Una nueva aproximación

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C /D 4CD C D 29M H %$ ' 9 C D C D94 4 M á x u ( c m ) t ( c t m t ) β t t t = 0 mt f ( kt ) + vt + ( δ ) kt + = ct + kt + mc%d t ( π ) t 6 9 CD 78 9 :8 d t log( M Pt ) = b0 + b log ct + b2 log + it!# i C#D ( C 9D ;)!$ C=D )C D ;! < 9 <=< $! I 4 / (C#$$@D H 9M2C%HJLDG+? K %$ / +!C%HIJDG/? K4 * 4

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C D %% 9 C D M f ( x) a x n = = 0 a i i= i i CLD '! % * 9 9 C D %# 6 C D )! CD %HH@+* %= %>! % 4 6C D 9 B %@ * C %% d log( x j / x ) i η i j = d log( f ( x ) / f ( x )) 9 d log x2 d log x η2 = = d log() %# - N- 7 9 C%HI>D %= *0!F02+00C%HH@DG2? K %> n Rt r it C t = f ( x) = xit i = Rt %@! i j 7

D %J M 9 C!*!9 ( D ( $ * * CD - 4 ) C D - 4 R ri p i = IP * + R C6D 2 CID * - * %L ( 2)( wi t + wi t ) n D D x i t M t = M t Π i= x i t ( n D D log M log M = w i t log x log x t t ( i t i t ) i = # * w = p x p x i t i t i t k t k t k = n CHD C%$D * / C D %J 9 % 9 C.*D M = f ( x ) = x + I D * x t t t 2 t d lo g x 2 d lo g x x 2 x η 2 = = d lo g () d lo g ID ID %L 7 8

4 M * B * 4 4 % &&' % %HI$#$$@ 4 4 4 ' -!) 6O% 90.00000 Gráfico Nº - M y M' en términos reales 70.00000 0.00000 30.00000 0.00000 90.00000 70.00000 0.00000 980.I 98.IV 983.III 98.II 987.I 988.IV 990.III 992.II 994.I 99.IV 997.III 999.II 200.I 2002.IV 2004.III M real M' real 4 trimestres móviles M real 4 trimestres móviles M' real 9

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6O# Ponderación del C 00 090 080 070 060 00 040 030 020 00 000 980.I 98.IV Gráfico Nº 2 - Diferencial de rentabilidad 983.III 98.II 987.I 988.IV 990.III Pond. C 992.II 994.I 99.IV 997.III Dif. Rent. / -!).6 999.II 200.I 2002.IV 2004.III ' 4 C %HI# %HI@ %HH$ 4 #$$% #$$# D 6O= C$J>D 40 400 30 300 20 200 0 00 00 000 Diferencial de rentabilidad Diferencial de rentabilidad (en puntos porcentuales) 40 400 30 300 20 200 0 00 00 000 Gráfico Nº 3 - Diferencial de rentabilidad y aceleración inflacionaria 980.I 98.IV 983.III 98.II 987.I 988.IV Dif. Rent. 990.III 992.II 994.I 99.IV 997.III Aceleración 999.II 200.I 2002.IV 2004.III /.6-!) 200000 0000 00000 0000 0000-0000 -00000 M Aceleración inflacionaria (en %)

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9 ' * * * 4 6 ; % 4 C D C#D * M = C + DV + IDCA CA C%=D p * %( )* B ' ) %$$& C D* #$ DCAt C At VC At C%>D IDCAt = = DDVt DVt V D Vt ###> #> > > #> ( 4 * C D # $% $ #$ ) -+7)-!) ; -+7)-!)

% 4 # - + #% %HI=%HH@ ## 9 ; ()$ - %HI= %HI> %HI@ %HIJ %HIL %HII %HIH %HH$ %HH% %HH# %HH= %HH> $$L $$H $%$ $%# $#% $%$ $%= $%H $%I $%L $#H $## %HH@ $=@ / -+7)-!) # 4 %HI$%HI# %HHJ#$$> # $% % B -+7) #= #>! #%HI$%HI#%HHJ#$$> #% G. K -!) ## %HH@ #=! -+7) /(C#$$@D #> ;-2.'C#$$$DG )K 6

%+ ) 4 #@ # %HI=%HH@ #J # 4 %%=@& #$$>I$& 4 # %HI$%HI#%HHJ %HI=%HH@* 4 %HI$%HI# 9 %HHJ! %HHL%HHH G K Gráfico Nº - IDCA -aprox. conservadora 09 08 07 06 0 04 03 02 0 0 980 982 984 986 988 990 992 994 996 998 2000 2002 2004 983-99 980-2004 ajustado / -+7)-!) %+ 7 > ()7* # /= 0.# + 9 : '# 3 =@=J >%@H =I>L 4 >=H@ J$$H @#$# =I$@ #@=@ =%L$ %HJ@ %>H= %L#H / -!) ) 4 #@ # ln( IDCA ) = β + β T + µ t - #J! # 4 0 t 7

%HHL # # %HI$%HHJ %%=@&%HHL '(2 9 6OJ 6O@# 4 %HHL '(2 9 #$$$%$$& #L #$$# %$$& ' - ()< > 4 $$@@ 4 $$J% 4 $$JI 4$ $$LJ 47 $$I@ 4< $$H> 42 $%$@ 43 $%%L 44 $%=$ 4 $%>@ $%J% $%I$ $#$$ $ $##= 7 $#>I < $#LJ 2 $=$I 3 $>#J 4 $J>L $I@= % % % $ % 7 % 09 08 07 06 0 04 03 02 0 0 980 Gráfico Nº 6 - IDCA - Aproximación ad hoc 982 984 986 988 990 992 994 996 998 2000 2002 2004 983-99 980-2004 / -+7)-!) %! ' # 6OL + M = C + D V C%@D P #L 4 4 6 4 8

* M = C + DV + IDCA CA C%JD p ah * #! 6OL %@ 'H$S C# D 0.000 40.000 30.000 20.000 0.000 00.000 90.000 80.000 70.000 60.000 Gráfico Nº 7 - M y M* en términos reales 980.I 98.IV 983.III 98.II 987.I 988.IV 990.III 992.II 994.I 99.IV 997.III 999.II 200.I 2002.IV 2004.III M real 4 trimestres móviles M real M* real 4 trimestres móviles M* real / -+7)-!).6 % - ' & 4 #I ' T #H! 4 4 m p = β + β y + β i + β T C%LD 0 2 3 9 & =$ - * M #I! #H ;-3 C#$$=D =$ 9!@A$ 4!$? 9

G KF M G K -( GK %./-0 % 2.6 -!) ) =% * 2 4 6? * %! & < ; /C>D2-!) %HL@ 4.;/.- %HLI %HH$ %HI= %HHH %HII %HI= '.;/.- 9 C#$$>D =# C C k + h k + h k + h k + h = k + h + C k C%ID T C C = C%HD k + h k + h k k k + h C k 4 * 4 =% ;-2.'C#$$$D =# 0C#$$>DG) K 20

! 4 C%HI=%HIID! & 2 6 4 9 2 F * 4 2 6 C4 D & ( 4 4 44 4 %$! ) 4 9 C D * -!) %HLI ' * 2% C D 6 *.;/.- 6OIH 2000 80 700 0 400 20 00 90 800 980.I / -!) 98.IV 983.III Gráfico Nº 8 - IVF PBI empalmado (promedio 983=00) 98.II 987.I 988.IV 990.III 992.II 994.I 99.IV 997.III 999.II 200.I 2002.IV 2004.III 20 00 80 60 40 20 0 Gráfico Nº 9 - Tasa de interés (plazo fijo moneda nacional) 980.I 98.IV 983.III 98.II 987.I 988.IV 990.III 992.II 994.I 99.IV 997.III 999.II 200.I 2002.IV 2004.III 2

% /% 9 R 4 * C% %HI$ % #$$@D %HI$%#$$=> %2 *M/' C'*/D == ) 6OJ )2*? @A*((#/ 0 : B 9 B! $$@ %$ =@@QQQ H % $=# %$ =JJQQQ H % 2 %$> I =$JQQQ L % '# C! 9 9 9 9 %%> J >#$QQQ @ % ; 6 ;4 QQQQQQ 4 %$&@&%& C D % 4 4 C D ) C D '*/ % 4 B C D % + 9 CB6D 4 == ' 42 22

4 0 3 => %$ 3 0 ;'+ 4I C D C D =@ 9 ;'+ 9 = #= > 'MM @?' ;'+C@D 4 @& 9 0 @ 2 6OLI 4 ' %& 4 4 C@& 4 D*0 4 94 %& 4 4 @& # 6 4 @& 4 B 9 4 => ) ' 42 =@!. 'MM N4 23

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log( M/ IPC) = β + β log( PIB ) + β log( i ) + β T + δ SD + ε t 0 t 2 t 3 j j t j= 2 4 * log( M / IPC) t = γ 0 + γ log( PIBt ) + γ 2 log( it ) + γ 3T + λ jsd j + vt j= 2 6 $#L%L@L #I@>$H #@@> =$=> #66 $#>IL=J #@L=HI %IHJ #=J@ QCQQD @&C%&D # $$>L>L> >=LL>> %##@ %J#J 24 # QCQQD CD@& @&C%&D 24 % 24 # CD CD@& %& 24 %& C#%D 3 6OH %$ 4

lo g ( M / IP C ) = 8 0 9 + 0 8 9 lo g ( P IB ) 0 lo g ( i ) 0 0 0 7T C##D * log( M / IPC ) = 97 + 06log( PIB ) 023log( i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

)9/ C%HHID log( M / IPC) = 0 0+ 0 488log( PIB) 832π -3 log( M / IPC ) = 8 29 + 080 log( PIB) 0 46 log( i) 0 007T! 3 * ' 9 '*/ =J 0 3 4 %$ / M! 4 4 %$ + % ' 4 ' ) 7 9 4 2 4! 36 Para un análisis más detallado del resultado de este contraste véase Fried y Trujillo (200) 26

4 4 4 R + =L B C4D ' 4 2 4 4 4 C D 4 9 ;!2 C@ D! C%%%#D @& %& 2 ( 4 4 24 4 4 ' 4 B '2 C D C D 4 37 ngle R.F.; Hendry D.F..; Richard J.F. (983) xogeneity. 27

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

# = %>B =#&=L& #>& #J& = @L&@I& #O ' =H B = 9 %HI#I= # %HH% %HI# C G KD M* &- C9CD %>%HI#$@=> %HI= $ %HH% & F9 $ #%HH%% 9 %&' #$$# % ' 4% %7 %76 + # $I$ $I# ==& =#& * C D * >$ =H ;-43(3!C%HL@DG.? K >$ )*2C%HH%D 2 % *2 % %HI=%HH$ >H&>I& 9 / C%HHHD%HI=%HHI 30

' 4 =& ) >% ># 4 %7 9 * N # * -4 2-3 / - 9 4 4 0- %$& N 4 / 4 * G G %7$ 0 9 +9(+ 4 2!7 =@& - 3 C#$$=D %HI$#$$# =L& 2 % >% + ) *R C%HH@D %=& ># ' R'C%HH#D =>& 3

%77 4 %77 C D 4! 2 % 6O%$ >= %HH=> #$$$% 6!)9)2!)9)2 >> C6O%%D. 2 D9 )* (( :/ 0.0 8.0 4.0 0 -.0 4 -.0 8 9 9 2 9 9 4 9 9 6 9 9 8 2 0 0 0 2 0 0 2 R e c u rs ive R e s id u a ls ± 2 S.. D9 )**A/ 0.6 30.2 0.8 0.4 0.0 20 0 0-0 -20-0.4 992 994 996 998 2000 2002-30 992 994 996 998 2000 2002 CUSUM of Squares % Significance CUSUM % Significance 43 +/- 2 desviaciones estándar para cada punto que es la especificación por defecto que surge del programa views. 44 Brown Durban y vans (97) 32

9 4 C6O%#D* D9 )*9 ( :/ 0 -.0.6 -. 0. -..4 -.2 0 -.2.3 -.3 0.2 -.3. -.4 0 9 4 9 9 6 9 7 9 8 9 9 00 0 0 2 0 3.0 9 4 9 9 6 9 7 9 8 9 9 0 0 0 0 2 0 3 T érm in o d e c o rre c c ión d e e rro r ± 2 S.. P IB ± 2 S...9.0 0.8.7 -.0.6 -. 0..4 -..3 -.2 0.2. -.2.0 9 4 9 9 6 9 7 9 8 9 9 00 0 0 2 0 3 -.3 0 9 4 9 9 6 9 7 9 8 9 9 0 0 0 0 2 0 3 P IB (- ) ± 2 S.. I ± 2 S...3 0.2.2 0.. 0.0.0 0 9 4 9 9 6 9 7 9 8 9 9 0 0 0 0 2 0 3 I(- ) ± 2 S..! >@ ' 9 C!)9)2D D9 )$* (( :/# : 0. 30.0 20.0 0.00 0 -.0-0 -.0-20 -. 84 86 88 90 92 94 96 98 00 02 Recursive Residuals ± 2 S.. -30 84 86 88 90 92 94 96 98 00 02 CUSUM % Significance >@ R %HH% ;? 33

2 % Q 9 6O%>%@ %J D9 )7* (( :/ 6 0.2.08.04.00 -.04 -.08 992 994 996 998 2000 2002 Recursive Residuals ± 2 S.. D9 )<*A/ 6 0.6 30 20.2 0 0.8 0 0.4-0 0.0-20 -0.4-30 992 994 996 998 2000 2002 992 994 996 998 2000 2002 CUSUM of Squares % Significance CUSUM % Significance 6 4! 6O%L 34

D9 )2*9 ( :/60 -.0.6 -.0. -..4 -.20.3 -.2.2 -.30. -.3 94 9 96 97 98 99 00 0 02 03.0 94 9 96 97 98 99 00 0 02 03 Término de corrección de error ± 2 S.. PIB ± 2 S...9.00.8.7 -.0.6 -.0..4 -..3 -.20.2. -.2.0 94 9 96 97 98 99 00 0 02 03 -.30 94 9 96 97 98 99 00 0 02 03 PIB(-) ± 2 S.. I ± 2 S...30.2.20..0.0.00 94 9 96 97 98 99 00 0 02 03 I(-) ± 2 S...6.2.08.04.00 -.04 -.08 -.2 -.6 84 86 88 90 92 94 96 98 00 02 Recursive Residuals D9 )3G (( : /C(A : 0 30 20 0 0-0 -20-30 ± 2 S.. CUSUM 84 86 88 90 92 94 96 98 00 02 % Significance 3

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4 [ λ traza n i= r + ^ ( r) = T ln( λ ) C'@D ^ ( ) T ln( r ) λ r r λ máx + = + C'JD ^ λ Π - ## $ 3 C%HILD!$ 2!7* y = β 0 + βx + β 2 x2 +... + β x + ε C'LD t t t k kt t ' ^ ε!$ 4 *M/* * C 3 ]2\ D C 4D + 0 9 3 j= ς y = α + α y +... + α y + β x +... + β x + η SD + ε C'ID t 0 t ρ t ρ t ρ t ρ j j t j= t 0 t ρ t ρ t ρ t ρ j j t j= j= ζ x = γ + γ x +... + γ x + δ y +... + δ y + ϕ SD + ν C'HD ρ '# C'ID 3 & C'HD & 3 H ) β = β =... = β = 0 C'%$D 0 2 0 2 ρ H ) δ = δ =... = δ = 0 C'%%D ρ 49

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