.
Exogenous:
(1) participation and unemployment patterns (vs. Fiscal Studies (2010))
(2) labour-augmenting technological progress (at rate ρt
)
Neoclassical production side

The GE model
Households Heterogeneity
Representative Households by cohort, that diﬀer by:
1 Education
2 Relative value of leisure → heterogeneity in retirement behavior

The GE model
Households Heterogeneity
Representative Households by cohort, that diﬀer by:
1 Education
2 Relative value of leisure → heterogeneity in retirement behavior
Within each Rep Household, the proportion of households with
one/two members changes with age (due to the action of mortality)
→ we have 4x80x10= 3200 diﬀerent agents each period & 250 periods per simulation;
still very computationally tractable.

The GE model
Life-cycle planning
Optimal behavior cohorts u > 1980, (for previous cohorts we solve for what
remains of their life-cycle)
i ∈ {20, 100}, t ∈ {u + 20, u + 100}, g = {1, 2}
Max I
i=1 βi−1
su
i U(ct
i , τu
, α)
τu
, {ct
i , at
i }I
i=1
ct
i + at+1
i+1 = LIt
i + (1 + rt
) at
i
W t
i,g = (1 − ϕt
) [wt
et
i g εi g − ς covt
i,g ]
LIt
i =
πt
i,1 W t
i,1 + πt
i,2 W t
i,2 + ¯πt
i ivt
i i < τ
πt
i,1 nbt
i,1 + πt
i,2 nbt
i,2 + ¯πt
i ivt
i i ≥ τ
au
1 = 0 au+I−1
I = 0 at
i ≥ 0 ∀ i ≥ τu

The GE model
Public Sector: contributive pension system
Contributions: covt
i = min{CMt
, max{Cmt
, (1 − χ) wt
et
i εt
i , };

The GE model
Contributions: covt
i = min{CMt
, max{Cmt
, (1 − χ) wt
et
i εt
i , };
Retirement pension:
Individual beneﬁt: b(τ, h, u) = αR
(τ, h)
τ−1
e=τ−D covu+e−1
e
D
αE
(τ, h) = Replacement rate (penalty for early retirement and short contribution record)
Gross pension income:
ibt
i (τ) = min{bMt
, max{bmt
, b(τ, h, t − i + 1)}}
Survival pension: ivt
i = max{bmt
V , αV BR(τ, h, u)}

The GE model
Contributions: covt
i = min{CMt
, max{Cmt
, (1 − χ) wt
et
i εt
i , };
Retirement pension:
(τ, h)
τ−1
e=τ−D covu+e−1
e
D
αE
ibt
i (τ) = min{bMt
, max{bmt
, b(τ, h, t − i + 1)}}
i = max{bmt
Pension System:
Balance: SSBt
c = COTt
c − PPt
c
Trust Fund: Surplus accumulate at a ﬁxed rate ωt
in Ft
. Deﬁcits are
split between the TF and the general budget (while Ft
> 0)

The GE model
Contributions: covt
i = min{CMt
, max{Cmt
, (1 − χ) wt
et
i εt
i , };
Retirement pension:
(τ, h)
τ−1
e=τ−D covu+e−1
e
D
αE
ibt
i (τ) = min{bMt
, max{bmt
, b(τ, h, t − i + 1)}}
i = max{bmt
Pension System:
Balance: SSBt
c = COTt
c − PPt
c
Trust Fund: Surplus accumulate at a ﬁxed rate ωt
in Ft
. Deﬁcits are
split between the TF and the general budget (while Ft
> 0)
Transfer to the Treasury: SSTt
= SSBt
nc + (1 − ωt
) SSBt

The GE model
Government Budget
Public Expenditure, CPt: health, running costs of pub sector,
unemployment, etc
Debt policy: Dt/Y t follows an exogenous path.

The GE model
Government Budget
unemployment, etc
Taxation of involuntary bequests, BIt.
Tax revenue needed to balance the budget:
RNt = CPt + rd Dt − (Dt+1 − Dt) − SSTt − BIt

The GE model
Government Budget
unemployment, etc
Taxation of involuntary bequests, BIt.
Tax revenue needed to balance the budget:
RNt = CPt + rd Dt − (Dt+1 − Dt) − SSTt − BIt
Proportional income tax is levied on all forms of labor and capital
income. The (marginal and average) tax rate ϕt, is adjusted annually
to raise RNt.

The GE model
Equilibrium
Households are rational (solve their LC problem taking the rest of the
equilibrium environment as given).
Factor markets clear
Kt
=
J
j=1
I−1
i=20
T
τ=tm
Pt
i j τ at
i j e Lt
= At
Ht
Ht
=
J
j=1
T
τ=tm
τj −1
i=20
Pt
i j τ lt
i j e
Prices are competitive:
PRICES : r + δ =
∂F
∂K
(Kt
, Lt
) wt
=
∂F
∂H
(Kt
, Lt
)
Public budget balances
Overall aggregate feasibility constraint

The Calibration
Aligning the artiﬁcial economy and the Spanish Economy

The Calibration
Demographic processes: two scenarios
Initial conditions & distrib: INE Censo 2011, Enc. Migr., T. Mort.
Alternative scenarios:
(1) AWG (2010);
(2) VAR : INE assumptions on TFR-LE + econometric projection of
immigration flows; INE Proyección de la población de España a Largo plazo (2012)
2010 2040 2070 2100
1.2
1.4
1.6
1.8
TFR
2010 2040 2070 2100
75
80
85
90
95
EV
INE
AWG
VAR
2010 2040 2070 2100
0
500
1000
Net Inmmigrant flow (1000s)
2010 2040 2070
0.1
0.2
0.3
Immigrant share of population

The Calibration
Demographic projection
2010 2040 2070
40
45
50
55
Total Population
INE AWG VAR
0 0.5 1 1.5 2
0
20
40
60
80
100
Distribution by age
2010 2040 2070
0.2
0.4
0.6
0.8
Dependency ratio
2010 2040 2070
−0.01
0
0.01
0.02
Population growth rate
INE
AWG
VAR

The Calibration
The Labor Market & Education
Education by gender and cohort, 4 categories (ECV 2004/2011) graph-edu

The Calibration
Eﬃciency labor units by education and gender (ECV panel 2004-2011) graph-ute

The Calibration
Participation by coh, educ, gender & age. graph-part
AWG aggregate time series (77.7 → 83) + EPA to disaggregate by education
2000 2020 2040 2060
50
60
70
80
90
100
Participation Rate
All hist.
All projec
Male hist.
Male projec

The Calibration
Retirement: HLSS cohort 1940/1945.
2000 2020 2040 2060
50
60
70
80
90
100
Participation Rate
All hist.
All projec
Male hist.
Male projec

The Calibration
Retirement: HLSS cohort 1940/1945.
Unemployment by coh, educ, gender & age. Two scenarios:
(1) AWG assumptions 12% (2025) 8% (2035); (2) VAR 27% (2013) 16% (2050)
2000 2020 2040 2060
50
60
70
80
90
100
Participation Rate
All hist.
All projec
Male hist.
Male projec
2010 2020 2030 2040 2050 2060
5
10
15
20
25
30
Projected Unemployment Rate
data VAR AWG

The Calibration
The pension system: RGSS / Ret & survivors
System in place in 2011: D =15, tN = 65, tm = 61, ...

The Calibration
Initial conditions: pensions by coh, g & educ (HLSS+ECV); wealth (EFF02)

The Calibration
Individual pensions
1 Gross income/covered earnings: continuous Bu HLSS/ECV. graph-BR
2 Rep. rates: contributed years Nh from LC act proﬁles graph-years

The Calibration
Individual pensions
Discretional elements: Initial values and dynamics
Pmin incidence: 0.2 vs 0.166/0.266 (RGSS/total);
DATA Model
Pmax 1.36 1.37
Pmin Jub 0.27/0.40 0.3
Pmin Viud 0.24/0.33 0.2
Cotmax 1.51 1.60
Cotmin 0.35/0.48 0.52
(ratios to average male worker)

The Calibration
Individual pensions
Discretional elements: Initial values and dynamics
Pmin incidence: 0.2 vs 0.166/0.266 (RGSS/total);
DATA Model
Pmax 1.36 1.37
Pmin Jub 0.27/0.40 0.3
Pmin Viud 0.24/0.33 0.2
Cotmax 1.51 1.60
Cotmin 0.35/0.48 0.52
(ratios to average male worker)
2010 2020 2030 2040 2050 2060 2070
0
10
20
30
40
50
60
70
Upper and lower bounds on pensions & contributions
bmin
cmax
bmax

The Calibration
The pension system: aggregates
units DATA Model
Aggregate pension expenditure (2010) (% GDP)
Total 10.24 10.5
Retirement & survivors 8.8 9.1
Retirement 6.9 7.3
Survivors 1.9 1.8
Social contributions (2010) (% GDP) 13.2 13.2
% imputed to contr. pensions 0.71 0.71
System balance
Contributive Ret & Surv(*) 1.1 0.9
Trust Fund (2010) (% GDP) 6.14 6.0
* excluding minimum pensions.
Number (mill) Average (ths. Euros )
DATA Model DATA Model
Total 7.9 7.3 11.6 13.4
Retirement 5.4 5.0 13.2 15.5
Survivors 2.5 2.3 8.1 7.9

The Calibration
Public Expenditure and Macro Aggregates
K/Y 2.8/3; I/Y =21/25 %; rk/Y :38%; TAX/Y=0.22
Parameters: β=0.988, δ=6.0%, θ=0.38

The Calibration
K/Y 2.8/3; I/Y =21/25 %; rk/Y :38%; TAX/Y=0.22
Parameters: β=0.988, δ=6.0%, θ=0.38
Exogenous growth rate of productivity, ρt
: 1.1 → 1.6

The Calibration
K/Y 2.8/3; I/Y =21/25 %; rk/Y :38%; TAX/Y=0.22
Parameters: β=0.988, δ=6.0%, θ=0.38
: 1.1 → 1.6
CP/Y: (i) Health + LTC +Educ (% Gdp, AWG)
+ (ii) rest of CP
+ (iii) Transfers: Unemployment + Other pensions
2000 2010 2020 2030 2040 2050 2060
15
20
25
30
data Pc Pc + var Tr
1980 2000 2020 2040 2060
1
1.5
2
2.5
3
3.5
Unem expediture to GDP ratio

The Calibration
K/Y 2.8/3; I/Y =21/25 %; rk/Y :38%; TAX/Y=0.22
Parameters: β=0.988, δ=6.0%, θ=0.38
: 1.1 → 1.6
CP/Y: (i) Health + LTC +Educ (% Gdp, AWG)
+ (ii) rest of CP
+ (iii) Transfers: Unemployment + Other pensions
Debt/Y: Linked to Unemp.
2000 2010 2020 2030 2040 2050 2060
15
20
25
30
data Pc Pc + var Tr
1980 2000 2020 2040 2060
1
1.5
2
2.5
3
3.5
Unem expediture to GDP ratio
1980 2000 2020 2040 2060
20
40
60
80
100
120
Debt to GDP ratio

The Calibration
Alternative ECOs
2000 2020 2040 2060
−400
−200
0
200
400
600
800
Net Inmmigrant flow (1000s)
VAR
AWG
2010 2020 2030 2040 2050 2060
5
10
15
20
25
30
Projected Unemployment Rate
data VAR AWG
2010 2020 2030 2040 2050 2060 2070
1
1.5
2
2.5
3
Productivity Index
ρ=1.0
ρ=1.6
ρ=2.0
SCENARIO Demography Unemployment Productivity Survival B ref(†)
BAD VAR (low) VAR (high) Low NO
FAIR VAR (low) VAR (high) Avrg YES
BASE AWG (high) VAR (high) Avrg YES
GOOD AWG (high) AWG (low) High YES
(†)=Reform of Survival Pensions: cohorts entering the labor market now will not get an additional widow/widower pension if
they already enjoy an old-age pension.

Simulation path
Status Quo simulation, in the BASE and Alternative ECOs

Simulation path Status quo in the BASE ECO
Status Quo in the BASE ECO
The Status Quo system is that in place after 2011’s reform (R11),
featuring:
(i) Delay of the Statutory Retirement age 65 → 67;
(ii) Delay of the Early Retirement age 61 → 63;
(iii) Increase in the length of the pensions’ averaging period (15 → 25);
(iv) Minimum pension expenditure is transferred to the general budget.

Status Quo in the BASE ECO
The Status Quo system is that in place after 2011’s reform (R11),
featuring:
(i) Delay of the Statutory Retirement age 65 → 67;
(ii) Delay of the Early Retirement age 61 → 63;
(iii) Increase in the length of the pensions’ averaging period (15 → 25);
(iv) Minimum pension expenditure is transferred to the general budget.
(v) We add the reform of the Survival pensions for cohorts entering the
labor market from 2010.

Pension Expenditure path
2020 2040 2060 2080
6
8
10
12
14
16
18
20
22
Cotiz y Gasto Pen Contrib. sobre PIB
Pen
Pen sin pmin
Cotiz pen
Contributive pensions in deﬁcit in 2025; Trust Fund exhaustion: 2044
Tax collection % GDP: up from 22.1 in 2010 to 32.4 in 2050 and 34.2 in 2070

Number of pensions & average value
2010 2020 2030 2040 2050 2060 2070
0
5
10
15
20
Number of pensions (in millions)
Ret
Surv
Total
Pob+65
2020 2030 2040 2050 2060 2070
10
15
20
25
30
35
40
45
50
Average pension (thousand of 2010 euros)
Avr pension
Avr Ret pension
B ret(*) growth ∆ Num B Ret (†) ∆ Num All
2004/2012 4,99 88,8 112,1
2010/2020 2.20 90.0 142.8
2020/2030 3.34 209.1 257.3
2030/2040 3.81 279.6 314.7
2040/2050 3.92 207.0 202.5
2050/2060 3.11 52.1 0.7
* average annual growth rate of ret. pension; †= averg annual increase Num. pen. (thousands)

Retirement
1950 1960 1970 1980 1990 2000
60
61
62
63
64
65
66
67
68
Average retirement age by education
Primary Secondary Secondary advanced Higher
6061626364656667686970
0
0.2
0.4
0.6
0.8
Low education, u=1950
6061626364656667686970
0
0.2
0.4
0.6
0.8
6061626364656667686970
0
0.2
0.4
0.6
0.8
6061626364656667686970
0
0.2
0.4
0.6
0.8
High education, u=1950
6061626364656667686970
0
0.2
0.4
0.6
0.8
6061626364656667686970
0
0.2
0.4
0.6
0.8

Simulation path Alternative ECOs
Alternative ECOs
Institutional environment R11 ≡ System in place in 2011
2010 2020 2030 2040 2050 2060 2070
5
10
15
20
25
Pension expenditure to GDP ratio
bad
fair
base
good
2020 2040 2060 2080
0.8
1
1.2
Pension coverage
2020 2040 2060 2080
0.4
0.6
0.8
Demographic dependency ratio
2020 2040 2060 2080
0.5
0.6
0.7
0.8
0.9
Employment rate
2020 2040 2060 2080
0.1
0.15
0.2
0.25
Replacement rate
PP/Y Decomposition of PP/Y

Simulation path Alternative ECOs
R11 under alternative ECOs
Deﬁcit Contrib./GDP, Reform 2011
BAD FAIR BASE GOOD
2010 -1.1 -1.1 -1.0 -0.6
2030 3.1 2.3 1.1 -0.5
2050 16.4 12.4 7.8 2.0
2070 16.2 11.7 7.8 2.4
TAX Burden % GDP, Reform 2011
BAD FAIR BASE GOOD
2010 22.2 22.1 22.1 22.1
2030 26.6 25.4 23.6 21.5
2050 42.0 37.6 32.4 28.7
2070 43.7 38.8 34.2 31.1

Reform proposals
Pension Reforms, in the BASE and Alternative ECOs

Reform proposals Reforms in the BASE ECO
The experts committee proposal: FEI,FS Factor Sostenibilidad
Since 2019, the initial pension benefit is reduced according to the observed
increases in Life Expectancy.
Bt = FSEV
t α(.) BRt IEV
t = EV 2019
67 /EV t
67
BR = BaseReguladora, α = penalizaciones por edad/historial; EV t
67 = Esp. de vida INE
a los 67 años en el año t.
2010 2020 2030 2040 2050 2060
0.6
0.7
0.8
0.9
1

FRA Factor de revalorización anual , IR Índice de Revalorización
One-period ahead financial balance in t:
Gt+1 = It+1 ⇔ Gt(1 + gt+1)(1 + gP
t+1)(1 + gs
t+1) = It(1 + gI
t+1)
gt+1= growth rate of pensions that remain. gP
t+1= growth rate of the
number of pensions. gs
t+1= growth rate due to the replacement of old,
smaller pensions.

Gt+1 = It+1 ⇔ Gt(1 + gt+1)(1 + gP
t+1)(1 + gs
t+1) = It(1 + gI
t+1)
smaller pensions.
(1 + gt+1) =
1 + gI
t+1
(1 + gP
t+1)(1 + gs
t+1)
It
Gt

Gt+1 = It+1 ⇔ Gt(1 + gt+1)(1 + gP
t+1)(1 + gs
t+1) = It(1 + gI
t+1)
smaller pensions.
(1 + gt+1) =
1 + gI
t+1
(1 + gP
t+1)(1 + gs
t+1)
It
Gt
Smoothing:
1 MA(11) of all growth rates.
2 MA(11) (geo) of It
Gt
3 Reaction to imbalances controlled by α: ( It
Gt
)α

Workings of the FRA in the GOOD ECO
2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070
0.9
0.95
1
1.05
1.1
Componentes: nivel
2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070
−0.02
−0.01
0
0.01
0.02
0.03
Componentes: tasas
COT growth
PEN growth
2020 2030 2040 2050 2060
−5
−4
−3
−2
−1
0
1
2
Tasa indexación
10 20 30 40
2015 1.04 1.07 0.97 0.82
2025 1.03 0.93 0.79 0.70
2035 0.91 0.76 0.68 0.62

Alternative simulated proposals
MAX-I: Maximum pension indexation: R11 + Life Exp. adjustment (FEI)+
indexation of pension payment according to the max. possible growth (+0.25%
real, 2.5% π assumed)
MIN-I: Minimum pension indexation: R11 + Life expectancy adjustment (FEI)+
indexation of pension payment according to the min. possible growth (-2.25% real)
BAA: Bounded Automatic Adjustment system: R11 + Life expectancy adjustment
(FEI)+ Indexation to the Pension system Balance (FRA) with upper and lower %
limits (−2.25 ≤ g ≤ +0.25) (MAX-I and MIN-I are BAA’s upper and lower
bounds)

Alternative simulated proposals
MAX-I: Maximum pension indexation: R11 + Life Exp. adjustment (FEI)+
indexation of pension payment according to the max. possible growth (+0.25%
real, 2.5% π assumed)
MIN-I: Minimum pension indexation: R11 + Life expectancy adjustment (FEI)+
indexation of pension payment according to the min. possible growth (-2.25% real)
BAA: Bounded Automatic Adjustment system: R11 + Life expectancy adjustment
(FEI)+ Indexation to the Pension system Balance (FRA) with upper and lower %
limits (−2.25 ≤ g ≤ +0.25) (MAX-I and MIN-I are BAA’s upper and lower
bounds)
NDC: Notional Deﬁned Contribution system: R11 + Linear transition (from 2015
to 2050) to a system of Notional Accounts where all cohorts get the same TIR on
their contributions. NDC

Workings of the BAA in the BASE ECO
2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070
0.9
0.95
1
1.05
1.1
Componentes: nivel
2020 2025 2030 2035 2040 2045 2050 2055 2060 2065 2070
−0.02
−0.01
0
0.01
0.02
0.03
Componentes: tasas
COT growth
PEN growth
2020 2030 2040 2050 2060 2070
−5
−4
−3
−2
−1
0
1
2
Tasa indexación
10 20 30 40
2015 1.02 0.89 0.71 0.57
2025 0.88 0.70 0.56 0.45
2035 0.82 0.63 0.52 0.42
Working of the Unbounded FRA graph-FRA

PP/Y in the reformed systems (BASE ECO)
2010 2020 2030 2040 2050 2060 2070
4
6
8
10
12
14
16
18
20
MAX−I
BAA
MIN−I
2010 2020 2030 2040 2050 2060 2070
4
6
8
10
12
14
16
18
20
R11
MAX−I
BAA
MIN−I
NDC
BAA and its ﬂoor/ceiling R11,BBA & NDC

Pension system balance
2010 2020 2030 2040 2050 2060 2070
−15
−10
−5
0
5
(Contributive) pension system balance (% of GDP)
MAX−I
BAA
MIN−I
2010 2020 2030 2040 2050 2060 2070
−15
−10
−5
0
5
(Contributive) pension system balance (% of GDP)
R11
MAX−I
BAA
MIN−I
NDC
BAA vs 2011 Reform, “savings”
BAD FAIR BASE GOOD
2020 0.2 0.1 -0.1 -0.2
2030 1.8 1.5 0.9 -0.1
2040 5.0 4.1 3.1 1.3
2050 8.6 7.3 5.5 3.6
2060 9.5 8.4 6.5 4.3

Pension expenditure: incidence of ﬂoor/ceiling
TAX Burden, Eco BASE
R11 BAA NDC
(-2.25%) ( 1.0%)
2010 22.1 22.1 22.1
2030 23.6 22.9 22.5
2050 32.4 26.8 24.7
2070 34.2 27.1 25.3

Pension expenditure: incidence of ﬂoor/ceiling
TAX Burden, Eco BASE
R11 BAA NDC
(-2.25%) ( 1.0%)
2010 22.1 22.1 22.1
2030 23.6 22.9 22.5
2050 32.4 26.8 24.7
2070 34.2 27.1 25.3
2020 2040 2060 2080 2100
0
0.05
0.1
0.15
0.2
0.25
Incidence of minimum pension (%)
R11 BAA NDC
2020 2040 2060 2080 2100
0
0.05
0.1
0.15
0.2
0.25
Incidence of maximum pension (%)
R11
BAA
NDC

Intergenerational redistribution (BASE ECO): cohorts born 1980 & 2010
40 60 80 100
5
10
15
20
25
30
35
40
45
Ingresos u= 1980
40 60 80 100
5
10
15
20
25
30
35
40
45
Ingresos u= 2010
Expected real income of the representative households born in 1980 & 2010 (secondary
education). Thousands of 2010-Euros;
Consumption life-cycle proﬁles graph-c

Reform proposals Reforms in the Alternative ECOs
Pension DEFICITS % GDP in the 4 ECOs
Eco BAD
R11 BAA NDC
(2.5%) ( 0.0%)
2010 -1.1 -1.1 -1.1
2030 3.1 1.3 0.8
2050 16.4 7.7 4.3
2070 16.2 6.4 2.2
Eco FAIR
R11 BAA NDC
(2.5%) ( 1.0%)
2010 -1.1 -1.1 -1.2
2030 2.3 0.8 0.2
2050 12.4 5.0 2.5
2070 11.7 2.9 0.3
Eco BASE
R11 BAA NDC
(2.5%) ( 1.0%)
2010 -1.1 -1.1 -1.1
2030 1.1 0.2 -0.7
2050 7.8 2.3 0.5
2070 7.8 0.9 -1.1
Eco GOOD
R11 BAA NDC
(2.5%) ( 3.0%)
2010 -1.1 -1.1 -1.2
2030 -0.9 -0.8 -2.3
2050 4.0 0.4 -0.7
2070 4.7 0.1 -0.3

FISCAL BURDEN % GDP in the 4 ECOs.
Eco BAD
R11 BAA NDC
(2.5%) ( 0.0%)
2010 22.2 22.1 22.1
2030 26.6 24.8 24.3
2050 42.0 33.3 30.1
2070 43.7 33.8 30.0
Eco FAIR
R11 BAA NDC
(2.5%) ( 1.0%)
2010 22.1 22.1 22.0
2030 25.4 23.7 23.7
2050 37.6 30.3 27.7
2070 38.8 30.0 27.6
Eco BASE
R11 BAA NDC
(2.5%) ( 1.0%)
2010 22.1 22.1 22.1
2030 23.6 22.9 22.5
2050 32.4 26.8 24.7
2070 34.2 27.1 25.3
Eco GOOD
R11 BAA NDC
(2.5%) ( 3.0%)
2010 22.1 22.1 22.0
2030 21.5 21.7 20.4
2050 28.7 24.2 24.2
2070 31.1 26.5 26.2

BAA reform: Welfare impact by cohort
Low educ
BAD FAIR BASE GOOD
1940. -0.8 -0.6 -0.3 0.0
1950. -3.0 -2.2 -1.0 0.1
1960. -5.7 -4.8 -3.3 -1.1
1970. -6.8 -5.9 -4.6 -2.9
1980. -6.3 -5.5 -4.4 -3.3
1990. -6.1 -5.1 -3.9 -3.2
2000. -2.5 -2.2 -1.9 -2.3
2010. 1.1 0.1 -0.3 -1.3
2020. 5.4 1.7 0.9 0.2
High edu
BAD FAIR BASE GOOD
1940. -0.9 -0.7 -0.4 -0.1
1950. -2.8 -2.1 -1.0 0.0
1960. -5.4 -4.5 -2.9 -1.1
1970. -6.4 -5.5 -4.1 -2.6
1980. -4.4 -4.3 -3.4 -2.9
1990. 0.3 -1.4 -1.3 -2.5
2000. 7.1 4.5 3.2 0.8
2010. 12.7 9.2 6.8 3.9
2020. 16.5 12.1 9.1 5.9
EV=% shift in the life-cycle consumption proﬁle under the status quo

Conclusions & future research
Wrapping up
1 Status Quo Path: Under R11, PP/Y will increase without
corresponding increases in income.
Depending on the environment, the deﬁcits (tax hikes) vary from
substantial to huge
Sizable behavioral reaction to eg. pmax/pmin policy.

Wrapping up
1 Status Quo Path: Under R11, PP/Y will increase without
corresponding increases in income.
Depending on the environment, the deficits (tax hikes) vary from
substantial to huge
Sizable behavioral reaction to eg. pmax/pmin policy.
2 Reforms: If implemented, the sept-2013 proposal will be the most
ambitious attempt to restore the financial balance of the pension
system.
In our BASE environment, it fails to fully restore the financial balance
(Adjustments needed are too strong, hitting the lower limits in pension
depreciation) . Notwithstanding, it goes a long way towards that target.
Large imbalances remain in tougher macro/demographic environments

Conclusions
Problems with BAA:
Ignores the implicit liabilities: no adjustment until the imbalance
emerges, Large diﬀerences in the treatment of current cohorts.
Contrast with Sweden: accumulate Trust Fund ex ante (imbalance in the Balance
Sheet vs ﬂows)

Conclusions
Problems with BAA:
Sheet vs ﬂows)
Is a downward sloping consumption path the best that can be
achieved?
Is transferring wealth via inﬂation-driven income erosion “right”?
Methodological Improvements (applied GE approach)
1 Microsimulation: move beyond the Representative Households
2 More precise calibration

Conclusions
Problems with BAA:
Sheet vs ﬂows)
Is a downward sloping consumption path the best that can be
achieved?
Is transferring wealth via inﬂation-driven income erosion “right”?
Methodological Improvements (applied GE approach)
1 Microsimulation: move beyond the Representative Households
2 More precise calibration
Thanks for your comments

Supplemental stuﬀ

Education
2000 2010 2020 2030 2040 2050 2060
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Education
Primary
Secondary 1st
Secondary 2nd
Higher
back

Eﬃciency Labor units
20 30 40 50 60 70
5
10
15
20
25
30
35
Educación Varones
baja
media/baja
media/alta
alta
20 30 40 50 60 70
5
10
15
20
25
30
35
Educación Mujeres
baja
media/baja
media/alta
alta
back

Participation
1920 1940 1960 1980 2000 2020
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Single earner households by cohort
Low
low/Avrg
Avrg/High
high
back

Initial Pensions
1940 1950 1960 1970 1980 1990 2000
0
0.2
0.4
0.6
0.8
1
1.2
Ratio B a salario medio, τ=65
low low/avr avr/high high
back

Number of contributed years
1940 1960 1980 2000
10
20
30
40
Primary educ
1940 1960 1980 2000
10
20
30
40
Secondary
1940 1960 1980 2000
10
20
30
40
Secondary advanced
1940 1960 1980 2000
10
20
30
40
Higher education
back

NDC
1950 1960 1970 1980 1990 2000
0
5
10
15
20
25
Transition DB−NDC High Educ Male
Mixed
NDC pure
SQ
1950 1960 1970 1980 1990 2000
0
5
10
15
20
25
Transition DB−NDC High Educ Female
Mixed
NDC pure
SQ
back

Unbounded FRA reform: Growth rate of indexation
2020 2030 2040 2050 2060 2070
−7
−6
−5
−4
−3
−2
−1
0
1
2
Indexation growth rate
bad
fair
base
good
back

Intergenerational redistribution (BASE ECO): cohorts born 1980 & 2010
40 60 80 100
10
20
30
40
50
Consumo, coh 1980
40 60 80 100
10
20
30
40
50
Consumo coh 2010
thousands of 2010-Euros; Representative Agents of households with secondary education.
back

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