Accurate estimates of the price and income elasticities of exports are valuable for growth policies based on trade promotion. However, not sufficient attention seems to have been paid to the specification of the relative price variable in some influential empirical works. This paper estimates the export equation for Fiji to show that inappropriate specification of the relative price variable may give under estimates of the price elasticity and over estimates of the income elasticity.Exports, Price and Income Elasticities, Export-lead Growth Policy.

B Bhaskara Rao

Rup Singh

English

Research Papers in Economics

Exports: August-2005 1
.
ESTIMATING EXPORT EQUATIONS
B. Bhaskara Rao and Rup Singh
University of the South Paciﬁc, Suva (Fiji)
Abstract
Accurate estimates of the price and income elasticities of exports are
valuable for growth policies based on trade promotion. However, not
suﬃcient attention seems to have been paid to the speciﬁcation of the
relative price variable in some inﬂuential empirical works. This paper
estimates the export equation for Fiji to show that inappropriate
speciﬁcation of the relative price variable may give under estimates
of the price elasticity and over estimates of the income elasticity.
JEL: F14, F41, E21, C22;
KEYWORDS: Exports, Price and Income Elasticities, Export-lead
Growth Policy.2 Exports: Fiji
.
1. INTRODUCTION
Estimating export demand functions for developing countries is im-
portant because the relative price and income elasticities indicate the
scope for export-lead growth policies. The higher are these elastici-
ties, the higher is the scope for export based growth policies. There-
fore, it is important to avoid misspeciﬁcation biases. However, in the
current empirical literature the speciﬁcation of the export equations
are unsatisfactory. The usual speciﬁcation for a country’s exports X
in the log-liner form is:
lnXt = α0 − α1ln
h PD
E × PF
i
+ α2lnYF (1)
where PD is domestic price of exports, PF is price level of trading
partners, E is exchange rate, measured as the price of foreign cur-
rency in domestic currency and YF is income of trading partners.
Note that the relative price variable has three components viz., PD,
E and (PF). A 1% percent decline in relative prices could be due to
a 1% decline in PD or a 1% increase in E (depreciation) or PF.
However, in some inﬂuential empirical works e.g., Senhadji and
Montenegro (1999), E is ignored in the relative price variable. This
procedure seems to be widely used to quickly obtain expected em-
pirical results with techniques like the fully modiﬁed OLS (FMOLS)
of Phillips and Hansen (1990) and the bounds test (ARDL) of Pe-
saran and Shin (1995); see Senhadji (1998) and Dutta and Ahmed
(2004) for ignoring E in imports. Although the eﬀects of omitting
E on the estimated elasticities are diﬃcult to estimate, it may be
said that this could lead to an under estimation (over estimation) of
the absolute value of price elasticity (α1) if devaluations (apprecia-
tions) dominate the sample. It is hard to say how this ommission
eﬀects the estimate of income elasticity.1 This paper illustrates the
1 A formal econometric proof is complicated because we have used non-linear
estimation methods. The approximate bias in OLS estimates can be computed by
estimating three equations: (A) is the correct speciﬁcation, (B) is the misspeciﬁed
equation and (C) is an auxiliary regression:Exports: August-2005 3
aforesaid biases by estimating the export demand function for Fiji
(1970-2002). We shall estimate the long run export equation, us-
ing the Phillips-Hansen FMOLS, the Johansen (1988) cointegration
approach (JML) and the LSE-Hendry general to speciﬁc approach
(GETS); see Hendry (1987). We have ignored the bounds approach
of Pesaran and Shin because of its large range of indeterminacy for
the cointegration test statistic. Although JML gave plausible point
estimates of these two elasticities, they were insigniﬁcant. In compar-
ison, both GETS and FMOLS gave good and signiﬁcant estimates.
2. EMPIRICAL RESULTS
The speciﬁcations of export equation, with and without E in the
relative price variable, are:
lnXt = α0 − α1ln
h PD
E × PF
i
+ α2lnYF (2)
lnXt = β0 − β1ln
hPD
PF
i
+ β2lnYF (3)
Deﬁnitions of the variables and sources of data are in the Appendix.
JML estimates of (2) and (3) are given in the ﬁrst two columns of
Table-1.2 The point estimates of the implied price and income elas-
lnXt = α0 − α1ln
h PD
E × PF
i
+ α2lnYF (A)
lnXt = β0 − β1ln
hPD
PF
i
+ β2lnYF (B)
lnPF = γ0 + γ1ln
hPD
PF
i
+ γ2lnYF (C)
Maddala (1992) shows that the expected values of the estimated coeﬃcients
from the misspeciﬁed equation (B) are: E(β1)=( 1+γ1) × α1 and E(β2)=
(1 + γ2) × α2. Thus, the magnitude of this bias depends on the coeﬃcients in
the auxiliary equation.
2 We have used a VAR(1) model, after determining its optimal order with both
AIC and SBC. However, we faced problems with the Johansen JML procedure.
The null that there is at least one cointegrating vector for equation (2) could be4 Exports: Fiji
ticities are correctly signed but in neither equation they are signiﬁ-
cant. Exogeneity tests showed that both the relative price variables
are weakly exogenous and the lagged ECM term is signiﬁcant only
at the 11.8% and 10% levels, respectively, in the VAR of equations
for (2) and (3). These estimates, normalized on lnX, are reported
as JML(2) and JML(3). They should be interpreted only as an indi-
cation that ignoring E, in the relative price variable, would lead to
an under estimation of the absolute value of relative price elasticity,
−2.578 against −1.357 and to an over estimation of income elasticity,
1.147 against 1.641.
Using these insights, we have estimated equations (2) and (3)
with GETS.3 The GETS estimates are in columns (3) and (4) of
Table-1. The estimated elasticities, in both equations, are correctly
signed and signiﬁcant. However, the point estimates of price elas-
ticities show that it is only slightly higher in (3) but the null that
these two estimates are equal could not be rejected at the 5% level of
signiﬁcance. The computed test statistic is χ2
1 =1 .022 (p =0 .312).
In contrast, there are signiﬁcant diﬀerence in the estimates of income
elasticities. While equation (2) implies an income elasticity of 1.164,
equation (3) gives an estimate of 1.652. The computed test statistic
for the null that these are equal is χ2
1 =1 5 .683 (p =0 .000) and the
null is rejected.
Estimates with FMOLS are in columns (5) and (6). Unlike the
Johansen JML and GETS, FMOLS does not seem to have the op-
tion to restrict the intercept and trend in the underlying VAR. Con-
sequently, it became necessary to add a supply shock variable (SS)
with a lag of two periods to get meaningful estimates of equation (2).
SS is retained in equation (3) for comparable results.4 The estimated
coeﬃcients in both equations, except that of SS, are signiﬁcant and
have the expected signs. It is noteworthy that, like in GETS, there
accepted only at the 90% level by the trace test. For equation (3) this null is
accepted by both the eigenvalue and trace tests at the 95% level.
3 In the Johansen JML, it was necessary to use a restricted intercept in the
VAR. Therefore, we have estimated the GETS equations with NLLS to allow for
this restriction. However, the intercept was signiﬁcant only in (2).
4 SS is found be I(1) with a long lag structure of 7 periods in the ADF test.Exports: August-2005 5
Table 1
Export Equations for Fiji
Alternative estimates
Variable JML(2) JML(3) GETS(2) GETS(3) FMOLS(2)FMOLS(3)
ln
PD
E×PF −2.578 −0.862 −1.018
(2.56) (3.27)
ln
PD
PF −1.357 −1.202 −1.024
(3.78) (4.74)
lnYF 1.147 1.641 1.164 1.652 0.995 1.379
(9.44) (64.48) (8.88) (15.88)
Const. 2.431 0.056 1.971 2.536 0.974
(3.75) (4.37) (1.99)
SS −0.001 −0.001
(0.12) (0.16)
Notes: The cointegrating vectors are normalized on lnX. JML(2) means JML
estimate of equation (2) etc. t-ratios are in the parentheses. t-ratios for the
GETS equations are based on the Newey-West adjustment. t-ratios for the JML
equations in columns (1) and (2) are not reported because they are highly in-
signiﬁcant. Microﬁt 4.1 of Pesaran and Pesaran (1997) is used for estimation.
is no signiﬁcant diﬀerences in the estimated relative price elasticities
of −1.018 against −1.024, but income elasticities are signiﬁcantly
diﬀerent at 0.995 against 1.379. The test statistics for the null of no
signiﬁcant diﬀerence between them is χ2 =1 1 .710 [p =0 .001] and
the null is rejected.
From these alternative estimates, it can be said that excluding
the exchange rate in the relative price variable is perhaps less serious
for the estimates of the price elasticity. This may be partly due to
the fact that depreciation regimes are relatively less dominant in our
sample for Fiji. The Fiji dollar was stable or appreciated in 19 out of
33 periods. It would be interesting to know whether the price elas-
ticity estimates would be close if depreciation regimes dominate in6 Exports: Fiji
the samples of other developing countries. However, in these alterna-
tive methods, the income elasticity is unequivocally overestimated by
40% to 65% when E is excluded in the relative price variable.5 Such
a magnitude of overestimation gives the misleading implication that
by liberalizing trade, a developing country can substantially increase
exports if its trading partners grow faster. What seems to be neces-
sary for the success of an export-lead growth policy is a substantial
reduction in the relative prices, either by decreasing domestic costs
of exports or through timely adjustments to the exchange rate.
3. CONCLUSIONS
In this paper we have empirically shown that neglecting the exchange
rate in the relative price variable of the export equation causes an
overestimation of the income elasticity. Although it could not be con-
clusively shown that this leads to an underestimation of the relative
price elasticity, because our sample is not dominated by depreciation
regimes, we conjectured that underestimation is likely for countries
in which depreciation regimes dominated the sample. Therefore, we
hope that our conjecture will be tested by other investigators. A clear
cut policy implication of our ﬁndings is that, since income elastici-
ties are substantially overestimated in the existing empirical works
that exclude the exchange rate in the relative prices, fresh estimates
are necessary to determine the scope for export-driven growth poli-
cies. It is also reasonable to conjecture that the relative price and
income elasticities in the import equations will be similarly biased if
the relative price variable is improperly speciﬁed. Since these biases
can be avoided by including the exchange rate in the relative price
variable, the current popular practice of ignoring the exchange rate
is unwarranted.
5 The insigniﬁcant bias in the relative price elasticity is due to a small value
of 0.046 for γ1 in the auxiliary regression. In contrast, the estimate of γ2 is
0.370 implying that income elasticity could be overestimated, in the misspeciﬁed
equation, by about 40%. See footnote 2.Exports: August-2005 7
Data Appendix
YF is the trade weighted average real income of Fiji’s major trading
partners, viz., Australia, New Zealand, USA, UK/EU and Japan.
Trade weights are computed as the share of trade to each of these
countries relative to Fiji’s total trade.
Xt is Fiji’s total exports of goods and services (FOB) deﬂated by the
export price index.
PD is the price of Fiji’s export goods, computed as the weighted
average of Fiji’s unit value index of major domestic exports.
Et is the weighted average exchange rate and is the price of a unit
of foreign currency in domestic currency.
PF is the import weighted average of major trading partners’ export
price indices. Import weights are computed as the share of respective
imports to total imports.
SS is a proxy for export productivity proxied with the average pro-
ductivity of sugar per hectare from the Key Economics Statistics,
various years. Sugar is the major export of Fiji.
Notes: Data on the are from the IFS CD-ROM 2003 and the Reserve Bank of
Fiji Quarterly Review, for various years.8 Exports: Fiji
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Econometrics methodology: a personal perspective”,

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Statistical analysis of cointegrating vectors”,

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ESTIMATING EXPORT EQUATIONS

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