Transcript Document

Intergenerational problem
Generation
G1
G2
Time t1
+$1
-$1
Time t2
Time t3
Time t4
+$1
G3
G4
-$1
+$1
-$1
+$1
Intergenerational problem
• Each generation lives for two periods
(young and old).
• The initial generation (G1) is old at time t1.
• They receive $1 per head by taxing
generation G2 at time t1.
• Similarly, G2 receives $1 by taxing G3 in
t2. G3, in turn, gets $1 in t3 by taxing G4.
• This process continues indefinitely.
Intergenerational problem
• Let us now consider two systems: pay as you go
and a switch to privatized system. We will
consider the outcomes in turn.
• Pay as you go: It is easy to see that each
generation (except the generation G1) pays $1 in
one period and gets $1 in the following period.
For example generation G2 pays $1 in t1 and gets
$1 in t2. Therefore, the rate of return is zero.
Intergenerational problem
• Privatized scheme: Let us assume that the
investors are only allowed to invest in bonds under
a privatized individual account system. Let us
suppose that the system starts at t2. Suppose the
rate of return on the bond is 5%.
Intergenerational problem
• It might seem that the individuals in generation G3
would now get $1.05 in period t3 rather than $1 in
the pay as you go regime. Note that the $1 that is
owed to G2 has to be paid from somewhere.
Suppose that the government pays G2 by selling
bonds in t2. The only way the government can
sell the bonds is to offer a market interest rate of
5%. In other words, the government owes $1.05
in t3.
Intergenerational problem
• If the government simply wants to keep the
principal of the loan at $1, it has to pay for the
interest payment in t3. If this five cents
($0.05=$1.05-$1.00) is to be paid for by taxes, it is
likely to tax the younger generation. Thus, the net
gain of G3 would be $1.05 (from bond holding)
minus $0.05 (from tax payment). Thus, once the
interest cost (through taxes) is included, G3 does
not gain anything from the new privatized system.
Intergenerational problem
• Once the government has borrowed that $1,
private accounts do not generate any additional
national savings. The $1 extra in private accounts
is exactly offset by $1 extra borrowed by the
government. With no added savings at the
national level, there would be no additional capital
formation and therefore no increased wealth for
future generations. In future years, nobody in the
society will have more income than they would
under a pay as you go system.
Intergenerational problem
• The result can be worse for the retired old.
If the taxes are paid (at least in part) by the
old, they will be worse off. Instead, if the
benefits are cut, the retired generation will
be worse off as well.
Intergenerational problem
• There is one way of making future generations
better off by privatization. Suppose young people
direct their $1 contribution to privatized individual
accounts. The $1 hole is now "financed" in two
parts. The government cuts the benefits of the
current old generation by $0.50 and imposes an
additional tax of $0.50 to the current young
generation. This means no new borrowing is
necessary to finance anything else in the future.
Future generations will be able to enjoy the 5%
without offsetting taxes.
Intergenerational problem
• Of course, there is no free lunch. The above
process will make the current old generation
worse off. They will see their benefits
dwindle by $0.50. In addition, even though
the current young people will get a 5% rate
of return on their investment, they will also
pay an additional tax of $0.50.
Intergenerational problem
• The essential nature of this argument does
not change if we have other forms of
financing schemes. For example, if all
generations hold diversified portfolios (with
bonds and stocks), it does not alter the
conclusion. The main insight is that higher
rates of return for stocks also have higher
risk.
Intergenerational problem
• In summary, privatization of accounts by
itself does not have any effect on the
economy as a whole. Benefits from
privatization only comes from raising taxes
or cutting benefits (or both) which might
then be used to raise national saving.
• Consider a worker who earns ws at time s,
assumed to grow exponentially at rate g:
• (1) ws = w0egs.
• The tax rate on these earnings is t. There is
a proportional front-load charge of f, so that
t(1-f) w0egs is deposited at time s.
• This accumulates until retirement age T.
• The accumulation occurs at rate r-c, where r
is the rate of return and c is the management
charge per dollar under management.
• Thus deposits made at time s have
accumulated to t(1-f) w0egs e(r-c)(T-s) at time
T.
• The total accumulation at time T is the integral
of this expression from time 0 until time T.
Integrating, the accumulation depends on f
and c and (for g+c unequal to r) is equal to:
• (2) A[f, c] = t(1-f)w0e(r-c)T{e(g+c-r)T - 1}/(g+c-r).
• For g+c=r, the accumulation satisfies
• (3) A[f, c] = t(1-f)w0e(r-c)T T.
• How do we get (3) from (2)?
• For r unequal to both g+c and g, the ratio of the
accumulation to what it would be without any
charges satisfies:
• (4) AR[f, c] = A[f, c]/A[0, 0]
=(1-f)e-cT{(e(g+c-r)T - 1)/(e(g-r)T - 1)}{(g-r)/(g+c-r)}.
• The charge ratio is one minus the accumulation
ratio:
• (5) CR[f, c] = 1 - AR[f, c].
Time
Value
Contribution
Fund return
Fee on flow
Fee on saldo
0
V0
-
1
V1
C1
r1
f1
s1
2
V2
C2
r2
f2
s2
…
…
…
…
…
…
t
Vt
Ct
rt
ft
st
• Let Vt denote the value of the fund at the
end of time t. The contribution during time t
is denoted by Ct (we will assume that the
entire payment occurs at the beginning of
the period so that the interest earned by the
contribution is the same as interest earned
by the balance Vt-1 brought in from the
previous period).
• The rate of return between time t-1 and time
t is denoted by rt. There are two types of
fees charged by the AFOREs: fees on flow
and fees on saldo. We denote the fee on
flow at period t by ft and the fee on saldo at
period t by st.
• Therefore, we can write the value of the fund at
time 1 as follows:
• V1 = [V0 + c1(1 - f1)](1 + r1)(1 – s1)
• Similarly, the value of the fund at time 2 can be
written as follows:
• V2 = [V1 + c2(1 –f2)](1 + r2)(1 – s2)
• In general, we can write this recursive relation that
connects period t-1 and t as follows:
• Vt = [Vt-1 + ct(1 – ft)](1 + rt)(1 – st)
• There is an additional contribution by the
government in the form of a cuota social.
• According to the law, cuota social is not subject to
fees on flow. Thus, we need to add the cuota social
in the formula ensuring that it stays outside the
fees ft. Let us denote the cuota social at time t by
cst. Then, the modified formula takes the
following form:
• Vt = [Vt-1 + cst + ct(1 – ft)](1 + rt)(1 – st)
• AFORE 2003 Spreadsheet
• Comparison with IMSS
Administrative cost as a proportion of total expenditure
0.26
0.24
0.22
ratio
0.2
0.18
ratio
0.16
0.14
0.12
0.1
1944
1949
1954
1959
1964
1969
year
1974
1979
1984
1989
1994
Reform in Mexico
1
0.9
0.8
0.7
0.6
tax
privatiz
internat
tariff
capital mkt
total
0.5
0.4
0.3
0.2
0.1
0
1970
1975
1980
1985
1990
1995
CONSAR
Comisiones Equivalentes sobre saldo a 25 años
Enero 2001
(Porcentaje anual)
Afore
Banamex
ING
Bancomer
Principal
XXI
Tepeyac
Allianz Dresdner
Garante
Banorte Generali
Profuturo GNP
Inbursa
Santander Mexicano
Promedio
Sobre Saldo
0.70
0.75
0.76
0.87
0.88
0.88
1.18
1.26
1.47
1.51
1.58
1.85
1.14
Junio 2004
(Porcentaje anual)
Afore
Actinver
Azteca
Inbursa
Banamex
IXE
XXI
ING
Bancomer
Santander Mexicano
Principal
HSBC
Banorte Generali
Profuturo GNP
Promedio
Sobre Saldo
0.54
0.56
0.64
0.67
0.69
0.71
0.74
0.76
0.79
0.80
0.88
0.98
1.05
0.75
Disminución
de 34%
Comparar ambos resultados
•
•
•
•
El Reforma dice 19% de las aportaciones
La CONSAR calcula sobre el saldo
El Reforma dice que ha sucedido hasta ahora
La CONSAR calcula con una proyección a 25
años
• Ademas, CONSAR supone que cada persona se
mantiene con la misma AFORE durante 25 años
• La verdadera competencia debe permitir la
posibilidad de cambiar de AFORE sin castigo
1.0
0.4
2004
2006
2008
2010
2012
2014
2016
2018
2020
2022
2024
2026
2028
2030
2032
2034
2036
2038
2040
2042
2044
2046
2048
2050
2052
2054
porcentaje del PIB
Seguro Social sin reforma y con reforma
1.2
Sin reforma
0.8
0.6
Con reforma
0.2
-
Costos fiscales comparativos
año
sin reforma con reforma
2004
4,0
42,6
2005
4,8
44,0
2006
5,8
45,5
2007
7,0
47,0
2008
8,3
48,4
2009
9,8
50,0
2010
11,5
52,1
2011
13,4
53,8
2012
15,5
55,3
Miles de milliones de pesos
Valor presente neto a diferentes
tasas de descuento
tasa desc. sin reforma con reforma
0%
6.217,24
4.462,17
3%
2.148,28
1.967,91
4%
1.555,03
1.566,34
5%
1.143,97
1.272,91
8%
502,65
762,33
10%
314,99
583,56
12%
209,70
467,23
15%
125,94
356,25
Portafolio de AFOREs
RBANA
RBANCO
RBANCRE
RBANOR
RBITAL
RGARAN
RINBURSA
RPRIN
RPROF
RSANTA
RTEPE
RXXI
RZURICH
RBANA RBANCO RBANCRE RBANOR
1.000000 0.970261 0.965125 0.979338
0.970261 1.000000 0.951128 0.965575
0.965125 0.951128 1.000000 0.985814
0.979338 0.965575 0.985814 1.000000
0.991506 0.947308 0.964006 0.976829
0.976777 0.953378 0.981639 0.977286
0.945123 0.962747 0.907559 0.936538
0.974113 0.971846 0.981446 0.988925
0.970116 0.938333 0.979318 0.973308
0.974260 0.992384 0.946852 0.970506
0.961615 0.959032 0.959835 0.971406
0.978015 0.984221 0.971962 0.985942
0.962033 0.968543 0.969118 0.985690
Rendimientos de las AFORES
0.6
BANAMEX
0.5
BANCOMER
BANCRECER
BANORTE
0.4
BITAL
GARANTE
INBURSA
PRINCIPAL
0.3
PROFUTURO
SANTANDER
TEPEYAC
0.2
XXI
ZURICH
INFLATION
0.1
0
1997:07
1997:10
1998:01
1998:04
1998:07
1998:10
1999:01
1999:04
1999:07
1999:10
2000:01
2000:04
Risk vs Return
0.09
0.085
efficient frontier
0.08
Return
0.075
0.07
0.065
0.06
0.055
0.05
0.065
0.07
0.075
0.08
0.085
Risk
0.09
0.095
0.1
0.105
Valor en Riesgo Historico Diario
0.3500%
0.3000%
ALLIANZ
BANAMEX
0.2500%
BANCOMER
BANORTE
INBURSA
0.2000%
ING
PRINCIPAL
PROFUTURO
0.1500%
SANTANDER
XXI
SISTEMA
0.1000%
0.0500%
10/21/2002 12/10/2002
1/29/2003
3/20/2003
5/9/2003
6/28/2003
8/17/2003
10/6/2003
11/25/2003
• Scenario 1: Affiliate with three minimum
salary (flat profile with the assumption of
the salario minimo at 16,931 per year), 5%
real interest rate (we assume it is the same
for all AFORES), 0% inflation, 0 initial
quantity brought into the system
years
Actinver
Allianz
Azteca
Banamex
Bancomer
Banorte
Inbursa
ING
Principal
Profuturo
Santander
XXI
10
48988
44096
48641
44741
44814
45586
51021
44802
44781
43229
44529
46797
25
184925
162062
184673
172367
170311
168286
186746
170861
171059
156911
172468
176669
40
457955
392843
463193
441144
431209
412130
451851
432929
431103
369977
433842
442068
45
600120
510765
609429
584866
570098
538395
586596
572441
567955
476267
571075
581403
• Scenario 2: Suppose we keep all the other
assumptions the same as in scenario 1 but
simply change the amount of money an
affiliate brings into the system. (3 times
salario minimo and 5% real return with 0%
inflation but an initial amount of 50,000.)
Actinver
Allianz
Azteca
Banamex
Bancomer
Banorte
Inbursa
ING
Principal
Profuturo
Santander
XXI
10
128499
121559
128873
126186
126259
123830
128484
126247
123380
119148
122144
126628
25
344371
311437
347755
341685
339629
323782
336122
340179
329309
298958
330233
337721
40
777697
680892
794679
793144
783208
721150
739899
784928
750361
635751
754521
766979
45
1003328
869296
1029334
1034116
1019349
926910
945127
1021691
971360
803762
977291
991950
• Impact of the real interest rate: If the real
interest rate is high and stays high (for
example, 10%), the charges of Inbursa
begin to have a bigger bite by the twentyseventh year. Azteca becomes the best
AFORE.
Actinver
Allianz
Azteca
Banamex
Bancomer
Banorte
Inbursa
ING
Principal
Profuturo
Santander
XXI
10
64872
58381
64466
59345
59465
60422
67600
59437
59283
57164
58929
62039
25
394691
344260
395199
370014
367399
360821
396993
368168
363976
331366
366540
377878
Actinver
Allianz
Azteca
Banamex
Bancomer
Banorte
Inbursa
ING
Principal
Profuturo
Santander
XXI
10
64872
58381
64466
59345
59465
60422
67600
59437
59283
57164
58929
62039
25
394691
344260
395199
370014
367399
360821
396993
368168
363976
331366
366540
377878
27
484327
420763
485810
456027
452418
442076
485273
453408
447351
403558
450768
464135
40
1724476
1457023
1749382
1673080
1653716
1560366
1679151
1657816
1607456
1362927
1625334
1663410
Comparación internacional
Comisión (%
aportación)
Kazajstán
El Salvador
Uruguay
Suecia
Chile
México
Argentina
Reino Unido
Polonia
Perú
21,4
12,5
13,5
15,2
15,0
23,1
36,2
21,3
19,3
22,1
Comisión
Equivalente
sobre Saldo
a 25 años
0,52
0,58
0,67
0,75
0,76
0,80
0,92
0,90
1,01
1,20
Edward Whitehouse study, 2000
Bolivia
Australia
Kazakhtan
Colombia
Sweden
Uruguay
El Salvador
Chile
Poland
Peru
UK(Stakeholder)
UK(Personal)
Argentina
Mexico
0%
5%
10%
15%
20%
25%