Real Asset Returns and Inflation a Structural VAR Analysis

8/2/2019 Real Asset Returns and Inflation a Structural VAR Analysis

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FAME - International Center for Financial Asset Management and Engineering

Research Paper N118October 2004

A Structural VAR Analysis

HEC-University of Lausanne and FAME

Matthias HAGMANN

Real Asset Returns andComponents of Inflation:

University of Basel, Department of EconomicsCarlos LENZ


2/41

! "##$

% & ' & & ( & !' )

+, - . +, - . +, -

& - / & (

& !

! . ) &)

0 0- &&0 & (

& ( !' &

& & *3! & - 4!!

!& & & ' ' ! & &

!' & (! '(. & & -

& 567#0

) . - . 0& &&0.

8$$. 45

8 8. 9) . &(

8* &&


3/41

3& - & !' )

. +, - . +, - . +

+(, - & ( & !

) F & 3& & ! &

(' & '. '&& & ) '&

3& ( & & ! &

& ('. ) ) &

& ( 2 ( !'

!( & / &

9 +56;H,. CF ) +56;H,. A +56;H,. ) +567:,I 9)& & +566:, 2 & & (

- '& & 3& &

!

+5675. 567:, & & !' )

D - & !

( &' & ( ) (

& & '& -

3&. &

! 2 ! & ( 3& ' F D

(. ! 4)

0 && ! & ! & ( &

3& - & '&

& & ' ( !

& '& &


4/41

&. 4!! +567", 2. & &

! ( '& ( & . & +5675,. '&& & (

( 3& & & & -

&& ( 3 2 & (. & 1!

& & & (

) F .

& - & ( !' &

= +567H, ( - 1!

( !' )

'(. ) ( * & !

=0 +567$, & & ( !'

- - ( ! &) 3& &) ( ! & !

1! '&& &

) & !& (

8- &)

) & - &) =

& 1! & +566",

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&). ! ( '& ! &) &.

- ) - . &0

'& ( ! &)

&) & & &( & & D2 ( !'

& & &).

( - & ( !' )

( ( C B& ?& +567@,


5/41

- ! &). '&

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&) * &)

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& !' ) +, - . +, - +(, & - ?( '

& !' ) -

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) 3& ! '

- F 3& &

! & & 3

& ' - &

) & F

& ! & ( '). ' ( ! 2 (

! & !

+5667,

& & !' ) -


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2 4!! +567",. ' +56

% ' &' & & & & ( ! &) '& F

F

3& ' " ! &' '

. & & &

( & & '

2 ' ) ( &) :

2 / . ! F

( ') $

% 2 ! & - -

( ( +, % &

+, F

&. ' ( - ( &

!

- & & !'

F .

&. CF )

&' +56;;,. ' +56;@, &

3& & - & &

/ & - F !' &

& ! & &. 9 +56;H,


7/41

& ! & 3& 2 &

( ( ! & 1 ' ' =)* +=, & ?&*? +??,

9& & ) &

= ' ! D & &

= )' &( ' ' 3& ??

'&& ) & 1 % & & (!

'&& ! ! ! "

'& & ( - & ! '&&

! 1 ! 1

& . - & - -

. (. !

'& & J ! (

( & & '&

3& ( & F

( . ' & D & & '

& & ( - - -

. - - &

- & ! 3&


8/41

. ' !

'& ( & ( & !' & ) F

9 . ) &

' 1 .

& & 1 % ) & & &

! & 2 & & ' 1 3&

& ) ! & (!

& +& !( ! ) ,. '

&. & !

- & & & 1 %. &. &

& -

" # #

& ! ' ' & 2 !(

&). & % & &

'&

. &

* 2

3&


9/41

3& '& & !

( ( '& . ! &!. & &) & (!

. ! -

3 ( &) !. '

& ! & %

& &

'& & - !

&) & ! +567#, 3 !

& & !' & (! '

! & &)

3& '

'& 9 & &) ' . & &) &

. '& & & ( (

&) 1. & & ' !

&) & (! F 3

& - . & . &


10/41

+567@, & ( 2 &

& 2 ! & ! ! ! F (! F

& ' (!. !

& (! '&& ! '& &

+567H,. 9& % +567H, +567H,

& (! 2

( &

+5676, & * &

'& & '&

&) ! & &(

& ( . ! 2. '

& - 3 & ) . 0 ( 2 & &

+566", 9 +566@, '& & !( . &

& J

(' 8 2 &) !

+5666, 3& !( )

&) ( & ' (! ' 9&

& &( * ) 3&

( !' )

&) & ') ! 2 (

! & &). & ( &

( +5666, ( &) 3& . &'(.

* &) &

& !' ) - 3&

L +&' +5675, "7, & (


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$

' & (! . ' &( &

& & - ' & ') !

! &* *

5*" 3 & & &) & ' &

&( * & ( )

: &) '

% : &) &( &* F

% :! 3& 0 !&( ! &

'& &

-

5 " * ! 9&

3& & 3& 2 (

&* ) 3& ( +:!, ( !

! ' ! ! '*) 3 +

+"##",,3& * & & *

& ' '

5*"

3& ' ( & &* &

&) +, & -

! +,. ( 3& 2 ( & & &*


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3& ( & !. & '

:!

'& ! ! ( ( !

. & & ' &* & !' & (!

3& !( 1 ! '

! 3& 2 &

& * . . *!

& & J (. & - 3& ')

!&( & 0 &

- '& F ( ( & &

3& +5 * :, & '& &

& &

. ' 4

& #

& ' &( 2 & !

( ( & ' '

( & ' )' &

' & & & & (

F '&& !

%& & (! '&& &


13/41

-. - & -

& ( &' & & & !D & ' !&

- & F. ' ( & ' (

3 ) & ' ( !'

& -

& ' ( !

A & ' ' & )

'& & & - 2

&) . & !

(

( ( (

3& ! -. (

& ( !' ) '&&

&) 3& ( ' &

!' ) + & (!,

( -. & !' )

&)

(


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& ' ( ) !

. ' &

( (

( (

9& ( &( ! ! ( &

& '. ' & (( ! & ( &) % 2 &

!' - ) .

3& ( !' ) -

(

( (

(

3& !' & (! ! & (

! ! & ( !. & ( !' )

!

(

( (

(

. & . & ( !' -

& - !

(


15/41

$

$ *

. ' 1 / & 2

56@$ & "##: 3& ( &

- +?, ! & 9 ! )

@## - +=, . & & :

! & 9 4( & (

$ ' ( + ,

& ! ' & ( F !' )

& F

' & !

2 . ' & -

- +& , - - @

3! 5 & 1 &

. & &( 2 '

& ( & 2 ( &

& ' ' 3! ". '&&

&' +56;;, % . &'(. & & (!.

. '&& & ) &

3& J & & !' & -

3& 0& &&0 & & J &

F 3 ! && ! & J '


16/41

' ( , ! '

& & ) - 5 &' &

:@P ) " &

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( - ) &

- . 5P

. '& & D ! "P .

- - & ! . '

& 5:P & -

- . '&& ( '& -

( )

3& & & J '&+56;H,. &' +56;;, CF ) +56;H, '&

2 & - & - ' &

' , , !

( & 5P

& $# ! - '&& & ( . !

3& & 0& &&0 .

&. ' & & @

HP & - :6P &

. H & & 2

& -

$$ ,


17/41

( :! 3& ( !

3& - '& ( 1 & ! & &

& F ( 1( 1(

" D & & (; 2

! & ! ! B

5 ". & & ' F

: :! & 3&. .

'& & ' F 2 : :!

( ) &' 2

&) 3& ( 2 &

& ' ( ( ( 1 &. & F

( 2 D 2

' ( = &) & )

F & 3& = &) & ( F & (

& &) & ( !

& & ! &&. & . '&& &* ).

6 . & F & = &) &

& & *

( ( 3& &) & ( 2

! (& ( 1 A & & '

) 3& &

& &&

( '&& ! !) ) &


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F ) & &) & & F &

&' 2 0- !)0 1 F ! &' ( 3& ! &

- 2 &)

$$ "

& ! ' & )

F ! ( !

3 & :

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D & :! ( & : (

: & !'

+ & , F ( "$ 2 ( &

! ! B +5667,5# 3& &

3! $ !& 2 &

' ( , ! 3& (

: & & &) &

& ) %& & &)

) . & = &

& &) &* *

& & !' )

&) A & & ' &) & ;#0 55 &. & & &

567# & & & 0

3& !( ( (

% & !


19/41

& ( ) & -

& ( ) !&. -. 3! : & & &

& &) 3& &) (

!& & &) &&

. & & &) ! ( '

&& ) 3&

&& +5675, 3& !'

! & &) ( ! 2 '(.

:! & - 3&

=& = +567H, & +566", 3& (

) &)

& & &) 3& ( !' ) & ( &

! ! +5666, !( . &

&)

3 & !' ) -

!' & (. &

'&( & & &) & & F

& &) 3& &) '&& & (

- '' '& - )

&) & ( !' )

A & & & ! &) !

- - 3& &

&) )

F ( ( - 8-

& ' '&& ( !' -

- 3& ( & &


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& & 1 9)& &

& & &&. '& & !' ) - & (

3! : & !& &). & (

! ( '& & &. &'(. 2

' , ! 3& (

& &

& & &) & !

& %

!' & - . '&& & (

- & ( & & && 1

& &). & !' &

( '(. & '& & & F

& &) '&& &( F

5 &' & & '&

3& !( ( &

3& & '& & ! &) ' &

- ( ( '& 4!! ! & *3!

& &). & 2 ( = ).

& ! -

& - 3& & -!)

' ! +& , ! ( (. '

&. & ( &

! 4!! +567", & -

'& - (

% & & & ( &


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&'(. !& ( ! (

2 ( & && & & && & . & ( !' &

! &) ( &

$$ "

& ( . & ! & &

567# ! & & & 0

+566#, & & ( !' )

& *% % & &

56;6K: ( & & '

( . 4& 3 +"##", 2 & !

')A & 2 &

! D2 & '&

&. &

56;6K$ * "##:K$ % '

& ( ' &

2 ! 56@$K5 * 56;6K: &&

'& . ! D & 2

& = & ?? 5: % &

56;6K$ * "##:K$ 3! @ & & &)

!' ) F

&'(. 2 '& && - 3 !' ) - +-,

( +(, ! 2 &

. & &) ') 2

A & & &


22/41

. 2 & '

2 (, F &)2 ! @ '&& & &

F & &) & ( &( &

& &) ' ( 2-

3& ( ( ! & = &) A &

& & 3&

&) & & '& &

+"##",

&

& ' - & ( )

'& F ( ( & '

') % -

. ' & &

( ! . ) &)

!' ) - . ' 2 &&0 !& ' ! +5675, . & &

) +-, & &

&). ! ( &

'& =& = +567$,. & +566", 2

+5666, '& & !' )

&. ' 2 & & ( !' -

- & &

'& & +566",

& ( !' &


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& & & 7#0 '

F &) &


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-

& ' ( &

& A 2 &

3 ( & ! '

% ' ' ( & - & - .

& D & F !' &

. &

3&. & - (

3 - (

!


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!( 3& - ( !

( !

9 & . & !

"$


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',

G5I . 4 4. 566;. L3 8

G"I 9. ?. 566@. L) . . & 0?- & =.L 8 . $7. $;*@:

G:I 9). 9 . 567H. L( 8- &

*& ?! ?. "@. $6*5##

G$I 9&. C = K&. 5676. L3& = 8F

=!.L 3& 8 ('. ;6. H@@*H

G@I 9&. C %. 567H. L 9

+,. 3& 9 . A98 /( &

GHI 9. >. 56;H. L ) .L 3

:5. $@6*$;#

G;I 9(. C 4. "##". L ? 9

?. ( 9) A' E)

G7I 9)&. C &. 566:. L)

?(.L 3& 8 ('. 7:. 5:$H*5:@@

G6I . 3 . 567@. L&

C 8. 5H. "7:*:#7

G5#I =&. C ? C =. 567H. L ?


27/41

G5:I . 8 4 % &'. 56;;. L

8. @. 55@*5$H

G5$I . 8 . 5675. L) . (.

8 ('. ;5. @$@*@H@

G5@I . 8 4!!. 567". L.

3& C 8. ":6*"@7

G5HI . 8 . 567:. L) . (.

8 ('. ;:. $;5*$;"

G5;I 4M. C. 566". L' % = & * ?' /

C 8. 5#;. ;#6*;:7

G57I 4&. ? 3. "##". L3& ) *

8 . ;@. 5$;*5@H

G56I 4). . 567:. L3& )

.L 3& C . :7. 5*::

G"#I . ? C 9 . 5666. L) '=!L. 3& (' . 5". 5"#:*5"57

G"5I CF. C 4 ). 56;H. L3& 0& 8F0 )

(.L 3& C . :5. $$;*$@7

G""I C. &. B&. ?&. 567@. L

) . . A

. $#. 5:;@*5:7$

G":I B. 4. 566#. L & !'

8 L 3& C K


28/41

G"HI . 9. "##:. L

=!.L (' K( . "

G";I . C. 56;@. L .L 3& C

G"7I &. = . 566". L

. $;. 5:5@*5:$"

G"6I . . 56H:. L .L C ?

G:#I A. . 56;H. L

. :5. $;5*$7:

G:5I &'. 4 %. 5675. L3& D ) ?

3& C . :H. 5@*"6

G:"I . . 567#. L .L 8.

G::I . . 567H. L !

9) . K ('. "*5H

G:$I ). 9. 567:. L3& !' ) ?

8(.L 3& C . :7. :@*$7

G:@I . .567H. L ? 8- .L 3& C

"#6*"":

G:HI 3!. C. 56H@. L 8 4'&.L 8. :


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Figure 1: Impulse respon


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Figure 2: Impulse response


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Figure 3: Structural decomposition of rea

(Time s


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Figure 4: Real stock returns, real in

(Scat


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Figure 5: Impulse respon


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c RSR(-1) RI (-1) INF(-1)

RSR(-2) RI (-2) INF(-2)

INF 0.35 -0.004 0.92 1.23

[ 1.22] [-1.00] [6.58] [ 9.18]

0.004 -0.82 -0.36[ 1.05] [ -5.91] [ -2.66]

R2

= 0.69

The variables are inflation (INF), the real interest rate (RI) and real stock ret

(RSR). Values in brackets indicate t-statistics.

Table 1: Regression Equation for Inflation


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c INF INFE INFU

R1 RSR 17.12 -3.47

[4.93] [-4.99]

R2 RSR 12.52 -2.32 -5.85

[3.19] [-2.79] [-4.67]

R3 RSR 3.27

[1.43]

R4 RI 2.94 -0.40

[12.92] [-8.69]

R5 RI 2.21 -0.20 -0.86

[9.70] [-4.18] [-11.77]

R6 RI 1.54

[8.36]

The variables are inflation (INF), expected inflation (INFE), unexpected infl

h i d i fl i (CHINFE) h l i (RI) d l

Table 2: Real Stock Returns, Real Interest Rate and Inflation Com


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37/41


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AS RD MM ASPanel A: Version A3a

RSR/INF -0.98 -0.11 -0.86 -0.85[-0.99 / -0.63] [-0.26 / -0.04] [-0.94 / 0.52] [-0.93 / 0.01] [

RSR/INFU 0.11 0.00 -0.97 -0.84[-0.46 / 0.17] [0.00 / 0.00] [-0.98 / 0.91] [-0.93 / 0.00]

RSR/INFE -0.99 -0.66 0.08 -0.25[-0.99 / -0.65] [-0.86 / -0.19] [-0.24 / 0.23] [-0.76 / 0.55] [

RSR/CHINFE -0.03 0.55 -0.09 -0.26[-0.49 / 0.04] [0.03 / 0.64] [-0.51 / 0.73] [-0.54 / 0.75] [

RI/INF -0.99 -0.78 -0.98 -0.41[-1.00 / -0.94] [-0.94 / -0.56] [-0.99 / -0.93] [-0.93 / 0.61] [

RI/INFU -0.12 -0.56 -0.94 -0.49[-0.57 / 0.01] [-0.61 / 0.60] [-0.98 / -0.89] [-0.78 / 0.43] [

RI/INFE -0.99 -0.78 -0.28 0.00[-1.00 / -0.79] [-0.94 / -0.56] [-0.40 / -0.06] [-0.88 / 0.73] [

RI/CHINFE -0.03 0.84 -0.29 0.16[-0.79 / 0.20] [0.34 / 0.89] [-0.54 / 0.48] [-0.11 / 0.85]

Panel B: Version A3b

RSR/INF -0.98 0.66 -0.72 -0.85[-0.99 / -0.66] [-0.91 / 0.82] [-0.84 / 0.50] [-0.94 / 0.02] [

RSR/INFU 0.11 0.97 -0.67 -0.84[-0.46 / 0.16] [-0.98 / 0.96] [-0.82 / 0.68] [-0.93 / 0.03] [

RSR/INFE -0.99 0.14 -0.33 -0.25

[-1.00 / -0.67] [-0.47 / 0.18] [-0.80 / -0.05] [-0.78 / 0.54] [

RSR/CHINFE -0.03 -0.06 0.23 -0.26[-0.59 / 0.04] [-0.53 / 0.77] [-0.20 / 0.56] [-0.53 / 0.75] [

RI/INF -0.99 -0.97 -0.91 -0.41[-1.00 / -0.93] [-0.99 / -0.78] [-0.96 / -0.78] [-0.93 / 0.62] [

RI/INFU -0.12 -0.96 -0.75 -0.49[-0.57 / 0.04] [-0.98 / -0.85] [-0.91 / -0.07] [-0.78 / 0.46] [

RI/INFE -0.99 -0.19 -0.54 0.00[-1.00 / -0.79] [-0.40 / -0.04] [-0.91 / -0.34] [-0.90 / 0.75] [

RI/CHINFE -0.03 0.16 -0.10 0.16[-0.83 / 0.24] [-0.45 / 0.65] [-0.39 / 0.80] [-0.08 / 0.87]

Conditional correlations and their 90% confidence intervals. Variables are real stock r

inflation (INF), expected inflation (INFE), unexpected inflation (INFU), changes in e

i fl ti (CHINFE) d th l i t t t (RI)

Early Period La

Table 5: Subperiod Analysis

The FAME Research Paper Ser


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p

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Education with interfacing activities such as the FAME lectures, the Research DResearch Paper Series.

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N 117 Equity Returns and Integration: Is Europe Changing?Kpate ADJAOUTE, HSBC Private Bank (Suisse) and FAME and Jean-Pierre DANT

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N 116 The Price Impact and Survival of Irrational Traders - Winner of the 2004 FAM

Leonid KOGAN, Sloan School of Management, MIT and NBER; Stephen ROSS, S

MIT and NBER; Jiang WANG, Sloan School of Management, MIT, CCFR and NBEconomics Department, MIT;August 2004

N 115 Predicting Tail-related Risk Measures: The Consequences of Using GARCH Fil

Amine JALAL, HEC - University of Lausanne and FAME and Michael ROCKINGE

FAME AND CEPR;June 2004

N 114 Further Evidence on Debt-Equity Choice

Philippe GAUD, HEC-University of Geneva; Martin HOESLI, HEC-University of G

Aberdeen (School of Business) and Andr BENDER, HEC-University of Geneva and

N 113 Geographic versus Industry Diversification: Constraints Matter

Paul EHLING, Smeal College of Business, Penn State University and Sofia B. RAMAugust 2004

N 112 Nonparametric Estimation of Conditional Expected Shortfall

Olivier SCAILLET, HEC - University of Geneva and FAME;July 2004

N 111 The Integration of Securitized Real Estate and Financial Assets

Sverine CAUCHIE, HEC-University of Geneva


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Real Asset Returns and Inflation a Structural VAR Analysis

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