- Email: [email protected]
Elasticities of substitution and export demands in a world trade model
EuropeanEconomic Review4 ( 1973) 347 - 380. Q North-HollandPubMing
Company
ELASTICITIES OF SUBSTIT9TION AND EXPORT DEMANDS IN A WORLD TRADE MODEL *
Bert G. HICKMAN and Lawrence J. LAU Stanford Univasit j*, Stan ford, California, US. A.
First versionreceivedOctober 1972, revisedversionreceivedJanuary 1973
Alternativecomplete models of world trade, based on the trade sharesmatrix approach,are specified and estimated for twenty-sevencountriesand regions.This model attempts to explain the composition of imports on the bases of reiativepricesand time trend, given the total quarttity of imports of each country. Elasticities of substitutionamongstimportsof different countries of origin in each import nuuket are obtained and used in the derivationof aggregateexpoxt demand functions for the individual countries. There is also a comparison of the predictive performanceof the alternativemodels.
1. introdu&ion
P
In this paper we present new estimates of elasticities of substitution between competing imports into 25 industrial countries and two regions (comprising respectively the socialist countries and the rest of the world). We use a constrained estimation procedure which takes explicit account of the adding up properties of world merchandise trade flows on both the import and export sides and guarantees that estimated world exports equals world imports. We then derive for each of the 27 regions an explicit export demand function incorporating the estimated substitution elasticities as coefficients of relative price terms and as weighting factors for export competitive price indexes. This same pro-
* A paper preparedfor the Europeanmeeting of the Econometric Society, Budapest, Sep tember 5, 1972. The authors gratefully adrnowkdge the assistance of Jens Christiansenand Chiranjib3en in the computational sections of the paper.They are grateful to Edward Learner for helphrlcommenta. The researchwas supportedby the National Scknce Foundation under its grant to ProjectLINK.
348
B. Hickman. L. Lou, Substitution and export demands
cedure is followed for four alternafive demand specifications and the structural pioperties and predictive rpbilities of the four models are compared. The results presented herein are an empirical implementation of the theoreiical export demand system developed in a recent paper by Hickman j4]. In that paper, the export demand functions arc incorporated into a system of riational models which determines import quantities and export and import prices as well as export quantities. In the present paper. however, import quantit,ies and export and import prices arc taken ;is exogenous. Thus the system of e*xport demand functions taken alone is best regarded as a model of import allocation which explains changes in market shares over time as a function of given prices and trends. This procedure is justified because we are following Armington’s utility tree approach to specification of demand functions in foreign trade [ I 1. according to which total import demand for any good is first determined and then independently allocated among competing sources of supply b;l geographic region. Thus we are assuming for present purposes that total imports in each courrtry have already been determined in the first step, and we deal herein only with the allocation decision. Our typical estimating equation has the form
(1) where xii = constant dollar quantity of exports from the ith country to the jth fiountry. Superscript zero refers to base year quantity. CY$= base year ith country’s share in ]th country’s imports. ml = constant dollar quantity of imports of the jth country. 0-J = elasticity of substi:ution between imports from any two countries in the /th market. fij = price index of the exports of country i to country 1. rn=p i=lat&j, price index of imports of country i. yi = time trend, set at zero in base year. r** = trend coefficient. This eiuation is the same basic form as proposed in Hickman’s earlier paper, exeept for the addition of the trend term. An explicit derivation
B. Hicknm, L. Lou, Substitution and export demands
349
of the specification is given in sect. 2 below. Just as before, Armington’s CES demand system I1 1 is the point of departure, but Hickman’s earlier results are extended in two ways. First, it is shown rigorously that the linear system is a first order approximation to Armington’s formulation and that the estimated coefficients of the relative price terms may therefore properly be interpreted as substitution elasticities - propositions which were stated but not proved in the earlier paper. Second, the approach is generalized to include trend terms with parameters to account for changing tastes over time, and it is shown that the adding up proper ties of the linear model are still preserved. ’ This last is important, since the basic appeal of the linear model over a CES system is the automatic satisfaction of the adding up criteria in complete model solutions. Thus the present model has the special property that the sum of the predicted exports from all the other countries to the jth country will equal the actual imports of the jth country. Consequently, total predicted world exports also add up automatica!,ly to total world imports. By summing the Xiis over j, the export demand funct-on of the ith country is derived and written as n
where Gi and ‘;i have the interpretations of being weighted averages of the elasticities of substitution and the trend terms respectively, and pTc is a weighted average of the import price indexes having the interpretation of an export competitive price index, and fl is the weighted export price index. The organization of the paper is as follows. The theoretical derivation of eqs. (I) and (2) is given in sect. 2. A dynamic variant of the system, allowing for the formation of price expectations, is presented in sect. 3. The data are described in sect. 4. The estimated substitution elasticities and the corresponding export demand functions and predictions are discu: sed and tested in sect. 5. ’ A method of allowing for other non-price factors ‘effective price’ concept is discussed in I41.
incorporating their influence illan
8. i!ickman, L. Lau. Substitution and =prKi’ demands
350
2. Theoretical development
Assume that there exists a qu or region of the CES type, i.e., 1, meI
index of imports for each country
?I - IlPj .._y.. -Pj c (J 4 11 I i= 1 I1
=
c
i= 1
Oj/(oj-1) Q.&.(ai11 11
l)/aj
9
(31
3
where uj = I/( I + pi) can be identified as the elasticity of substitution between the imports of any two countries or regions in the jth market. 2 In addition we set
since we are allowed an arbitrary scalar transformation of the quantity index. Then according to Armington [ I], the cost minimizing quantities of imports demanded for attaining a specified level of rn,!@ are given by “ij
= a,.yojm.1*
6
- *j
( )
(4)
-yz Pi
where Pi”-- =
[
n Of XWOI) i”x 1 aij Pij
1
l/(1- oj,
is the price index of imports with the property that n pr’m;
=
is
Ptxij
= Mj
(9
’ The basic aswmptions for the existence of such a quantity index are (0 independence,i.e., the marginalrate of substitutionbetween imports from any two countriesis independentof the level of imports of any other country, or, for that matter, the level of domestic consumption; and (ii) homotheticity, i.e., the relative composition of imports is independent of the level of total imports, for a given set of pricer In fact, the CES quantity index is the only quurtity index that satisfies both assumptions(i) and (ii). This approach may be compared to that of Barten 131, who assumes the existence of an import ‘production’ function with siinikt properties.
0. blickwmn. L. Lou. Substitution and export demands
351
i.e.. the product of the CES price and quantity indexes is equal to the actual totaf value of the imports. The individual import demand functions may be written alternatively as a= “ij PI
x -. uj
m*(a/-
’ “~~I~pij pj
xij
I)
X--Ul = UTMjPij Pj
t?l'(Uj-
1)
s
(61
In the base period, all export prices are set equal to unity, and given our normalization rule, all import prices are equal to unity as well. Hence 0
xij
=
a7Mj)
(7)
.
Further, define n mj s c+,
U.0
xi/
as the total quantity of imports to the jth country or region. Note that mj is the simple arithmetic sum of the imports in constant prices from all countries or regions to the jth region, and should not be confused with m;,the CES quantity index of imports. Then by using eqs. (5) and (8), eq. (7) may be rewritten as 0 Xij
=
al
Lc 6 1= *i
aij mj0
i:,
(9)
where rn;is the quantity of the base year imports to the jth country. The base year share of the ith country’s quantity of imports can be identified as 0 = a!1 0 =% m/l ‘j
(%j
’
(11) (12) Now the total quantity of imports to the jth country, mj, is given by
B. Hickman,L. Lau, Substitu?ionand export dewmnds n
mj =
c
il 1 “ij
c uijPijX--Oj11 c ’ ijPijx(1-q) [ 11
=
-tl
0
0
i= 1
1
-1 M
(13)
j*
i=l
In other worrts. n
=
Mj
mi
ll
C i=l
Id
I[c aijPijx-o1 1
atpi] x(1-Uj)
-1
cl
.
i=l
(14)
Substituting eq. (14) into eq. ( 1 I), we obtain
“ij
n
0 X-O/
= Uijpij
c k=l
x- aj &kjPkj
1 -1
rij
(15;
.
Thus far eq. (15) is an exact expression for any given level of the total quantity of imports. However, eq. (15) is non-linear and hence difficult to estimate and aggregate. We therefore linearize eq. ( 15) in the gjs by a Taylor’s series expansion around fij = 1, all i and 1. This is equivalent to choosing a base period in which all the export prices are set equal to unity. First order expansion of eq. (15) resu!ts in , Xij
=
U$9Zj
+
a$mji-- uj) @$ - 1) -
Lkel a&@&-l>1
a))?lj(-Uj)
- (16)
0
Observing that ci=t x** II
=
0
Qijmj
a& s 1, eq. ( 16) simplifies to
-
ujt&j
-
,q
= a&&h$mj -
(17)
If we now define a new import price index,
having the interpretation of a fixed-weighted average of the export prices of all countries in the fth market, eq. (17) may be rewritten as xij =
a&mj
-
Oj@$
-
pi”
h+j
l
(19)
8. Hickman, L. Lou, Substitution and export demands
353
Hickman 141 has shown that individual export demand functions of the type given in eq. (19) have the adding-up property, i.e.,
c i:,xu=mj. To see this, observe that
Now cy=ra$ = 1 and~~=r~$& =py; thus Cy=rXii =mj. This adding up property also automatically assures that predicted total world exports will equal actual total world imports, provided that the appropriate c.i.f.-f.o.b. valuation adjustments are made. If we further linearize Xii ill terms of mj around rnf , we have
which is the same basic linearized form proposed by Hickman (41. A similar derivation applies to the case in which the original CES quantity index of imports for each country or region is a function a&o of time, i.e., n
rn.J*, -
c i=l
[
Oj/bj-11
a..e II
7#~,~j_l)/~j
(22)
1J
I
where the YijS may be considered to be parameters indicating taste changes over time. The individual export demand functions are then given by xij
= CYije ’ 7’tujp~eaj
2 0 Ykjtoj x(1-oj) kPl akjt? Pkj
1 Ml (2% -1
and total quantity of imports by n c mj=+, xij 2 =
i=l
0 aije
r#tUj x-a/ Pfj
I[
2
0
kzl
aWe
i 1 i*
7kjt”jp;(L-uf)
-1
M
(24)
8. Hickmn, L. Lou. Substitution and export &wutnds
Note that if rij = rkj for all i and k, then the individual export demand functions as well as the quantity of total imports remain unchanged, as it should be, for such is a case of a neutral change in tastes. Solving eq. (24) for Mi and substituting the solution into eq. (23) yields
xij
Again,
= aO,w~l ij
x-“i
pij
II2
k=, a&.Pj
to
x-oj
jPkj
1 . --*
(25)
rr$
eq. (25) in a Taylor’s series
order,
(26) we have Xij
=
t
atrnj - oja~mitp$ -ply> + atmioj that eq. (27)
l
(271
up criterion, we observe
cy_,,t = 1. Hence even in the case with trend terms, our system still satisfies the adding up criterion. Finally, we further linearize eq. (27) in mi around m!, obtaining
+ atrnfrift = aQm J / - u&Wj
where
Pirn)
uflij Orij t
(28)
B. Hichan,
L. Law Substitution and export demands
355
It is clear that given the rijs one can determine the rijs and vice versa. it is also clear that the rijS are not ~11independent. In fact,
In other words, the sum of the atrijs must be zero. This is a fact that must be taken into account in the emp2cal implementation. Thus, we have shown that the linear world trade system proposed by Hickman 143 and the generalization to include trend terms can be properly regarded as a first order approximation of a theoretical d%mand model -of the Armington [ 1] type. The estimated coefficients corresponding to the relative price variables in this system can therefore be interpreted as the elasticities of substitution between imports in given markets. We now turn our attention to the aggregate export demand functions. These are given by summing eq. (28) across all the jth markets: ’ n xj
= r I Xij
j=l n
=
c
j*l
0 Oijmj
C j=l
a@j
UjrijXCf 0
n
n
=
UjXP,(p;i-?I;",+,$
-6
‘gjXpt,$
- c j-1 'j.0
i
4 Ip1 0 u*r .."i'txp . Uj.OPj Xi +k j=l I 'lx0 i
(29)
i
Now define (30) the base year share of the jth country’s imports from the ith country in the ith country’s exports,
6, =jg u&
(31)
the weighted average elasticity of substitution in the export markets of ’ This derivation follows Hickman [ 4 J.
B. Hickman, L. Lau. &botinrrion and export demunds
356
the ith country, and
(32)
the export competitive price index of the ith country, with weights summing to unity. In this expression, p,? is a weighted index of the prices charged by all exporting countries in the ith market and the #s are in turn weighted by the relative elasticities of substitution and the shares of the j markets in the total exports of country i to yield an overall index of prices competitive to the exports of the ith country. The same weighting scheme defines the export price index of country i: (33) and also n !.!L
r;. = c
qij
(34)
j=l iji
the weighted :lver+~.‘ of thf, trend terms of the exports of the ith country-to all its markets. Given these definitions, eq. (29) may be rewritten as n
Xi =
c j-1
0
&ijmj
-
(GiXp)@f -tic)
+ (ZiXFQ)t
a
(35)
Thus, given the estimated ois and ri/s, one can construct ZiS,@, ds and #s and obtain aggregate export demand functions of the form in eq. (35). 3. Expectations and adjustment lap In the preceding derivations we implicitly assumed static price expectations and the absence of adjustment lags. In this section we discuss two alternative specifications to allow for such dynamic factors and show that only the second is useful for our purposes.
IA Hickman. L. Lau, Substitution and export demands
357
First, we retain tic assumption of static price expectations but adopt the following familiar partial adjustment hypothesis: Xi~=siXi;++(l_61)(-~i,)_,,
O< hi< 1,
(36)
where xii is the quantity of imports desired by the ith country from the ith supplying country. If eq. (21) is now rewritten to refer to the desired quantity demanded from i by i, we have
Combining (36) and (2la) yields Xij
=
6jabm,-
f!3/ujx@?$-pi”>
+
(1 - i5$ (Xj&
.
(37)
Eq. (37) could be rewritten for estimation purposes as follows:
At first sight this is a perfectly acceptable specification, since Sj and dj are just identified. It cannot be used in our system, however, because it violates i the additiviky criterion. To show this, we sum eq. (37) over i after substituting .ut= a&my :
X
where
t&a$+(1 -6jl,$
use
(xij)-1
=
6jmj
+
(1 -
s/l
(mj)_l9
(38)
has been made of Cyz 1ai = 1, Cy= 1a$pFj = pi” and Cy= 1Xii of course, is that the left-hand side is identically equal to mj,SO the equation cannot hold in a world where mi changes from period to period unless 8j = 1, in which case there is no adjustment lag and the model reduces to the original static version. Thus the lagged adjustment specification (37) is inconsistent with the adding up criterion and is unacceptable for our purposes. This is not an admissible method for introducing dynamic elements into the static models represented by eqs. (2 1) and (28). An alternative is available which does yield an acceptable specifica-
= mj. The difficulty,
358
B. Hickwtan, L. Lau, Substihtcion and export demands
tion under plausible assumptions concerning the formation of price expectations. however. Instead of assuming an adjustment lag with static price expectations, we assume immediate adjustment with an (adaptive) expectations lag. In its most general form, the adaptive expectations hypothesis we use is:
ogij5
Thus each rebtive of the expt;rctation
1.
(39)
yicc expectaWn of this period is a weighted average r&d last period and the actual relative price of this
period, plus an ir~d~pend~nt trend whether or not the expectation is realized. Notice that we are assuming the same adaptive expectations parameter fii for AI relative prices in market j, but are allowing different trend factors for the expected prices of the several supplying countries. Let us now rewrite our most general static model (28) in terms of expected prices:
If we now substitute (39) in (28a) and then use (28a) lagged one period to eliminate the lagged expected price term, the result is
where all variables are observable. The parameters 6j and Uj are identifiable, but the others are not. In particular, it is not possible to estimate both the trend coefficient of tastes (r,i) and the trend coefficient of price expectations (rjj). If either trend coefficient is assumed to be zero for all i and j, however, the other is identifiable. If rjj s 0, for example, so that tastes are assumed constant over time and the trend term drops out of (28a), the second term of (40) will identify flij and the third term will identify y4j. Similariy , assuming rjj = 0 permits identification Of&j and rjj. In the sequel, we present actual estimates of an equation of the form (40), and we arbitrarily interpret the results as if the trend coefficient represents price expectations rather than tastes, though we admittedly cannot distinguish that hypothesis from its converse. We also
B. Hickman, L. Lau. Substitution and export demands
359
give estimates for a model in which we assume ‘ii z rii 5 0, permitting identification of flii, u1 and $. For estimation, eq. (40) is rewritten with the term CY@Z~ transferred to the left-hand side in order to impose its coefficient of unity. it is then easy to see that the last variable on the right-hand side is simply the lagged dependent variable. The estimated coefficient of the relative price variable, Of( 1 - S,), is the short-run value of the elasticity of substitution. In long-run equilibrium. however, xii = (Xii)._1 and mi = (mi)_, , so that the long-run coefficient of the relative price term is oi( 1- $)/ (1 - S$ = ai. Since 0 < SI < 1 in the estimates, the elasticity of substitution is greater in the long-run, since the short-run response to a relative price change is moderated by the expectations lag. Unlike the lagged adjustment model, the adaptive expectations model is consistent with the adding up criterion, providing t trend coefficients are appropriately constrained in the estimation procedure. To sholw this for our assumption of constant tastes, we set rj/ 5 0 in eq. (40) and sum over i:
(41) where use has been made of the same definitional relations as in the simplification of eq. (20). Since c :=I xii I nlj, the additivity criterion will hold if (Cy*r a&) = ( Cy* 1Qt+Yi/)= 0, or in other words, if the constant terms and the trend coefficients of the pooled Xii regressions for market i are constrained to sum to zero. It remains to derive the export demand function for country i by aggregating (40) over 1, again after setting rij z 0. The result is y. = 1
n Ei + fq t
n U$j
-
SiXfQ7fb
- tic’)
+ ~iXi _ 1 - ,_l C
6 J4rOm rj j-1
-zs -
0
uirixi tp
(42)
8. Hickman, L. Lou, Substitution and ew-t
demands
where (43)
(44) the weighted average short-run elasticity of substitution markets of’ the ith country
ai =~~ oih~~ .
(45)
the weighted average long-run elasticity of substitution markets of the ith country
.= _i j=l SC
in the export
in the export
N
hjX,i
_ 1
(46)
9
the weighted average adaptive exceptation parameter in the export markets of ith country using the previous period’s export shares as weights = I.
n
1
=
j=l c(
i $Q ai j
,
(47)
the weighted average of the trend terms of the exports of the ith country in all its markets ,
(48)
the short-run weighted export price index of country i
the short-run weighted export competitive price index of country i. Note that 8, will in general vary from period to period. The expression
B. Hickmun, 1.. Lau. Substitution and exprt demands
361
(50) has the interpretation of an effective lagged external demand index. Eq. (42) is the dynamic counterpart to eq. (35) above. From eq. (35) one may compute the export price elasticities of demand of the static model in the year f as
-pZ dXit
Ti
Z----_ Xit
J$
=$. a i xoi xit
l
(52)
Similarly, one may compute from eq. (42) the short-run (~2) and long-run (r#-) export price elasticities of demand of the dynamic model in the year t as (53)
4. Data The data were supplied by Grant B. Taplin of the International Monetary Fund and are the same as are used in the IME’ Expanded World Trade Model. Basically, they consist of a series of nine annual export trade matrices developed at the lnternational Monetary Fund by Taplin for the years 1961 through 1969. The original export flows are valued at f.o.b. prices and in current US dollars, but Taplin has also provided export price deflators for each exporting country or region to convert the flows to constant dollars. Altogether, 27 countries or regions are distinguished. ’ ‘The CMEA group include:s member countries of the Council of Mutual Economic Assistance bllbania, Bulgaria, Czclchoslovakia, Eastern Germany, Hungary, Mongolia, Poland, Rumania and the Union of Soviet Socialist Republics), mainland China, and other countries poBticaBy and economicady associated with these twc areas, including North Korea and North Vietnam.
362
B. Hickmm. L. Lau. Substitutim and export donwnda
The base year for aif countries or regions is chosen to be 1963. In other words, all price indexes are set equal to one in 1963. in addition, the a& are taken from the 1963 constant dollar import share matrix. Exports and imports are measured f.o.b. The export price indexes were converted to a c.i.f. basis for comparability with the import price indexes. as explained in [ 5 1.
5. Empirical results The actual equations used in the estimation of the elasticities of substitution of the different countries are of the forms
- OjX$*rijt + &j(Xij - a$m$_ I e
(56)
Estimates are also presented for both forms with time trends suppressed. Note that Oj appears in every Xii equation. Hence it is necessary to pool a!1 the Xii observations for each i and estimate the equations jointly. Where constant terms or trends are included, their coefficients are constrained to sum to zero in order to preserve the additivity property. as explained above. With regard to the stochastic specification, three alternative assumntions are attempted. Assume that the stochastic disturbance term is additive, such that in the case of eq. (55), we have xijt -
= - UjXg@fj*
c&t
- @I
+ O,Xsrijt
+ ‘ijt
where the t subscript refers to the time period of the observation. Then the tnree alternative assumptions are: (9
Eteijt)
=
0
)
all i, j, t
All other covariances are zero. (To avoid confusion with the elasticity of substitution, we have denoted the population variance by S* rather than the customary oz.)
B. Hickman, L. Lau, Substttution and export demands
(ii)
E&j,) = 0 )
all i, j, t
V(t+ = $xQ’,
all i, t .
363
All other covariances are zero. (iii)
E(Q) Q..
w
=09 ) = s?x!? I 11’
all i, j, 1 all i, : .
All other covariances are zero. In addition, for all three specifications,
assume that
n
c ei/t=o,
+,
all j, t .
Corresponding to each of these three stochastic specifications, a complete set of estimates of the elasticities of substitution is obtained for each of our four functional specifications. One final set of estimates is chosen for each of the four cases. The criteria for selection are: (i) the estimated elasticity of substitution must have the correct sign, (ii) it must have the highest t-ratio, and (iii) for the dynamic models the estimated values of the adaptive expectation parameter must be less than unity. The resulting estimates are presented in table 1. We show the coefficient estimates and their t-ratios for both variants of the static model (SS), with and without trend terms. In the case of the adaptive expectations model, we show t-ratios for the short-run elasticities u/ (1 - $), but not for the long-run elasticities Gj, which are obtained as the quotient of the estimated coefficients on the relative price and lagged dependent variables (see eq. 56). In general, the estimated substitution elasticities are significant for all models. The conventional goodness-of-fit statistics are not given in table 1, for two reasons. First, within each of the four functional specifications, the R-squares and standard errors of estimate are not comparable across different stochastic specifications, since the variables are scaled differently in each of the latter. Second, as between functional specifications, even when the stochastic specification is the same, the R-squares are not comparable for the forms including and excluding a constant term, and indeed, the concept of a coefficient of determination is not even well defined when the regression is forced through the origin. In the case of the first static model, in which the only explanatory
364
B. Hickman. I.. Lou. Substitution and export demand;
h
$2 maD
dir; Y
h
38
zs .d h
2:3
“r .
z
25 33 “i Y
(z6zC'S) (Z6zC‘5) ,699L.t ,,699L'Z
(8868'8) (zsrcr*s) PZdZZ'C P658T.Z
(S8W'S) PLTTT'E
(CLE6'2) (9090'9) ,ct9z-z PsLzz'z
(6;dSC'8) (9869-L) pZT9Z'E p6Tz6'z
(EtSO'T) (~OZC'E) PS6LO'T PT6TO'Z
(OL06'E) PS)9S'T
ZT8Z'S
t0ZTi.Z) (C9TL'C) P88Ez'z
Ubt9't) P9SC9.T
O8VS'f 9800-t p6SSZ lZ
tosocrel) P?xlC'f
80V!?'Z S6LZ'C
OSCZ'ci 099O'lr
(86~s.~ &lSZ'C
tSZZ8'Oi &6Zz'T
TTLZ'O l
(O?f6E'T) t89SC.O) ,OiTS'O $69T'O
(COST-91 (SZ86W aL88L'c a6ZOC'E
t8LSS.9) PSWC
f6?7tr'O
(TTVT i 1
69L6'9
tOUS-T) &9TZ'Z
ZTBZ'S
9ZOE'O
(SZSL lcl
899L'Z 9LZ8'0
("'1 ,O'O
(9S6Z.L) (956Z'f) T96tr'O T9Lf'0
t69LO.S) (0~98.U OLZS'O 9cOL'O 9fZ8.0
(TOZL'S) PS6T8.0
tmco*9)
(S6ZC'9) (S6ZE.9) LO81r'O LO8t'0
SL90'T 8VZL.B
trs!?s*E) 6Z8Z.O
(~806.T) h886=6~) TST6'0 LMT'O ZC89.t
(Z689.Z) #ZTL'O
(6z8~-z) (Z09t.T) PSSEZ'T JSLTi'z _A
P-l& anwarn
(CD,TaPaW va*as 'UOTlnafa~pS 30 -TaT3P~T3
WnI
PrulJ
(ZT69'T) &tS&'T) &dZS'V 3TSTO'Z
(TLt9'Z) p6688'T
(626L'O) tS9LZ*VT) LqO6'0 ET8O'O
0909-T E68C'O
p-2 a*orllffi
966T‘5
ZLW'L
(9tre9*r)ttTSt*tT) Z9SS'O 2558'0
Z8CL.S F=i wm
(T606'T) tT69O'TT) 9ZT9'0 LOTZ'O
_ mqa8aaadx3
cF* ) 8;loaaw3wd (panu!luw) I a1qe.L
=Ws
*nalOd
‘OZ
‘61
366
B. Hickman. L. Law Substitution and export demands
B. Hickman, L. Lou, Substitution and export demnds
367
vziable for changes in market shares is relative prices, the estimated elasticities of substitution range from near zero to about 15 and average to 3.03. interestingly enough, a value of 3 was assumed for all markets by Armington in an empirical application of his original model, on the grounds thal: the figure was roughly of the order of magnitude to be expected from past research and a priori reasoning (2). When a trend term is added to the static model, the effect is to reduce the average estimated elasticity to 1.84 and to reduce the range of estimates to values between 0 ant8 6. The model without time trend is probably mrsspecified because of omitted variables, and since the addition of the trend term makes some allowance for omitted variables which are correlated with time, such as changes in tastes or preferences, it should tend to reduce misspecification bias in the estimates of the uIs. The trend-adjusted set of estimated static substitution elasticities is therefore to be preferred to the unadjusted set, but it still is subject to the deficiency that it makes no allowance for expectational Lagsand hence, may be providing estimates basically of the short-run rather than the long-run elasticities. This last inference is consistent with the results on the estimation of the adaptive expectations model. Whether estimated with or without a trend, the expectations model results in short-run elasticities which are mucir closer to 1.8 than to 3 in value. The values for the trendless expectations model range from 0 to 3 and average 1.18, whereas those with allowance for trend range from 0 to 4.5 and average 1SO. The presence or absence of a trend term in the expectations model makes a greater difference for the estimates of the long-run substitution elasticities than for the short-run values. This is because the adaptive expectations parameter is estimated as the coefficient on the lagged dependent variable, which itself is correlated with time. When time ia, excluded, the average value of the expectations parameter $ is 0.73, whereas inclusion of a trend term yields an average estimate of 0.34. Since (I- 6i, measures the rate at which price expectations are adapted to experienced price changes, the trendless model implies a slower ap preach to long-run equilibrium and hence a larger ratio of long-run to short-run substitution elasticities. Thus, although the trendless model has smaller average estimated short-run elasticities (1.18 as compared with 1SO) it has considerably larger long-run elasticities (5.2 instead of 2.5). In our judgment, the expectations model with allowance for trend gives the best results in terms of estimation of substitution elasticities in
368
B. Iiickman. 1.. Lau. 22ubstitution nnd export demmds
import markets. lmmcdiatc revision of price expectations seems implausible to us ;LSan assumption in behavior, SO we prefer the ciy?llamic model on intuitive grounds. The trcndless version yields estimates of long-run elastizitics of substitution that appear implausibly high, whereas allowance for an expectation4 trend results in an average of 2.5 and ;t range from 0 to 9, and these figures seem rcz:sonable to ‘US.Further criteria for sclcction among the alternative models will be considered below. and wiil be fdund to confirm this initial judgment based largely on our prior beliefs. For the moment, we merely observe that our best ly an average short-run substitution elasticity of about 1.5 oncerned the substitution elasticities f course. It is equally relevant to ask what substitution elasticity faces each exporting country on the average in all its markets. TabIt 2 lists the estimated average long-run (Gi) and short-run (Gi) elasticities of substitution in the export markets of country i, weighted by the base-period importance of each market in its exports (Xv.) x 11* s Thus a low oi indicates that the country in question sells its exports predominantly in markets with low U/S, and hence its export sales are rather insensitive to changes in its export prices relative to its competitors. To judge from the long-run OiS computed from the preferred adaptive expectations model with trend, the exports of the socialist countries ithe CMEA group and Yugoslavia) are not very sensitive to increases or decreases in their prices relative to those of non-socialist countries as a group. Many of the non-socialist industrialized countries show a higher estimated degree of price sensitivity, but even they seldom exceed a value of 2 for ?ii. Let us now turn our attention to the predictive ability of the alternative models when it comes to forecasting exports. Specifically, we are interested in how well the export vector xi, i = I, .. . . n, can be predicted conditional on the known vector of import quantities mj and matrix of export prices p$ ’ Given the estimated structural parameters implicit in eqs. (55) and (56) and their trendless counterparts, it is simple arithmetic to form aggregative export demand functions for each country as given in eqs. (35) and (42) and their trendless counterparts. These export demand functions contain as arguments the given import quan’ See formulas (44). (45) and (30) for the exact definitions. 6 Az noted in the introduction, the present import allocation model is intended for eventual incorporation in a complete world system with endogenous imports and prices.
Norway
Sweden
Switzerland
United
Finland
Greece
Iceland
ire land
Il.
12.
13.
14.
15.
16.
17.
18.
Kingdom
Dark
10.
Austria
9.
Gerrangi
6.
Italy
S. France
Netherlands
2.4857
Eelgim
8.
2.7924
Japan
3.
4.
7.
2.2543
Canada
0.4617
1.8335
2.8337
2.3092
2.5710
2.4070
2.1600
1.6291
1.7757
3.0401
2.4507
2.8244
2.4121
1.1952
United
2.
2.9856
zthout
1.
State8
Country
of SubacituModel (3,)
l
l
.1483
0.88S2
1.1027
1.2619
i
1.4483
1.2443
1.3383
1.1255
1.1677
1.4273
1 3451
1.5087
1.4324
1.5218
1.2219
1.2700
0.8918
1 3343
Trend With Trend
Elsleticitiee tion Static
0.4824
0.6654
0.7060
0.6335
0.9626
0.742s
0.8285
0.5817
0.6499
0.6658
0.7386
0.7411
0.7785
0.8531
0.5678
0.9099
0.8042
0.9153
Without Trend
0.9654
0.9682
0.9825
0.9145
1.2023
1.0590
1.4744
1.0026
1.2658
1.1642
1.2034
1.2919
1.2938
1.2527
1.1994
0.9494
0.9452
1.1023
With Trend
Short-run (8,)
Elastkities
4.8686
3.7941
4.3828
3.7927
5.7002
4.5851
4.4209
3.8425
4.2072
4.2830
4.8749
4.9183
4.4964
5.5756
3.4423
6.4395
5.3238
7.2547
Trend
Without
d
1.1962
1.3796
1.4500
1.3629
2.1121
1.7048
2.0768
1.5345
1.7919
1.6818
1.7843
1.9574
1.9532
1.7450
1.8345
1.4471
1.3844
1.6975
Trend
With
Long-run @,)
of Substitution, Dynsxaic Model
trend
0.8961
0.7955
0.8150
0.8040
0.7940
0.8178
0.7798
0.8234
0.8312
0.8227
0.8403
0.8287
0.7944
0.83l3
0.7929
0.8470
0.8420
0.8442
Without
O.i742
0.2i84
3.2930
0.2797
0.3360
0.3264
0.2790
0.3113
0.2859
0.2814
0.3050
0.3248
0.3246
0.2699
0.3382
0.2926
0.2818
0.3080
With trend
Expectations Parameters (;3,Ia
Table 2 FZs,gtimates of weighted averageelasticitiesof substitution and weighted averagea&ptive expectations parametersin export mtirkets.
370
R. Hickmn,
L. Law Substitution and
3 f
c;
;
exportdemands
B. Hi&man,
1.. Lou,
Substitution
and export
371
demands
Table 3 Comparisons of goodness-of-fit of the export demand functions (standard errors of estimate ad-
justed by degreesoffreedom). Static Model Without With Trend Trend
Dynamic Model Without With Trend Trend
1.
United states
0.7669
0.6449
0.8190
0.6064
2.
Cfmaaa
0.6332
0.2390
0.3495
0.2421
3.
Japan
3.0396
0.7312
0.8236
0.5797
4. c,.
Belgium
0.3951
0.1661
0.1936
0.2058
France
0.4561
0.1749
0.2916
6.
Germany
1.oG99
0.6714
0.3357 0.4446
7.
Italy
1.2589
a,
Netherlands
0.3482
0.3133 0.1881
0.5363 0.3261
9. Austria 10. Denmark
O.l&i5
0.0945
0.0454
0.0710
0.1669
0.1182
0.0717
0.1072
11. Norway
0.1891
0.0468
0.0551
0.0285
12.
0.1164
0.0506
0.0430
0.0646
13. Switzerland
0.2994
0.0447
0.1130
0.0430
14. United Kingdom
1.9275 0.0810
0.4709
0.4215
0.3503
0.0487
0.0422
0.0455
0.0609
0.0387
0.0513
0.0443
0.0253
0.0184
0.0229
0.0233
0.0358
0.0248 o. 0261
Sweden
15. Finland Greece 16.
0.1853 ~1.1864 0.1'184
17.
Iceland
la.
Ireland
0.0395 0.0287
19.
Portugal
O.lOil
0.02h5
0.0304
20.
Spairi
0.3340 # 0.1290
0.1748
0.0913
a.
Turkey
0.0711
G.0400
0.0505
0.0348
22.
Yugoslavia
0.2785
0.0898
0.0576
0.0722
0.9777 0.2028
0.2645
0.2475
0.0822
0.0689
0.1973 0.0831
25. South Africa
0.0772
0.0999
0.1201
0.1098
26.
CMEA Countries
0.4101
27.
Rest of World
0.4344 4.5782
0.4004 1.0857
0.2956 0.4218
23. Australia 24.
New Zealand
0.9752
372
B tlickwzan, L. Lau. Substitution and export demands
tities and certain price indexes that are weighted averages of the given export prices. and hence they can be used to predict exp:7rts for each country. The export demand functions were obtained by aggregation of the underlying market share equations rather than by direct estimation, of course, but it is an easy matter to compute goodness-of-fit and error statistics for the synthetic equations which are directly analogous to the measures usually computed for multiple regressions. Comparisons of goodness-of-fit statistics in the form of standard errors of estimate are shown for the export demand functions of the four m:ldels in table 3. Even after correction for loss of degrees of freedom, the smallest prediction errors are obtained from the preferred ations with allowance for trend - in 14 of the of the 1 I countries or regions which had more than 1O billions of exports ( i 963 US dollars) in 1970. Where the preferred model is beaten on this criterion, the best fits are divided about equally between the static model with time trend and the trendless expectations model. Clearly the preferred model is dominant when it comes to explaining changes m annual exports of the individual countries or regions over the sample period, so it should also provide the best cross-country predictions of exports on the average. This last expectation is confirmed by the cross-section error measures presented in table 4. Four error measures are presented for each model and are defined as follows. Let Cit = (Xit - X,) be the error in prediction of exports of country i in year t, ei,* = (cit/Xit) be the corresponding proportional error, and wp = (x$x0) be the base period share of the exports of country i in world exports. Then, for year t is the root-mean-square
error,
(ii)
(RWSF), = ($ w+?f
is the root-weighted-square ror
(iii)
(RMsPE), = [ l$ (e:,)2/n]H
is the root-mean-square-proportional error, and
(iv;
(RWSPE),= [fi is the root-weighted-square-pro= w;(e;)'lK portional error.
er-
1963
0.2493
0.0795
0.3816
0.1693
III
IV
0.0000
0.4195
0.5543
0.7634
0.2952
II
III
IV
0.0721
0.0675
0.0326
II
III
IV
0.0352
0.0444
0.0444
0.0616
0.0560
0.0543
3.0667
0.1206
0.3163
0.4706
0.3292
0.0283
0.0471
0.0479
0.0497
0.0136
0.0400
o.oooo‘
0.0000
0.0240
0.0278
0.0283
0.0378
0.0222
0.0317
0.0221
0.0662
(ma
0.0207
0.0191
0.0224
0.0839
error
0.0614
0.0444
0.0661
0.1315
error
0.2474
0.2791
0.3261
1.8073
0.0232
0.0250
0.0204
3 51070
(IWSPE)’
0.0456
0.0684
0.0457
0.1572
0.2466
0.2977
0.2463
2.5189
0.2002
0.207;
0.1780
1.2305
1967 1.0698
0.2787
1.0592 0.5177
0.6961 0.3102
0.0190
0.0308
0.0210
0.1381
0.0541
0.0784
0.0782
0.2254
0.2636
0.0589
0.0173
0.0287
0.0242
0.1448
0.1673
0.0309
0.0381
0.0425
0.0215
0.0323
0.0390
0.0888
0.0469
0.0564 0.0255
0.0639
0.0747 0.0362
0.0689
0.1966
0.1952 0.0481
0.1396
0.4952 0.5272
0.9450
0.5044
0.2314 0.6330
5.6737
3.9327
2.0193
0.1759
0.2928
0.2784
3.1662
0.5706 0.3496
0.4049 0.2083
0.3414 0.1744
2.9257
0.5597
2.1329 0.3060
1.6953 0.1571
Pooled Sal&@@ b
’ Weights are 1963 shares of exports of each country in total world exports.
a The models are as follows: 1 Static mAeI without trend. II Static model with trend. ill Dynamic model without ttcndIV Dynamic model witk trend. b Based on pooled errors over sample rather than averages of annual enor measures. For Modeb 1 and II, sample pcuod is 1961-69, and for Models 111and IV, it is 1962-69.
IV
III
II
0.0316
0.0649
0.0000
0.0000
0.1616
0.1514
0.1950
0.8966
1966
@51SE)C
0.9128
error
0.1766
0.2748
0.1807
0.5372
(BlQ)
1965
D. Root-weldted-squarepropo+t~Onal
0.0919
I
I
0.3621
0.4377
0.4721
0.3936
C. Boot-mkm-sauere-pr:sportiona.l
0.1234
o.oooo
0.5219
I
0.2034
0.2377
0.2598
0.2769
error
1964
&et-weighted-square
0.0000
0.3029
If
B.
o.oooo
0.2887
I
A. Boot-rscan-rauare
1962
Table 4 Comparison of cross-section prediction errors, four models.
374
B. Hickmen, L. Lau, Substitution and
exportdemmds
Corresponding pooled error measures can be computed by summing over f as well as II. A number of points emerge from a study of ,these error measures. (1) The largest errors by far result from the simplest specification, the static model without trend (Model I in table 4) whereas the smallest errors come from our preferl.ed adaptive expectations model with trend (Model IV). (2) Weighting the absolute errors increases the avera els, whereas the reverse is true of the proportional errors. atic tendency to make larger absolute errors for are larger exporters, but the errors for the larger ~~tio~ately smaller on the average. (3) The errors for nit with time from the 1963 base period, Of other models. Indeed, the unweighted e preferred Mode1 IV is smaller for 1969 than in any earlier year in the sample period, whereas the weighted proportional error is smaller in 1969 than in any other year except 1963. There is a similar, though less striking, absence of significant error buildup within the sample period for the absolute error measures from Model IV. (4) Despite the last observation, it is unfortunately true, though not surprising, that the 1970 post-sample prediction errors for Model IV (as well as the other models) are larger than for any year during the sample period itself. Thus Mode1 IV appears to be the best of our four specifications not only a priori but for prediction as well. It should be possible to reduce prediction errors still further in future work, however. It is likely that post-sample errors can be reduced by shifting the base period to the end of the sample period, since this will tend to minimize the change away from the base period shares to be explained by the price and trend terms. Another possible device for reducing prediction error is to combine the best fitting import allocation functions for each country from among the four models. We have organized this paper so as to ‘run a race’ between the four specifications in order to pick the ‘best model’. This is surely a rational procedure for the general structural analysis of export demand functions and for the purpose of estimating elasticities of substitution in import markets. When it comes to prediction, however, at least some marginal improvement should be achievable by choosing the best fitting specifications for each import .market to form a fifth complete system, but this remains to be tried. Other useful facts of some practical interest at? the values of the
R. Hickman,L. Lou. Substrtution and export demands
375
Tatle S Export price elasticities ofdemand. Dynamic model
Short-Run(+
Static model Long-Run(nf;)
(n,)
1. UnitedStattee
0.8937
1.3781
Le.653
2. Canada 3. Japan
0.5936 0.3485
0.8447
4.
Belgiun
0.6585
0.5590 0.4636 0.6695
5.
France cermeny
0.7947 0.6909
1.0945
6.
1.0360
0.9615 0.7609
7.
Italy
0.4936 1.0198
0.6103
0.9284
0.7092
a. Netherlands
0.6482
0.9490
0.7217
9. Allsb~'if%
0.6186
10. Denmark
0.8911
0.9315 1.2765
11. Norway 12. Sweden
0.5559 1.0438
0.8081
0.7585 0.8173 o.6ug
1.9887
019404
13.
Salt zerland
0.7648
1.0110
14.
United Kingdom
0.8735
1.2744 0.8136
0.8953 1.0469
15. Finland 16. Greece
0.5783 0.4669
17.
0.619s
0.7266 0.6004
0.8094
1.1616
0.9221
O.B567
0.6363
19. Portugal
0.6956 0.7382
1.0253
20. spala
0.4230
0.6107
0.8777 0.4540
21. mey 22. Yugoslavia
0.7410
1.0345
0.5760
0.7894
23- Australia 24. New Zealand
0.5303 0.5626
0.7411
0.8529 0.9183 0.6692
0.7466
0.5656
25. South Airics
0.6583
26. CMEA Countries
0.3156 0.6716
0.8777 0.4336
0.8836
Iceland
la. Ire?.and
27.
Rest 0r World Aver .we
0.6292
0.9638 0.9542
0.6998 0.7808 0.7622
8. Iiickman,
376
I_. 1,~
Substitution
and
expor#
demands
'fable b Coefftcients of aggregate exportdemand funtions, adaptiveexpectations with trenda coeffi&ntof:
country
Ei -
1. Lnited States
0.2261
l.OQOO
-25.2660
2.3515
2.
0.0657
1.0000
-6.1174
0.2973
3.
0.2747
1.0000
-5.1422
0.29ko
4.
0.0131
1.0000
-5.8206
0.3543
5.
1.0000
-10.1211
0.2739
6.
0.334
Canada
Germmy
1.0000
-18.9090
0.0950
1.0000
-6.5560
0.3426
-r).ooo2
I. 0000
-5.9708
0.370
0.0225
1.0000
-1.5437
0.33559
-0.0076
1.0000
-2.3595
-0.0470
nds
11.
Norway
0.0311
1.0000
-1.0763
0.3019 0.3121
12.
'Sweden
0.0211
1.0000
-4.7172
0.2769
33. Switzerland
-0.0278
1.0000
-2.5434
0.2435
14. UnitedKingdom -0.2593 15. Finland 0.0009
1.0000
-13.7355
0.3.146
1.0000
-1.0511
0.2892
16. Creefie
1.0000
-0.2850
0.21r67
0.0076
l.ooc)O
-0.0912
0.3032
-0.0092
1.0000
-0.5171
0.1880 0.2800
17. Icelmd 18. Irehnd
-0.0157
lr. Portugal 20. Spain
0.0175 O.nl96
1.0000
-0.4360
l.OoQO
-0.8302
0.347&
21. Turkey
0.0108
1.0000
-0.4190
0.2837
22. Yugoelavla
0.0389
1.0000
-9.6014
0.2703
-0.1229
1.0000
-2.3583
0.2&k
-0.079
-0.0111
1.000
-0.8588
0.2L65
-0.029;
-0.0118
1.0000
-1.2535
0.2500
26. CWA Countrice -0.0520 27. Rest of World -0.2599
l.ooOo
-8.1828 -30.0706
0.2722
0.0051 -0.088;
Q.3032
-0.5521
23. Australia 24.
New Zealand
25. South Africa
a Seeeq.(42). b TM
vahcs
are for 1969.
l.Oooo
-0.008i O.OlQC
us
CA
JA
BE
FR
GE
17
NE
A7
OE
I
2
3
4
5
6
7
8
9
80
6.7544 6.9591 -0.2iJ47
5.4162 5. s9ue -U. 1746
l-b?55 1. I+024 -0.1269
1.1819 1.1273 0.0546
+.Ybiti
4.6782 4.5652 0.1130
1.6641 1*&?93 0.0348
1.3259 1.3381 -O.OlZL
U. 0010
4.9608
5.0747 5.1642 - 0.0895
14.6155 A40 5235 0.0921
8.0413 0.0384
8.07Yb
0.0313
2.014V I *WC3
1.4d95 1 .CIlC -b#.o313
5.6YC2 5.6363 o,ost9
5.9466 -0.13>3
5.8113
i6.&9d8 lb. 5245 -0.3257
8 -6546 8. I4LU -O.OOVl
5.5622 5.5816 -D*OlYC
7.585r) 7.2111 0.3073
6.4719 6.4552 0*3167
1964
25.&!77 25. ZASl O.6126
4a 8528 4.8214
Table 7
2. IS50 d.kO70 o.o?*d
U,!.Ji)iJ3
1.5338 1.5105
6.1474 b.L405 -0,393l
7.1j:u 0. =,-74 0.103b
-0.3lll
il.l;760 Lt. b930
9.5879 9.5348 -iL 0069
6.2565 6.1911 LO654
trr65Yb 0.4661 0. I%9
7.8943 8.2165 -0.3224
25-9149 LB.2 807 -0.J650
-
1965
2.2239 1.1344 0. r)895
i-6157 1.6492 -u*3334
-0. JO56
6.4926 b.?OBZ
-3.0268
1.1645
8.1317
19IIZLO 19.6388 -3.16b8
LO.2612 -0.L279
hl.0333
-0.1947
6.69&a
b-5038
10-3085 l&l*lW;, -3.1524
0.9265 tl.947k -O,iJ206
21.8133 27.3290 0.4840
1966
1
0.1152
2.3550 2.2406
1.7426 1.7154 0.0272
7.0153
7.1409 -0.0656
8.7118 8.7986 -0.0268
21.2677 21.2616 0.0062
10.6431 10.8679 -0.2248
7.052 -0.2902
6.7619
JO, 3690 11,1871 -& 6181
9.5609 9.4L57 0.1452
2LIc4189 28.0963 0.3226
1967
2. LmO7 l.PIIIU r)r 0161
0.1781 1.2472 -3. QbYl
9.9543 Ym8727 0.0616
24. d672 24.2 tm 0.5884
A1.8544 LL. WIA ‘U. 45&I
(1.ObZ3 -0.1561
7.9202
11.1117 AL-O476 0.0641
actual and predicted values - adaptive expectations model with
22b9217 23.1547 -062331
1963
4.755A 4.5162 0.23&B
1% 5636 12.9923 0.2714
7.4486 7.4426 010060
4s j&&3 4.3290 0.0593
4.8582 4.4566 0.4017
5*9157 5.9900 -0.0751
21.2952 LL.5845 -0.2894
1962
Exports1969 35,i(ill
9,319)
L.7VuL
2.7164 J*313c(
2,43/9 2.314L lLl117
0.4906 9.5r)OV -O.&J>
I?.l:?r: 11.2Lt13 -0.1105
LtebL9Y 0.33tl4
LP.POB~
13.6214 13.9a73 -3.3659
9.2uZl 3.1174
i! 09905 5.0736 “Q.3831
2. b450 2.~951 r). 0493
lo.&954 10.7876 3.1i)ta
:P-v8e?
id.5161 -0.5672
AC WAL PREDfCTEO HESIDUAL
AC 7UdL PREDICTFD RESIPUAL
HESIDUIN
At TUAL PREOIC TfD
PREOIClEO RE SlOuAL
ACTgcI!.
WEDIC TED RESIDUAL
AC 7UAL ?9. v900 LO.6304 0.3596
2 J
g
ii
%
2
4 i3 ;: 2
2. z 2. o 3
g $
PRCDICTFD RESIDUAL ACYUAL PREOICTFD RESIDUAL
s f: AC TuAL
.
3
-E
AC TUAL PREDICTED RESIDUAL
AC 7UAL f’RE9KfED RESIDUAL
15.6382 15.9765 -3.1383
lUr26ll AU.3439 -3,0827
1.1167
16.442ll
3.617L
17.3615
16)s
A3.1175 lZ.II5lU 0.2665
34.9313 0.2698
l9?U
L+.%b80
15a
-O.c)brO
l1.(1?7rr 11.94*1
-0.bO7f
32.5035 s3.1112
time
8. Hickman, L. Lou. Substitution and export demands
378
. . .
-ro
i 4 0’
B. Hickman, L. Lau, Substitution and export demands
-54 PcQ@ .--In
000
. . . 440 1
I
n)lw
I
379
3x0
B. Hickman. L. Law Suhstirution aud export demands
export price elasticities of demands. These elasticities have been computed for the year 19h9. using the formulact in eqs. (52) through (54), far both the static and dynamic with trend models, and are presented in table 5. For the static model. the cstimatcs range from a low of 0.45 (Spain) to a high of 1.W (US). with an avcragc of f_L7C1. For the dynamic modei. the short-run elasticities range from a low of 0.32 (Council of Mutual Economic kssistancc) to a high of I .04 (Sweden) with an aver-
age of 0.66: whereas the long-run elasticities ra,lge from a low of 0.43 (Council of ~~ut~lat Economic Assistance) to a high of 1.99 (Sweden) e of 0.95. The ;.anking b:J the magnitudes of the elasticiross the short and long runs. It is worthy to las consistently a n;latively low value for her export ereas the United States has consistently a relatively We conclude an already lengthy paper by presenting additional information on the preferred model for stt.idy by the interested reader without comment on our part. Table 6 contains a listing of the coefficients of the export demand functions for Model IV as specified in eq. (42), whereas table 7 shows the sample (1962 -69) and post-sample (1970) predictions and residuals from these equations.
keferences [ 11 P.S. Armington, + theory of demand for poducrs distinguished by place of production, International Man-ta.-y Fund Stiff Papers, Vol. XVI, No. 1 (March 1969) 159-176. [ 21 P.S. Armington, The geographic pattern of trade and the effects of price changes, lnternational Monetary Fund Staff Papers, Vol. XVI, No. 2 (July 1969) 177-199. I31 A.P. Barten, An import allocation model for the common market, Cahiers Economiques de Bruxelles, No. 50 (2e trimestre 19? I) 3- 14. [41 B.G. Hickmanv A general linear model of world trade, in: R. J. Ball and C. Moriguchi teds.), International linkage of national economic models (North-Holland, Amsterdam, 1972). IS) B.C. Hickman, Prices and quantities in a world trade system, Paper No. I, Project LINK Working Paper Se*ies, Economic Research Unit, University of Perz*ylvania, Philadelphia (August 197 1).
Company
ELASTICITIES OF SUBSTIT9TION AND EXPORT DEMANDS IN A WORLD TRADE MODEL *
Bert G. HICKMAN and Lawrence J. LAU Stanford Univasit j*, Stan ford, California, US. A.
First versionreceivedOctober 1972, revisedversionreceivedJanuary 1973
Alternativecomplete models of world trade, based on the trade sharesmatrix approach,are specified and estimated for twenty-sevencountriesand regions.This model attempts to explain the composition of imports on the bases of reiativepricesand time trend, given the total quarttity of imports of each country. Elasticities of substitutionamongstimportsof different countries of origin in each import nuuket are obtained and used in the derivationof aggregateexpoxt demand functions for the individual countries. There is also a comparison of the predictive performanceof the alternativemodels.
1. introdu&ion
P
In this paper we present new estimates of elasticities of substitution between competing imports into 25 industrial countries and two regions (comprising respectively the socialist countries and the rest of the world). We use a constrained estimation procedure which takes explicit account of the adding up properties of world merchandise trade flows on both the import and export sides and guarantees that estimated world exports equals world imports. We then derive for each of the 27 regions an explicit export demand function incorporating the estimated substitution elasticities as coefficients of relative price terms and as weighting factors for export competitive price indexes. This same pro-
* A paper preparedfor the Europeanmeeting of the Econometric Society, Budapest, Sep tember 5, 1972. The authors gratefully adrnowkdge the assistance of Jens Christiansenand Chiranjib3en in the computational sections of the paper.They are grateful to Edward Learner for helphrlcommenta. The researchwas supportedby the National Scknce Foundation under its grant to ProjectLINK.
348
B. Hickman. L. Lou, Substitution and export demands
cedure is followed for four alternafive demand specifications and the structural pioperties and predictive rpbilities of the four models are compared. The results presented herein are an empirical implementation of the theoreiical export demand system developed in a recent paper by Hickman j4]. In that paper, the export demand functions arc incorporated into a system of riational models which determines import quantities and export and import prices as well as export quantities. In the present paper. however, import quantit,ies and export and import prices arc taken ;is exogenous. Thus the system of e*xport demand functions taken alone is best regarded as a model of import allocation which explains changes in market shares over time as a function of given prices and trends. This procedure is justified because we are following Armington’s utility tree approach to specification of demand functions in foreign trade [ I 1. according to which total import demand for any good is first determined and then independently allocated among competing sources of supply b;l geographic region. Thus we are assuming for present purposes that total imports in each courrtry have already been determined in the first step, and we deal herein only with the allocation decision. Our typical estimating equation has the form
(1) where xii = constant dollar quantity of exports from the ith country to the jth fiountry. Superscript zero refers to base year quantity. CY$= base year ith country’s share in ]th country’s imports. ml = constant dollar quantity of imports of the jth country. 0-J = elasticity of substi:ution between imports from any two countries in the /th market. fij = price index of the exports of country i to country 1. rn=p i=lat&j, price index of imports of country i. yi = time trend, set at zero in base year. r** = trend coefficient. This eiuation is the same basic form as proposed in Hickman’s earlier paper, exeept for the addition of the trend term. An explicit derivation
B. Hicknm, L. Lou, Substitution and export demands
349
of the specification is given in sect. 2 below. Just as before, Armington’s CES demand system I1 1 is the point of departure, but Hickman’s earlier results are extended in two ways. First, it is shown rigorously that the linear system is a first order approximation to Armington’s formulation and that the estimated coefficients of the relative price terms may therefore properly be interpreted as substitution elasticities - propositions which were stated but not proved in the earlier paper. Second, the approach is generalized to include trend terms with parameters to account for changing tastes over time, and it is shown that the adding up proper ties of the linear model are still preserved. ’ This last is important, since the basic appeal of the linear model over a CES system is the automatic satisfaction of the adding up criteria in complete model solutions. Thus the present model has the special property that the sum of the predicted exports from all the other countries to the jth country will equal the actual imports of the jth country. Consequently, total predicted world exports also add up automatica!,ly to total world imports. By summing the Xiis over j, the export demand funct-on of the ith country is derived and written as n
where Gi and ‘;i have the interpretations of being weighted averages of the elasticities of substitution and the trend terms respectively, and pTc is a weighted average of the import price indexes having the interpretation of an export competitive price index, and fl is the weighted export price index. The organization of the paper is as follows. The theoretical derivation of eqs. (I) and (2) is given in sect. 2. A dynamic variant of the system, allowing for the formation of price expectations, is presented in sect. 3. The data are described in sect. 4. The estimated substitution elasticities and the corresponding export demand functions and predictions are discu: sed and tested in sect. 5. ’ A method of allowing for other non-price factors ‘effective price’ concept is discussed in I41.
incorporating their influence illan
8. i!ickman, L. Lau. Substitution and =prKi’ demands
350
2. Theoretical development
Assume that there exists a qu or region of the CES type, i.e., 1, meI
index of imports for each country
?I - IlPj .._y.. -Pj c (J 4 11 I i= 1 I1
=
c
i= 1
Oj/(oj-1) Q.&.(ai11 11
l)/aj
9
(31
3
where uj = I/( I + pi) can be identified as the elasticity of substitution between the imports of any two countries or regions in the jth market. 2 In addition we set
since we are allowed an arbitrary scalar transformation of the quantity index. Then according to Armington [ I], the cost minimizing quantities of imports demanded for attaining a specified level of rn,!@ are given by “ij
= a,.yojm.1*
6
- *j
( )
(4)
-yz Pi
where Pi”-- =
[
n Of XWOI) i”x 1 aij Pij
1
l/(1- oj,
is the price index of imports with the property that n pr’m;
=
is
Ptxij
= Mj
(9
’ The basic aswmptions for the existence of such a quantity index are (0 independence,i.e., the marginalrate of substitutionbetween imports from any two countriesis independentof the level of imports of any other country, or, for that matter, the level of domestic consumption; and (ii) homotheticity, i.e., the relative composition of imports is independent of the level of total imports, for a given set of pricer In fact, the CES quantity index is the only quurtity index that satisfies both assumptions(i) and (ii). This approach may be compared to that of Barten 131, who assumes the existence of an import ‘production’ function with siinikt properties.
0. blickwmn. L. Lou. Substitution and export demands
351
i.e.. the product of the CES price and quantity indexes is equal to the actual totaf value of the imports. The individual import demand functions may be written alternatively as a= “ij PI
x -. uj
m*(a/-
’ “~~I~pij pj
xij
I)
X--Ul = UTMjPij Pj
t?l'(Uj-
1)
s
(61
In the base period, all export prices are set equal to unity, and given our normalization rule, all import prices are equal to unity as well. Hence 0
xij
=
a7Mj)
(7)
.
Further, define n mj s c+,
U.0
xi/
as the total quantity of imports to the jth country or region. Note that mj is the simple arithmetic sum of the imports in constant prices from all countries or regions to the jth region, and should not be confused with m;,the CES quantity index of imports. Then by using eqs. (5) and (8), eq. (7) may be rewritten as 0 Xij
=
al
Lc 6 1= *i
aij mj0
i:,
(9)
where rn;is the quantity of the base year imports to the jth country. The base year share of the ith country’s quantity of imports can be identified as 0 = a!1 0 =% m/l ‘j
(%j
’
(11) (12) Now the total quantity of imports to the jth country, mj, is given by
B. Hickman,L. Lau, Substitu?ionand export dewmnds n
mj =
c
il 1 “ij
c uijPijX--Oj11 c ’ ijPijx(1-q) [ 11
=
-tl
0
0
i= 1
1
-1 M
(13)
j*
i=l
In other worrts. n
=
Mj
mi
ll
C i=l
Id
I[c aijPijx-o1 1
atpi] x(1-Uj)
-1
cl
.
i=l
(14)
Substituting eq. (14) into eq. ( 1 I), we obtain
“ij
n
0 X-O/
= Uijpij
c k=l
x- aj &kjPkj
1 -1
rij
(15;
.
Thus far eq. (15) is an exact expression for any given level of the total quantity of imports. However, eq. (15) is non-linear and hence difficult to estimate and aggregate. We therefore linearize eq. ( 15) in the gjs by a Taylor’s series expansion around fij = 1, all i and 1. This is equivalent to choosing a base period in which all the export prices are set equal to unity. First order expansion of eq. (15) resu!ts in , Xij
=
U$9Zj
+
a$mji-- uj) @$ - 1) -
Lkel a&@&-l>1
a))?lj(-Uj)
- (16)
0
Observing that ci=t x** II
=
0
Qijmj
a& s 1, eq. ( 16) simplifies to
-
ujt&j
-
,q
= a&&h$mj -
(17)
If we now define a new import price index,
having the interpretation of a fixed-weighted average of the export prices of all countries in the fth market, eq. (17) may be rewritten as xij =
a&mj
-
Oj@$
-
pi”
h+j
l
(19)
8. Hickman, L. Lou, Substitution and export demands
353
Hickman 141 has shown that individual export demand functions of the type given in eq. (19) have the adding-up property, i.e.,
c i:,xu=mj. To see this, observe that
Now cy=ra$ = 1 and~~=r~$& =py; thus Cy=rXii =mj. This adding up property also automatically assures that predicted total world exports will equal actual total world imports, provided that the appropriate c.i.f.-f.o.b. valuation adjustments are made. If we further linearize Xii ill terms of mj around rnf , we have
which is the same basic linearized form proposed by Hickman (41. A similar derivation applies to the case in which the original CES quantity index of imports for each country or region is a function a&o of time, i.e., n
rn.J*, -
c i=l
[
Oj/bj-11
a..e II
7#~,~j_l)/~j
(22)
1J
I
where the YijS may be considered to be parameters indicating taste changes over time. The individual export demand functions are then given by xij
= CYije ’ 7’tujp~eaj
2 0 Ykjtoj x(1-oj) kPl akjt? Pkj
1 Ml (2% -1
and total quantity of imports by n c mj=+, xij 2 =
i=l
0 aije
r#tUj x-a/ Pfj
I[
2
0
kzl
aWe
i 1 i*
7kjt”jp;(L-uf)
-1
M
(24)
8. Hickmn, L. Lou. Substitution and export &wutnds
Note that if rij = rkj for all i and k, then the individual export demand functions as well as the quantity of total imports remain unchanged, as it should be, for such is a case of a neutral change in tastes. Solving eq. (24) for Mi and substituting the solution into eq. (23) yields
xij
Again,
= aO,w~l ij
x-“i
pij
II2
k=, a&.Pj
to
x-oj
jPkj
1 . --*
(25)
rr$
eq. (25) in a Taylor’s series
order,
(26) we have Xij
=
t
atrnj - oja~mitp$ -ply> + atmioj that eq. (27)
l
(271
up criterion, we observe
cy_,,t = 1. Hence even in the case with trend terms, our system still satisfies the adding up criterion. Finally, we further linearize eq. (27) in mi around m!, obtaining
+ atrnfrift = aQm J / - u&Wj
where
Pirn)
uflij Orij t
(28)
B. Hichan,
L. Law Substitution and export demands
355
It is clear that given the rijs one can determine the rijs and vice versa. it is also clear that the rijS are not ~11independent. In fact,
In other words, the sum of the atrijs must be zero. This is a fact that must be taken into account in the emp2cal implementation. Thus, we have shown that the linear world trade system proposed by Hickman 143 and the generalization to include trend terms can be properly regarded as a first order approximation of a theoretical d%mand model -of the Armington [ 1] type. The estimated coefficients corresponding to the relative price variables in this system can therefore be interpreted as the elasticities of substitution between imports in given markets. We now turn our attention to the aggregate export demand functions. These are given by summing eq. (28) across all the jth markets: ’ n xj
= r I Xij
j=l n
=
c
j*l
0 Oijmj
C j=l
a@j
UjrijXCf 0
n
n
=
UjXP,(p;i-?I;",+,$
-6
‘gjXpt,$
- c j-1 'j.0
i
4 Ip1 0 u*r .."i'txp . Uj.OPj Xi +k j=l I 'lx0 i
(29)
i
Now define (30) the base year share of the jth country’s imports from the ith country in the ith country’s exports,
6, =jg u&
(31)
the weighted average elasticity of substitution in the export markets of ’ This derivation follows Hickman [ 4 J.
B. Hickman, L. Lau. &botinrrion and export demunds
356
the ith country, and
(32)
the export competitive price index of the ith country, with weights summing to unity. In this expression, p,? is a weighted index of the prices charged by all exporting countries in the ith market and the #s are in turn weighted by the relative elasticities of substitution and the shares of the j markets in the total exports of country i to yield an overall index of prices competitive to the exports of the ith country. The same weighting scheme defines the export price index of country i: (33) and also n !.!L
r;. = c
qij
(34)
j=l iji
the weighted :lver+~.‘ of thf, trend terms of the exports of the ith country-to all its markets. Given these definitions, eq. (29) may be rewritten as n
Xi =
c j-1
0
&ijmj
-
(GiXp)@f -tic)
+ (ZiXFQ)t
a
(35)
Thus, given the estimated ois and ri/s, one can construct ZiS,@, ds and #s and obtain aggregate export demand functions of the form in eq. (35). 3. Expectations and adjustment lap In the preceding derivations we implicitly assumed static price expectations and the absence of adjustment lags. In this section we discuss two alternative specifications to allow for such dynamic factors and show that only the second is useful for our purposes.
IA Hickman. L. Lau, Substitution and export demands
357
First, we retain tic assumption of static price expectations but adopt the following familiar partial adjustment hypothesis: Xi~=siXi;++(l_61)(-~i,)_,,
O< hi< 1,
(36)
where xii is the quantity of imports desired by the ith country from the ith supplying country. If eq. (21) is now rewritten to refer to the desired quantity demanded from i by i, we have
Combining (36) and (2la) yields Xij
=
6jabm,-
f!3/ujx@?$-pi”>
+
(1 - i5$ (Xj&
.
(37)
Eq. (37) could be rewritten for estimation purposes as follows:
At first sight this is a perfectly acceptable specification, since Sj and dj are just identified. It cannot be used in our system, however, because it violates i the additiviky criterion. To show this, we sum eq. (37) over i after substituting .ut= a&my :
X
where
t&a$+(1 -6jl,$
use
(xij)-1
=
6jmj
+
(1 -
s/l
(mj)_l9
(38)
has been made of Cyz 1ai = 1, Cy= 1a$pFj = pi” and Cy= 1Xii of course, is that the left-hand side is identically equal to mj,SO the equation cannot hold in a world where mi changes from period to period unless 8j = 1, in which case there is no adjustment lag and the model reduces to the original static version. Thus the lagged adjustment specification (37) is inconsistent with the adding up criterion and is unacceptable for our purposes. This is not an admissible method for introducing dynamic elements into the static models represented by eqs. (2 1) and (28). An alternative is available which does yield an acceptable specifica-
= mj. The difficulty,
358
B. Hickwtan, L. Lau, Substihtcion and export demands
tion under plausible assumptions concerning the formation of price expectations. however. Instead of assuming an adjustment lag with static price expectations, we assume immediate adjustment with an (adaptive) expectations lag. In its most general form, the adaptive expectations hypothesis we use is:
ogij5
Thus each rebtive of the expt;rctation
1.
(39)
yicc expectaWn of this period is a weighted average r&d last period and the actual relative price of this
period, plus an ir~d~pend~nt trend whether or not the expectation is realized. Notice that we are assuming the same adaptive expectations parameter fii for AI relative prices in market j, but are allowing different trend factors for the expected prices of the several supplying countries. Let us now rewrite our most general static model (28) in terms of expected prices:
If we now substitute (39) in (28a) and then use (28a) lagged one period to eliminate the lagged expected price term, the result is
where all variables are observable. The parameters 6j and Uj are identifiable, but the others are not. In particular, it is not possible to estimate both the trend coefficient of tastes (r,i) and the trend coefficient of price expectations (rjj). If either trend coefficient is assumed to be zero for all i and j, however, the other is identifiable. If rjj s 0, for example, so that tastes are assumed constant over time and the trend term drops out of (28a), the second term of (40) will identify flij and the third term will identify y4j. Similariy , assuming rjj = 0 permits identification Of&j and rjj. In the sequel, we present actual estimates of an equation of the form (40), and we arbitrarily interpret the results as if the trend coefficient represents price expectations rather than tastes, though we admittedly cannot distinguish that hypothesis from its converse. We also
B. Hickman, L. Lau. Substitution and export demands
359
give estimates for a model in which we assume ‘ii z rii 5 0, permitting identification of flii, u1 and $. For estimation, eq. (40) is rewritten with the term CY@Z~ transferred to the left-hand side in order to impose its coefficient of unity. it is then easy to see that the last variable on the right-hand side is simply the lagged dependent variable. The estimated coefficient of the relative price variable, Of( 1 - S,), is the short-run value of the elasticity of substitution. In long-run equilibrium. however, xii = (Xii)._1 and mi = (mi)_, , so that the long-run coefficient of the relative price term is oi( 1- $)/ (1 - S$ = ai. Since 0 < SI < 1 in the estimates, the elasticity of substitution is greater in the long-run, since the short-run response to a relative price change is moderated by the expectations lag. Unlike the lagged adjustment model, the adaptive expectations model is consistent with the adding up criterion, providing t trend coefficients are appropriately constrained in the estimation procedure. To sholw this for our assumption of constant tastes, we set rj/ 5 0 in eq. (40) and sum over i:
(41) where use has been made of the same definitional relations as in the simplification of eq. (20). Since c :=I xii I nlj, the additivity criterion will hold if (Cy*r a&) = ( Cy* 1Qt+Yi/)= 0, or in other words, if the constant terms and the trend coefficients of the pooled Xii regressions for market i are constrained to sum to zero. It remains to derive the export demand function for country i by aggregating (40) over 1, again after setting rij z 0. The result is y. = 1
n Ei + fq t
n U$j
-
SiXfQ7fb
- tic’)
+ ~iXi _ 1 - ,_l C
6 J4rOm rj j-1
-zs -
0
uirixi tp
(42)
8. Hickman, L. Lou, Substitution and ew-t
demands
where (43)
(44) the weighted average short-run elasticity of substitution markets of’ the ith country
ai =~~ oih~~ .
(45)
the weighted average long-run elasticity of substitution markets of the ith country
.= _i j=l SC
in the export
in the export
N
hjX,i
_ 1
(46)
9
the weighted average adaptive exceptation parameter in the export markets of ith country using the previous period’s export shares as weights = I.
n
1
=
j=l c(
i $Q ai j
,
(47)
the weighted average of the trend terms of the exports of the ith country in all its markets ,
(48)
the short-run weighted export price index of country i
the short-run weighted export competitive price index of country i. Note that 8, will in general vary from period to period. The expression
B. Hickmun, 1.. Lau. Substitution and exprt demands
361
(50) has the interpretation of an effective lagged external demand index. Eq. (42) is the dynamic counterpart to eq. (35) above. From eq. (35) one may compute the export price elasticities of demand of the static model in the year f as
-pZ dXit
Ti
Z----_ Xit
J$
=$. a i xoi xit
l
(52)
Similarly, one may compute from eq. (42) the short-run (~2) and long-run (r#-) export price elasticities of demand of the dynamic model in the year t as (53)
4. Data The data were supplied by Grant B. Taplin of the International Monetary Fund and are the same as are used in the IME’ Expanded World Trade Model. Basically, they consist of a series of nine annual export trade matrices developed at the lnternational Monetary Fund by Taplin for the years 1961 through 1969. The original export flows are valued at f.o.b. prices and in current US dollars, but Taplin has also provided export price deflators for each exporting country or region to convert the flows to constant dollars. Altogether, 27 countries or regions are distinguished. ’ ‘The CMEA group include:s member countries of the Council of Mutual Economic Assistance bllbania, Bulgaria, Czclchoslovakia, Eastern Germany, Hungary, Mongolia, Poland, Rumania and the Union of Soviet Socialist Republics), mainland China, and other countries poBticaBy and economicady associated with these twc areas, including North Korea and North Vietnam.
362
B. Hickmm. L. Lau. Substitutim and export donwnda
The base year for aif countries or regions is chosen to be 1963. In other words, all price indexes are set equal to one in 1963. in addition, the a& are taken from the 1963 constant dollar import share matrix. Exports and imports are measured f.o.b. The export price indexes were converted to a c.i.f. basis for comparability with the import price indexes. as explained in [ 5 1.
5. Empirical results The actual equations used in the estimation of the elasticities of substitution of the different countries are of the forms
- OjX$*rijt + &j(Xij - a$m$_ I e
(56)
Estimates are also presented for both forms with time trends suppressed. Note that Oj appears in every Xii equation. Hence it is necessary to pool a!1 the Xii observations for each i and estimate the equations jointly. Where constant terms or trends are included, their coefficients are constrained to sum to zero in order to preserve the additivity property. as explained above. With regard to the stochastic specification, three alternative assumntions are attempted. Assume that the stochastic disturbance term is additive, such that in the case of eq. (55), we have xijt -
= - UjXg@fj*
c&t
- @I
+ O,Xsrijt
+ ‘ijt
where the t subscript refers to the time period of the observation. Then the tnree alternative assumptions are: (9
Eteijt)
=
0
)
all i, j, t
All other covariances are zero. (To avoid confusion with the elasticity of substitution, we have denoted the population variance by S* rather than the customary oz.)
B. Hickman, L. Lau, Substttution and export demands
(ii)
E&j,) = 0 )
all i, j, t
V(t+ = $xQ’,
all i, t .
363
All other covariances are zero. (iii)
E(Q) Q..
w
=09 ) = s?x!? I 11’
all i, j, 1 all i, : .
All other covariances are zero. In addition, for all three specifications,
assume that
n
c ei/t=o,
+,
all j, t .
Corresponding to each of these three stochastic specifications, a complete set of estimates of the elasticities of substitution is obtained for each of our four functional specifications. One final set of estimates is chosen for each of the four cases. The criteria for selection are: (i) the estimated elasticity of substitution must have the correct sign, (ii) it must have the highest t-ratio, and (iii) for the dynamic models the estimated values of the adaptive expectation parameter must be less than unity. The resulting estimates are presented in table 1. We show the coefficient estimates and their t-ratios for both variants of the static model (SS), with and without trend terms. In the case of the adaptive expectations model, we show t-ratios for the short-run elasticities u/ (1 - $), but not for the long-run elasticities Gj, which are obtained as the quotient of the estimated coefficients on the relative price and lagged dependent variables (see eq. 56). In general, the estimated substitution elasticities are significant for all models. The conventional goodness-of-fit statistics are not given in table 1, for two reasons. First, within each of the four functional specifications, the R-squares and standard errors of estimate are not comparable across different stochastic specifications, since the variables are scaled differently in each of the latter. Second, as between functional specifications, even when the stochastic specification is the same, the R-squares are not comparable for the forms including and excluding a constant term, and indeed, the concept of a coefficient of determination is not even well defined when the regression is forced through the origin. In the case of the first static model, in which the only explanatory
364
B. Hickman. I.. Lou. Substitution and export demand;
h
$2 maD
dir; Y
h
38
zs .d h
2:3
“r .
z
25 33 “i Y
(z6zC'S) (Z6zC‘5) ,699L.t ,,699L'Z
(8868'8) (zsrcr*s) PZdZZ'C P658T.Z
(S8W'S) PLTTT'E
(CLE6'2) (9090'9) ,ct9z-z PsLzz'z
(6;dSC'8) (9869-L) pZT9Z'E p6Tz6'z
(EtSO'T) (~OZC'E) PS6LO'T PT6TO'Z
(OL06'E) PS)9S'T
ZT8Z'S
t0ZTi.Z) (C9TL'C) P88Ez'z
Ubt9't) P9SC9.T
O8VS'f 9800-t p6SSZ lZ
tosocrel) P?xlC'f
80V!?'Z S6LZ'C
OSCZ'ci 099O'lr
(86~s.~ &lSZ'C
tSZZ8'Oi &6Zz'T
TTLZ'O l
(O?f6E'T) t89SC.O) ,OiTS'O $69T'O
(COST-91 (SZ86W aL88L'c a6ZOC'E
t8LSS.9) PSWC
f6?7tr'O
(TTVT i 1
69L6'9
tOUS-T) &9TZ'Z
ZTBZ'S
9ZOE'O
(SZSL lcl
899L'Z 9LZ8'0
("'1 ,O'O
(9S6Z.L) (956Z'f) T96tr'O T9Lf'0
t69LO.S) (0~98.U OLZS'O 9cOL'O 9fZ8.0
(TOZL'S) PS6T8.0
tmco*9)
(S6ZC'9) (S6ZE.9) LO81r'O LO8t'0
SL90'T 8VZL.B
trs!?s*E) 6Z8Z.O
(~806.T) h886=6~) TST6'0 LMT'O ZC89.t
(Z689.Z) #ZTL'O
(6z8~-z) (Z09t.T) PSSEZ'T JSLTi'z _A
P-l& anwarn
(CD,TaPaW va*as 'UOTlnafa~pS 30 -TaT3P~T3
WnI
PrulJ
(ZT69'T) &tS&'T) &dZS'V 3TSTO'Z
(TLt9'Z) p6688'T
(626L'O) tS9LZ*VT) LqO6'0 ET8O'O
0909-T E68C'O
p-2 a*orllffi
966T‘5
ZLW'L
(9tre9*r)ttTSt*tT) Z9SS'O 2558'0
Z8CL.S F=i wm
(T606'T) tT69O'TT) 9ZT9'0 LOTZ'O
_ mqa8aaadx3
cF* ) 8;loaaw3wd (panu!luw) I a1qe.L
=Ws
*nalOd
‘OZ
‘61
366
B. Hickman. L. Law Substitution and export demands
B. Hickman, L. Lou, Substitution and export demnds
367
vziable for changes in market shares is relative prices, the estimated elasticities of substitution range from near zero to about 15 and average to 3.03. interestingly enough, a value of 3 was assumed for all markets by Armington in an empirical application of his original model, on the grounds thal: the figure was roughly of the order of magnitude to be expected from past research and a priori reasoning (2). When a trend term is added to the static model, the effect is to reduce the average estimated elasticity to 1.84 and to reduce the range of estimates to values between 0 ant8 6. The model without time trend is probably mrsspecified because of omitted variables, and since the addition of the trend term makes some allowance for omitted variables which are correlated with time, such as changes in tastes or preferences, it should tend to reduce misspecification bias in the estimates of the uIs. The trend-adjusted set of estimated static substitution elasticities is therefore to be preferred to the unadjusted set, but it still is subject to the deficiency that it makes no allowance for expectational Lagsand hence, may be providing estimates basically of the short-run rather than the long-run elasticities. This last inference is consistent with the results on the estimation of the adaptive expectations model. Whether estimated with or without a trend, the expectations model results in short-run elasticities which are mucir closer to 1.8 than to 3 in value. The values for the trendless expectations model range from 0 to 3 and average 1.18, whereas those with allowance for trend range from 0 to 4.5 and average 1SO. The presence or absence of a trend term in the expectations model makes a greater difference for the estimates of the long-run substitution elasticities than for the short-run values. This is because the adaptive expectations parameter is estimated as the coefficient on the lagged dependent variable, which itself is correlated with time. When time ia, excluded, the average value of the expectations parameter $ is 0.73, whereas inclusion of a trend term yields an average estimate of 0.34. Since (I- 6i, measures the rate at which price expectations are adapted to experienced price changes, the trendless model implies a slower ap preach to long-run equilibrium and hence a larger ratio of long-run to short-run substitution elasticities. Thus, although the trendless model has smaller average estimated short-run elasticities (1.18 as compared with 1SO) it has considerably larger long-run elasticities (5.2 instead of 2.5). In our judgment, the expectations model with allowance for trend gives the best results in terms of estimation of substitution elasticities in
368
B. Iiickman. 1.. Lau. 22ubstitution nnd export demmds
import markets. lmmcdiatc revision of price expectations seems implausible to us ;LSan assumption in behavior, SO we prefer the ciy?llamic model on intuitive grounds. The trcndless version yields estimates of long-run elastizitics of substitution that appear implausibly high, whereas allowance for an expectation4 trend results in an average of 2.5 and ;t range from 0 to 9, and these figures seem rcz:sonable to ‘US.Further criteria for sclcction among the alternative models will be considered below. and wiil be fdund to confirm this initial judgment based largely on our prior beliefs. For the moment, we merely observe that our best ly an average short-run substitution elasticity of about 1.5 oncerned the substitution elasticities f course. It is equally relevant to ask what substitution elasticity faces each exporting country on the average in all its markets. TabIt 2 lists the estimated average long-run (Gi) and short-run (Gi) elasticities of substitution in the export markets of country i, weighted by the base-period importance of each market in its exports (Xv.) x 11* s Thus a low oi indicates that the country in question sells its exports predominantly in markets with low U/S, and hence its export sales are rather insensitive to changes in its export prices relative to its competitors. To judge from the long-run OiS computed from the preferred adaptive expectations model with trend, the exports of the socialist countries ithe CMEA group and Yugoslavia) are not very sensitive to increases or decreases in their prices relative to those of non-socialist countries as a group. Many of the non-socialist industrialized countries show a higher estimated degree of price sensitivity, but even they seldom exceed a value of 2 for ?ii. Let us now turn our attention to the predictive ability of the alternative models when it comes to forecasting exports. Specifically, we are interested in how well the export vector xi, i = I, .. . . n, can be predicted conditional on the known vector of import quantities mj and matrix of export prices p$ ’ Given the estimated structural parameters implicit in eqs. (55) and (56) and their trendless counterparts, it is simple arithmetic to form aggregative export demand functions for each country as given in eqs. (35) and (42) and their trendless counterparts. These export demand functions contain as arguments the given import quan’ See formulas (44). (45) and (30) for the exact definitions. 6 Az noted in the introduction, the present import allocation model is intended for eventual incorporation in a complete world system with endogenous imports and prices.
Norway
Sweden
Switzerland
United
Finland
Greece
Iceland
ire land
Il.
12.
13.
14.
15.
16.
17.
18.
Kingdom
Dark
10.
Austria
9.
Gerrangi
6.
Italy
S. France
Netherlands
2.4857
Eelgim
8.
2.7924
Japan
3.
4.
7.
2.2543
Canada
0.4617
1.8335
2.8337
2.3092
2.5710
2.4070
2.1600
1.6291
1.7757
3.0401
2.4507
2.8244
2.4121
1.1952
United
2.
2.9856
zthout
1.
State8
Country
of SubacituModel (3,)
l
l
.1483
0.88S2
1.1027
1.2619
i
1.4483
1.2443
1.3383
1.1255
1.1677
1.4273
1 3451
1.5087
1.4324
1.5218
1.2219
1.2700
0.8918
1 3343
Trend With Trend
Elsleticitiee tion Static
0.4824
0.6654
0.7060
0.6335
0.9626
0.742s
0.8285
0.5817
0.6499
0.6658
0.7386
0.7411
0.7785
0.8531
0.5678
0.9099
0.8042
0.9153
Without Trend
0.9654
0.9682
0.9825
0.9145
1.2023
1.0590
1.4744
1.0026
1.2658
1.1642
1.2034
1.2919
1.2938
1.2527
1.1994
0.9494
0.9452
1.1023
With Trend
Short-run (8,)
Elastkities
4.8686
3.7941
4.3828
3.7927
5.7002
4.5851
4.4209
3.8425
4.2072
4.2830
4.8749
4.9183
4.4964
5.5756
3.4423
6.4395
5.3238
7.2547
Trend
Without
d
1.1962
1.3796
1.4500
1.3629
2.1121
1.7048
2.0768
1.5345
1.7919
1.6818
1.7843
1.9574
1.9532
1.7450
1.8345
1.4471
1.3844
1.6975
Trend
With
Long-run @,)
of Substitution, Dynsxaic Model
trend
0.8961
0.7955
0.8150
0.8040
0.7940
0.8178
0.7798
0.8234
0.8312
0.8227
0.8403
0.8287
0.7944
0.83l3
0.7929
0.8470
0.8420
0.8442
Without
O.i742
0.2i84
3.2930
0.2797
0.3360
0.3264
0.2790
0.3113
0.2859
0.2814
0.3050
0.3248
0.3246
0.2699
0.3382
0.2926
0.2818
0.3080
With trend
Expectations Parameters (;3,Ia
Table 2 FZs,gtimates of weighted averageelasticitiesof substitution and weighted averagea&ptive expectations parametersin export mtirkets.
370
R. Hickmn,
L. Law Substitution and
3 f
c;
;
exportdemands
B. Hi&man,
1.. Lou,
Substitution
and export
371
demands
Table 3 Comparisons of goodness-of-fit of the export demand functions (standard errors of estimate ad-
justed by degreesoffreedom). Static Model Without With Trend Trend
Dynamic Model Without With Trend Trend
1.
United states
0.7669
0.6449
0.8190
0.6064
2.
Cfmaaa
0.6332
0.2390
0.3495
0.2421
3.
Japan
3.0396
0.7312
0.8236
0.5797
4. c,.
Belgium
0.3951
0.1661
0.1936
0.2058
France
0.4561
0.1749
0.2916
6.
Germany
1.oG99
0.6714
0.3357 0.4446
7.
Italy
1.2589
a,
Netherlands
0.3482
0.3133 0.1881
0.5363 0.3261
9. Austria 10. Denmark
O.l&i5
0.0945
0.0454
0.0710
0.1669
0.1182
0.0717
0.1072
11. Norway
0.1891
0.0468
0.0551
0.0285
12.
0.1164
0.0506
0.0430
0.0646
13. Switzerland
0.2994
0.0447
0.1130
0.0430
14. United Kingdom
1.9275 0.0810
0.4709
0.4215
0.3503
0.0487
0.0422
0.0455
0.0609
0.0387
0.0513
0.0443
0.0253
0.0184
0.0229
0.0233
0.0358
0.0248 o. 0261
Sweden
15. Finland Greece 16.
0.1853 ~1.1864 0.1'184
17.
Iceland
la.
Ireland
0.0395 0.0287
19.
Portugal
O.lOil
0.02h5
0.0304
20.
Spairi
0.3340 # 0.1290
0.1748
0.0913
a.
Turkey
0.0711
G.0400
0.0505
0.0348
22.
Yugoslavia
0.2785
0.0898
0.0576
0.0722
0.9777 0.2028
0.2645
0.2475
0.0822
0.0689
0.1973 0.0831
25. South Africa
0.0772
0.0999
0.1201
0.1098
26.
CMEA Countries
0.4101
27.
Rest of World
0.4344 4.5782
0.4004 1.0857
0.2956 0.4218
23. Australia 24.
New Zealand
0.9752
372
B tlickwzan, L. Lau. Substitution and export demands
tities and certain price indexes that are weighted averages of the given export prices. and hence they can be used to predict exp:7rts for each country. The export demand functions were obtained by aggregation of the underlying market share equations rather than by direct estimation, of course, but it is an easy matter to compute goodness-of-fit and error statistics for the synthetic equations which are directly analogous to the measures usually computed for multiple regressions. Comparisons of goodness-of-fit statistics in the form of standard errors of estimate are shown for the export demand functions of the four m:ldels in table 3. Even after correction for loss of degrees of freedom, the smallest prediction errors are obtained from the preferred ations with allowance for trend - in 14 of the of the 1 I countries or regions which had more than 1O billions of exports ( i 963 US dollars) in 1970. Where the preferred model is beaten on this criterion, the best fits are divided about equally between the static model with time trend and the trendless expectations model. Clearly the preferred model is dominant when it comes to explaining changes m annual exports of the individual countries or regions over the sample period, so it should also provide the best cross-country predictions of exports on the average. This last expectation is confirmed by the cross-section error measures presented in table 4. Four error measures are presented for each model and are defined as follows. Let Cit = (Xit - X,) be the error in prediction of exports of country i in year t, ei,* = (cit/Xit) be the corresponding proportional error, and wp = (x$x0) be the base period share of the exports of country i in world exports. Then, for year t is the root-mean-square
error,
(ii)
(RWSF), = ($ w+?f
is the root-weighted-square ror
(iii)
(RMsPE), = [ l$ (e:,)2/n]H
is the root-mean-square-proportional error, and
(iv;
(RWSPE),= [fi is the root-weighted-square-pro= w;(e;)'lK portional error.
er-
1963
0.2493
0.0795
0.3816
0.1693
III
IV
0.0000
0.4195
0.5543
0.7634
0.2952
II
III
IV
0.0721
0.0675
0.0326
II
III
IV
0.0352
0.0444
0.0444
0.0616
0.0560
0.0543
3.0667
0.1206
0.3163
0.4706
0.3292
0.0283
0.0471
0.0479
0.0497
0.0136
0.0400
o.oooo‘
0.0000
0.0240
0.0278
0.0283
0.0378
0.0222
0.0317
0.0221
0.0662
(ma
0.0207
0.0191
0.0224
0.0839
error
0.0614
0.0444
0.0661
0.1315
error
0.2474
0.2791
0.3261
1.8073
0.0232
0.0250
0.0204
3 51070
(IWSPE)’
0.0456
0.0684
0.0457
0.1572
0.2466
0.2977
0.2463
2.5189
0.2002
0.207;
0.1780
1.2305
1967 1.0698
0.2787
1.0592 0.5177
0.6961 0.3102
0.0190
0.0308
0.0210
0.1381
0.0541
0.0784
0.0782
0.2254
0.2636
0.0589
0.0173
0.0287
0.0242
0.1448
0.1673
0.0309
0.0381
0.0425
0.0215
0.0323
0.0390
0.0888
0.0469
0.0564 0.0255
0.0639
0.0747 0.0362
0.0689
0.1966
0.1952 0.0481
0.1396
0.4952 0.5272
0.9450
0.5044
0.2314 0.6330
5.6737
3.9327
2.0193
0.1759
0.2928
0.2784
3.1662
0.5706 0.3496
0.4049 0.2083
0.3414 0.1744
2.9257
0.5597
2.1329 0.3060
1.6953 0.1571
Pooled Sal&@@ b
’ Weights are 1963 shares of exports of each country in total world exports.
a The models are as follows: 1 Static mAeI without trend. II Static model with trend. ill Dynamic model without ttcndIV Dynamic model witk trend. b Based on pooled errors over sample rather than averages of annual enor measures. For Modeb 1 and II, sample pcuod is 1961-69, and for Models 111and IV, it is 1962-69.
IV
III
II
0.0316
0.0649
0.0000
0.0000
0.1616
0.1514
0.1950
0.8966
1966
@51SE)C
0.9128
error
0.1766
0.2748
0.1807
0.5372
(BlQ)
1965
D. Root-weldted-squarepropo+t~Onal
0.0919
I
I
0.3621
0.4377
0.4721
0.3936
C. Boot-mkm-sauere-pr:sportiona.l
0.1234
o.oooo
0.5219
I
0.2034
0.2377
0.2598
0.2769
error
1964
&et-weighted-square
0.0000
0.3029
If
B.
o.oooo
0.2887
I
A. Boot-rscan-rauare
1962
Table 4 Comparison of cross-section prediction errors, four models.
374
B. Hickmen, L. Lau, Substitution and
exportdemmds
Corresponding pooled error measures can be computed by summing over f as well as II. A number of points emerge from a study of ,these error measures. (1) The largest errors by far result from the simplest specification, the static model without trend (Model I in table 4) whereas the smallest errors come from our preferl.ed adaptive expectations model with trend (Model IV). (2) Weighting the absolute errors increases the avera els, whereas the reverse is true of the proportional errors. atic tendency to make larger absolute errors for are larger exporters, but the errors for the larger ~~tio~ately smaller on the average. (3) The errors for nit with time from the 1963 base period, Of other models. Indeed, the unweighted e preferred Mode1 IV is smaller for 1969 than in any earlier year in the sample period, whereas the weighted proportional error is smaller in 1969 than in any other year except 1963. There is a similar, though less striking, absence of significant error buildup within the sample period for the absolute error measures from Model IV. (4) Despite the last observation, it is unfortunately true, though not surprising, that the 1970 post-sample prediction errors for Model IV (as well as the other models) are larger than for any year during the sample period itself. Thus Mode1 IV appears to be the best of our four specifications not only a priori but for prediction as well. It should be possible to reduce prediction errors still further in future work, however. It is likely that post-sample errors can be reduced by shifting the base period to the end of the sample period, since this will tend to minimize the change away from the base period shares to be explained by the price and trend terms. Another possible device for reducing prediction error is to combine the best fitting import allocation functions for each country from among the four models. We have organized this paper so as to ‘run a race’ between the four specifications in order to pick the ‘best model’. This is surely a rational procedure for the general structural analysis of export demand functions and for the purpose of estimating elasticities of substitution in import markets. When it comes to prediction, however, at least some marginal improvement should be achievable by choosing the best fitting specifications for each import .market to form a fifth complete system, but this remains to be tried. Other useful facts of some practical interest at? the values of the
R. Hickman,L. Lou. Substrtution and export demands
375
Tatle S Export price elasticities ofdemand. Dynamic model
Short-Run(+
Static model Long-Run(nf;)
(n,)
1. UnitedStattee
0.8937
1.3781
Le.653
2. Canada 3. Japan
0.5936 0.3485
0.8447
4.
Belgiun
0.6585
0.5590 0.4636 0.6695
5.
France cermeny
0.7947 0.6909
1.0945
6.
1.0360
0.9615 0.7609
7.
Italy
0.4936 1.0198
0.6103
0.9284
0.7092
a. Netherlands
0.6482
0.9490
0.7217
9. Allsb~'if%
0.6186
10. Denmark
0.8911
0.9315 1.2765
11. Norway 12. Sweden
0.5559 1.0438
0.8081
0.7585 0.8173 o.6ug
1.9887
019404
13.
Salt zerland
0.7648
1.0110
14.
United Kingdom
0.8735
1.2744 0.8136
0.8953 1.0469
15. Finland 16. Greece
0.5783 0.4669
17.
0.619s
0.7266 0.6004
0.8094
1.1616
0.9221
O.B567
0.6363
19. Portugal
0.6956 0.7382
1.0253
20. spala
0.4230
0.6107
0.8777 0.4540
21. mey 22. Yugoslavia
0.7410
1.0345
0.5760
0.7894
23- Australia 24. New Zealand
0.5303 0.5626
0.7411
0.8529 0.9183 0.6692
0.7466
0.5656
25. South Airics
0.6583
26. CMEA Countries
0.3156 0.6716
0.8777 0.4336
0.8836
Iceland
la. Ire?.and
27.
Rest 0r World Aver .we
0.6292
0.9638 0.9542
0.6998 0.7808 0.7622
8. Iiickman,
376
I_. 1,~
Substitution
and
expor#
demands
'fable b Coefftcients of aggregate exportdemand funtions, adaptiveexpectations with trenda coeffi&ntof:
country
Ei -
1. Lnited States
0.2261
l.OQOO
-25.2660
2.3515
2.
0.0657
1.0000
-6.1174
0.2973
3.
0.2747
1.0000
-5.1422
0.29ko
4.
0.0131
1.0000
-5.8206
0.3543
5.
1.0000
-10.1211
0.2739
6.
0.334
Canada
Germmy
1.0000
-18.9090
0.0950
1.0000
-6.5560
0.3426
-r).ooo2
I. 0000
-5.9708
0.370
0.0225
1.0000
-1.5437
0.33559
-0.0076
1.0000
-2.3595
-0.0470
nds
11.
Norway
0.0311
1.0000
-1.0763
0.3019 0.3121
12.
'Sweden
0.0211
1.0000
-4.7172
0.2769
33. Switzerland
-0.0278
1.0000
-2.5434
0.2435
14. UnitedKingdom -0.2593 15. Finland 0.0009
1.0000
-13.7355
0.3.146
1.0000
-1.0511
0.2892
16. Creefie
1.0000
-0.2850
0.21r67
0.0076
l.ooc)O
-0.0912
0.3032
-0.0092
1.0000
-0.5171
0.1880 0.2800
17. Icelmd 18. Irehnd
-0.0157
lr. Portugal 20. Spain
0.0175 O.nl96
1.0000
-0.4360
l.OoQO
-0.8302
0.347&
21. Turkey
0.0108
1.0000
-0.4190
0.2837
22. Yugoelavla
0.0389
1.0000
-9.6014
0.2703
-0.1229
1.0000
-2.3583
0.2&k
-0.079
-0.0111
1.000
-0.8588
0.2L65
-0.029;
-0.0118
1.0000
-1.2535
0.2500
26. CWA Countrice -0.0520 27. Rest of World -0.2599
l.ooOo
-8.1828 -30.0706
0.2722
0.0051 -0.088;
Q.3032
-0.5521
23. Australia 24.
New Zealand
25. South Africa
a Seeeq.(42). b TM
vahcs
are for 1969.
l.Oooo
-0.008i O.OlQC
us
CA
JA
BE
FR
GE
17
NE
A7
OE
I
2
3
4
5
6
7
8
9
80
6.7544 6.9591 -0.2iJ47
5.4162 5. s9ue -U. 1746
l-b?55 1. I+024 -0.1269
1.1819 1.1273 0.0546
+.Ybiti
4.6782 4.5652 0.1130
1.6641 1*&?93 0.0348
1.3259 1.3381 -O.OlZL
U. 0010
4.9608
5.0747 5.1642 - 0.0895
14.6155 A40 5235 0.0921
8.0413 0.0384
8.07Yb
0.0313
2.014V I *WC3
1.4d95 1 .CIlC -b#.o313
5.6YC2 5.6363 o,ost9
5.9466 -0.13>3
5.8113
i6.&9d8 lb. 5245 -0.3257
8 -6546 8. I4LU -O.OOVl
5.5622 5.5816 -D*OlYC
7.585r) 7.2111 0.3073
6.4719 6.4552 0*3167
1964
25.&!77 25. ZASl O.6126
4a 8528 4.8214
Table 7
2. IS50 d.kO70 o.o?*d
U,!.Ji)iJ3
1.5338 1.5105
6.1474 b.L405 -0,393l
7.1j:u 0. =,-74 0.103b
-0.3lll
il.l;760 Lt. b930
9.5879 9.5348 -iL 0069
6.2565 6.1911 LO654
trr65Yb 0.4661 0. I%9
7.8943 8.2165 -0.3224
25-9149 LB.2 807 -0.J650
-
1965
2.2239 1.1344 0. r)895
i-6157 1.6492 -u*3334
-0. JO56
6.4926 b.?OBZ
-3.0268
1.1645
8.1317
19IIZLO 19.6388 -3.16b8
LO.2612 -0.L279
hl.0333
-0.1947
6.69&a
b-5038
10-3085 l&l*lW;, -3.1524
0.9265 tl.947k -O,iJ206
21.8133 27.3290 0.4840
1966
1
0.1152
2.3550 2.2406
1.7426 1.7154 0.0272
7.0153
7.1409 -0.0656
8.7118 8.7986 -0.0268
21.2677 21.2616 0.0062
10.6431 10.8679 -0.2248
7.052 -0.2902
6.7619
JO, 3690 11,1871 -& 6181
9.5609 9.4L57 0.1452
2LIc4189 28.0963 0.3226
1967
2. LmO7 l.PIIIU r)r 0161
0.1781 1.2472 -3. QbYl
9.9543 Ym8727 0.0616
24. d672 24.2 tm 0.5884
A1.8544 LL. WIA ‘U. 45&I
(1.ObZ3 -0.1561
7.9202
11.1117 AL-O476 0.0641
actual and predicted values - adaptive expectations model with
22b9217 23.1547 -062331
1963
4.755A 4.5162 0.23&B
1% 5636 12.9923 0.2714
7.4486 7.4426 010060
4s j&&3 4.3290 0.0593
4.8582 4.4566 0.4017
5*9157 5.9900 -0.0751
21.2952 LL.5845 -0.2894
1962
Exports1969 35,i(ill
9,319)
L.7VuL
2.7164 J*313c(
2,43/9 2.314L lLl117
0.4906 9.5r)OV -O.&J>
I?.l:?r: 11.2Lt13 -0.1105
LtebL9Y 0.33tl4
LP.POB~
13.6214 13.9a73 -3.3659
9.2uZl 3.1174
i! 09905 5.0736 “Q.3831
2. b450 2.~951 r). 0493
lo.&954 10.7876 3.1i)ta
:P-v8e?
id.5161 -0.5672
AC WAL PREDfCTEO HESIDUAL
AC 7UdL PREDICTFD RESIPUAL
HESIDUIN
At TUAL PREOIC TfD
PREOIClEO RE SlOuAL
ACTgcI!.
WEDIC TED RESIDUAL
AC 7UAL ?9. v900 LO.6304 0.3596
2 J
g
ii
%
2
4 i3 ;: 2
2. z 2. o 3
g $
PRCDICTFD RESIDUAL ACYUAL PREOICTFD RESIDUAL
s f: AC TuAL
.
3
-E
AC TUAL PREDICTED RESIDUAL
AC 7UAL f’RE9KfED RESIDUAL
15.6382 15.9765 -3.1383
lUr26ll AU.3439 -3,0827
1.1167
16.442ll
3.617L
17.3615
16)s
A3.1175 lZ.II5lU 0.2665
34.9313 0.2698
l9?U
L+.%b80
15a
-O.c)brO
l1.(1?7rr 11.94*1
-0.bO7f
32.5035 s3.1112
time
8. Hickman, L. Lou. Substitution and export demands
378
. . .
-ro
i 4 0’
B. Hickman, L. Lau, Substitution and export demands
-54 PcQ@ .--In
000
. . . 440 1
I
n)lw
I
379
3x0
B. Hickman. L. Law Suhstirution aud export demands
export price elasticities of demands. These elasticities have been computed for the year 19h9. using the formulact in eqs. (52) through (54), far both the static and dynamic with trend models, and are presented in table 5. For the static model. the cstimatcs range from a low of 0.45 (Spain) to a high of 1.W (US). with an avcragc of f_L7C1. For the dynamic modei. the short-run elasticities range from a low of 0.32 (Council of Mutual Economic kssistancc) to a high of I .04 (Sweden) with an aver-
age of 0.66: whereas the long-run elasticities ra,lge from a low of 0.43 (Council of ~~ut~lat Economic Assistance) to a high of 1.99 (Sweden) e of 0.95. The ;.anking b:J the magnitudes of the elasticiross the short and long runs. It is worthy to las consistently a n;latively low value for her export ereas the United States has consistently a relatively We conclude an already lengthy paper by presenting additional information on the preferred model for stt.idy by the interested reader without comment on our part. Table 6 contains a listing of the coefficients of the export demand functions for Model IV as specified in eq. (42), whereas table 7 shows the sample (1962 -69) and post-sample (1970) predictions and residuals from these equations.
keferences [ 11 P.S. Armington, + theory of demand for poducrs distinguished by place of production, International Man-ta.-y Fund Stiff Papers, Vol. XVI, No. 1 (March 1969) 159-176. [ 21 P.S. Armington, The geographic pattern of trade and the effects of price changes, lnternational Monetary Fund Staff Papers, Vol. XVI, No. 2 (July 1969) 177-199. I31 A.P. Barten, An import allocation model for the common market, Cahiers Economiques de Bruxelles, No. 50 (2e trimestre 19? I) 3- 14. [41 B.G. Hickmanv A general linear model of world trade, in: R. J. Ball and C. Moriguchi teds.), International linkage of national economic models (North-Holland, Amsterdam, 1972). IS) B.C. Hickman, Prices and quantities in a world trade system, Paper No. I, Project LINK Working Paper Se*ies, Economic Research Unit, University of Perz*ylvania, Philadelphia (August 197 1).