Le en akis, John A.
A icle
In la ion and he Fo ma ion o Expec a ions: Some
Empi ical Resul s
K edi und Kapi al
P o ided in Coope a ion wi h:
Duncke & Humblo , Be lin
Sugges ed Ci a ion: Le en akis, John A. (1985) : In la ion and he Fo ma ion o Expec a ions: Some
Empi ical Resul s, K edi und Kapi al, ISSN 0023-4591, Duncke & Humblo , Be lin, Vol. 18, Iss. 4, pp.
515-526,
h ps://doi.o g/10.3790/ccm.18.4.515
This Ve sion is a ailable a :
h ps://hdl.handle.ne /10419/293037
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In la ion and he Fo ma ion o Expec a ions:
Some Empi ical Resul s
By John A. Le en akis*, A hens
I. In oduc ion
The ole o expec a ions and hei ea men is pe haps he mos impo -
an issue conce ning he p ocess o in la ion. Since in la iona y expec a-
ions a e no an obse able a iable, in es ima ing he e ec s o p ice expec-
a ions on ac ual in la ion a ious p oxies ha e gene ally been used o he
unobse able expec ed a e o in la ion (see e.g., Tu no sky and Wach e ,
1972; Lahi i, 1976; Mullineaux, 1980). One p ocedu e o modelling p ice
expec a ions is he a ional expec a ions app oach, in which he exp ession
o he expec ed a e o in la ion is de i ed om he gene al a ional expec-
a ions solu ion o he s uc u al model o he p ocess gene a ing in la ion.
An al e na i e p ocedu e is o use independen measu es o in la iona y ex-
pec a ions which a e employed o es ima ing p ice equa ions.
In his pape we ollow he second app oach. In pa icula , we de elop
and es ima e a model o p ice de e mina ion using al e na i e expec a ions
hypo heses, all aking in o accoun he ole o money g ow h in he o ma-
ion o in la iona y expec a ions. The model is es ima ed wi h qua e ly
da a om he small open economy o G eece o e he pe iod 1975.1 -
1983.IV.
The plan o he pape is as ollows: sec ion II se s up he model o p ice
o ma ion. In sec ion III we discuss a ious hypo heses on he o ma ion o
expec a ions. Empi ical esul s a e p esen ed in sec ion IV and concluding
ema ks a e gi en in sec ion V.
II. The Model
The model p esen ed in his sec ion is a a ian o a gene al model de-
eloped by Tobin (1972) and is ep esen a i e o much o he ecen empi -
* The au ho is g a e ul o S. N. B issimis and A. S. Cou akis o hei help ul com-
men s.
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516 John A. Le en akis
ical wo k on p ice and wage beha iou (see Ecks ein and Gi ola, 1978;
Spi alle , 1978). The model con ains i e equa ions - an iden i y o he gen-
e al p ice le el, a p ice adjus men equa ion, a wage adjus men equa ion,
an equa ion ela ing he unemploymen a e o he ou pu gap, and an
equa ion o p ice expec a ions wi h al e na i e hypo heses as o how
in la iona y expec a ions a e o med.
The o e all a e o in la ion is exp essed as a weigh ed a e age o he a e
o change o he p ice le el o domes ically p oduced goods and he a e o
change o p ice o impo ed goods
(1) Ap =
¡iAph
+ (1 - ^)Ap?
whe e p is he log o he gene al p ice le el, ph is he log o p ice o domes-
ically p oduced goods, pm is he log o he domes ic p ice o impo ed goods,
[i and (1 - (i) a e he weigh s o domes ically p oduced and impo ed goods
espec i ely and A is he i s di e ence ope a o ; AX is a e o change on an
annual basis.
The p ices o domes ic goods a e assumed o espond o bo h domes ic and
o eign ac o s
(2) Aph
= a0 + ax Aw + a2 Aq + a3 Aph
+ a4 (y - y)
al a3, a4 > 0; a2 < 0
whe e w is he log o he money wage a e, q is he log o p oduc i i y (ou -
pu pe man-hou ), y is he log o eal ou pu and y is he log o no mal p o-
duc ion capaci y p oxied by he end le el o ac ual ou pu .
The i s e m in eq. (2) gi es he in luence o he a e o change o wage
a e on in la ion, while he second e m ep esen s ha o he a e o change
o p oduc i i y. The hi d e m cap u es he in luence o o eign in la ion (in
domes ic cu ency) on domes ic in la ion. The ou h e m ep esen s he ex-
en o which p ices adjus o a gap be ween ac ual and he no mal le el o
ou pu . When ac ual ou pu is abo e i s capaci y le el, in la iona y p essu e
is p esen in he goods ma ke .
The wage equa ion is he well known expec a ions augmen ed Phillips
hypo hesis whe e he a e o change o money wages is posi i ely ela ed o
he expec ed a e o in la ion and o he a e o change o p oduc i i y, and
nega i ely ela ed o he unemploymen a e.
(3) Aw = b0 + b xAp + b2Aq + bzU
bu b2 > 0: b3 < 0
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In la ion and he Fo ma ion o Expec a ions 517
whe e pe is he log o he expec ed p ice le el in pe iod and U is he un-
employmen a e. The expec ed a e o in la ion en e s equa ion (3) o allow
wage ea ne s o p o ec hei pu chasing powe agains in la ion.
Assuming Okun's law (1962), in which he ou pu gap is ela ed o he
unemploymen a e, we ha e
(4) U = y0 4- 7l (y-y)
Yo
> 0; Yi < 0
whe e he cons an e m, y0> ep esen s some ic ional unemploymen which
i is assumed ha does no espond sys ema ically o he a ia ions in he
demand p essu e in he ma ke o goods. The abo e o mula ion in ol es
he es ic i e assump ion ha all changes in he ou pu gap necessa ily
cause changes in unemploymen a e in he opposi e di ec ion.
Combining equa ions (1) - (4), we ob ain
(5) Ap = c0 + cx Apm + c2 (y-y) + c3Aq + c4z p
Ci, C2, c4 >0; c3 ^ 0.
The sign o he coe icien c3 can be ei he posi i e o nega i e depending on
he ela i e magni udes o he coe icien s a2 and b2 = b2a The expec ed
alue o a2 is be ween minus one and ze o while ha o b2 lies be ween ze o
and one. Thus, wo opposing o ces a e p esen in he e ec o he a e o
change o p oduc i i y on he a e o in la ion.
III. Al e na i e Hypo heses o he Fo ma ion
o In la iona y Expec a ions
To comple e he model we need o speci y how expec a ions a e o med.
Since he p ima y pu pose o he s udy is o es al e na i e hypo heses o
in la iona y expec a ions which ake accoun o he ole o mone a y
changes in he o ma ion o expec a ions, he selec ed hypo heses include
mone a y changes as one a iable a ec ing in la iona y expec a ions. One
hypo hesis ha omi s mone a y changes has been conside ed bu only as a
basis o compa ison o he se o hypo heses con aining mone a y changes.
Thus, in es ima ing he p ice equa ion (5) he ollowing hypo heses o he
expec a ional a iable a e conside ed:
(i) The i s hypo hesis we conside is he s anda d adap i e expec a ions
lea ning model (see Cagan, 1956; F enkel, 1975)
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518 John A. Le en akis
(6) A p - A pU = (A p .x - A pUi)
whe e X is he e o adjus men coe icien . Recu si e subs i u ion o he
expec ed a e o in la ion in he abo e equa ion allows us o exp ess he
expec ed a e o in la ion as he weigh ed sum o pas (ac ual) in la ion a es
(V A Pi= SoiP -i-l
i =
0
whe e a = A.(l - X)1
(ii) The second model o expec a ions o ma ion conside ed is called mon-
e a y model, which e e s o he hypo hesis ha p ice expec a ions a e
o med as a weigh ed a e age o cu en and pas a es o g ow h o he
money supply
(8) Ape = ^biAm -
i
=
0
whe e m is he log o he money supply. This ype o hypo hesis was
sugges ed by Flemming (1976, p. 58) who w i es ha "on his basis a
mone a is is equi ed o assume ha o he people's p ice expec a ions a e
based on ecen changes in he money supply"1.
(iii) The hi d model o expec a ions o ma ion is he model ha combines
bo h adap i e and mone a y hypo heses
(9) Ape =
1
+
i=0 i=0
The basic idea unde lying he abo e hypo hesis, which has been o mula ed
by Ru ledge (1974), is ha in la ion expec a ions a e o med on he basis no
only o pas alues o he a iable i sel , bu also o he in o ma ion con-
ained in he his o y o he a e o g ow h o he money supply2.
Subs i u ing equa ions (7), (8) and (9) in o (5) we ob ain he al e na i e
p ice equa ions:
(10) Ap = c0 + cxAp? + c2{y - y) + czAq + ^MP -z-i
i
=
0
1
McGui e (1976) and Holden and Peel (1977), among o he s, p o ide suppo o
his hypo hesis by explaining he expec ed a e o in la ion in e ms o mone a y
changes.
2 Recen suppo o his hypo hesis is p o ided by Mullineaux (1980) who shows
ha in la ion o ecas s a e sys ema ically in luenced by pas in la ion a es and pas
a es o money g ow h.
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In la ion and he Fo ma ion o Expec a ions 519
(11) Ap = c0 + ClApT + c2(y - y) + c3Aq + ^M^-*
i = 0
Ap
=
c0 + CiAp? + c2(y-y) + c3Aq + 2M P -i-
-1
i = 0
(12) + 2 M m - i
i = 0
which a e all in e ms o obse able a iables and can be di ec ly es ima ed.
As is immedia ely ob ious, equa ions (10) o (12) a e a se o nes ed models.
Equa ion (12) comp ises he comple e se o explana o y a iables con ained
in he o he models. P oceeding in e ms o he concep ual amewo k ex-
pounded by Cou akis3, we can examine he alidi y o al e na i e hypo h-
eses ega ding he o ma ion o p ice expec a ions. In pa icula , compa i-
son o (12) wi h (10) can h ow ligh on he alidi y o he mone a y expec-
a ions hypo hesis. The null hypo hesis ha Z = 0 can be es ed by using
an F-Tes on he nes ed models. I he hypo hesis is ejec ed, i can be a gued
ha mone a y changes ac ing as a p oxy o in la iona y expec a ions a ec
ac ual in la ion. On he o he hand, compa ison o (12) wi h (11) enables us
o examine he alidi y o he adap i e expec a ions hypo hesis.
I will be no iced ha he abo e ela ionships do no commi us o any
pa icula lag con igu a ion. On he o he hand, he gene al endency has
been o p oceed in e ms o speci ic lagged s uc u es. Typical o he la e
ype o s udy a e ela ionships ha employ Almon lags. In wha ollows he
esul s de i ed om ela ionships cons ained o con o m o Almon s uc-
u es a e p esen ed while subsequen ly he pe inence o such cons ain s is
examined.
The esul s o es ima ion a e p esen ed in Table 1. All coe icien s ha e he
co ec signs and, wi h he excep ion o he in e cep , a e signi ican a he
5 pe cen le el. The es ima es indica e ha expec a ions play an impo an
ole in he de e mina ion o ac ual in la ion. In equa ion (10') he expec ed
a e o in la ion is ep esen ed by a dis ibu ed lag in pas a es o in la ion.
I is in e es ing o no ice ha he sum o he coe icien s on lagged in la ion
is signi ican ly less han uni y (0.153), implying ha he long- un Phillips
cu e is no e ical. Mo eo e , lagged alues o he a e o in la ion, excep
he i s lag, a e insigni ican , a inding indica ing ha in o ming hei ex-
pec a ions people a ach g ea signi icance o he mos ecen his o y o he
IV. Empi ical Resul s
3 See o example Cou akis (1978, 1981).
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520 John A. Le en akis
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In la ion and he Fo ma ion o Expec a ions 521
a iable i sel . The signi ican e ec s o he o he a iables dese e special
men ion. The magni ude o he o eign in la ion on domes ic in la ion is
smalle han ha one migh expec in he small open economy o G eece,
which impo s mo e han one- i h o i s inal goods. Excess demand, as
measu ed by de ia ions o ac ual ou pu om i s no mal capaci y le el4 (o
he p e ious pe iod), appea s o ha e a a he weak e ec , while he in lu-
ence o he a e o change o p oduc i i y is s ong and nega i e.
Equa ion (11') inco po a es he hypo hesis ha p ice expec a ions a e
p oxied by changes in money supply. I appea s ha only he hi d lag o
money g ow h is signi ican . The sum o he coe icien s o cu en and lag-
ged alues o money g ow h is conside ably less han uni y (0.112), a inding
indica ing he weak in luence o money g ow h on ac ual in la ion. Thus
he e is li le e idence o sys ema ic changes in p ices in esponse o changes
in money supply. As o he e ec s o he o he a iables, i can be seen ha
on he whole he e a e no subs an ial di e ences be ween he es ima es o
eq. (11') and hose o eq. (10').
Equa ion (12') embodies he hypo hesis ha pas a es o in la ion as well
as cu en and pas alues o money g ow h ac as a p oxy o in la iona y
expec a ions. Inspec ion o Table 1 e eals ha in la ion is explained a li le
be e by his model han by he o he wo models. The F- es s indica e,
howe e , ha money g ow h does no con ibu e o he explana ion o ac-
ual in la ion, gi en he e ec o pas in la ion. The hypo hesis ha money
g ow h coe icien s all equal ze o canno be ejec ed (see Table 2 o he F-
s a is ics). In addi ion, he e idence does no enable us o ejec he
hypo hesis ha all he pas in la ion coe icien s equal ze o. The esul s
he e o e do no yield conclusi e e idence as ega ds he selec ion o he ap-
p op ia e expec a ional a iable.
Table 2: A Compa ison o Al e na i e Hypo heses: Gene al Fo m (12)
Compa ed C i ical
equa ions Hypo hesis F-s a is ic F (0.05)
(12) -(10) Ißi = 0 1.15 2.92
(12) -(11) Zai = 0 1.63 2.92
(12a)-(10a) 2ßi = 0 0.71 2.92
(12a)-(11a) lai = 0 0.92 2.92
No e: The le e a deno es a a ian including he uni labou cos a iable.
4 Capaci y ou pu is measu ed by i s end alue, which is gi en by
Y = 4.911 + 0.009 R2 = 0.753 DW = 0.436.
34 K edi und Kapi al 4/1985
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