For the United Kingdom, the income elasticity estimate varies
from 1.5 to 2.1. The own-price elasticity ranges from -0.1 to -0.2,
whereas the cross-price elasticity is not significantly different from
zero. The data support the hypotheses of normality, homoskedasticity,
price: homogeneity, parameter constancy, and dynamic specification.
However, the residuals have serial correlation of order greater than
one, a problem not detected by the Durbin-Watson statistic. In view of
this serial correlation, it is difficult to give full credit to the test
resu..ts for the United Kingdom, which suggests that the associated
estinates should be seen as tentative.17

For the United States, the income elasticity ranges from 1.8
to 2.2. The estimate of the own-price elasticity ranges from -0.5 to
-2.9, whereas the cross-price elasticity varies from -0.4 to -2.9. The
test results reveal that, of the three hypotheses for the error term,
only homoskedasticity is rejected by the data with any consistency.
The Almon distributed lag with cross-price effects produces the more
reasonable estimates, even though this lag structure is not fully
supported by the data. The alternative specifications, while consistent
with the statistical criteria, do not have significant price
elasticities which is in direct contradiction to the available evidence
(Grossman 1982, Warner and Kreinin 1983).

The evidence of table 3 suggests several general propositions.
First, income elasticities estimated at the country level do not display

any tendency towards the estimates of either Cline (1984) or Dornbusch

1Twren the serial correlation problem is corrected, the estimates for
inecme, own- and cross price elasticities remain virtually unchanged.
The reason to present the specification with the serially correlated
errors is to maintain uniformity of specification across countries.


Almon

Homosked.

Koyck
‘Serial
Indep.

Normality

Table A3
Non-0il Imports from Non-OPEC Developing Countries

Homosked.

(Notes at the End of Table)

Indep.

Almon
Serial

Box-Cox Tests and Testing of Error Properties

Normality

Homosked.

koyek
‘Serial
Indep.

Normality

38

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43

Appendix 2

Definitions of Variables and Data Used

All data are in billions of U.S. dollars, quarterly at annual rates,

unless otherwise noted. Where source data differs, it has been scaled

to conform to this convention. A complete explanation of all source

abbreviations follows the data definitions.

Mi

MiLV

MiLO

MiPETV

iER

MiTO

LPXNO

= real non-oil imports of the jth developed country from

non-OPEC developing countries.

CMiLV - (MiLO * (MiPETV * iER/MiTO))]/LPXNO.

goods imports of country i from non-OPEC developing
countries (millions of $US, FOB), DOT line 71.

oil (crude and refined) imports of country i from non-OPEC
developing countries (thousand metric tons), OECD, divided by
0.136 (metric tons/barrel).

Petroleum imports of country i (local currency), IFS line Tia
{for Germany, Japan, U.K., U.S.J; BOC Cansim series BA3154
(erude) and B43157 (refined) [for Canada].

U.S. dollar exchange rate ($U.S./local currency), MDL:
quarterly average of series SXMBCD (Canada), SXMBDM
(Germany), SCDBJY (Japan), and SXDBUKP (U.K.).

Total oil imports of country i (thousand metric tons), OECD
divided by 0.136 (metric tons/barrels).

Non-OPEC developing countries non-oil export price index:
Weighted average of external trade deflators for manufacturers

and non-oil primary products (WB), rebased to 1972 = 1,


1

Although this test is powerless to discriminate among various
specifications for which the null hypothesis is not rejected, it
indicates whether a given dynamic specification is not valid.

Constancy in structural parameter estimates is needed to
forecast accurately the consequences of either policy decisions or
changes in the exogenous variables. However, structural parameters may
be changing because of changes in trade patterns during the process of
economic development or in government policies. Furthermore, one may
question the hypothesis of parameter constancy in light of the
pronounced changes in oil prices and exchange rates of the seventies.
To test for this hypothesis, (2) is first estimated with data through
1979 and then used to forecast non-oil imports through 1981. Under the
null hypothesis of parameter constancy the expected forecast error is
zero, and the associated test-statistic is (Chow 1960, p. 560)

“G(t)2/(T, - K)) ~ F(Ta, Ti" K).

T Ty
(6) ( Yat)? - YF acty?)/t, 7(
= =1 1

1 t

ima

t

where T, = number of observations in the estimation period,
T, = number of observations in the forecast period.

Price homogeneity may not hold in empirical analysis with
maercdata such as ours. Aggregation across commodities or use of unit
value indexes as a proxy for transaction prices may account for an
empirical rejection of price homogeneity. Therefore, it might be of
interest to examine whether price homogeneity holds. Given the
log-linear specification, testing for price homogeneity amounts to

expressing (2) in terms of price levels and then testing whether the sum


IFDP

NUMBER

269

268

267

265

264

263

262

261

260

259

258

257

256

255

254

International Finance Discussion Papers

TITLES

Canadian Financial Markets: The Government's
Proposal for Reform

Was It Real? The Exchange Rate Interest
Differential Relation, 1973-1984

The U.K. Sector of the Federal Reserve's
Multicountry Model: The Effects of
Monetary and Fiscal Policies

Optimal Currency Basket in a World of
Generalized Floating: An Application to
the Nordic Countries

Money Demand in Open Economies: A Currency
Substitution Model for Venezuela

Comparing Costs of Note Issuance Facilities
and Eurocredits

Some Implications of the President's Tax
Proposals for U.S. Banks with Claims on
Developing Countries

Monetary Stabilization Policy in an Open
Economy

Anticipatory Capital Flows and the Behaviour
of the Dollar

Simulating Exchange Rate Shocks in the MPS
and MCM Models: An Evaluation

Trade Policy for the Multiple Product
Declining Industry

Long Memory Models of Interest Rates, the
Term Structure, and Variance Bounds Tests

Currency Substitution and the New Divisia
Monetary Aggregates: The U.S. Case

The International Transmission of Oil Price
Effects and OPEC's Pricing Policy

U.S. Banks' Lending to Developing Countries:
A Longer-Term View

Conditional Econometric Modelling:
An Application to New House Prices
in the United Kingdom

51

OR(s)
Garry J. Schinasi
Richard Meese
Kenneth Rogoff

Hali J. Edison

Hali J. Edison
Erling Vardal

Jaime Marquez

Rodney H. Mills

Allen B. Frankel

Marcus H. Miller
Arnold Kling
Arnold Kling
Catherine Mann
Gary S. Shea
Jaime Marquez
Jaime Marquez
Henry S. Terrell

Rod Mills

Neil R. Ericsson
David F. Hendry


49

Jarque, C. and A. Bera, 1980, Efficient tests for normality,
homoscedasticity, and serial independence of regression residuals,
Economic Letters, 6, 255-259.

Khan, M. and K. Ross, 1975, Cyclical and secular income elasticity of
the denand for imports, Review of Economics and Statistics, 57, 357-61.

Khan, M. and K. Ross, 1977, The functional form of aggregate import
demand, Journal of International Economics, 7, 149-169.

Klein, L., 1984, World recovery and debt prospects, in B. Hickman (ed.)
International monetary stabilization and the foreign debt problem,
Proceedings of a Conference Co-sponsored by Project Link and the Federal
Reserve Bank of San Francisco.

Klein, L. and M. Nakamura, 1985, Singularity in the equation systems of
econometrics: Some aspects of the multicollinearity problem, in J.
Marquez (ed.), Economic theory and econometrics (Basil Blackwell,
Oxford).

Magee, S., 1975, Prices, income, and foreign trade, in P. Kenen (ed.),
International trade and finance: Frontiers for research (Cambridge
University Press, Cambridge).

Marston, R., 1971, Income effects and delivery lags in British import
demand: 1955-67, Journal of International Economics, 1, 375-399.

Riedel, J., 1984, Trade as the engine of growth in developing countries,
revisited, Economic Journal, 94, 56-73.

Seaks, T. and S. Layson, 1983, Box-Cox estimation with standard
econometric problems, Review of Economics and Statistics, 65, 160-164.

Thursby, J. and M. Thursby, 1984, How reliable are simple, single
equation specifications of import demand? Review of Economics and
Statistics, 66, 120-128.

United States Congress, Joint Economic Committee, 1984, Hearings on
International Debt, March 28.

Warner, D. and M. Kreinin, 1983, Determinants of international trade
flows, Review of Economics and Statistics, 65, 96-104.


21

rate.£1 To the extent that OECD countries, as a whole, will not
sustain a 4.3 growth rate, these findings suggest that OECD growth,
important as it may be, will not be the decisive factor in enabling

borrowing countries to service their debt on a sustainable basis.

6. Coriclusions
The objective of this paper has been to estimate income and price
elasticities of non-oil imports of major industrial countries from
non-OFPEC developing countries. These elasticities have been the subject
of increased attention recently in view of their importance for
designing policy responses to the debt crisis. Despite their
importance, a review of the literature reveals sharply divided views
regarding their magnitudes. This lack of consensus stems from three
sources: use of multilateral trade flows aggregated across countries,
omission of price effects, and reliance on ordinary least squares for
parameter estimation, The elasticity estimates derived in this study
eliminate each of these limitations.

The empirical results at the country level yield an aggregate

income elasticity that varies from 1.3 to 1.6, a relatively narrow range

21cline has pointed out to us that his average elasticity is approximately
2, be:.ow his marginal elasticity estimate of 3. The lower average
elasticity is due to both a subjective interpretation of what the
average OECD growth rate is and a negative intercept in his estimating
equations (see Cline 1985). A negative intercept implies a declining
trend in imports of industrial countries from developing countries, a
trend not borne out by the data. More likely, a negative intercept is
the result of omitted variables and measurement errors that impart an
upward bias to the marginal income elasticity. More importantly,
Cline's (1984) long-term projection model relies on the marginal and not
the average elasticity. In any event, substitution of his average
elast:.city and zero price elasticity into (9) yields a critical growth
rate of 2.7 percent, well below our growth estimate.


Homosked.

Almon
Serial
Indep.

Normality

Homosked.

Koyck
Indep.

Normality

Table A3
(continued)

Homosked.

Almon
Serial
Indep.

Normality

Homosked.

Koyck
Indep.

Normality

a

39

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Japan 1
Japan 2
Japan 3
Japan 4


Despite the increased attention given to these elasticities,
an examination of the more influential studies reveals a lack of
consensus regarding their values. Dornbusch (1985) states that

"...the elasticity estimate of LDC export growth with respect

to OECD growth cannot be pinned down. ... At this stage there

is certainly no firm finding, here or in the literature,

regarding the elasticity." (p. 336-37)

Unsatisfactory as it may be, Dornbusch's characterization is quite
accurate. Existing estimates of the income elasticity for non-oil
exports of developing countries range from 1.3 (Goldstein and Khan 1982)
to 4.7 (Dornbusch 1985). Differences this large in elasticity
estimates need to be addressed because of their importance for policy
design in both debtor and creditor countries.

To place the analysis in perspective, section 2 reviews the
more influential papers in this area. This review reveals that existing
elasticity estimates are subject to biases arising from the omission of
relevant variables, country aggregation, and simultaneity, all 2f which
“Limit the applicability of existing estimates to practical problems,
Section 3 describes the import demand model used to estimate income and
price elasticities of non-oil imports of Canada, Germany, Japan, the
United Kingdom, and the United States from non-OPEC developing countries.
Econometric estimation of these elasticities requires a fair amount of
sensitivity analysis coupled with hypothesis testing. This paper tests
the maintained assumptions for the error term (normality, serial
independence and homoskedasticity), the structural Stability of
parameter estimates, the homogeneity of degree zero in prices, and the

dynamic specification.


32

Figure Al displays the log-likelihood function for each value
of \ for all specifications for all countries. The results reveal a
log-likelihood function almost invariant to the choice of Box-Cox
parameter. One possible reason for this invariance is the constancy of
the import-GDP ratio (see Appendix 2), which would give the same income
elasticity estimate for either A=0 or A=1.

However, to find that elasticity estimates might be invariant
to the choice of A is not equivalent to saying that the properties of
the error term are invariant to the choice of 4, a point stressed dy
Seaks and Layson (1983). They argue that the optimal A is influenced by
the presence of heteroskedasticity. To recognize this influence, they
derive the log-likelihood function with (proportional )
heteroskedasticity, under the assumption of normality. The approach
followed here is to test the assumptions behind the error term before
altering the likelihood function. After all, if the residuals do not
behave according to the normal distribution, then there is no point in
deriving its log-likelihood function with or without heteroskedastic
errors.

Table A3 indicates whether a given specification passes (P)
or fails (F) the assumptions of normality, serial independence, and
homoskedasticity for each value of 4. Out of 440 cases (11x8x5), the
hypothesis of normality is rejected in 14 instances (Canada 9, Japan 1,
United States 4), the hypothesis of serial independence is rejected in
81 instances (Canada 1, United Kingdom 80), and the hypothesis of
homoskedasticity is rejected in 57 instances, all of them for the United
States. The results for the United Kingdom indicate serial correlation

of order four, which does not necessarily invalidate the choice oF ),


(1985). Rather, they reveal a tendency towards a value of 1.5, which is
consistent with the evidence of Thursby and Thursby (1984) and Goldstein
and Khan (1985). To emphasize these differences, table 4 uses the
results of table 3 to compute income and price elasticities for an
OECD-aggregate. The results indicate that the aggregate income
elasticity varies between 1.3 and 1.6, which is not only a narrow range
of variation, but one that is far below the elasticity estimates of
Cline and Dornbusch. 18

Second, with the exception of Canada and the United Kingdom,
the estimates of the own-price elasticity are smaller than both -1 and
the cross-price elasticity. This evidence suggests that non-oil imports
from developing countries face greater competition from domestic gcods
than from exports of developed countries, which is consistent with
the findings of Grossman (1982). From a commercial policy standpoint,
large own-price elasticities suggest that protectionist actions might be
effective in eliminating competition from developing countries. But by
the same token, this effectiveness might exacerbate debt-servicing
difficulties of the latter countries with a potentially adverse feedback
effect on OECD countries. Third, the Koyck lag adjustment seems tc
receive greater support from the data than the Almon specification, a
finding already noted by Thursby and Thursby (1984).

Overall, the elasticity estimates shown in table 3 are

consistent with both economic theory and estimates from independent.

18xote that Riedel estimates an income elasticity close to ours, despite
his assumption of no price effects. However, his analysis is valid

until 1978 and refers to manufactured goods only, which because of their
relatively high price elasticity, tend to display relatively small price
variations that might lead to statistically insignificant price effects.


24

Table 2
Non-oil Imports from Non-OPEC Developing Countries
Income Elasticities and Country Aggregation Biases

1974-1981
Income Ho: ni=Nus Ho N{=N

Level of Elasticity - F(2,145) F(5,145)
Aggregation n R? (sig.level) (sig.level)
Canada 1.265* -0.03 6.162

(0.003)
Germany 1.013* -0.01 6.036

(0.003)
Japan -1.209* -0.03 6.112

(0.003)
United 0.239* -0.03 6.108
Kingdom (0.003)
United 5.931 0.27
States
Pooled data: 1.595* 0.01 2.546
fixed effects (0.03)
Aggregate of 2.858 0.16

5 Countries

* Coefficient not significant at the 5 percent significance level.

The dependent variable is the growth rate of non-oil imports from. non-
OPEC developing countries, and the explanatory variable is the ir.come
growth rate for the associated country bloc.

Column 3 presents test-results for the hypothesis that the income
elasticity of the itn country equals the U.S. income elasticity.

Column 4 presents the test-result for the hypothesis of a common income
elasticity across countries.


20

derive a relation between OECD growth and interest rates consistent with
sustainable debt servicing:
(9) Yes 2 1/((Py/Y) C1 +e) +n),
where %* is the threshold OECD growth rate and r is the nominal interest
rate. According to (9), {* is inversely related to both the
terms-of-trade effect and the income elasticity, but directly related to
both the own-price elasticity (e<0) and nominal interest rates.
Substituting n=1.6, e=-0.7, and Py/Y-0.97 into equation (9),
we find that an increase in interest rates of 1 percent must be
accompanied by a 1/2 percent increase in OECD growth for debtor
countries to service their debts on a sustainable basis.19 Thus if
interest rates are equal to 8 percent (as in Cline 1984, p.60), then
servicing sustainability requires an OECD growth rate of at least 4,3
percent, which is above Cline's (1984, p.67) estimate of 3 percent, 20
The difference between these two growth estimates can be traced to
Cline's assumption of a zero price elasticity and to his relatively high
income elasticity estimate, since both of these considerations tend to

lower the critical growth rate associated with a given interest

19hese parameter estimates are found in table 4, and they provide the
lowest threshold growth rate. According to the regression results of
footnote 14, a one percent increase in Y raises Px by 0.97 percent. Chu
and Morrison (1984) estimate an income-price elasticity of 2, but their
analysis excludes manufactured goods, which tend to have large price
elasticities for demand and supply, and thus relatively small price
changes in response to demand-supply shifts.

20The critical growth rate is derived as 4.3= 8/(0.97(1-0.7)+1.6). With
simulations of the LINK model, Klein (1984) finds a critical growth rate
of 4.66 percent per year.


33

since there is no evidence of first-order serial correlation. The
results for the United States indicate a fairly well grounded
heteroskedasticity problem for the Almon distributed lag. In contrast,
the data supports the three hypotheses for the Koyck distributed lag for
d>0.4, for which the hypothesis of A=0 cannot be rejected. These

results, when combined with the ease of interpretation of a logarithmic

formulation, provides some basis for the choice of functional form of

(2).


15

equations per country. Table 3 displays the long-run estimates of
income: and price elasticities and the significance levels associated
with each of the six hypotheses described in section 3.14

For Canada, the long-run income elasticity ranges between 1.0
and 1.5. The own-price elasticity ranges between -0.3 and -0.9 whereas
the cross-price elasticity varies between -0.4 and ~0.9. Based on the
test-results, the best specification for Canada allows cross-price
effects with a Koyck distributed lag. For this specification, it is not
possible to reject the hypotheses of normality, serial independence, and
homoskedasticity. Furthermore, the data support the hypotheses of price
homogeneity and parameter constancy.

For Germany, the income elasticity ranges between 1.9 and
2.0, which is a narrow range of variation. The own-price elasticity
ranges from -1.0 to -1.3, whereas the cross-price elasticity varies from
-0.1 to -0.5. The only specification fully supported by the data has a
Koyek distributed lag with no eross-price effects. For this
specification, all three hypotheses about the residual are accepted;
similarly, the hypotheses of price homogeneity, and parameter constancy

cannot be rejected by the data.

14predicted values for the export price are generated according to
(t-statistics in parentheses):

Pyt = 0.82 + 0.000757%¢-1 ~ 0-0173EXt=1 + 0.0174PDOME-1, R2=0.95,
(0.9) (1.8) (-4.6) (3.0) 19711-1981IV

where Y is our five-country GDP aggregate, in 1972 dollars and exchange
rates; EX is the weighted average value of the dollar, and PDOM is the
weigited average value of consumer price indexes for the five countries
with 1972 exchange rates. The sample means of these variables are 1.885
for Px, 2313 for Y, 100.841 for EX, and 60.69 for PDOM.


3. Empirical modeling of import demand

3.1 The imperfect substitute model

This analysis assumes that domestically produced goods are imperfect
substitutes for non-oil imports from developing countries, and that these
imports are separable with respect to oil purchases. As a result, the
demand for these imports can be expressed as

(1) Me = F(Yt, Pts Qt),

>
where Fy>0, Fp<o, Fq.0,

Me = quantity of non-oil imports from developing countries,
Yt = importer's real income,

Pt = price of imports relative to the price of domestic goods;
= (Pxt/Ep)/Pyt 5

Pxyt = dollar price for non-oil exports of developing countries;

Et = exchange rate, dollar/foreign currency;

Pyt = GDP deflator for the importer;

Q, = price of imports relative to price of developed countries;

Pxt/Qxts
Qxt = dollar price for exports from developed countries.

According to (1), increases in either domestic income or domestic prices
raises non-oil imports from developing countries, In addition, (1)
allows imports from developed countries to be either complements (Fg>0)

or substitutes (Fg<0) to non-oil imports from developing countries.

3,2 Econometric Specification and Hypothesis Testing

For empirical applications, economic theory provides generally little
more than the selection of relevant variables and their anticipated
effects. As a result, pinning down elasticity estimates requires a
significant amount of hypothesis testing. This paper tests for the
functional form of (1), for the maintained assumptions of the error term
(normality, homoskedasticity, and serial independence), for the parameter

restrictions imposed in the dynamic specifications, for parameter


30

zero in estimation. But, for the sake of sensitivity, the results
presented here include the case where 6 is non-zero.

Table Al presents long-run elasticity estimates following the
format of Table 3. On the whole, a comparison of the results between
these two tables reveals that the use of potential output (as
constructed here) produces no major changes in the elasticity estimates
or in the various test-statistics. The two exceptions are the United
Kingdom (where there the income elasticy increases and the own-prive
elasticity declines) and Canada (where there is an increase in the
significance levels of the various hypotheses). It must be emphasized
that this robustness of parameter estimates rests on the assumption that
potential output can be estimated as trend of actual output. A more
complete sensitivty analysis should address the issues raised by Haynes

and Stone (1983).

A1.2 Quantum Effects
A second limitation of equation (2) is the assumption of no quantun
effects -- that is, the response of imports to changes in either prices
or income is the same regardless of the magnitude of the changes in
these variables. The hypothesis of quantum effects is examined here by
postulating the following parameter behavior:

ay(L) = a = a9 + ayy AlnY,

ag(L) = ag = agg + apy AlnPy,

a3(L) = ag = a39 + a3, AlnQ,.

With the above formulation, testing for the hypothesis of

no-quantum effects amounts to testing whether 411, 421 and a3; are

zero. Once again, it is assumed that the lagged response of imports is


27

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Higher growth in industrial countries is certain to increase non-oil
imports from developing countries with a corresponding impact on their
price, Although the small country assumption might be relaxed by using
two-stage least squares, many studies in this area rely on ordinary
least squares for parameter estimation.2

Third, an examination of the nature of the data used in
previous studies suggests that available elasticity estimates are not
strictly comparable to each other. On the one hand, Cline (1984)
focuses on multilateral non-oil imports of the bloc of industrial
countries, which include non-oil imports of OECD countries from
themselves.3 On the other hand, Dornbusch examines multilateral
non-oil exports of developing countries, which include non-oil exports
of developing countries to themselves. It is immediately clear that
neither of these two measures of multilateral trade are suitable for
estimating the income response of imports of industrial countries from
developing countries. Furthermore, changes in the country composition

of multilateral trade flows might be responsible for the erratic

2crossman's (1982) analysis does not suffer from the limitations
mentioned above, but it only applies to 0.7 percent of U.S. imports.
(The 1978 value of U.S. imports from developing countries in Grossnan's
paper is $1.2 billion, whereas U. S. total imports in 1978 were $183
billion, $42 billion of which were imports from non-oil developing
countries (IMF, Direction of Trade, Yearbook 1981, p. 380).) This study
makes it possible to establish the extent to which Grossman's findings
extend to a non-oil commodity aggregate and the degree to which they
apply to other industrial countries.

3this point has already been observed by Dornbusch (1985). Note that
according to IMF data (Supplement on Trade Statistics, 1982, p.80), only
16 percent of total imports of the OECD region come from non-oil
developing countries. This share is even lower for non-oil imports.
Similarly, according to IMF data only 57 percent of exports of
developing countries flow to industrial countries.



A second contribution of this paper is the construction of
quarterly time series for non-oil imports for the above five countries
from rion-OPEC developing countries. To our knowledge, this kind of
information is not publicly available and thus section 4 describes the
methodology used to construct the data. Section 5 presents our
empirical estimates for income and price elasticities for each of the
five countries and uses them to examine the relation between OECD growth
and interest rates consistent with sustainable debt servicing by
developing countries. The main findings are that the OECD-aggregate
income elasticity varies between 1.3 and 1.6, and that sustainable debt
servicing requires a 1/2 percent increase in OECD growth for every 1
percent increase in interest rates. Section 6 summarizes the paper and

suggests avenues for further research.

2. Review of Existing Studies
Table 1 lists the more salient features of several studies of developing
count:ies' exports. An examination of these features reveals important
limitations that limit the applicability of their findings to practical
questions. First, the own-price elasticity of import demand is commonly
assumed to be zero. In addition to being unrealistic, this assumption
might induce a bias in the estimate of the income elasticity and thus be
respoisible for much of the controversy about its magnitude.

Second, importers are generally treated as if they were small
econonies, a tenable assumption for countries with little participation
in international trade, but an untenable one for most of the countries

considered here, either separately or when they are treated as a bloc.


For Japan, the own-price elasticity ranges from -1.3 to -1.4
whereas the cross-price elasticity turns out to be not statistically
significant. The results also point to a negative income elasticity
that ranges from -0.2 to -0.4, being rather significant for the Almon
specification. A negative income elasticity for imports is not
necessarily in contradiction with economic theory if domestic goods are
perfect substitutes for imports. Under this assumption, Magee (1975)
establishes that imports will have a negative income elasticity when the
income response of the domestic demand for importables is sufficiently
gsmall.15 In this case, an increase in income is associated with
greater production of domestic importables, which reduces the import gap.
Because the composition of developing countries' exports has been
shifting towards the kind of goods that Japan produces, an increase in
real income in Japan means greater availability of domestic importables,
which reduces Japan's imports from developing countries.16 Note that
this negative income elasticity is not due to a violation of the
maintained hypotheses for the error term, Furthermore, the data support
the hypotheses of price homogeneity, lag structure, and parameter

constancy.

15~his condition can be stated as (SI/DI)ns,y>nd,y» Where ng,y and ng,y
are the domestic income elasticity of supply and demand respective.y,
and SI and DI are the domestic supply and demand for importables.

16Japan's negative income elasticity for these imports might be the result
of a sustained shift away from developing countries and towards

developed countries as a source of inputs. Lower quality and unreliable
supply of the former countries may account for such a shift. Khan and
Ross (1975) find a negative elasticity for potential income in total,
multilateral imports of Japan. Appendix 1 allows for cyclical and
secular income effects, but the results still point to a negative income
elasticity.


differences in country elasticities are significant, they are estjimated
with a pooled sample of our five countries (fixed effects). With an
F-test for the hypothesis of equal elasticity across countries, the
evidence suggests that such differences are indeed significant. The
results of table 2 also suggest that the behavior of U.S. imports might
be the dominant force in explaining the behavior of aggregate imports
and thus largely responsible for the differences in estimates due to
country aggregation. This last possibility is empirically supported by
F-tests rejecting the null hypothesis of equality between the U.5.
income elasticity and any other country's income elasticity.

Several conclusions emerge from this review and from the
results of table 2. First, growth in non-oil exports of developing
countries is inadequately explained by growth of importers alone,
Failure to account for price effects and dynamic adjustments could result
in biased and erratic income elasticities. Second, estimation methods
need to recognize that ordinary least squares do not capture general
equilibrium effects, which might be responsible for a simultaneit:y bias.
Finally, reliance on multilateral trade flows aggregated across countries
might impart a certain instability to parameter estimates. Changes in
the country composition of an aggregate trade flow could lead to changes
in the aggregate elasticity estimate even if the elasticities at the

country level remain unchanged.


22

of variation, and one which suggests an upward bias for estimates of
previous studies. With respect to the question of debt-servicing
sustainability, our elasticity estimate suggests that reliance on growth
of industrial countries to pull out the developing countries from the
present debt crisis is not warranted.

This conclusion is subject to a number of qualifications.
First, the analysis has dealt with the bloc of non-OPEC developing
countries that is a larger aggregate than just debtor countries. It is
conceivable that bilateral trade between the United States and major
debtors is characterized by higher income elasticities than those
obtained here. We are not aware of any available evidence on the
magnitude of these elasticities, and it seems that their estimation is a
natural avenue for future research. Second, interest rates and OECD
growth are not independent of each other, as the analysis of this paper
has assumed; a more general equilibrium analysis is needed. Finally,
some of the elasticity estimates need further refinement and further
testing. Though this analysis has not exactly pinned down the
elasticities, it has narrowed down considerably the range of
disagreement. Given these limitations, and the importance of this

subject, it seems that further research will yield positive returns.


International Finance Discussion Papers
Number 277

April 1986

CAN DEBTOR COUNTRIES SERVICE THEIR DEBTS?
INCOME AND PRICE ELASTICITIES FOR EXPORTS
OF DEVELOPING. COUNTRIES

by

Jaime Marquez
Caryl McNeilly

NOTE: International Finance Discussion Papers are preliminary materials
circulated to stimulate discussion and critical comment. References in
publications to International Finance Discussion Papers (other than an
acknowledgment by a writer that he has had access to unpublished
material) should be cleared with the author or authors.


45

Canadian Statistical Review, published quarterly by Statistics

"Lange Reihen der vierteljahrlichen volkswirtschaftlichen

Gesamtrechnung fur die Bundesrepublik Deutschland", published

Economic Trends, published monthly by U.K. Central Statistical

Macro Data Library of the Federal Reserve Board of Governors.

published monthly by U.S. Department of Commerce, Bureau of

Sources

BOC Bank of Canada .

BOJ Bank of Japan.

CSR
Canada.

DIW
quarterly by Deutsches Institut fur Wirtschaftsforshung,
Berlin,

DOT Direction of Trade Statistics, published monthly by the
International Monetary -Fund.

ET
Office.

IFS International Financial Statistics, published by the
International Monetary Fund.

MDL

NCA National Income Accounts in Survey of Current Business,
Economic Analysis.

OECD Quarterly Oil Statistics, Tables B1 (Crude + Natural Gas
Liquids + Refinery Feed Stocks) and B2 (Total Products),
published quarterly by OECD International Energy Agency.

WB

World Bank, Economic Analysis and Projections Department,

Division of Global Analysis & Projections.


The error term is generally assumed to satisfy the
assumptions needed for classical inference -- namely, serial
independence, normality, and homoskedasticity. While serial correlation
is usually tested, the other two assumptions are taken as valid. This
paper follows the suggestion of Thursby and Thursby (1984) to examine
the possibility of serial correlation of order greater than one, in
addition to the Durbin-Watson statistic. To this end, we test the null
hypothesis that all the coefficients of an AR(4) for the residual are
equal to zero.

The hypothesis that the residuals behave according to the
normal distribution is tested with the Jarque-Bera statistic (Jarque and

Bera 1980), denoted here as JB:
(3) JB = T(u3/(6u2) + (1/24) (u4/u2 - 3)2)~ x2(2),

where T is sample size and Wy is the jth central moment of the
distribution of the estimated residuals, i. The first term of (3)
measu*es the skewness of the distribution of & whereas the second term
measures the departure of the estimated kurtosis from the kurtosis
associated with the normal distribution. The test for homoskedasticity
is based on the work of Engle (1982) on autoregressive conditional

heteroskedasticity (ARCH). Based on the following model
a a a?
(4) E(G?;0,-1) = Yo + Yi Ot-1,

the null hypothesis of homoskedasticity cannot be rejected if Y1;=0,
which is tested with a t-statistic.
The response of imports to changes in either income or prices

is generally subject to some delay. Contracts, delivery lags, and


constancy, and finally, for price homogeneity. Appendix 1 tests
these hypotheses when the income elasticity is allowed to vary over the
business eyele.®

The results from Box-Cox tests (presented in appendix 1),
provide partial support for a log-linear formulation:7
(2) Img = a9 + Seo, gbtinyy + Tyo, ghtinPy + Dpa, gh&ind, + s1nMe-

+ TieiSa + OD + ug,

where L is the lag operator, S; iS a seasonal dummy for the ith quarter,
D is a dummy for one-time events (e.g., dock strikes), and u is a white
noise random term. Besides being the more commonly used formulation,
the choice of (2) allows the parameters to be.interpreted as
elasticities, which facilitates the computation of the test-statistic

for the hypothesis of price homogeneity.

5The above tests are performed with the GIVE computer software developed
by David Hendry. With the exception of normality and homoskedastiicity,
Thursby and Thursby (1984) test for these hypotheses as well as for the
independence between residuals and predetermined variables. Because
this paper uses two-stage least squares for parameter estimation, such
independence is not being assumed here.

6This possibility has been examined by Marston (1971), Khan and Ross
(1975), and Haynes and Stone (1983), among others. In the present
context, such distinction might be useful to determine the long-run
prospects for the balance of payments of developing countries.

Tthe Box-Cox tests of Khan and Ross (1977) for total multilatera:. imports
Suggest a log-linear formulation. For non-oil imports from non-oil
developing countries, the Box-Cox tests provide only partial support for
a log-linear formulation because the log-likelihood function is very
flat. In turn, this flatness is due to a relatively constant import-GDP
ratio throughout the sample (see data appendix). Although this
constancy suggests that the elasticity estimates are invariant to a
choice between a logarithmic or a linear specification, this invariance
does not apply to the properties of the error term, a point stressed by
Seaks and Layson (1983). The Box-Cox tests performed here check for
serial correlation, homoskedasticity, and normality, the last of which
is the fundamental basis for standard Box-Cox tests.


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29

Appendix 1

Estimates for Alternative Specifications

This appendix presents elasticity estimates which allow for both
business cycle and quantum effects. In addition, it examines the extent

to which the functional form of (2) is supported by the data.

A1.1 Cyclical and Secular Responses to Output

A number of empirical studies have shown that the income elasticity
might vary over the business cycle. From an empirical standpoint, the
key question is to decompose a given income path into its secular and
its cyelical components. Khan and Ross (1975) and Marston (1971)
estimaze secular (or potential) income as a trend of actual income,
which permits computing income fluctuations as the difference between
potential and actual income. This approach has been criticized by
Haynes and Stone (1983), who argue that a spectral decomposition of
output provides a more reliable estimation procedure.

Given that the Multi-Country Model operates in time domain
only, and given that Haynes and Stone acknowledge that their approach
has certain limitations, this paper estimates potential output as a
trend of actual output. Under this assumption, equation (2) becomes
(a1) In Mg = a9 + a, 1m YPOTE + ag In (GDP/YPOT)4 +

+ a3 (L) In Py + oy (L) In Qe + 6 In Me-4,
where YPOT = EXP(8q + 8, TIME) with the B's estimated by OLS. Note that
(A1) implicitly assumes that a decomposition of output into its cyclical
and secular components eliminates lagged effects of income on imports

(Marston 1971). This observation suggests that the value of 6 should be


Figure A2
Non-Oil Imports from Non-OPEC Developing Countries 46
Relative Prices

United States = 418

==
a

~ =
[es a | | pili iit es
1975 1977 1979 1981

Japan = — 0.9

| | | 1 Lititiittitity
1975 1977 1979 1981

Germany i= > —~ 12

——— wee eo
== ys

| | | | Liritiii titi og

1975 1977 1979 1981

United Kingdom

| | i | [iiitiittitity,
1975 1977 1979 1981
— —21
Canad. = _--—— qu
anada SI, =< a
| l a I Lirrtittiiitt gs
1975 1977 1979 1981


28

Table 4
Income and Own-Price Elasticities
Country Level and Aggregate Level

OECD4
Shares Income elasticity Own-Price elasticities
smallest largest smallest largest

Canada 47 0.95 1.52 -0.85 -0.25
Germany 16.0 1.93 2.02 -1.30 -0.95
Japan 21.0 -0.38 -0.13 1.39 -1.25
U.K. 8.6 1.35 2.06 -0.22 -0.11
U.S. 49.7 1.81 2.20 -2.90 -0.50
Aggregate 100 1.29 1.64 2.00 -0.68

a. Normalized shares in OECD GDP. For the actual shares in the OECD
aggregate, multiply by 0.70; these shares are obtained from the OECD
Economic Outlook, 1981, p. 16.


behavior of the aggregate elasticity estimates noted by Dornbusch
(1985).4

Finally, almost all of these studies rely on import relations
between country blocs. From a policy standpoint, aggregation across
countries allows us to study how exports of developing countries
fluctuate in response to the business cycle of all industrial countries.
But unless all importing countries are identical, the resulting
elasticity estimates are not helpful for analyzing the effects on trade
of developing countries of stabilization policies of a particular
importing country. From an econometric standpoint, the chief drawback
of country aggregation is the potential for aggregation biases.

To emphasize these biases, table 2 presents income
elasticities estimated using data at different levels of aggregation:
data for our five countries (Canada, Germany, Japan, the United Kingdom,
the United States) considered as one bloc, data at the country level,
and a pooled sample of our five countries. The elasticity estimates are
based on a linear regression of the growth rate of non-oil imports on
the GNP growth rate, which is the specification used by Cline (1984).
The elasticity estimated with data aggregated across countries is 2.9,
wrich is relatively close to the estimate of Cline (1984). However, the
elasticity estimates using individual country data range from -1.2 for

Japan to 5.9 for the United States. To determine whether these

4ane use of multilateral trade flows might bias the price elasticity.
For example, Bergsten and Cline (1983) do not allow for price effects in
their estimating equation. However, empirical tests using their
published data reveal that prices exert a negative, but insignificant,
influence on imports. This apparent absence of price effects might be
the result of a negative price elasticity for imports from non-OECD
countries being offset by a positive price elasticity for OECD exports
to themselves, which Bergsten and Cline include in their import data.


studies, possess a narrow range of variation, and satisfy a number of

statistical criteria. All of these considerations give some credence to

our estimates.

5.2 Implications of Our Findings for Debt Servicing

One of the most important questions currently faced by policy makers is
whether exports of debtor countries can grow faster than their interest
payments--that is, whether their debt-servicing requirements are
sustainable. Because these exports are tied to growth in industrial
countries, it might be of interest to estimate the OECD growth rate
consis’sent with sustainable debt servicing. To this end, total export
revenues are modeled as

(1) X = Px(¥) M(PX(Y)/(E Py)» ¥)/B,

where 8 represents the share of exports of developing countries to
industrial countries. Under the assumption of constant 8,

differentiation of (7) with respect to Y yields

(8) & = ((B,/f)1 + €) + nlf,
where x = growth rate of total exports in nominal terms,
Py = growth rate of the dollar price of exports,
Y = growth rate of industrial countries,
€ = own-price elasticity <0,
n = income elasticity >0.

According to (8), higher growth in industrial countries
translates into higher export revenues of developing countries through
two channels: an income effect, represented by n, and a price effect
which is decomposed into a terms-of-trade effect, By/t, and a direct
price effect, e. Both equation (8) and the sustainability condition

(growt:h in nominal exports2nominal interest rate) might be used to


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Table A2

Non-oil imports from Non-OPEC Developing Countries
Income and Price Elasticities

Quantum Effects

37

Long Run Elasticities Canada U.K. Germany Japan U.S.
Income

a10 1.17 0.89% 2.28 -0.17* 2,07

a44 0.04% 0.04% 0.54 0.06* -0.09*
Own--Price

220 -0.77* — -0.16* -1.16 -0.70  -0.71*

021 -1.68* 0. 38* -4,39 -2.78* 0.25%
Cross-Price

230 -0.06* 0.25% -0.49 -0.63* 0.25*

034 4.35% -0.95* 8.30 -0.89* -2.00*
R? (adj.) 0.39 0.47 0.94 0.22 0.90
Normality: JB 0.68 0.59 0.10 0.21 0.99
Homoskedasticity ARCH? -0.54 -0.70 0.69 1.36 4.75
Serial Indep.@ 0.23 0.99 0.80 0.98 0.99

* Coefficient estimate
level.

a. See notes in Table 3.

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Introduction
This paper estimates income and price elasticities of non-oil imports of
major industrial countries from developing countries. Besides their
traditional role in analyses of international linkages and trade
policies, knowledge of these elasticities is crucial to designing policy
responses to the existing debt erisis.! From the debtors!
standpoint, both stabilization policies and debt rescheduling agreements
hinge on balance of payment projections that are crucially dependent on
the choice of elasticity estimates. Moreover, whether these countries
will, in general, be able to service their external debt depends on the
response of their exports to growth in industrial countries, a response
that is ultimately determined by income and price elasticities.
Knowledge of these elasticities is also relevant for
policymaking in industrial countries. A restrictive monetary policy
stance in the United States makes it more difficult for debtor countries
to service their debt. Both the increase in interest rates and the
induced contraction in U.S. imports reduce the debt-servicing capacity
of debtor countries, a reduction that might feed back to the United
States as declines in exports and disruptions in financial markets. An
important component in determining the magnitude of these feedback
effects is the income elasticity for industrial-country imports from

developing countries.

lgee the studies of Cline (1984, 1985), Dooley et. al. (1983), Adams et.
al. (1983), Dornbusch (1985), Riedel (1984), Goldstein and Khan (1982),
and Bond (1985). For the debate on the policy implications of different
elasticity estimates for the United States, see the testimonies of
William Cline and Rudiger Dornbusch before the Joint Economic Committee,
March 28, 1984. See also the exchange between Cline and Dornbusch in
the Brookings Papers No.2, 1985.


Yi

LPXNO

iPGNP

44

converted from annual to quarterly data according to seasonal

pattern of non-OPEC LDC export unit value index, IFS line 74D.

Real income of ith developed country.

iGNP (1972 prices).

Canada: nominal GNP, Cansim series D40551 (millions of

Canadian $), divided by constructed absorption deflator, CSR

Table 1.2.

Germany: constructed from components (billions of DM), DIh.

Japan : constructed from components (billions of Yen), BCJ.

U.K. : nominal GDP (billions of pounds sterling), ET, Table 2,
multiplied by 0.62113 (implicit GDP deflator), ET, Table 4,

U.S. : NIA Table 1.2, line 1.

Relative price (foreign prices/domestic prices).

(LPXNO/iEI)/iPGNP.

Non-OPEC developing country non-oil export price index (WE,

defined above), divided by 1972 average value.

Spot Exchange Rate Index --$US/local currency exchange rate

(MDL, defined above), divided by 1972 average value.

GNP Deflator.

Canada: Nominal GNP (millions of Canadian $), CSR Table 1,2,

series D40551, Germany: Nominal GNP (billions of DM), DIW,

defined above).

Japan: Nominal GNP constructed from components (billions of

Yen), BOJ, divided by Real GNP (BOJ, defined above).

U.K.: Nominal GNP (billion of pounds sterling), ET Table 2,

divided by real GNP (ET, defined above).

U.S.: NIA Table 7.1, line 1.


42

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12

of price coefficients is zero, The test-statistic for this hypothesis

is distributed as F(1, T-K).10

4, Data construction
Central to this analysis is the availability of quarterly time series of
non-oil imports for Canada, Germany, Japan, the United Kingdom, and the
United States from non-OPEC developing countries. Since, as far as we
are aware, data of this nature are not publicly available, a deta:.led
explanation of the methodology for its construction and the associated
sources appears in the data appendix.'1

Non-oil imports from developing countries are derived as the
difference between total and oil imports, both from developing countries.
Data for each country's total imports from developing countries,
measured in dollars, are obtained from the Direction of Trade compiled
by the International Monetary Fund.'!2 pata for each country's oil
imports from non-OPEC developing countries, in value terms, are not
readily available. However, data on bilateral oil imports (crude plus

products) for each of the five countries from non-OPEC developing

10The validity of price homogeneity is tested at each point in time and
not just in the long-run. For the Koyck lag, the null hypothesis is epy
+ Ent Eqx=0 where ej is the compensated price elasticity for the ith
price; for the Almon lag, the null hypothesis is y, x,2 + Vp,2 +

Vqx, 2705 where Vi,2 is the quadratic term in the almon polynomial for
the ith price. If there are no cross-price effects, then gx, 2=€x=0-

11~he Yearbook of International Trade Statistics, published by the United
Nations, presents bilateral trade flows with commodity disaggregation,
but on an annual basis.

l2phe Direction of Trade does not include bilateral trade flows
disaggregated by commodity. In addition, data for Ecuador and Gaon
need to be excluded from the group of non-oil developing countries and
included in the group of oil-exporting countries, which is the basis for
our calculations.


United States. The aggregate of these imports account for 56.6 percent
of total exports of developing countries to industrial countries.

The price for non-oil exports of developing countries, P,,, is
a weighted geometric average of the prices of non-oil raw materials and
of manufactures. The weights vary over time and are equal to the
(normalized) shares of these two classes of goods in merchandise exports
of non-OPEC developing countries. Note that this export price is based
on multilateral trade weights, which is a limitation of our analysis.
However, we found no better alternative. Each country's real non-oil
imports from non-OPEC, M, are obtained by deflating their nominal
non-oil imports by the non-oil dollar export price of developing
countries.

The export price of developed countries, Qy, is a weighted
geometric average of their dollar export prices, with weights changing
over time and equal to bilateral trade shares. Finally, the exchange
rate, the GDP deflator and real GNP for each country are conventionally
defined. The data appendix contains the official data sources, the
details regarding the constructions of our data set, and time-series

plots of the more relevant relations.

5. Empirical Results

5.1 Elasticity Estimates

The parameters associated with (2) are estimated using two-stage least
squares with quarterly data for the period 19741 to 1981IV. In adcition
to considering two lag adjustments, we test for the importance of

cross-price effects, which results in a total of four estimating


Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports
of Developing Countries

Jaime Marquez
International Finance Division
Federal Reserve Board
Washington, D.C. 20551

and

Caryl McNeilly
Woodrow Wilson School of Public and International Affairs
Princeton University
Princeton, N.J. 08544

April 1986
(Revised October 1985)

Interest in income and price elasticities for international trade has
increasec| recently because of the debt crisis that many developing
countries are experiencing. Estimates of income elasticities of import
demand, however, range from a low of 1.3 to a high of 4.7. Such
differences have important implications for debtor and creditor
countries, alike. Using quarterly data for the period 1973-1981, this
paper estimates income and price elasticities for non-oil imports of
five major industrial countries from non-OPEC developing countries. The
empirical results suggest that the income elasticity is closer to 1 than
to 4,

This paper is part of a larger modeling effort of trade and financial
relations between major industrial countries and developing countries
for the Multi-Country Model of the Federal Reserve Board. The work of
McNeilly was completed while she was at the Board. We have benefited
from the comments of F. Gerard Adams, William Cline, Russell Cooper,
Vittorio Corbo, Jonathan Eaton, Neil Ericsson, Mike Gavin, Peter Hooper,
Mohsin Khan, Cathy Mann, Mare Noland, Charles Siegman, and Ralph Tryon.
Woodrow Bellamy provided helpful research assistance. This paper has
been presented in seminars at the Federal Reserve Board and the World
Bank. This paper represents the views of the authors and should not be
interpreted as reflecting the views of the Board of Governors of the
Federal Feserve System or other members of its staff.


5

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Table 1
Non-oil Exports of Developing Countries

Comparison of Selected Studies

23

Country Aggregation Elasticity
Author Exporter Importer Data Commodity Income Price
Bond (1985)? Non-Oil Industrial Annual All -0.1,
LDC 1967-81 Goods 2.4 -0.8
Goldstein Non-0il Industrial Annual Non-0il 1.3 0.0
Khan (1982)> LDC 1963-80
Cline (1984)° World Industrial Annual Non-0 il 3.1 0.0
1961-81
Dornbusch® Non-Oil World Annual Non-0il 2.4, 71.2
(1985) LDC 1960-83 WAT
Grossman4 Non-Oil U.S. Quarterly 7-digit 0.2, -4.5,
(1982) LDC 1968-78 SITC 1.5 70.5
Riedel? Non-0il Industrial Annual Non-Oil 0.9, (0)
(1984) LDC 1960-78 1.3

a. The estimation method is indirect least squares.

b. The estimation
the ratio between

ec. The estimation method is ordinary least squares.

d. The estimation method is two-stages least squares.

method uses the average of the percentage changes of
LDC exports to OECD countries and the OECD real GDP.


ABSTRACT

Interest in income and price elasticities for international trade
has increased recently because of the debt crisis that many developing
countries are experiencing. Estimates of income elasticities of import
demand, however, range from a low of 1.3 to a high of 4.7. Such
differer.ces have important implications for debtor and creditor
countries alike. Using quarterly data for the period 1973-1981, this
paper estimates income and price elasticities for non-oil imports of
five major industrial countries from non-OPEC developing countries. The
empirical results suggest that the income elasticity is closer to 1 than

to 4,


Figure A3
Non-Oil Imports from Non-OPEC Developing Countries
Import-GDP Ratio

— 2
United States Va 1
| | i Litiiiiitiitt,

1975 197 1979 1981
— 43
Japan — 4e2
| | | | Jisitititiity,

1975 1977 1979 1981

a3
Germany
= 2

i ! | l Lisidiiitint
1975 1977 1979 1981

ES Pa NO ‘

| | | | Lirttitiliiit,
1975 1977 1979 1981

Canada iia 0.8

i | L I Lisitiritiry
1975 1977 1979 1981



31

due to the omission of quantum effects, and that once these effects are
recognized, there is no need for additional lagged variables.
Elasticity estimates presented in table A2 reveal a relatively
robust income elasticity but a good deal of sensitivity in the own- and
eross-price elasticities. Several reasons may account for this
sensitivity. First, dynamic adjustments are not solely due to quantum
effects, as it is implicitly assumed in the results of table A2.
Second, already high levels of collinearity might be exacerbated, which

prevents isolation of coefficient estimates.

A1.3 Choice of Functional Form

The general functional form of equation (2) is
ny d

(a2) (Mp - 1)/ A= ag + (a, (L)76(L)) (Xe = wa) +

a
+ (a, (L)78(L)) (Pt

1)/x)

+ (1, (19/8(4)) (Cae - 1A) + ug
where \ is the Box-Cox parameter, 8(L) = 1 - 6L, aj(L) = } ajgh®,
(for j=1,2,3), up~ NID(O, o?), and L is the lag operator. The value of A
is determined by maximizing £, + (A-1)JinY,, where £, is the concentrated
log-likelihood function for \=1. The maximizing value of A is found
through a grid-search on which } is allowed to vary from 0 to 1 with a
0.1 step size. This procedure is applied to a total of eight
specifications for each country: with and without cross-price effects,
with and without potential output, and two distributed lags (Koyck and

Almon).


effects
Ffects

potential output and

no cross-price effects

Case 4: potential output and

: no cross-price

cross-price ¢&.

Case 1
Case 2

Case 3

Homosked.

Almon
Indep.

Normality

Table A3
(continued)
Homosked.

Koyck

cross-price effects

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10

uncertainty over future supply conditions may account for such a celayed
response. Failure to recognize lagged responses could potentially bias
the income elasticity estimates with implications for the design of
policy responses to the debt crisis. From an empirical standpoint, the
key issues are the length of time that it takes for imports to adjust
fully and the nature of the adjustment process. To maintain the
analysis at a manageable scale, it is assumed that the full response
takes place in one year (Grossman 1982 and Goldstein and Khan 1985) and
that the dynamic response follows either a Koyck adjustment lag or an
Almon distributed lag.8
Testing for the validity of the restrictions imposed by these

two dynamic specifications involves comparing the sum of squared
residuals for both the original and an "unrestricted" dynamic
specification. The latter is constructed by eliminating the parameter
restrictions associated with the original dynamic specification ard
adding, as regressors, all predetermined variables lagged one
period.9 The associated test-statistic under the null hypothesis is
(5) F=((SSR, - SSR,)/n)/(SSR,/(T-K)) ~F(n, T-K),
where SSR = sum of squared residuals under the null hypothesis,

SSR,= sum of squared residuals under the alternative hypothesis,

n = number of additional parameters,
K = number of regressors.

8ror the Koyck distributed lag, a5Q is set to zero for &%>1 and all j.
For the Almon distributed lag, 6 is set to zero. The Almon lag is
assumed to follow a second degree polynomial as in Thursby and Thursby
(1984). Endpoint restrictions in this polynomial were needed to avoid
the multicollinearity problems, which are also indicated by Grossman
(1982). As Klein et. al. (1985) point out, multicollinearity problems
are more serious for two-stage least squares than for OLS.

QNote that the construction of the unrestricted specification will not
include the lagged dependent variable if this variable already exists in
the original specification.


48

REFERENCES,

Adams, F.G., E. Sanchez, and M. Adams, 1983, Can Latin America carry its
international debt? A prospective analysis using the Wharton Latin
American debt simulation model, Journal of Policy Modeling, 5, 41-41.

Bergsten, F. and W. Cline, 1983, Trade policy in the 1980's: An
overview, in Cline (ed.), Trade Policy in the 1980's (MIT Press,
Cambridge).

Bond, M., 1985, Export demand and supply for groups of non-oil
developing countries, IMF Staff Papers, 32, 56-77.

Chow, G., 1960, Tests of equality between sets of coefficients in two
linear regressions, Econometrica, 28, 591-605.

Chu, K. and T. Morrison, 1984, The 1981-82 recession and non-oil primary
commodity prices, IMF Staff Papers, 31, 93-140.

Cline, W., 1984, International debt (MIT Press, Cambridge).

Cline, W., 1985, International debt: Analysis, experience and prospects,
Journal of Development Planning, No. 16, 25-55.

Dooley, M., W. Helkie, R. Tryon, and J. Underwood, 1983, An analysis of
external debt positions of eight developing countries through 1990,
International Finance Discussion Paper No. 227, Federal Reserve Board.

Dornbusch, R., 1985, Policy performance links between LDC debtors and
industrial nations, Brookings Papers on Economic Activity, No. 2,
303-366.

Engle, R., 1982, Autoregressive conditional heteroskedasticity with
estimates of the variance of the United Kingdom inflation, Econometrica,
50, 997-1008.

Goldstein, M. and M. Khan, 1982, Effects of slowdown in industrial
countries on growth in non-oil developing countries, Occasional Paper
No. 12, International Monetary Fund.

Goldstein, M. and M. Khan, 1985, Income and price effects in foreign
trade, in R. Jones and P. Kenen (eds.), Handbook of International
Economics, vol. II (North-Holland, Amsterdam).

Grossman, G., 1982, Import competition from developed and developing
countries, Review of Economics and Statistics, 64, 271-281.

Haynes, S. and J. Stone, 1983, Secular and cyclical responses of |J.S.
trade to income: An evaluation of traditional models, Review of
Economies and Statistics, 65, 87-95.


IFDP
NUMBER

280

279

278

277

276

275

274

273

272

271

270

International Finance Discussion Papers

TITLES

1986

Taxation of Capital Gains on Foreign
Exchange Transactions and the Non-neutrality
of Changes in Anticipated Inflation

The Prospect of a Depreciating Dollar
and Possible Tension Inside the EMS

The Stock Market and Exchange Rate Dynamics
Can Debtor Countries Service Their Debts?
Income and Price Elasticities for Exports

of Developing Countries

Post-simulation Analysis of Monte Carlo
Experiments: Interpreting Pesaran's (1974)

Study of Non-nested Hypothesis Test Statistics

A Method for Solving Systems of First Order
Linear Homogeneous Differential Equations
When the Elements of the Forcing Vector
are Modelled as Step Functions

International Comparisons of Fiscal Policy:
The OECD and the IMF Measures of Fiscal
Impulse

An Analysis of the Welfare Implications of
Alternative Exchange Rate Regimes: An
Intertemporal Model with an Application

1985
(partial listing)

Expected Fiscal Policy and the Recession
of 1982

Elections and Macroeconomic Policy Cycles

Assertion Without Empirical Basis: An
Econometric Appraisal of Monetary Trends

in ... the United Kingdom by Milton Friedman
and Anna J. Schwartz

Please address requests for copies to International Finance Discussion
Papers, Division of International Finance, Stop 24, Board of Governors of

the Federal Reserve System, Washington, D.C.

20551.

50

AUTHOR(S)

Garry J. Schinasi

Jacques Melitz

Michael K. Gavin
Jaime Marquez

Caryl McNeilly

Neil 8. Ericsson

Robert A. Johnson

Garry Schinasi

Andrew Feltenst.ein
David Lebow
Anne Sibert

William H. Braason
Arminio Fraga
Robert A. Johnson

Kenneth Rogoff
Anne Sibert

David F. Hendry
Neil R. Ericsson


13

countries, measured in barrels per day, can be obtained from the

Quarterly Oil Statistics compiled by the Organization for Economic

Cooperation and Development .13

With data on oil import prices, one can estimate the value of
oil imports from developing countries. Note, however, that neither
OPEC's: official price nor the spot price are ideally suited to value
oil imports from non-OPEC developing countries. Differences in the
sulphur content of oil imports from alternative suppliers, in the
erude~product composition of imports, and in transportation costs
limit considerably the usefulness of the above prices in our study. To
bypass this problem, the paper computes first a price of oil for each
country as the ratio between the value of total oil imports and the
total volume of oil imports. This average price, which is influenced by
oil purchases from OPEC, is then adjusted to take into account the
existing country-differences in the crude-product composition of oil
imports, the different regional sources for imports, and the different
gravities of crude oil.

With data on the value of oil imports from developing
countries, non-oil imports are computed as the difference between total
and oil imports, both from developing countries. As a percentage in
1981, non-oil imports from developing countries account for 5.2 percent
of total imports for Canada, 12.3 percent for Germany, 13.9 percent for

Japan, 13.6 percent for the United Kingdom, and 18.9 percent for the

13The earliest date covered by this source, on a quarterly basis, is
1973, which determines the starting period of our analysis. This data
source measures oil in metric tons; the data in this study are converted
to barrels using standard conversion factors.