■ ^ \^L·. -i? ■ 1S *.· V :;· ‘i¿ ■«’■'Г f" n f Щ І J ,ir4 i¿ , л кь; í i· ; Fjúí·^· , i> . ü f- «w··»»'·»·* . Ѵ ^ ч іі'·^*, Ѵ'іЫ 1
,ϊ-itv t'.lft . ,ar 4i«'
Î i E ï ' î i - o í ' В ш п о п і і ш ' ' ■'ili'»;» ■ 1ІЭ кЫ І.Л . S C ' i S i l O e í í í V, " '«í‘ '·>*'>’ iiiŞ' τ'* '»û. і4І'ІлА -· *·^<4 ■’гіІііШjV'İ'iİİ/ϊ ί Α '■ 'Τ,^^ΐ.'ΐί^ * î^.<л’-1f*“! i î ' ^‘·>·.-.« · «i*Ѵч «T . . ».■ *.·.···*..ν. ч0?0 I '¿íS W'l Sf.'·**’ . ‘ * 'ч '“ ¿i. . ‘ !■.''■?■■. .í"^.l·’*·‘í,Γ·^■чЧ■^■‘ i ·>'ι Pif·.*.·! » V / 0 9 0 c · /
Rationality of Inflation Expectations
in a Financially Repressed Economy
E c o n o m i c s
Soc i a l S c i e n c e s A T h e s i s
S u b m i t t e d to the D e p a r t m e n t of and the I n s t i t u t e of E c o n o m i c and
of B i l k e n t U n i v e r s i t y in P a r t i a l F u l f i l l m e n t of the R e q u i r e m e n t s for the D e g r e e of M a s t e r of A r t s in E c o n o m i c s by E R D E M B A SÇI O c t o b e r , 1'990 a<> <-i ... :.r;tir.
і г о ^ - г •в39~
с.i
I c e r t i f y that T hav e read this t h e s i s is f u l l y a d e q u a t e In s c ope and In qu a l i t y , d e c r e e of M a s t e r of Art s In E c o n o m i c s . and In my ov.)lnion it a s a t h e s i s f o r t h e Co CJ P r o f . S u b i d e y To.^an
T c e r t i f y that I have read t h i s t h e s i s is fu L L y a d e q u a t e in scope and in qual i t y , d e c r e e of M a s t e r of A r t s in E c o n o m i c s .
a nd in m y o p i n i o n it as a t h e s i s for the
Dr. U m i t Erol
T c e r t i f y that I h a v e read this t h e s i s is f u l l y a d e q u a t e in s c o p e a nd in q u a l i t y , d e c r e e of M a s t e r of A r t s in E c o n o m i c s .
a n d in my o p i n i o n it as a thes i s for the
Dr. E r i n ç Y e l d a n
A B S T R A C T R A T I O N A L I T Y O F I N F L A T I O N E X P E C T A T I O N S IN A F I N A N C I A L L Y R E P R E S S E D E C O N O M Y E R D E M BASÇI M * A. in E c o n o m i c s S u p e r v i s o r : P r o f e s s o r S u b i d e y T o ^ a n O c t o b e r 1990, 25 pag'es T h i s s t u d y a t t e m p t s to a s s e s s the q u a l i t y of p u b l i c ’s e x p e c t a t i o n s of i n f l a t i o n by i n v e s t i g a t i n g the d y n a m i c i n t e r a c t i o n s b e t w e e n money, prices, income and i n t e r e s t rates in T urkey. Four a l t e r n a t i v e h y p o t h e s e s on p u b l i c e x p e c t a t i o n
f o r m a t i o n rule are p r o p o s e d and tes t e d in the c o n t e x t of the same real m o n e y b a l a n c e s model. The fact th a t i n t e r e s t rates w e r e not d e t e r m i n e d by the m a r k e t f o r c e s in the i n v e s t i g a t e d p e r i o d p r o v i d e s s u f f i c i e n t v o l a t i l i t y in the real i n t e r e s t rates, and h e n c e r e d u c e s the c o n f i d e n c e b a n d s of the e s t i m a t e s of the i n t e r e s t s e n s i t i v i t y p a r a m e t e r of the real m o n e y d e m a n d function. The e s t i m a t i o n of p a r a m e t e r s and t e s t s of h y p o t h e s e s are c a r r i e d out on r e s t r i c t e d and u n r e s t r i c t e d v e c t o r - a u t o r e g r e s s i v e r e p r e s e n t a t i o n s of the time s e r i e s of four e c o n o m i c v a r i a b l e s , n a m e l y g r o w t h rates of money, prices, o u t p u t and i n t e r e s t rates. Out of s a m p l e f o r e c a s t s are also c a r r i e d out and c o mpared. M o s t of the r e s u l t s are in f a v o r of the a d a p t i v e and less i n f o r m e d e x p e c t a t i o n s h y p o t h e s i s r a t h e r t h a n r a t i o n a l or m o r e i n f o r m e d ones .
K e y w o r d s : R a t i o n a l e x p e c t a t i o n s , m o n e y d e m a n d function, v e c t o r - a u t o r e g r e s s i o n , s t a t i o n a r i t y , c r o s s - e q u a t i o n r e s t r i c t i o n s .
Ö Z E T
M A L t P İ Y A S A L A R I AZ G E L İ Ş M İ Ş B İ R E K O N O M İ D E
E N F L A S Y O N B E K L E N T İ L E R İ N İ N A K I L C I L I Ğ I
ER D E M BASOr
Y ü k s e k Lisans Tezi, E k o n o m i k ve So s y a l B i l i m l e r E n s t i t ü s ü
Tez Yöneticisi: Prof* Dr. S ü b i d e y T o ^ a n
E k i m 1990, 25 sa y f a
Bu ç a l ı ş m a h a l k ı n e n f l a s y o n b e k l e n t i l e r i n i n n i t e l i ğ i h a k k ı n d a bir f i k i r e d i n m e k a m a c ı y l a T ü r k i y e M e k i para, fiyat, mi l l i ^ e l i r ve f ai z o r a n l a r ı a r a s ı n d a k i d inami k etk i leşimi i n c e i e m e k t e d i r . H a l k ı n b e k l e n t i l e r i n i m o d e l l e y e n dör t ayrı h i p o t e z ö n e r i l m i ş ve b u n l a r aynı p a r a talebi m o d e l i ç e r ç e v e s i n d e s ı n a n m ı ş t ı r . tncelenerı d ö n e m d e f a i z l e r i n s e r b e s t p i y a s a d a o l u ş m a m ı ş b u l u n m a s ı , p a r a t a l e b i n i n faiz h a s s a s i y e t i yıarametresinin e t k i n bir ş e k i l d e t a h m i n e d i l e b i l m e s i n e imkan v e r e c e k şekilde, reel f a i z l e r d e d a l g a l a n m a y a n e d e n o l m u ş t u r . M o d e l p a r a m e t r e l e r i n i n tah m i n i ve h i p o 1. ez test 1 e r i d ö t m a k r o e k o n o m i k d e ğ i ş k e n i n z a m a n ser i .1 e r i r) i n k ı s ı t l a n m ı ş ve s e r b e s t p a r a m e t r e l i v e k t ö r o t o r e ^ r e s y o n m o d e l l e r i ü z e r i n d e y a p ı 1m ı ş t ı r . Bu d e ğ i ş k e n l e r p a r a n ı n , f i y a t l a r ı n , reel m i l l i ^'elirin ve f a i z l e r i n y ı l l ı k d e ğ i ş i m m i k t a r l a r ı d ı r . A y r ı c a her h i p o t e z için ö r n e k dışı k e s t i r i m l e r de y a p ı l m ı ş ve k a r ş ı l a ş t ı r ı l m ı ş t ı r . S o n u ç l a r ı n ç o ğ u az bilğ i l e n d i r i l m i ş ve a d a p t i f b e k l e n t i l e r h i p o t e z i n i , çok b i l g i l e n d i r i l m i ş veya akılcı beki en t i 1er al t e m a t i f 1er inden d a h a f a z l a de s tek I e m e k t ed i r .
A n a h t a r K e l i m e l e r : A k ı I c ı b e k l e n t i l e r , a d a p t i f b e k l e n t i l e r , par a talebi f o n k s i y o n u , v e k t ö r o t o r e ğ r e s y o n m o d e l i , d u r a ğ a n l ı k , d e n k i e m l e r araşı kısa t l a m a l a r .
ACKNOWLEDGEMENTS
I w o u l d like to e x p r e s s my g r a t i t u t e to P r o f e s s o r S u b i d e y T o g a n for his i n v a l u a b l e s u p e r v i s i o n d u r i n g the d e v e l o p m e n t of this thesis· I also w o u l d like to e x p r e s s my t h a n k s to the E c o n o m i c s D e p a r t m e n t of B i l k e n t U n i v e r s i t y for p r o v i d i n g me both the n e c e s s a r y b a c k g r o u n d and all the f a c i J i t i e s th a t I n e e d e d to c o m p l e t e this study. S]-)ecial t h a n k s go to Dr· Umi t Erol for p r o v i d i n g the n e c e s s a r y b a c k g r o u n d in m a c r o e c o n o m i c s and time s e r i e s a n a l y s i s and to Dr. Erinc Y e l d a n for u s e f u l c o m m e n t s . I am i n d e b t e d to P r o f e s s o r H i r o f u m i U z a w a of the J a p a n A c a d e m y for his e n c o u r a g e m e n t and u s e f u l c o mments. I al s o t h a n k to P r o f e s s o r P e t e r H a m m o n d for his a d v i c e s on the use of t e r m i n o l o g y .
TABLE OF CONTENTS A b s t r a c t O z e t A c k n o w l e d g e m e n t s T a b l e of C o n t e n t s List of T a b l e s List of F i g u r e s ). i i i i i. i V V V i I. I n t r o d u c t i o n II. The M o d e l III. E s t i m a t i o n R e s u l t s and T e s t s IV. P a r a m e t e r S t a b i l i t y and O u t of S a m p l e F o r e c a s t s 12 V. C o n c l u s i o n s 18 VI. L i s t of R e f e r e n c e s 19
LIST OF TABLES T a b l e 1. C r o s s E q u a t i o n R e s t r i c t i o n s T a b l e 2. T he L i k e l i h o o d R a t i o T e s t s for F o u r A l t e r n a t i v e S p e c i f i c a t i o n s 7 9 T a b l e 3. P a r a m e t e r E s t i m a t e s of four A l t e r n a t i v e Spec i f i c a t i o n s T a b l e 4. The C h a n g e in P o l i c y Rviles I m p l i e d by P a r a m e t e r C h a n g e s in M o n e y and I n t e r e s t P r o c e s s e s T a b l e 5. T he L i k e l i h o o d R a t i o T e s t s for Fo u r A l t e r n a t i v e S p e c i f i c a t i o n s in Two T i m e P e r i o d s Tat)le 6, P a r a m e t e r E s t i m a t e s of F o u r A l t e r n a t i v e S p e c i f i c a t i o n s in Two T i m e P e r i o d s
T a b l e 7. The L i k e l i h o o d R a t i o T e s t s for Fou r A l t e r n a t i v e S p e c i f i c a t i o n s in 1 9 7 6 - 8 8 P e r i o d w i t h P a r a m e t e r s E s t i m a t e d for 1 9 6 3-75 P e r i o d T a b l e 8. R o o t M e a n S q u a r e d F o r e c a s t E r r o r s of I n f l a t i o n ( 1 976-88) P e r i o d 10 11 1 2 13 14 15 L i s t of F i g u r e s F i g u r e 1 . F o r e c a s t s of I n f l a t i o n U n d e r Case A S p e c i f i c a t i o n 16 F i g u r e 2 . F o r e c a s t s of I n f l a t i o n U n d e r C a s e B S p e c i f i c a t i o n 16 F i g u r e 3. F o r e c a s t s of M o n e y G r o w t h U n d e r C a s e A S p e c i f i c a t i o n 17 F i g u r e 4. F o r e c a s t s of M o n e y G r o w t h U n d e r C a s e B S p e c i f i c a t i o n 17
Turkey used to have a bank based financial system until 1980’s
and despite the recent efforts to develop the capital markets,
money deposits in banks still constitute the major medium for
savings. Moreover, toj^ether with extensive credit rationin.iC, the
nominal interest rates have been fixed at rates lower than their
free market values at re;p;ular intervals by the Turkish
authorities during most of the 60-80 period. This resulted in
ex-post real interest rates on bank deposits that were very
volatile and mostly negative.
In such an environment, due to non availability of alternative
securities, the anticipated real return on money savings will
effect the speed of spending on commodities, hence on prices.
Therefore the real value of money balances will vary positively
with the public’s real return expectation on money deposits. And
the real return expectation is solely determined by inflation
expectations, ^iven the nominal interest rate.
As a financially repressed economy, Turkey provides a good case
for investigating this phenomena. In this paper, the effect of
expectations of inflation on the path of prices is discussed.
The rationality of expectations is questioned and tested in the
contexts of rational and adaptive expectations specifications.
Two versions of each specification is considered based on
differences in the assumed information sets for the agents,
section II presents the models and methodology. Section III
gives the estimation results. Comparisons of out of sample
forecasts of alternative models are presented in section IV. A
summary of main findings are in section V.
I. Introduction
II. The Model
According to the model used here, the logarithm of real money
balances is a linearly increasing function of both real income
and real rate of return available from holding money.^
ln(M/p) = a + nlny + A(R-7T) + u (1)
with T)>0, ^>0, where
M; Money Stock (Currency+Demand Deposits+Time Deposits)
p: Price Level (GNP Deflator)
y: Real Income (GNP in constant prices)
R; Nominal Rate of Interest on Money (Weighted Average)
n: Public’s expected rate of inflation
u; Unobserved disturbance term due to public’s preferences and technological conditions.
The important problem in estimation of the parameters of the
above model is that T( is not observable by the economist.
Cagan(1956) has proposed using adaptive expectations in the form
00
(2)
i = 0
with P<^[0,1J where =ln(pyp^ ,,) is the realized inflation rate
of period t. One should note that this model requires the
knowledge of x^ i.e. the current period’s inflation rate before
it is realized and announced. Moreover, as it is shown in
^The model in principle the same as the one used by Togan(1987) for 1960-1983 period in Turkey. As a specific case one obtains Cagan’s (1956) model when 0=0 and R=0.
Sar,^'ent& Waliace( 1973) usiiiii (2) to estimate (1) by OLS will
yield statistically inconsistent results since is correlated
with u t
An alternative form assumes yuiblic has the knowled,s>'e of the
latest announce inflation i*e. they are less informed but they
still form their expectations adaptively.
00
(3) i=0
Togan(1987) has estimated model (1) by using both
specifications (2) and (3) for expected inflation. Although
2
specification (2) gave higher R values, in all the simulations it
performed worse than specification (3) which gives consistent
estimates of X.
Sargentfe Wallace(1973) and Sargent(1977) show that unless the
money supply process has feedback from inflation in a specific
way, the adaptive expectations cannot be rational in the sense of
being consistent with the model’s expectations. In this paper
the validity of the rational expectations hypothesis as opposed
to adaptive expectations assumption will be tested for Turkish
data in the context of the money demand function presented as
equation (1). The test is based on the suitability of imposing
the restrictions implied by model (1) and various expectation
specifications on a vector autoregressive representation of four
Differenciii9; (1), one obtains,
x,= n.s;\+ (4)
where
= ln(M^/M^ is the rate of .s^rowth in money,
= ln(y^/y^ is the real income i^rowth rate,
is the change in interest rate
is due to chang'es in technology or S = H - V.
preferences. 3 It will be assumed that ^(e )=0.'
Rationality of expectations require
7T = E X
t t t +1 (5)
provided that the agents posess information about variables of
the period they are in. If their information set contains only
previous period’s announced variables, then rational expectations
take the less informed form
n = E ,x, ,
t t -1 t +1 (61
To obtain the cross equation restrictions on a vector
autoregressive representation of four variables imposed by the
model and various public expectation specifications, the expected
value of both sides of equation (4) is taken.
(71
^The reader can note that (4) is a theory of inflation if money growth, expected inflation and income growth are regarded as exogenous.
^E (.) is the mathematical expectation operation given all the ievant information of period t-1.
Specit'icly, consider the representation below where rate of
growth in income is taken as econometricLy exogenous and the
change in interest rates is formulated to be Grcvnger caused by
past inflation rates. Furthermore money growth and inflation are
assumed not to be caused by past income growth or interest rate
changes. 4 n n
I
i = 1 i = l r4 n X =c + t X V r li i = l+ S
i = l (Ba) (Bb) g =c + ‘X ♦- g g. (8c) r =c + e + e x _ + « t r 1 t -1 2 t - 2 r (BdlNow equation (7) together with any of equations (2),(B),{5) or
(6) Impose its own restriction on the parameters of
representation (8). The testing of these restrictions are
carried out in the following section.
III. Estimation Results and Tests
First consider the adaptive expectations hyi)oth<,'ses. The
optimal value of ¡3 for 1961-88 period is found to be very close
to 1 on the basis on minimum mean squared errors. The same value
^The reader can note that the unrestricted version presented above is not a complete vector autoregressive representation and has a total of lln+1 exclusion restrictions. The reason is the shortage of degrees of freedom due to shortness of time series. The value of n is selected as 2 for the same reason. The ad hoc restrictions however are all .justified by prior analysis.
of p is reported in Tog'an (1987) as estimated from the money
demand equation (1) for his more satisfactory model. Given a
value for /?, it is straii?htforward to obtain the cross equation
restrictions on parameters of (8). The restrictions for less and
more informed expectation formulations are presented on table 1
as cases A and B respectively.
Under model consistent expectations of the form (5), the
restrictions are presented as case C. The reader can verify the
validity of tliese by directly substititin^ VAR expectations in 5
(7) and (5). Under the less informed formulation (6), quite
simpler lookini:^ restrictions are derived and presented as case D
on table 1.
Table 1
Cross Equation Restrictions
Hypothesis:
Model (1) holds and
Restrictions on parameters of (8)
(n=2)
A. Adaptive Expectations Model (2) 0=1) rjc + Xc +c g r X (Less Informed) a. = 1 c. 1 i=l,2 b = d -X +Xe 1 1 1 d +A +Xe^ 2 2 2 B. Adaptive Expectations "/-r 17c +X.C + c g r X Model (3) (P=l) (More Informed) a . — 1 (l-X)c. i=l,2 d^-Xd^+ X+ Xe ^ V ^2“ '^2more detailed derivation method of restrictions for this case can be found in Salemi&Sargent(1979) where income and interest effects do not appear.
(T ab J.e 1 c o w t i 11ii e d ) C* Rational Expectations Model (5) (More Informed) c . . = --- ^ ^ + rj c +^ c y r // ■■ (l+>c^) (l-Xd^)c^-X(c2-c^) a = --- ^---(1+Xc^) (l->.d^)c^+Ac^ ^2“ (1+^C^) (l->.d;)d^-X(d2-d^) b = = +Xe (1+XcJ b = --- +Xe (1+^cp D. Rational Expectations Model (6) (Less Informed) c = Xc + Xc +c JL/ g r V a =c.=0 1 1 d,=0 bi= d^-Ad^+Xe^ b_= ^d^+^e_ 2 1 2 i=l,2
The unrestricted and restricted versions of (8) for n=2 are
estimated for 1963-1988 period by iterative Zellner’s seemingly
unrelated regression technique which is asymptoticly equivalent
to full information maximum likelihood estimation. The
suitability of restrictions is tested by the likelihood ratio
test calculated as
L = T d n I V !-lnlV ! ) ,
where V and V are the variance covariance matrix of residuals of
restricted and unrestricted models respectively and T is the
number of observations. The statistic is asymptotically
distributed chi-squared with k de,^rees of freedom, where k is the
number of independent restrictions,under the null hypothesis that
the restrictions are correct. The values of this statistic and
the marginal significance levels are reported as Table 2 for the
1963-88 ))eriod. The results lead to the rejection of all
specifications except A at 95% and to the rejection of the
more informed cases B and C at 99% confidence levels.
Table 2
The Likelihood Ratio Tests
for Four Alternative Specifications (1963-1988)
Case: q* X^(q) Marginal Significance At 95% Hypothesis
A 3 5.9 0.117 Not Rejected
B 3 13.9 0.003 Rejected
C 3 14.4 0.002 Rejected
D 6 16.0 0.014 Rejected
Number of Independent Restrictions
The estimated parameters are seen on Table 3. All the income
elasticities T] are of plausible magnitudes. The interest rate
coefficient ^ however is significantly positive only for cases A
and D, i.e. the cases of less informed expectations. For cases B
and C the estimated X is negative but not significantly different
from zero. Both the likelihood ratio test and parameter
estimates seems to justify the less informed adaptive
expectations specification over the other three.
Table 3
Parameter Estimates
of Four Alternative Specifications (1963-88)
Case: Estimate of r> Estimate of X
A 1.003 0.494 (0.2909) (3.297) B 1.140 -0.335 (0.362) (-0.805) c 1.282 -1.062 (0.910) (-1.257) D 0.878 0.793 (0.318) (2.903)
Asymptotic Standard Errors in Parantheses t-ratios in parantheses
Refiarding money supply and interest rate as policy variables,
the above type of analysis determines the stochastic process of
inflation given the money growth, interest rate and income
processes. The strategic dependence of behavior on policy is the
key argument of the rational expectations "school" . For our
case there has been an apparent change in the money supply rule
and the interest determination rule after the 1973 and 1974 oil
shocks. Substantial feedback from inflation to money creation
has took place in 1976-88 period whereas it has been negligible
in 1963-75. If there is such a switching in the stochastic
policy processes within 1963-88 period, the above results will be
biased and misleading. For this reason the time period is
Sargent(1986,p.101) point out that there is not a unique school of rational expectations. The common feature of the very diverse class of such models is the model consistency of expectations.
seperated into two equal intervals 1963-75 and 1976-88. The
unrestricted system estimates of money growth and interest change
processes are given on Table 4 for the two periods. The changes
especially in the money growtl> rule but also the interest
determination rule are remarkable. The restricted estimation
Table 4
The Change in Policy Rules
Implied by Parameter Changes in Money and Interest Processes
Parameter: 1963-75* 1976-88 c.. 0.05 0.13 M (3.18) (3.49) 1.39 -0.07 1 (7.65) (-0.29) -0.68 0.20 c . (-0.84) (1.44) b, -0.11 0.45 (-0.84) (5.88) b 0.28 0.21 (1.75) (1.79) c 0.003 -0.037 r (2.517) (-0.966) e, 0.049 0.184 1 (2.905) (1.640) -0.078 0.030 2 (-3.704) (0.250) t-ratios in parantheses
results are on Tables 5 & 6. The likelihood ratio test (Table 5)
this time fails to reject rational expectation hypotheses of
cases C and D at 95 per cent confidence level, for the 76-88
period. For the 63-75 period however case D is rejected at 99
percent confidence level. Case A passes the 95% test in both
periods but Case B is rejected for the second half at 95%. The
interest sensitivity coefficients on Table 6 hcwe the correct
si^n except for case B in the first half. However none of the
rational expectations estimates are si^ificantly g'reater than
zero. Similarly the confidence band for income elasicity
estimates is lar^e. They are lar^e enough to include plus one,
with one exception for case C, although some point estimates are
negative. Still, the reduction in the value of this estimate in
the second half is common to all cases. These results weaken the
evidence against validity of the rational expectations as
depicted by estimation on the entire 1963-88 period. The next
section compares forecasting power of the alternative models on
out of sample data.
Table 5
The Likelihood Ratio Tests for Four Alternative Specifications
in Two Time Periods
Case: q X (n)2/ . 1963-75 1976-88 Marginal 1963-75 Significance 1976-88 A 3 2.4 7.8 0.494 0.051 B 3 0.8 10.8 0.850 0.013 C 3 6.4 7.1 0.094 0.069 D 6 26.1 7.9 0.001 0.246
Table 6
Parameter Estimates
of Four Alternative Specifications in Two Time Periods
Case: Estimate of rt Estimate o f A
1963-75 1976-88 1963-75 1976-88 A 1.387 0.493 0.794 0.498 (0.186) (0.720) (2.587) (2.537) B 1.005 -0.653 -1.072 0.323 (0.201) (1.506) (-1.225) (2.243) C 0.503 -0.423 3.046 1.684 (0.105) (1.399) (1.522) (1.392) D 1.329 -0.790 1.532 2.035 (0.188) (1.565) (2.299) (1.570)
Asymptotic standard errors in parantheses t-ratios in parantheses
IV. Parameter Stability and Out-of-Sample Forecasts
The basic task of the econometric rational expectations models
is reported in Sargent (1986) to be the isolation of the
parameters related to preferences, technology or more generally
the parameters that are independent of the strategy of policy
makers. For our case, this means that the expectation generation
rule of the public, rather than being fixed over time, depends on
the policy rules of authorities in determining money growth and
interest rates.
If the policy dependence were to hold in our case, and if the
parameters > and 17 were stable over time, one would expect the
rational expectations models to perform better than the adaptive
expectation models in forecasting the inflation rates of the
1976-88 period, since there has been an apparent change in policy
rules^.
To have an idea about stability of \ and ri the point estimates
of them for the 1963-75 period is put as additional restrictions
on the same models in the 1976-88 period. The likelihood ratio
statistics on table 7 fail to reject the hypotheses of no
parameter change and model validity for cases A, C and D at 99
percent confidence.
Table 7
The Likelihood Ratio Tests
for Four Alternative Specifications (1976-1988) With Parameters Estimated for 1963-75 Period
Case: q X^(q) Marginal Si.^ni f icance At 99% Hypothesis
A 5 11.2 0.048 Not Rejected
B 5 15.2 0.001 Rejected
C 5 9.8 0.081 Not Rejected
D 8 11.7 0.165 Not Rejected
Number of Independent Restrictions
Next, to compare the out of sample forecasting performances,
the estimates of X and H in 1963-75 period, and the money growth,
interest rate and income growth parameters for the 1976-88 period
rj
It is assumed by most rational expectations models that people are aware of the new policy rule as soon as it is in tact. Whether the rule is announced beforehand or whether it is felt by the individuals is an issue not much discussed in empirical studies.
are used to calculate the parameters of the inflation process g
implied for this period by the restrictions of Table 8 . The 9 root mean stpiare forecast errors (RMSE) are reported on Table 8 .
For comparison, the RMSE of adaptive expectations for ,8=1 which
is the public’s RMSE under case A is also presented. Quite
interestingly, case A results are superior to all other cases in
forecasting inflation. Figures 1 and 2 show the paths of
forecasted and realized inflation rates for cases A and C
respectively. A common observation in all cases, is that
explaining and forecasting money growth is much more easier by
this model which may be an implication of exogeity of inflation
during the investigated time interval (Figures 3 and 4).
Table 8
Root Mean Squared Forecast Errors of Inflation (1976-88 Period)
Case: RMSE Parameter
n Values Used X A. 0.116 1.39 0.79 B. 0.151 1.00 -1.07 c . 0.148 0.50 3.05 D. 0.141 1.33 1.53 Naive 0.152 -
-Adaptive Expectations 0=1) is identical to previous period’s realized inflation rate.
Q
The estimation of policy processes were done seperately for
each case under its own restrictions.
^The forecasts are "static" in the sense that the past realized
vaues are used to forecast current values.
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-RESIDITAL ---ACTUAL - — TITTEU
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V. Conclusions
This paper looked for evideru'e of policy dependence in
expectations of inflation in Turkey, The time period
investi <4ated is one in which interest rates are not allowed to
move toR'ether with expected inflation, hence the effect of
expected inflation rate on real money balances becomes
emphasized.
The data on price, money, income and interest rates for Turkey
in 1963-88 period does not provide stron.9; evidence on the
existence of policy dependence in inflation expectations of the
a^^ents in the context of the rational expectations imbedded money
demand function. An adaptive expectations specification fits the
data better and the so constructed model has the best forecasting
performance.
However when the data is seperated to two time periods, it
is seen that the rational expectations models fit better in the
second period.
Another finding of this study is that, the less informed
cases where the agents are assumed to posess only the previous
period’s information, in general seem to be more valid as
compared to more informed cases.
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3. Salem i , M.K. and Sargent, T.J. 1979. "The Demand For Money During Hyperinflation Under Rational Exp'r'ctations: II",
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4. Sargent, T. .1. and Wallace, N. 1973. "Rational Expectations and The Dynamics of Hyperinflation", International Economic
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5. Sargent , T. J. 1977. "The Demand For Money During Hyperinflations Under Rational Expectations: 1", International
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