The effects of longevity and distortions on education and retirement

(1)

No ₅₉₀ _{ISSN 0104-8910}

The Effects of Longevity and Distortions on

Education and Retirement

Pedro Cavalcanti Ferreira, Samuel de Abreu Pess ˆoa

(2)

Os artigos publicados são de inteira responsabilidade de seus autores. As opiniões

neles emitidas não exprimem, necessariamente, o ponto de vista da Fundação

(3)

∗

†

! "

" # $ % &

% ' # % "

& ' %

% # ! " (

" " % # $

& " "

# )# #

& % #

% * )# # % +,- %

+.-# $ & ! &

& &

* # / "

0 ! #

∗_/ _' _% _{1 2 $} _{& 3} _4# _&

% % # #

' % ( 5 *"4 0 & 65 7 8 #

†₄ ₉ _: _{9 ;&} _{<2 9} ₌ _&

4 >?,& >>+.& 1 & 1& +++.@"?,,& 4 0 # & &

A # A #

(4)

6 %

# $ >??,& +.

)# #& 9 5 :>?BC; &

% B#D # 4 +,,, E >+ :1 :+,,+;;#

#

& ! % & & CD &

5 = :+,,+;# 6 %

FF # % &

( # ! +,

>?,, % C+#D & +,,, % ! .F#D

& >." #

% # 9 % !

% ' & * & G % %

# H

& & %

" #

& "

# :+,,>; !

+#B >DD, >@#> >?@,#

3 & " B. % .D- >?@,

>B- >?D. :I "60 / :+,,C;;# $ &

' % ! & % '

% # H % & 9 :>??+; (

C . >?.,& % # 3

BB#? >?.,".. B+#B >?D.">??,# 3

& %

G E

#

$ % # $

% & % ' #

% % %

(5)

# 8 ' # $ ! & % & % % '

& ! " (

: # #& H ' & :+,,@;& ;#

% ' J & % % % &

% % '

' #

$ & &

# / ! ( % ' %

" # )# # #

/ * * # 3 & "

"

" %

% # % ' %

& & # %

% % & %

% #

% ! #

/ %

! # % :K L

K L; * !

# & ! % '" &

" " &

% ' # %

# * & E ( &

: ;&

! # & % % " !

! &

% :>??,;& #

/ ! #

& & % %

& ! % &

# $ :+,,@;& :>??>; I ' "60 &

(6)

/ :+,,,; 4 '' & ! :+,,+;

( " ! #

& ! 4 '' &

! :+,,@;& )# # >?.,# I ' :+,,@; %

% ' % & !

)# # >_#

& % '

& % # 4

I % :+,,,; I :+,,,; & !

# 3 & " &

1 :+,,+;#

' % "

# I ' "60 / :+,,C; % !

& % % &

# ! & %

" & &

# " & #

! ! %& % ' # $ &

! 9 :>?D,;&

% & '

# $ "

& # H % & !

# 5 & &

! #

& % " &

! # $ & :>??@; 4 I %:+,,+;& %

" & # / %

% '& ! ! (

# ' :>??.; H ' :>???;

> ₄ _I _{% :+,,,;} ₃ _" _{:+,,>;& %} _{3 "}

% " # 5

% M ! !

* " " #

(7)

% & # :>??@;% &

" % '# $ % :>??,;& %

" 0 ! #

% * * #

0 % # $ ! % G

! ! # @

# ' %

C& % & &

.# B #

( % & : ;&

# H * %

" "E & % ! # $ %

! 0 # " "

& & ! ! ( & #

G ! ( N

& E #

& % " K L K L "

% "

# 9 " ! & " #

* % # !

" #

& % & ! ! &

E # :>?F.; %

% E

! # & &

& % # H &

% % !

% % N %

>?B, % O>,, O.,, >,">+ !

(8)

% >?@,# :+,,@; >??, P (

& ! # H %

% O.,,, >??. !

>,-% >?B,

:>?F.; ! P "

F."?, % ! % %

% >?@, >?B, ! E

% #

>@#F ! & ,#C $ P

@ :>?D,;& I ' :>??B; "

:>?FF;& & ( ! ! ! &

% #

0 % N ! %

% # /

* #

% &

M

# Y1 " K1

' H1 N

Y1 =A1K1α H11−α ,

% A1 " # ' N

H1 =L1eφ(TS)

% L1 % # * & % ' %

TS eφ(TS) % ' %

# φ(TS) !

& φ′₍_T

S)eφ(TS) !

# ' % & N

Y2 =A2K2α (L2eφ(TS))1−α ,

(9)

pi i" # ( ! 0 (

Ri =piαiAikiαi−1 wi =pi(1−αi)Aikiαi&

% Ri & wi % : % % " "E

! ;&

ki≡

Ki

Lieφ(T )

, :>;

i" Q #

$ &

# > & % N

R≡R1 =α1A1k1α −1 =pα2A2k2α −1 =R2

w≡w1 = (1−α1)A1k1α =p(1−α2)A2k2α =w2,

% p # "

!#

% " & % " & %

& p k, "% ' ' Q N

yi(p, k) =Aileφ(T )li(p, k) [ki(p)]αi, i= 1,2 :+;

% yi i, l G % %

li i.

% " % ' %

# 3 & % & !

% * #

$ T TR #

# $ ( & :K L& TY), (

TC TS # 6 &

# E ' & % ' TW # %

" N T/1& % % % " "E " % !

(10)

" T/2& % : % ;#

% : # #& H ' & 1#& # # &

+,,@; " : ; " ! ( % ' J " #

% %

% ' # " " %

& % * T

# N

T

0

e−ρa

[βlnc(a) + (1−β) ln (1−l(a))] a, :@;

% c(a) l(a) a "

& % ρ # / 0 % #

$ " % & &

" % # $

N

TR+T/

TR

e−ra

(1−τ )w(Ts, a, x)l(a) a+ T

0

e−ra

χ a :C;

=

T

0

e−ra

c(a) a+ (1 +τH)

TR

T

e−ra

ηp a&

% r &w(Ts, a, x) % "a% ' % Ts

! x, τ ! : ; % χ #

! & % τH ! : ;

η

+_# _!

% *

#

+_/ _" _{# $}

& η #

(11)

w(Ts, a, x) % N

w(Ts, a, x) =weφ(TS)x(a),

% x(a) K ! L % % '#

& % ' J ! "

( % % # H ' &

:+,,@;& & >?C, >??,& %

' & % & &

% ! #

" "E :x) % N

x(a) = e

γ(a−TR) T

R ≤a≤TR+T/1

eγT/ −ξ(a−(TR+T/ )) a≥T

R+T/1,

:.;

& % ' E ' : TY ;

TW1 ! γ.

& ξ % ' @_#

( "

N

l(a) = 1− 1−β e

(r−ρ)a

(1−τ )weφ(T )_x₍_a₎, :B;

% :C;#

$ # 9 &

% E '

E ' % #

E ' & % 0 N

1−β

= (1−τ )weφ(T )_e−(r−ρ)(TR+T/)_x₍_T

R +T/).

@ _{x a} _{x a} _eγ a−TR ξ a−TR _, _% _{γ >}

ξ < . H % & !

% ! & % ! :.; #

(12)

$ % TR +T/ > TR +T/1 % & :.;

! & N

e−ρ(TR+T/)1−β ₌_e−r(TR+T/)₍₁₋_τ ₎_weφ(T )_eγT/ −ξT/ _. _:F;

* * & &

% #

$ & ! 0 :@; E :C;# "

& % J ( N

c(a) =c(0)e(r−ρ)a_. _:D;

$ ( % ' % "

# : * C ; ! :D;&

:.;& :B; % N

c(0)1−e−

ρT

ρ + (1 +τH)pηe

−rT 1−e−rT

r +e

−ρTR1−β1−e

−ρT/ ρ

= (1−τ )weφ(T )e−rTR 1−e

−(r−γ)T/

r−γ +e

−(r−γ)T/ 1−e

−(r+ξ)T/

r+ξ +χ

1−e−rT

r ,

" J % &

' % C _#

% : " ; & & #

5 % * " *

#

!

$ & *

# $ & ' *

C _' _% _% _& _' _# ₍

% ! γ %

ζ

(13)

! 0 % & :C;N

max

T

 

T +T +T/

T +T

e−ra

(1−τ )weφ(T )x(a)l(a) a−(1 +τH)

T +T

T

e−ra

ηp a

 .

$ ' : (! ;&

& :T/;& ! # 3 "

& % & # /

% ' &T +T/1& !

M ( " ._#

$ & ( " % B_N

(φ′₍_T ₎₋_γ₎_{ ₍₁₋_τ ₎_weφ(T ) 1−e−(r−γ)T/

r−γ +e

−(r−γ)T/ 1−e

−(r+ξ)T/

r+ξ −

1−β

e(r−ρ)TR1−e

−ρT/

ρ }= (1−τ )we

φ(T )₋ 1−β_e(r−ρ)TR _{+ (1 +}_τ

H)ηp. :?;

! * &

" & & " # "

: ; % ' : # #& % ;

# % :

; " % %

& ! F_#

5 * :?; 1 +τH : :F;

(1−β)/ weφ(T )_; _! _& _!

& * ! # 5 %

& ! ! % % &

. _T

W ! # ! "

( H ' & :+,,@; ' !

& % #

B _{& :?;} ₍ _" _% _& _' ₍ _%

:F; & % : ; 0 #

F_$ _& _& _' _%

! # $ * ( N weφ T _φ′ _T

S −e

−

r we

φ T _τ

H ηq,

% * : " ;

% ' : " ;#

(14)

! (1 +τH) (1−τ ) % ! :

weφ(T )₎ _& _* _& _#

"

0 ment _{& %} _m_≡_n/ ₁₋_e−nT _&

t

t−T

mens _s₌_ent_.

/ & # N(a) a" #

# t a" s =t−a# / N

N(a) = me

ns

ent =me

−na_. _:>,;

N , N , N/, N & & & & % ' &

# / N

N =

T +T

T

me−na _a₌_e−nT 1−e−nT

1−e−nT .

' % & % N

N = 1−e

−nT

1−e−nT , N/ =e

−nTR1−e

−nT/

1−e−nT N =e

−n(T−TR)1−e

−nT

1−e−nT .

$ 0 (2)% l&

G % % # % ' TR TR +T/, %

N

l=

TR+T/

TR

N(a)l(a)x(a) a.

! ( :.;& :B;& ! N(a) :>,;

:F; & & % N

l=me−n(TR+TW>)_eγT/ _× _:>>; 1−e−(γ−n)T/

γ −n +e

−(n+ξ)T/ e

(n+ξ)T/ ₋₁

n+ξ −

1−e−(r−(ρ+n))T/ r−(ρ+n) .

(15)

#

$ %

& !

& # ( N

τHp

TR

T

N(a)η a=τHp m ηe−nT

1−e−nT

n ,

τ

TR+T/

TR

N(a)weφ(T )_x₍_a₎_l₍_a₎ _a,

∇ τIRK. * &

@ ent _:

χ=τHpηme−nT

1−e−nT

nent +

τIRK ent +

τ ent

TR+T/

TR

N(a)weφ(T )_x₍_a₎_l₍_a₎ _a, _:>+;

#

&

!'

4 * & % !

& % * ' #

N

c≡ C(t) ent =

T

0

N(a)c(a) a.

$ % * :D; * %

c=c(0)me

(r−(ρ+n))T ₋₁

r−(ρ+n) :>@;

( ! ! "

! #

/ % " * & %

% * N

(16)

• * ' N

y2(p, k) =ηme−nT

1−e−nT

n . :>C;

• * ' N

r = (1−τI)R−δ= (1−τI)α1A1k1α −1−δ, :>.;

• " ' * N

y1(p, k) =c+ (δ+n)

K

ent, :>B;

% c * :>@;& !

& :>+;& #

• * % & % :?;

* :F; (1−β)/ #

5 * '

y1(p, k) y2(p, k)#

(

%

"

)# # & "

* # % # $ (

% "

" * # /

& % %

)# # & 5 # $

% #

α1 α2 % * ,#C ,#,.& & %

)# # 5 $

:5$ ;# & l2,

(17)

5$ & >?DF">??F " *

" * %

,#,FF# i& ,#+& % 5$ ">?B,

% " & κ, % %

k δ# / 0 & y, & % #

! T % 77,% 5 =

:+,,+; +,,,# % n= ln(1,013),%

>#@- % >?,,& )# # #

% r = ln(1.05).

TS % ' "

:+. ;# $ % >@# $

% % 1 :+,,+;& ! +,,,&

>??@#

φ(TS) ' 4 I % :+,,,;N

φ(TS) =

θ 1−ψT

1−ψ

S . :>F;

/ % ψ = 0.58 θ= 0.32# H &

& %

% : # #&

:>??C;; ( % E

4 I %:+,,,;#

T/1& γ ξ % H ' & 1#& # # & :+,,@;D#

" * ! " (

# % % : & TW1;& ( γ %

E ' TW1. / %

( ξ. ! &

# $ ' &γ % * >#+.- ξ >-#

%

" & ( N

l≡ 1

T −TR

TR+T/

TR

l(a) a.

D_{/ %} _' _' _% _#

(18)

:B; :F; % N

l = T/ T −TR

− 1

T −TR

1−e−(r+ξ−ρ)T/ r+ξ−ρ +e

−(r+ξ−ρ)T/ 1−e

−(r−(ρ+γ))T/

r−(ρ+γ) . :>D;

3 9 :>??D; % '

>D % '# $ l, %

% ' % '& % +C D :

; # / l= 0.161.

/ % ! &

#

) y= 1 κ= 3, % " & K

ent =

3. / i, κ n ( " " ! (δ+n)κ= i "

& % % 0.053. $ TY =TC+TS S

>?& * TR+T/1 = 51, % ' #

:>D; % T/2 = 16.22, :>>; % l= 0.15, : ;

G % # $ % ( : !; k = 2.23,

"% ' ' Q # !&

& % Q &

k1 = 2.39 k2 = 0.19.

* :>C; " &A2 = 2.37.

α1 α2 * :+>; !&

p/A1 = 0.41. ( y : y1 +py2)& 0

A1 = 0.54 p= 0.22#

! N *

' & * :>.;& % τI = 0.20. τH τ % E

( " " * :?; " '

* " * :>B; " τH = 0.02 τ = 0.45.

ρ% " (

3 9 :>??D;# +"C

% ' : ! )

;# & (

'& % % '

# 4 ρ = r − γ + ln(1.0035) %

(19)

( # 4 ! (6) ' a,

l(a) % a = TY +TW1 &

?_#

& ( % ' % _c₍₀₎β =

% :C;# ( "

% ' % & & 1−β

∆ &= %

∆ = (1−τ )weφ(T )e−(r−ρ)(TR+T/)_x₍_T

R+T/)

* &

β = c(0)

c(0) + ∆ = 0.20.

% % ( " & % β =l,

% β. %

T % ' &

( # 3 &

# 5 & % ( " (

& % #

6 % '

% # &

9 ,#@.-& 5$ ( #

! :+,,+;& C,-#

#

" %

)

!

( " "

' # / ' & & %

&γ ζ./ ' % &

% % TR+T/1 = (51/77)∗T. % &

?_$ _{3 9} _:>??D; _& _G

'# 6 & % '

% & '# :>#,,@.; ! %

( #

(20)

# '& %

# & T, & &

& & #

( % % #

50 55 60 65 70 75

T

8 9 10 11 12 13

s

T

>N

% !

# / CD"FF &

! # 9 % !

J % ' * G %

% # H

# ,#FC>,_#

5 " # 1

:+,,+; & % &

>, _% _" ₍ _#

(21)

% " &

)# # % G

% % # ( "

%

# $ & % &

# H &

! ) ! & &

" N T TS.

5

% & %

! # $ >?>, +. &

9 5 :>?BC;& % B#D # !

& 5 = & % .>#C. # $

( TS = 8.5. / % % (

& % % & % "

#

' % "

: # #& >??, +,,,; & n, " #

H % & ! ( & &

& %

# / % & %

& >>_#

% &

)# # / ! CD & ( >?,,&

% % ' # H % &

+,,,& FF & %

# ( ! & % &

>> _& ₍ _{% &} _&

% >#C,- # ) ' % TS . >?>,&

( # H & % %

! & * %

& * # I ' :+,,@;

% % #

(22)

% #

$ & % ! N

% % # &

# 3 & T,

% ' & & % &

% ' # &

E ' % # $

% & % & % '

& & % '

% # !

& % ' %

#

+ % ( ! CD BD

FF# % # &

' : >;# % '

% & % #

% # &

' #

(23)

0 20 40 60

Age

0.1 0.2 0.3 0.4 0.5

r

o

b

a

L

eli

f

or

P

48 T=68

77

+N ( %

6 & % %

& %

# /

( % # & %

BF#+ +,,,& BB#@ >??,& B.#C >?D, B@#. >?F,#

5 &

& % # 6

Q γ ζ.

# & (

>?C, % >??, # $ γ

>??, >?C,& % % ' (

& # @ % % ( &

' :γ = 1.25%) * +#,-#

(24)

0 20 40 60 Age

0.1 0.2 0.3 0.4 0.5

r

o

b

a

L

eli

f

or

P

γ=0.0125, ξ=0.01

γ=0.02, ξ=0.01

@N ( %

$ % : # #& ; ( % ' &

% % ' #

% '

% #

5 E ' & * #

& & % &

# $ :+,,@; I "60 / :+,,,;&

% & "

# 6 & &

! % % & %

# H % & %

! E & & %

% * # $ E &

! " # #& ' " %

@>+#

>+₅ _& _% _& _γ _#

(25)

> % %

& ' #

>N " $

T TS y TR Retirement

FF >@ > BF#++ ?#FD F, >+#> ,#?+ B@#>, B#?, B. >>#+ ,#DB B,#>, C#?, B, >,#C ,#D, .F#,. +#?. .. ?#C ,#F@ .@#?. >#,.

., D#, ,#B@ .,#,, ,

! & % # & %

T = 60, D,- ' # 6

% * )# # %

+,- ! % >F #

: ;# H % U $ >??F&

! 4 % B> )# # % ?-# H &

! # &

% % &

>@_#

& % &

N % T FF %

>@- & >- % T .. %

.+ #

$ & % % &

! #

>@ _! _# _*

) % D,- " %

F,-# &

% A .

(26)

&

) !

) % ' % % # /

! ( "

# $ %

( #

" & %

& * &

! # "

! &

# $ %

# & ! "

& '#

" " &

% # ! & & #

$ & % ' "

#

% ( τL * ,#+& ,#C ,#B# 5

% τL & &

& ! % ' # % & %

N % ' # $ (

! " &

# $ " "

# ( ( !

# 3 & &

* & % #

(27)

0 20 40 60 Age

0.1 0.2 0.3 0.4 0.5

r

o

b

a

L

eli

f

or

P

0.2

τ_L=0.4

0.6

CN ( !

+ % ! % τL

' ' & N#

+N " $ !

τL TS y TR

,#C. >@ > BF#++ ,#, >D#@ >#?@ FF ,#+ >D#+ >#D. FF ,#C >C#? >#+@ B?#D ,#B >#.@ ,#>? .F#.

& ' " )# # "

* ! % ,#C.& ( # $

C& τL

& : % ;# & %

(28)

! ,#+,& )# # ( & %

( &

% ' # G

! & %

:τL = 0.20; % D. # $ & ! % *

,#B,& % +,- &

# & !

! : ; #

C τH τK. : !;#

@ % &

τH. ( & & ' #

#

@ " $

H !

τH y Ts TR

,#,+ > >@ BF#++ ,#+, ,#D. >,#CB BB#.+ ,#C, ,#@D @#,+ B+#F. ,#B ,#+, ,#B. .?#B?

! ( #

* )# # τH * ,#+ ' ,#,+&

% >.- % +#. #

. %

! & % % : % ! ;

#

(29)

0 0.2 0.4 0.6 0.8 1 0.25

0.5 0.75 1 1.25

1.5 1.75 2

y

τ_L τ_K

τH

.N !

5 ,#F+&

! % % % τH, τK τL. %

! & % ! "

& % τK,% & τH.

! ( &

" # 5

# $ ( & !

! #

$ & ( & %

C& τL " ( %

τK τH. 3 & %

! & % %

! # $ ! & #

& !

# ! *

& % ! #

(30)

*

$ % ( % ! !

" # (

3 & % #

/ )# # ! %

% +,- & & %

>.- #

% & "

& ! (

( # % % &

% ' % & E ' #

% E # $ & &

( E & %

& #

! % " "

! # 6

& ( & "

! & ! & " ! (

" &

" # " ! & % &

! " ! & ! "

& % # 6

! &

' # H % & %

* %

% : # #& ;& " ! "

% " #

(31)

+

,

-$ &

# > & % N

R≡R1 =α1A1k1α −1 =pα2A2k2α −1 =R2

w≡w1 = (1−α1)A1k1α =p(1−α2)A2k2α =w2,

% p #

* ( % % " "

i" N

ω≡ w

R =

1−αi

αi

ki. :>?;

$ ! (

% 0 " ( &# ( N

p= A1k

α −1 1

A2k2α −1

α1

α2

.

$ % :>?; * % !

N

ω = A2 A1

αα₂ αα₁

(1−α2)1−α

(1−α1)1−α

.p

α −α

, :+,;

:>?; :+,; % "

( N

ki =

αi

1−αi

A2

A1

αα₂ αα₁

(1−α2)1−α

(1−α1)1−α

p

α −α

. :+>;

% " % (

# li i" & l : ; G %

k : ; % #

N

l1k1+l2k2 = k

l1+l2 = 1,

(32)

% k ≡ K

lent_eφ(T ) "% ' ' Q # % * "

li ki k#

& k p % % N

yi(p, k) =Aileφ(T )li(p, k) [ki(p)]αi, i= 1,2 :++;

% ki(p) :+>;&yi ≡ _eYnti &ent N

l1(p, k) =

k2(p)−k

k2(p)−k1(p)

, and l2(p, k) =

k−k1(p)

k2(p)−k1(p)

$ % :

; k1 k2:

k1 =

α

1−α α

1−α l1+ α

1−α l2

k k2 =

α

1−α α

1−α l1 + α

1−α l2

k

(33)

+

,

"

0 20 40 60

Age 0.1

0.2 0.3 0.4 0.5

r

o

b

a

L

eli

f

or

P

τH=0

0.2

0.4

#>N " ( !

0 20 40 60

Age 0.1

0.2 0.3 0.4 0.5

r

o

b

a

L

eli

f

or

P

τκ=0

0.2

0.4

#+N " ( !

(34)

>N " $ !

τK y Ts TR

,#+ > >@ BF#++ ,#, >#BF >B#B> F@#@+ ,#C, ,#., D#@F B+#,> ,#B, ,#+> C#+> .F#BB

.

V>W / ) 0 1 2 333 K 9 % U&L

& ?,:.;N >>B,">>D@#

V+W / 44 ) 5 + 6 ) 33 )K= &

% &L & >,C& @C," @F.

V@W / 44 ) 5 + 6 ) 33 & L 3

% 3 9 % L& & >,.& C,>"C>D#

VCW ! ) ) 77 )K$ & & $ "

9 % &L 1 & ??:.;& >,+?">,.?#

V.W " ) 8 1 / 9 L L& &

# >& +CF"+.F#

VBW $ ) 8 " ) 77 & K !& >?.,"+,,.&L 3 %& 1 & ++"+?#

VFW $ ) : ) 7;3 K H N 3

$ & >DD.">?FD& 5 % H & 6N R ) #

VDW $ % ) 6 / 9 ) 7*;& L J J "

) >?>, >?B,L& & # .& o _{>& C>,"C+>}

(35)

V?W 4 ) 8 ) 0 ) 33 ) R 3 "

& 3 & ) #

V>,W 4 ) 777 K ! " 9 % &L

C@N C>>"C@C#

V>>W 8 ) 33 K )# # 9 % / $ &L

& ?+N ++,"+@?#

V>+W 1 4 )8 0 ) 33 & L9 % & X $ * % "

L& & 6 ) #

V>@W 1 -6< ) 5 ! 9 : & +,,,& L3 & H

$ & 9 % L& & #

B+& >"+@#

V>CW 1 -6< ) 9 : ) 33#& K3 & ) "

& L& #

V>.W 1 4) ) 77*)K L& & .,:@;& @B>"DF#

V>BW 1 " ) / ) ) 333 K 9 % N / / UL

54 / ' 5 # F.?>& 3 #

V>FW ) ) 33 K ! 3 ) & >D.?"

>??,&L 1 & =#>C& BC>"B.,#

V>DW ) ) 7;3 L H

! N " L& & #&

:) ;#

V>?W ) 8 ) ! ) 773& K " N %L&

! " # " #C+& o _{+& +?@"@>B#}

V+,W -0 ) = 33 K = 3 &L

CN >+F">.D#

V+>W $ ) ! " ) 77;& K H / ' >?.,L&

$ % & ' " # ++& o _{>& +">?}

(36)

V++W 9 > ) 33 & 5 H #

V+@W 0 ) ! 33#) Y/ / ' 3 3 UY

$ % & ' & # +D& o _{>& +">@#}

V+CW 0 ) ) 7?&) K % 3 "

L&! "+?& +#& +@>"+CD#

V+.W 0 ) ) 7??& K3 L& & @& >B@"FD#

V+BW 0 ) $ 77# K $ N 9 ) &L

( & ++:?;& >@+.">@C@#

V+FW ) ) 33 ) K3 & &

L& & ) 3 #

V+DW 4 ) 9 ) ) 77& K9 % " ! &L ! >,@:@;N .>?"..,#

V+?W ) 0 77 K ! H &L !

>,>:+;N @+F"@.,#

(37)

´

Ultimos Ensaios Econˆomicos da EPGE

[565] Marcelo Casal de Xerez e Marcelo Cˆortes Neri. Desenho de um sistema de

metas sociais. Ensaios Econˆomicos da EPGE 565, EPGE–FGV, Set 2004.

[566] Paulo Klinger Monteiro, Rubens Penha Cysne, e Wilfredo Maldonado. Inflation

and Income Inequality: A Shopping–Time Aproach (Forthcoming, Journal of Development Economics). Ensaios Econˆomicos da EPGE 566, EPGE–FGV, Set

2004.

[567] Rubens Penha Cysne. Solving the Non–Convexity Problem in Some Shopping–

Time and Human–Capital Models. Ensaios Econˆomicos da EPGE 567, EPGE–

FGV, Set 2004.

[568] Paulo Klinger Monteiro. First–Price auction symmetric equlibria with a general

distribution. Ensaios Econˆomicos da EPGE 568, EPGE–FGV, Set 2004.

[569] Samuel de Abreu Pessˆoa, Pedro Cavalcanti Gomes Ferreira, e Fernando A. Ve-loso. On The Tyranny of Numbers: East Asian Miracles in World Perspective. Ensaios Econˆomicos da EPGE 569, EPGE–FGV, Out 2004.

[570] Rubens Penha Cysne. On the Statistical Estimation of Diffusion Processes –

A Partial Survey (Revised Version, Forthcoming Brazilian Review of Econome-trics). Ensaios Econˆomicos da EPGE 570, EPGE–FGV, Out 2004.

[571] Aloisio Pessoa de Ara´ujo, Humberto Luiz Ataide Moreira, e Luciano I. de Cas-tro Filho. Pure strategy equilibria of multidimensional and Non–monotonic

auc-tions. Ensaios Econˆomicos da EPGE 571, EPGE–FGV, Nov 2004.

[572] Paulo César Coimbra Lisbôa e Rubens Penha Cysne. Imposto Inflacionário

e Transferˆencias Inflacion´arias no Mercosul e nos Estados Unidos. Ensaios

Econˆomicos da EPGE 572, EPGE–FGV, Nov 2004.

[573] Renato Galvão Flôres Junior. Os desafios da integração legal. Ensaios Econômicos da EPGE 573, EPGE–FGV, Dez 2004.

[574] Renato Galv˜ao Flˆores Junior e Gustavo M. de Athayde. Do Higher Moments

Really Matter in Portfolio Choice?. Ensaios Econˆomicos da EPGE 574, EPGE–

FGV, Dez 2004.

[575] Renato Galvão Flôres Junior e Germán Calfat. The EU–Mercosul free trade

agreement: Quantifying mutual gains. Ensaios Econˆomicos da EPGE 575, EPGE–FGV, Dez 2004.

[576] Renato Galv˜ao Flˆores Junior e Andrew W. Horowitz. Beyond indifferent players:

(38)

[577] Rubens Penha Cysne. Is There a Price Puzzle in Brazil? An Application of

Bias–Corrected Bootstrap. Ensaios Econˆomicos da EPGE 577, EPGE–FGV,

Dez 2004.

[578] Fernando de Holanda Barbosa, Elvia Mureb Sallum, e Alexandre Barros da Cu-nha. Competitive Equilibrium Hyperinflation under Rational Expectations. En-saios Econˆomicos da EPGE 578, EPGE–FGV, Jan 2005.

[579] Rubens Penha Cysne. Public Debt Indexation and Denomination, The Case

of Brazil: A Comment. Ensaios Econˆomicos da EPGE 579, EPGE–FGV, Mar

2005.

[580] Renato Galvão Flôres Junior, Germán Calfat, e Gina E. Acosta Rojas. Trade and

Infrastructure: evidences from the Andean Community. Ensaios Econˆomicos da

EPGE 580, EPGE–FGV, Mar 2005.

[581] Edmundo Maia de Oliveira Ribeiro e Fernando de Holanda Barbosa. A Demanda

de Reservas Banc´arias no Brasil. Ensaios Econˆomicos da EPGE 581, EPGE–

FGV, Mar 2005.

[582] Fernando de Holanda Barbosa. A Paridade do Poder de Compra: Existe um

Quebra–Cabec¸a?. Ensaios Econˆomicos da EPGE 582, EPGE–FGV, Mar 2005.

[583] Fabio Araujo, Jo˜ao Victor Issler, e Marcelo Fernandes. Estimating the Stochastic

Discount Factor without a Utility Function. Ensaios Econˆomicos da EPGE 583,

EPGE–FGV, Mar 2005.

[584] Rubens Penha Cysne. What Happens After the Central Bank of Brazil Increases

the Target Interbank Rate by 1%?. Ensaios Econˆomicos da EPGE 584, EPGE–

FGV, Mar 2005.

[585] Gustavo Gonzaga, Na´ercio Menezes Filho, e Maria Cristina Trindade Terra.

Trade Liberalization and the Evolution of Skill Earnings Differentials in Bra-zil. Ensaios Econˆomicos da EPGE 585, EPGE–FGV, Abr 2005.

[586] Rubens Penha Cysne. Equity–Premium Puzzle: Evidence From Brazilian Data. Ensaios Econˆomicos da EPGE 586, EPGE–FGV, Abr 2005.

[587] Luiz Renato Regis de Oliveira Lima e Andrei Simonassi. Dinˆamica N˜ao–Linear

e Sustentabilidade da D´ıvida P´ublica Brasileira. Ensaios Econˆomicos da EPGE

587, EPGE–FGV, Abr 2005.

[588] Maria Cristina Trindade Terra e Ana Lucia Vahia de Abreu. Purchasing Power

Parity: The Choice of Price Index. Ensaios Econˆomicos da EPGE 588, EPGE–

FGV, Abr 2005.

[589] Osmani Teixeira de Carvalho Guill´en, Jo˜ao Victor Issler, e George Athanasopou-los. Forecasting Accuracy and Estimation Uncertainty using VAR Models with

Short– and Long–Term Economic Restrictions: A Monte–Carlo Study. Ensaios