1) Professor, Graduate School of International Cooperation Studies, Kobe University. 2) Associate Professor, Kobe City University of Foreign Studies.
Kobe
University Repository : Kernel
Title
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION OF IMPORTS : SPECIFICATION AND ESTIMATION OF A BILATERAL TRADE LINKAGE MODEL
Author(s)
Toyoda, Toshihisa / Kuramoto, Mikio
Citation
Kobe University Economic Review, 43: 1-21
Issue date
1997
Resource Type
Departmental Bulletin Paper / 紀要論文
Resource Version
publisher
URL
http://www.lib.kobe-u.ac.jp/handle_kernel/81000909
Create Date: 2015-04-30
Kobe University Economic Review 43, (1997)
1
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION OF" IMPORTS: SPECIFICATION AND ESTIMATION OF A BILATERAL TRADE LINKAGE MODEL * TOSHIHISA TOYODA 1) AND MIKlO KUHAMOT0 2)
This paper is based on an empirical examination of the shifting patterns of the elasticities of substitution of imports from different trading partners for an importing country, when applied to a world trade linkage model. Among various trade linkage models that have been developed, that by Hickman and Lau (1973), which seems to be most theoretically satisfying, provides an estimate of a constant elasticity of substitution. However, the notion of constant elasticities of substitution, as given by Hickman and Lau, is too restrictive and awkward for an analysis of both differential elasticities among different combinations of trade partners and their shifting patterns over a certain time period. Specifically, we first approximate the cost-minimizing import price index for an importing country into a translog function and derive a multi-equation import share demand system based on recent developments of theory. We estimate this new trade linkage model by the SUR method using the data covering the period 1965-81 for Japan, North America, Western Europe, Oceania, other Asian countries, the Middle East and the rest of the world for four different goods and also for total goods. We conduct some simulation exercises of the predictive ability of the model using some additional observations for later years. Finally, we examine some implications of the results of the shifting patterns of the elasticities of substitution of imports for some selected countries (or regions) and goods. This is an interim report of our final goal of analyzing similar shifting patterns of the elasticities of substitution of imports over a longer time period including the 1990s, that research program being still in progress. The elasticity figures capture both the degrees of trade liberalization and competitiveness and therefore should provide us with some interesting information for the development of world trade.
*
This paper was completed when the first author was visiting the Australia-Japan Research Centre, the Australian National University (ANU). He wishes to thank Dr. Peter Drysdale of ANU and Dr. Richard Tyres of the University of Adelaide for their valuable comments. He also benefited from useful comments made by participants at seminars at the University of Essex, ANU and University of Western Australia. Finally, we are indebted to Mrs. P. Phillips of the International Economic Data Bank, ANU, for her assistance with our use of the international trade data.
1) Professor, Graduate School of International Cooperation Studies, Kobe University. 2) Associate Professor, Kobe City University of Foreign Studies.
2
TOSHIHISA TOYODA AND MIKIO KURAMOTO
I.
INTRODUCTION
Over the last three decades the economic interdependence of countries or geographical regions has been strengthened enormously, though some recent phenomena have weakened it somewhat. The clearest index that shows this strengthened interdependence is the growth rate of world trade as compared with that of world income or the elasticity of world trade with respect to world income; the average elasticity value for the period 19651985 was around 1.5, which is significantly greater than 1. Since the middle of the 1970s the world economy has undergone various changes. Reflecting these, the elasticity of world trade with respect to world income during the period from the 1950s through the early 1970s declined from a value that was probably close to 2 to around 1.2 during the 1980s. There are some special reasons for this decline. First, the volume of trade in primary commodities, including agricultural products and oil, has shown a stagnant or falling tendency. Second, the share of services in national incomes, has grown significantly, while it has remained practically unchanged in international trade. Third, some large debtor countries have been forced to curtail their imports as part of their domestic adjustment programs. And finally, despite some liberalization efforts, growing protectionism has been observed, particularly during the later period. Nevertheless, trade in manufactures has continued to increase, though more slowly than in the past. The annual rate of growth of exports of manufactured products declined from around 11 per cent during the 1960s to around 5 per cent during 1980-1985. Even so, it was still much higher than the rate of growth of commodity trade and higher than that of world income: in fact, the elasticity of trade in manufactures with respect to world income has increased somewhat in the 1980s compared with that of the 1970s. Also, since the 1970s we have observed some significant international transmissions of inflation, stagflation and disinflation, and also of some effects of the economic policies implemented in big countries. Therefore, many economists and policy makers have directed their attention to clarifying the channels of varIOUS aspects of the interdependence of countries or regions. All these facts may be interpreted as evidence that actual economic interdependence has not been weakened but strengthened. Corresponding to this development of the world economy, a substantial number of so-called international linkage models have emerged over the last two decades. An international linkage model may be defined as a set
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION
3
of two or more open-economy macro-econometric models each of which contains at least one variable belonging to another model as an endogenous variable t). The variables of one model appearing in another model are mostly related to merchandise trade, which is the major factor that links different individual models, though it may be desirable to accomplish a thorough, consistent linkage not only of merchandise, but also of other international transactions such as services, income transfers, and financial assets and liabilities. Individual open-economy macro-econometric models are usually linked in such a way that the exogenous variables in each model relating to foreign trade are made endogenous. Each open-economy model usually has its volume of exports determined exogenously, or explained as a function of (exogenous) foreign demand, and also the import price set exogenously, or determined by (exogenous) foreign prices. In this way merchandise exports and import prices usually play major roles in linking several open-economy models. However, there are several different approaches to modelling world trade linkage. In fact, some authors have made comprehensive surveys of representative models of world trade linkage; see, e.g., Amano et. al. (1980), Helliwell and Padmore (1984) and Italianer (1986). Therefore, we do not make any surveys of the topic in this paper. The purpose of our present paper is two-fold. First, we present a new approach to the modeling of bilateral trade linkage. Specifically, we apply a transcendental logarithmic functional form, a relatively flexible functional form, in specifying a bilateral import demand function. In this way, we can relax a serious limitation of an approach frequently proposed by Hickman and Lau (1973), which seems to be the most theoretically satisfying of the various approaches that have been presented. Secondly, analyzing and comparing the shifting patterns of the elasticities of substitution between imports from any two countries or regions and the price elasticities of imports, both for a certain country or region, we can figure out and assess quantitatively some aspects of structural change in world trade. The paper contains seven sections. The next section develops and specifies our general framework using a translog bilateral import demand function. Section ill gives a brief explanation of the data used in this study. Section IV explains estimates of the trade linkage model. Section V analyzes the shifting patterns of some of the elasticities derived from the 1 ) We owe this definition to Italianer (1986) p.2 ..
TOSHIHISA TOYODA AND MIKIO KURAMOTO
4
estimates of our model. Section VI looks at the predictive accuracy of our proposed model. The final section concludes our analysis indicating that our model can be a theoretically and practically reasonable alternative to the existing trade linkage models.
n.
THE TRANSLOG BILATERAL IMPORT DEMAND FUNCTION
Following Armington's utility tree approach 2) to specifying demand functions in foreign trade, we assume that total import demand for any good in a certain region is first determined and independently allocated among competing sources of supply by geographic regions. In this paper, we assume that not only total imports, but also export prices in each region, have already been determined in a first step, the values of which are usually provided by a macro-econometric model for each region in an international linkage model. Thus we deal herein only with the allocation decision of total imports. 3 ) Hickman and Lau (1973) used a quantity index of imports for each country or region of the CES type and obtained a bilateral import demand function as a result of cost minimizing behaviour. Although their approach is theoretically justifiable, it has fatal limitations in its application, at least in the following two respects. First, their use of identical and constant elasticities of substitution between the imports from any two countries or regions in a certain importing market can hardly be supported. For instance, there is no reason to justify the assumption that in the U.S. the elasticity of substitution between imports from Japan and from Europe and that between imports from Japan and from the Middle East are the same and that they remain constant over a sample period. Secondly, since their derived model was nonlinear, it was necessary for them to linearize it by Taylor's series expansion in which all export prices were set equal to unity at an arbitrarily chosen base period. However, we have found that the choice of the base period severely affects the model's predictive ability and that it accumulates significantly more predictive errors as the prediction period diverges further from the base period. 4) Our approach in this paper is an attempt to avoid these serious limitations. As in Hickman and Lau (973), we also start by assuming that there 2) See Armington (1969). 3) Recently, for example, Adams, Gangnes and Shishido (1993) have adopted this kind of two-step determination of imports for their analysis of the U.S.-Japan-World economy. 4) See Toyoda et. al. (1983).
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION
5
exists a quantity index of imports for each country or regIOn and that it can be expressed as: 5)
M ·= M·(Xt· X 2' . ••• X .) }
}
},
},
,
(1)
II}
where Xij is the constant dollar quantity of imports from the i-th region in the j-th market, or, in other words, the quantity of exports from the i-th region to the j-th region; we assume that the world economy consists of n countries or regions. Suppose that the j-th importing region attains a specified level of M j at n
its minimum import cost
L PXi)(ji,
where PXij is the export price index
i=l
from the i-th region to the j-th. Then, we have the following import price index as a dual import cost function: PMt = PMt (PXIj,PX2j,'" ,PXllj,Mt) n
=min xij
(L
PXjXij; Mi(Xij»Mt)
(2)
i=l
where PM*j is the import price index in the j-th market and the function PMt has the same characteristics that M j has. We further assume that the following transcendental logarithmic functional form provides an approximate description of the the exact minimum cost of imports in the j-th importing market given the vector of export prices and the quantity index of imports: 6) n 1 n n lnPMt = a OJ+ L a dnPXij+ 2 L L /3 ikjlnPXiJnPXkj i=l i=l=j
i=l k=l i=F-j k=l=j
n
(3) i=l
where the parameters are assumed to satisfy the following restriction: n
L i=l
a i j = 1 ; /3 ikj= /3 kij
for all k,j;
n
n
k=l
i=l
(4) 5) We assume that the function M j is pOSItIve, linearly homogeneous, nondecreasing, concave and at least twice differentiable. 6) Probably, Burges (1974) was the first attempt at specifying import demands in the form of a translog function. However, the present paper considers a completely different problem: we consider an elasticity of substitution between imported products from any two different trading partners in a consistent trade linkage framework, while he analyzed an elasticity of substitution between any two pairs of such production factors as capital, labor, and imports.
TOSHIHISA TOYODA AND MIKIOKURAMOTO
6
The restrictions ensure that PM defined above is linearly homogeneous in PMij and arbitrarily twice, continuously differentiable. Differentiating InPMt partially with respect to InPXij and using the Shephard lemma: fJPM fJPXij
(5)
Xij,
we get PXij PMj
fJlnPM fJlnPXij
fJPM fJPXij
PXijXij
(6)
PM
Note that this last expression in (6) shows the nominal relative share of imports from the i-th region in the j-th market since the numerator show the nominal values of imports from the i-th region and the denominator shows the nominal aggregate values of imports, both in the j-th region. Denoting this nominal relative share by Vij, and referring to equation (3), we obtain the following import share equation from the i-th region in the j-th market: n
Vij= a ij+
L
{3 ikjlnPXij+ {3 iMlnM (i,j = 1,2, ... ,n;i =1= j)
(7)
k=l
k*j
Let us define aikj as Allen-Uzawa partial elasticity of substitution between imports from the i-th and the k-th region in the j-th market. Then, we can obtain the following expressions in the case of the transcendental logarithmic price function: 7) aikj
aiij
{3 ikj+ v~- Vij 2
(i,j,k= 1,2, ... ,n;i=l=k)
(8)
(i,j, = 1,2, ••• ,n)
(9)
Vij
Also, the price elasticity of the j-th region's import demand for the i-th region's product when the k-th region's export price changes can be obtained as follows:' E ikj
f)
InXij
f) InPXkj
Note that in general
=Vij aikj (i,k,j=1,2,···,n;j=l=i,k) E ikj
is not equal to
E
(10)
ikj even if aikj has symmetry.
7) According to the definition of U;kj, it is expressed as Uikj =CjCikj/CijCIrj where Cj is the import price (cost) function in the j-th market, and Cij and Cikj are the first and the second derivatives of Cj with respect to export prices, respectively. Then, utilising equations (4), (5) and (8), we obtain (9) and (0).
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION
m.
7
THE DATA USED
We have used annual bilateral trade figures for the period 1965-1981, which were compiled by the United Nations. They are values of bilateral imports and exports of traded goods measured in current U.S. dollars. They cover trade values for 72 countries or regions, in addition to the world grand totals of imports and exports, and therefore comprise a 73 x 73 matrix for each year. Also, we have used data for two categories of commodities classified by the one digit Standard International Trade Classification (SITC) of the United Nations; they are manufactured products (SITC 5-8) and all goods (SITC 0-9). For our particular purpose, we have further compiled these figures into 8 X8 matrices aggregating countries and regions. Our final geographical regions consist of the following codes: 1. JA
2. NA 3. EU 4.0C 5. AS 6. ME
7. RW
Japan North America (U.S. and Canada) Western Europe Oceania (Australia and New Zealand) Asia except Japan and socialist countries The Middle East : The rest of the world other than the above listed countries or regions listed above.
We would expect the world balance measured in current U.S. dollars in a consistent way to be equal to zero since what are exports for one country are necessarily imports for another country. However, this is not the case in reality, particularly when we aggregate trade across commodities and/ or countries or regions. Therefore, in aggregating the data across countries or regions, we have paid particular attention to adjust them so that the values of the world exports equal those of the world imports. Export price indices were originally constructed in the following way: for primary goods, world price indices for 72 kinds of commodities were first made and then an aggregated commodity export price index for each country was compiled as a weighted average of the world price indices reflecting the export share of each commodity in the country. For manufactured goods, an export price index was compiled as a weighted average of unit values of individual traded goods. We have further aggregated these export price indices across individual countries or regions, reflecting their export shares, to get an export price index of each
8
TOSHIHISA TOYODA AND MIKIO KURAMOTO
commodity class for each €ountry or region. In a later stage of our research, we obtained similar trade figures compiled by the Inernational Economic Data Bank, ANU, for the period 1965-1986. Although the principal source of these data is also the UN's bilateral trade figures, they are not completely consistent with the data set mentioned above, reflecting differences In aggregation levels in commodities and geographical regions. Therefore, we have used the extended new data set only for our post-sample prediction simulations in Section VI.
IV ESTIMATES OF SHARE EQUATIONS We have estimated the system of import share equations (7), for the jth importing market by the Zellner ISUR. Specifically, we put such restrictions on parameters as in (4)8) and used an iteration in estimating a sample variance-covariance matrix of error terms to obtain consistent estimates of parameters. In each case we have estimated simultaneous equations for 5 regions, excluding each importing region and the rest of the world. The import price index defined by equation (2) is well-behaved if it is concave in bilateral export price indices, PXij , and if it is monotonously increasing. We can check our fitted translog import price index function for monotonicity and concavity based on our ISUR parameter estimates. First, as a necessary condition for monotonicity, at least the partial derivatives evaluated for the base year, when we put PXij = 1,9) a PMj / aPXij= a i, should be positive. In each case our parameter estimates of ai are revealed to be positive so that the monotonicity condition is satisfied. Second, the concavity of the import price index function is satisfied if the Hessian matrix, based on the ISUR parameter estimates, is negative semidefinite. Since it is known that every element of the Hessian matrix of the trans log function changes· at each point and that the concavity is not ensured globally, we check the Hessian matrix evaluated for the base year for the concavity condition as in the monotonicity one. We find that, except for AS market for SITe 0-9, and AS and ME markets for SITe 5-8, the concavity conditions are satisfied. Although it is not 8) The hypothesis of the linear homogeneity in PXij was rejected by likelihood ratio test statistics, expect for JA and RW markets for SITC 0-9, and JA and ME for SITC 5-8. 9) Of course, if the regularity conditions are not satisfied at the point of approximation, they are not so globally. However, on the other hand, satisfaction of the conditions at the point does not imply satisfaction in any neigborhood of the point.
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION
9
determined whether or not the Hessian matrices are statistically significant, the results cast doubt on the validity of the concavity assumption for the two importing markets, AS and ME. Some of the results for two particular importing markets, i.e., for Japan and North America, are exhibited in Tables 1-4. Tables 1 and 2 show the results for all goods, while Tables 3 and 4 show those for manufactured products. In the Tables, the first column shows exporting regions to the importing market concerned and the second column implies an estimate of each constant term. Other figures are estimates of {3 ikj in the share equation. Di exhibits estimates of coefficients for dummy variables, which are introduced whenever necessary to the regularity conditions, monotonicity and concavity. S.E. and D.W. stand for a standard error of the regression and a Durbin-Watson statistic for each equation, respectively. TABLE 1. ESTIMATES OF IMPORT SHARE FUNCTION WITH DUMMY VARIABLE FOR JAPAN: SITC 0-9 Canst. NA .2540a
PXNA
PXEU
PXoc
.0280
.0266
.0852
.0544
PXAS
PXME PXRW M D a a .0423 -.0503 -.1318 -.0,163 -.0272 a
S.E.
D.W.
.0104
1.91
-.0254
.0505 -.0387
-.0675
.0355
.0010
.0036
1.84
-.0380
-.1325 -.0280
.1388
-.0115
.0279
.0043
1.63
ED
.0758
OC AS
.0529 .1410
.1063 -.0238
-.0428
.0193
.0711
.0132
1.11
ME
.2744
.1341
.0068
-.0231
.0083
.0206
1.03
RW
.2020 .0965 -.0039 -.0811 a Where the t-value is greater than 2. b Where the t-value is between 1.5 and 2. Dummy variable takes 0 through sample period 1965-72, and 1 through 1973-81.
TABLE 2. ESTIMATES OF IMPORT SHARE FUNCTION FOR NORTH AMERICA: SITC 0-9 Canst. JA .1525a ED .2969a
.0179a
OC AS . 1289a ME
PXNA
.0222
PXEU . 1106a
.0691
PXoc
PXAS
PXME
PXRW
M
-.0406' .0111 .0019 -.1051 a .0745a .0181 a -.0449 -.0119 -.1410a -.0486 .0114" .0230a -.0142 a .0023 .0037a .,.0435 -.0389 a .0883a .0607a
.0731 a
RW .3307 a Where the t-value is greater than 2. b Where the t-value is between 1.5 and 2.
.0467"
.0114
.0107 a .1443 -.101Oa
S.E.
D.W.
.0148
1.31
.0135
1.05
.0016
1.48
.0069
1.67
.0096
0.96
TOSHIHISA TOYODA AND MIKIO KURAMOTO
10
TABLE 3. ESTIMATES OF IMPORT SHARE FUNCTION WITH DUMMY VARIABLE FOR JAPAN: SITC 5-8 Const.
NA .3835" EU
PXNA
PXEU
.1971" -14.66" -.0168
.3186a
PXME
PXRW
S.E.
D.W.
-.0438" .0145
1.76
-.0275" -.020P .0095
1.50
M
D
.0124
.0995" -.0281" -.0468
.0141 b
.1080
-.0057
b
.0179
.0007
.0029
.0035
1.88
.0219
b
.1223
.0481"
.0916" .0115
1.81
-.0415"
.0023
.0131" .0029
1.41
.0143
b
.0184 -.2122"
.0025
-.0011
RW .1661"
-.1425" 1.0207
b
.0964"
OC .0199" AS .1095" ME
PXAS
PXoc
-.0643
-.0029
-.0437
b
a Where the t-value is greater than 2. b Where the t-value is between 1.5 and 2. Dummy variable takes 0 through sample period 1965-72, and 1 through 1973-81.
TABLE 4. ESTIMATES OF IMPORT SHARE FUNCTION FOR NORTH AMERICA: SITC5-8 Const.
PXNA
PXEU
PXoc
JA .2837"
.1074
-.0476
-.0279"
-.1216
.0032 .0014
EU
.4728"
OC AS
.0074"
ME
.1501" .0007"
RW .0853"
S.E.
D.W.
-.0042
.0561" .0152
1.47
.0003
.0336
-.1596" .0228
1.24
-.0000
.0147"
.0051" .0013
1.81
-.0019
b
.0868" .0118
1.34
.0008
.0002
1.67
.0342"
.0105
PXAS
PXME
-.0314
.0037
.1321 " .0087 -.0285
-.0028
PXRlV
-.0790 b
M
.0004
a Where the t-value is greater than 2. b Where the t-value is between 1.5 and 2.
Generally speaking, the coefficients for export prices in each import share equation are revealed to be highly signficant for a demand system. For instance, there are 23 coefficients with t-values greater than 2 among the 39 coefficients for the Japanese market case for SITe 0-9 and 21 coefficients among the 33 for the North American market as can be observed in Tables 1 and 2, respectively: remember that the estimated values of the lower left-hand elements, which are symmetrical to the upper right-hand ones, have been omitted from these tables for simplicity. Furthermore, we observe that the coefficients for the import quantity index are mostly significant, implying that bilateral import share depends not only on bilateral export prices but also on import quantities.
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION
v.
11
SHIFTING PATTTERNS OF ELASTICITIES OF IMPORT DEMAND
The noted Hickman-Lau approach to modelling world trade linkage provides us with only one value of elasticity of substitution for an importing market regardless of the pair of importing partners. It also assumes that this value remains constant over a sample period. For instance, the elasticity of substitution of import demands for all products in the Japanese market for the period 1962-1969 was estimated as being 1.03 and 1.54 for the short-run and long-run values, respectively, by HickmanLan (1973). Similarly, Amano et. al. (1983) estimated the same elasticity for the Japanese economy as 0.01 and 0.05 for the short-run and long-run values, respectively, using quarterly data for the period 1970-1980. However, we have no supportable evidence that an elasticity of substitution of imported products is unique and constant over a sample period; it may vary for different pairs of trading partners and also from time to time, reflecting changes in the competitiveness of exporting regions and also in tastes in the importing market. 10) As mentioned earlier, an estimated elasticity of substitution of imported products based on the Hickman-Lau model should be considered as a value valid only around the base year, on which their final specification of the equation crucially depends. ll ) Therefore, in order to compare our estimated results with the ones based on the Hickman-Lau approach, we first re-estimated the Hickman-Lau model using our data set for the period 1965-1981 and choosing 1975 as the base year. We obtained the values of the elasticity for the Japanese market, for instance, which were 0.17 and 0.56 for the short-run and long-run values, respectively, for SITe 0-9, and 0.44 and 0.91 for the short-run and long-run values, respectively, for SITe 5_8. 12 ) To compare our results based on the translog function approach with these values of the elasticity of substitution between any pair of imported products in the Japanese market for 1975 for SITe 0-9 and SITe 5-8, Tables 5 and 6, are provided respectively, although we obtained such values for every year between 1965 and 1981. According to our results, it is easily seen that the unique and constant values based on the HickmanLau model, i.e., 0.17 in the short-run and 0.56 in the long-run for SITe 0-9, 10) Marquez (1990) estimated the bilateral trade elasticities using Engle's Band Spectrum estimator. Using the bilateral elasticities as raw data, he obtained associated multrateral estimates and noted the evidence that sole reliance on multilateral elasticities concealed valuable informations for international trade. 11) For further explanations of this point see Section II above or Hickman-Lau (1973) 12) We estimated the Hickman-Lau model assuming that the variance of the error term is proportional to the squared nominal share of trade in the base year, 1975.
TOSHIHISA TOYODA AND MIKIO KURAMOTO
12
hardly provide us with any important findings. For this product category in the Japanese market, for instance, the elasticity of substitution between imports from NA and OC is around 6.0 while that of imports from NA and AS is around 2.0. These differential values for the different pairs of trading partners are understandable because the main components of Japan's imports from OC are raw materials, fossil fuels and foodstuffs which may be highly substitutable for those from NA, while Japan's imports from AS were dominated by raw materials, oil and processed goods, in addition to foodstuffs, over the sample period which might be less substitutable with the imports from NA. That is, the choice of two trading partners may, in principle, give either a positive or a negative value and also differential absolute values for the elasticity of substitution, as we can observe in Tables 5 and 6. TABLE 5.
L
ESTIMATED VALUES OF ELASTICITIES IN THE JAPANESE IMPORTING MARKET FOR 1975. :SITC 0-9
~
k
Elasticities of Substitution: NA EU OC
-2.876
NA EU
°iki AS
ME
RW
2.630
5.990
1.996
0.282
-3.546
-2.422
-3.651
4.725
-0.726
-6.294
-18.905
-8.342
-0.197
15.323
-1.310
0.591
-0.776
-0.831
1.171
OC AS ME
-0.930
RW
S
k
NA
Price Elasticity : Ciki EU OC
AS
ME
RW
NA
-0.650
0.190
0.453
0.379
0.087
-0.455
EU
0.595
-0.175
-0.276
0.887
-0.225
-0.806
OC
1.354
-0.264
-1.428
-1.567
-0.061
1.965
AS
0.451
0.341
-0.630
-0.246
0.183
-0.100
ME
0.064
-0.052
-0.015
0.111
-0.258
0.150
RW
-0.802
-0.454
1.157
-0.146
0.363
-0.119
SHIFTING P ATTERNSOF ELASTICITIES OF SUBSTITUTION
TABLE 6.
1-
ESTIMATED V ALVES OF ELASTICITIES IN THE JAPANFSE IMPORTING MARKET FOR 1975. :SITC 5-8
S
k
Elasticities of Substitution: NA EU OC -0.247
NA EU
Uikj
AS
ME
RW
-0.386
-0.499
2.575
3.358
-2.255
-1.217
-1.889
0.119
4.092
3.844
-16.272
4.274
-10.838
5.452
-11.610
9.311
6.567
-70.616
-21.032
OC AS ME RW
1-
13
S
-11.074
k
NA
Price Elasticity: Cikj EU OC
AS
ME
RW
NA
-0.086
-0.117
-0.016
0.451
0.050
-0.283
EU
-0.135
-0.367
-0.061
0.021
0.061
0.482
OC
-0.174
-0.573
-0.523
0.749
-0.163
0.683
AS
0.899
0.036
0.137
-2.035
0.140
0.823
ME
1.173
1.240
-0.348
1.162
-1.061
-2.636
RW
-0.787
1.165
0.175
1.151
-0.316
-1.388
The lower parts of Tables 5 and 6 show the estimated values of the price elasticity of Japan's import demands for SITC 0-9 and SITC 5-8, respectively, for 1975. Note that, in our approach, not only own price elasticity but also cross price elasticities for each importing or exporting region can be calculated for each year. The values of the latter are exhibited in off-diagonal elements in Tables 5 and 6. Since the price elasticity depends on both the values of the elasticity of substitution between imports and of the nominal trade share as shown in equation (10), for example, it may be relatively large for many trading partners in particular years, such as 1975 just after the first oil crisis. It is seen from Table 5 that own price elasticities in the Japanese market for SITC 0-9 in 1975 are considerably different from each other. This result, reflecting the fact that the own price elasticities of imports from EU, AS, ME and RW have relatively low values, implies that the imports from these regions are more of the necessities for the Japanese market than those from other regions. We can also get the estimated values of the own price elasticity based on the Hickman-Lau model and on the same data base as we are using in this study, and we find that the values for NA, OC and AS, for instance, are -0.13, -0.16 and -0.14 so that the regional differences are
TOSHIHISA TOYODA AND MIKIO KURAMOTO
14
small. On the other hand, since our translog function approach puts very weak restrictions on a's, a's and also E 's can be more flexibly estimated and divergent from each other than in the case of the Hickman-Lau CES function approach. We have observed above that the cross-section values of a's and E 's for a particular importing region and for a particular year, i.e., for the Japanese market and for 1975, are to what degree different among chosen pairs of trading partners. Our approach can also provide us with the varying time-series values of these over the sample period. In the following, we look at the shifting patterns of a's and E 's In some interesting cases. FIGURE
1.
U231 :
SITC
5-8
0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 65
66
67
68
69
70
71
FIGURE
72
73
74
e 321, e 331
2.
:
75
76
77
78
79
80
81
77
78
79
80
81
SrTc 5-8
0.05 0 -0.05 -0.1 -0.15 -0.2 -0.25
e 331
-0.3
~
-0.35 -0.4 65
66
67
68
69
70
71
72
73
74
75
76
SHIFTING PATTERNS OF ELASTICITIES OF SUBSTITUTION
15
Figures 1 and 2 show how the export patterns of North American and European manufactures to the Japanese market have changed, in the form of the shifts in both elasticities. Over the sample period, the imports of manufactures took around 20-30 per cent of all imports into the Japanese market, but the shares of the imports of North American and European products in the Japanese market declined from 36 and 9 per cent to 20 and 6 per cent, respectively, over the sample period. The main reason for these declines is, of course, the steadily rising price competitiveness of Asian NIES and ASEAN countries. The U.S. has continued to keep its share, particularly in the area of high technology products, of the Japanese market but European products seem to have been replaced by Asian products, so that the elasticity of substitution between imports from NA and EU, 023l, has negative values, implying complementarity between NA and EU products, and an apparent tendency to grow more negative as in Figure 1. In any case, such unique and constant values of the elasticity of substitution among imports from NA and EU as those obtained by the Hickman-Lau approach, 0.44, cannot be supported by this clearly declining tendency of values. In Figure 2, let us examine the declining tendency of exports of European products to Japan in terms of the cross price elasticity of import demand, c 321, i.e., the upward shifts in the elasticity during the periods of the oil price hikes probably occur because European currencies depreciated vis-a-vis the U.s. dollar which temporarily restored the price competitiveness of European products. Figure 2 also shows the movement of the values of the own price elasticity of import demand for European manufactures in the Japanese market, implying that it was relatively stable until 1978 but gradually decreased subsequently. FIGURE
3.
71
72
