Error Correction, Cointegration
and
Aggregate Import Demand for Syria
Dr. Mamdouh ALKHATIB ALKSWANI Dr. Abdullah A. ALSHEBL
Professor Assistant Professor
E-mail: alkswani@ksu.edu.sa E-mail: : ashebel@ksu.edu.sa
College Business
Department of Economics
P.O.Box: 2459
Introduction
In
Economic Literature, many studies focused on traditional import demand
function, in static as well as dynamic forms.[1]
Their goals were seeking for variables and factors that determine the level of
aggregate demand import and estimating the long and short run elasticities.
These studies followed two approaches. The first one was the traditional
estimation by single equation, whereas the second followed the recent
development of time series technique: unit root and cointegration.
The
main purpose of this paper is to analyze the behavior of the aggregate import
demand function for
Analyzing
the import demand function for Syria has a special importance due to the high
degree of dependence of the Syrian economy on the international trade.
Econometrics wise, the estimation of import demand functions have some problems
resulting from administrative obstacles, pricing behavior of imports and
estimation methods of other related variables. Because of the special
administrative organization of imports in Syria, it is expected that, the
estimation of import demand function may face some econometrics problems. We
can summarize the most important factors qualifying the imports flows as
follows:
1-
Importance of imports and Instability: Imports has a
special importance in the Syrian economy. During the period 1970-1995, imports
value of goods and services have increased from 8.3 billion Syrian Pound (SP)
to 26.5 billion SP, with an annual average growth equals to 4.1 %. The average import share of GDP during the
study period was about 25.4 %. The instability of this share ranged between
18.8 % in 1983 and 31.4 % in 1979.
2-
Multiplicity of the exchange rates: the government
uses multiple exchange rates to allocate foreign reserves to imports, depending
on the type of the imported goods: raw materials, capital goods, final
consumption goods, intermediate consumption goods, and luxury goods. Therefore,
imports can be funded according to different exchange rates against the US
dollar. Among them are the following
official rates : 3.8 SP, 11.25 SP and 22 SP for one US dollar. The dollar
exchange rate in the parrell markets was equal to 45 SP, whereas it was about
50 SP in the black market. Thus, any modification in the official exchange rate
will lead to an artificial increase in import values.
3-
Differentiation in the exchange rates according to
the import sector: the public sector was given exchange rates to finance its
imports differed of those given to the private sector.
4-
Multiplicity
of tariffs according to the importing sectors (public, private or cooperative)
and according to the purpose of imports whether they were for final
consumption, intermediate goods, or capital accumulation. This would lead to
different extra costs which would lesd, in its turn, to price variations for
the same imported product.
5-
Interelationship between imports and exports
revenue. This is being done through
allowing exporters to use percentage of their exports revenue to finance their
import needs from consumers goods and raw materials. Another use is to sell the
foreign currency (US $) that comes from exports to the importers at higher
exchange rate than the going rate in the parrell markets or even in black
market. This regulation had lead to the differences in the exchange rates of US
$ which ranged from 10% to 15% between the black market (about 45 SP) and the export
price (it ranges between 55 SP to 65 SP
depending on the domestic demand). This linkage increases artificially
the exports values and decreases the import values, because of scarcity of
foreign currency and complicated steps on obtaining it in Syria.
6-
Smuggling of illegal imports. The prohibition of
importing some goods and raw materials, and the restriction of imports other
goods encouraged the smuggling from the neighboring countries, especially from
Lebanon. This had been noticed especially during the period 1981-1984 when
illegal market for the smuggled goods has spread across the country. In
addition, it led to spread of black markets, smugglers, and mediators for
several goods and raw materials.
Because of these factors, it
is expected that imports relative prices in the Syrian economy may play a
limited role in explaining the import demand function. The price concept is
destorded by many deficiencies that drove it away from reality. Import prices
are misrepresented and characterized by artificiality and unreality. As the US
$ has many exchange rates, the same good may have many prices. The noticeable
smuggling activities during some years lowered
imports and decreased their share in the GDP. So, the introduction of a
dummy variable is justified to take account for these activities. The
statistical significance of the dummy proved the existing of this phenomenon in
the Syrian economy.
This study is divided into three
sections. The first one deals with the theoretical aggregate import demand
functions. In the second section, the Error Correction Model is applied whereas
the last section is devoted to the Johansen method for Cointegration.
1.
Theoretical Aggregate Import Demand Functions:
Aggregate
import demand functions take the following general form:
Where:
: Aggregate import demand in period (t) .
:Real
gross domestic product in period (t).
: Relative
import prices in period (t).
:Other explanatory variables in period (t).
:Random error term in period (t).
The
relation shown in (1) indicates that variations in aggregate import demand are
explained by variations in gross domestic product, relative import prices, and
other explanatory variables. For example, population, financing level, export
revenues, availability of foreign currencies, time trend, and dummy variables
can be included. The random term 
represents other
variables not included explicitly in this relation as well as the estimation
errors.
The
aggregate import demand function can take the linear form:
Where it is
expected that 
.
The linear form assumes constant
response of import demand variations due to variations in relative import
prices and/or gross domestic product. If the response is not constant, the
exponential function, which takes the following form is preferable,
Taking the
linear logarithmic transformation to equation (3), we get:
The choice of the logarithmic model is dictated by the objective to
reduce the heteroscedasticity. To use a time series characterized by constant
mean and variance over time, it is
recommended to use the logarithmic form of the variables. Moreover, the
logarithmic model would facilitate the estimation of elasticities .
There are theoretical reasons to expect the price elasticity of
aggregate import to be negative, 
. Regarding the income elasticity, there is ambiguity in its
sign; but it is expected mostly to be positive. However, it is possible to have
a negative sign if the government followed a development policy for import
substitution in which the increase in gross national product may be associated
with decreasing import demand.
Applying
the OLS method to estimate equation (4), it is based on the assumption of stationarity time series of imports, relative
prices and gross domestic product. If this assumption does not hold, a new
methodology will be used to estimate our equations. Therefore, we will discuss
first the meaning of the stationarity of the time series and cointegration.
Then, we will test for existing of unit root in the time series that included
in the import demand function (imports, relative prices, and gross domestic
product). Finally, we will apply the cointegration concept on the import demand
function using Engle & Granger methodology of Error Correction Model (ECM) and
Johansen cointegration method.
Based on Wold’s theorem, a
stationary time series with no deterministic components has an infinite moving
average representation (ARMA) that can approximated by a finite process. A
priori, many economic time series will be non-stationary integrated processes.
Thus, if a non-stationary time series (X) needs to be differenced (d) times
until reaching stationarity, then the time series is said to be integrated of
order (d), denoted by 
.
For a pair of series, Xt
and Yt, which are both integrated of the same order (d) or 
, then any linear combination of the form 
, will be integrated of order 
, where 
is a constant. If fulfills the relation,
, then Xt and Yt are integrated. However,
the variables contained in the vector do not necessarily have
the same order of integrability. Johansen demonstrated that if 
and 
, then Y and 
could be cointegrable.
The Granger representation indicates that if Xt and Yt are integrated, they have an error
correction representation as follow:
Where a (L), b (L) and c (L) are
stable and invertible polynomials, respectively. Such models provide a more
attractive way of presenting and modeling cointegrating series. The error
correction models combine the long run 
and the short run
dynamics.
Following
the analysis of Engle and Granger, equation (2) and (4) can be employed
directly to test for cointegration. If the variables contained in the import
demand function are cointegrated, then models (2) and (4) would present
estimates of the long run equilibrium, and consistent estimates for
elasticities can be obtained directly from these models.
According to Engle
and Granger
methodology, the first step is to examine whether the series contained in the
import demand function has a unit root. In the cointegration literature, the
more frequently used tests for a unit root are the Dickey-Fuller (1979 and
1981), Philips-Perron (1988), and Perron (1986 and 1988) test. These tests
agreed in their treatment to the intercept parameter 
. Thus, the null
model to test for unit root has the following form:
and the model under the alternative
hypothesis:
Where Xt is the logarithm
of the time series, and under the null hypothesis; 
, and T represent the number of observations. In this paper,
we use the Augmented Dickey-Fuller (ADF) and the Philips-Perron (PP) to test for the stationarity of the time
series.
The ADF test can be obtained by applying OLS
to estimate the coefficients of the following relation:
Where 
is chosen to eliminate
the autocorrelation. If a unit root exists, then 
would not be statistically different from zero
. The ADF test can be conducted by comparing the t-value on the coefficient of 
by either the critical values presented by
Fuller (1976) or by the extended tables of Dickey-Fuller that presented by
Guilkey and Schmidt (1989) and denoted
by 
.
This study try to confirm
that there is a stable long-run equilibrium relationship between aggregate
import demand, price and income in the Syrian economy.
II.
Import demand and Error Correction Model:
The
aggregate import demand (Mt), and gross domestic product (Yt)
are measured at constant prices of 1985. The price variable (Pt) is
calculated by dividing import price index (Pm) on domestic price as
expressed by implicit of GDP price index (Pd), Pt = Pmt/Pdt.
The dummy variable is included to take into account illusory decreasing in the legal import level during
the period 1981 – 1984.
Table
(1) shows the t values on the level obtained from ADF and PP tests. These
values are clearly less than the critical values and therefore the null
hypothesis of a unit root cannot be rejected for each series at the 5 per cent
significant level.[3] Thus,
import, price and income are non stationary time series.
Table (1
)
ADF
and PP Unit Roots tests
|
First Differences |
Levels |
Lags |
Specifications |
Variables |
||
|
PP |
ADF |
PP |
ADF |
|||
|
-4.706 -4.705 -4.71 |
-4.706 -2.742 -2.187 |
1.787 1.893 1.893 |
1.787 1.711 1.425 |
0 1 2 |
No intercept No trend |
lm |
|
-5.233 -5.233 -5.229 |
-5.233 -3.193 -2.831 |
-1.834 -1.848 -1.854 |
-1.834 -1.834 -2.028 |
0 1 2 |
With intercept No trend |
|
|
-5.297 -5.298 -5.304 |
-5.297 -3.320 -3.208 |
-2.274 -2.262 -2.273 |
-2.274 -2.204 -2.645 |
0 1 2 |
With intercept and trend |
|
|
-3.834 -3.774 -3.830 |
-3.834 -2.578 -1.121 |
3.587 3.913 3.871 |
3.587 3.137 2.357 |
0 1 2 |
No intercept No trend |
ly |
|
-5.612 -5.623 -5.595 |
-5.612 -3.717 -1.948 |
-2.116 -2.355 -2.419 |
-2.116 -2.396 -1.436 |
0 1 2 |
With intercept No trend |
|
|
-5.997 -5.997 -5.992 |
-5.997 -3.698 -2.241 |
-2.435 -2.432 -2.433 |
-2.434 -2.587 -1.787 |
0 1 2 |
With intercept and trend |
|
|
-3.681 -3.669 -3.631 |
-3.681 -3.469 -2.534 |
-0.409 -0.636 -0.709 |
-0.409 -0.971 -0.316 |
0 1 2 |
No intercept No trend |
lp |
|
-3.826 -3.826 -3.778 |
-3.826 -3.529 -2.642 |
-1.680 -1.372 -1.797 |
-1.680 -2.169 -1.277 |
0 1 2 |
With intercept No trend |
|
|
-3.731 -3.734 -3.686 |
-3.731 -3.457 -2.593 |
-1.901 -2.042 -2.086 |
-1.901 -2.511 -1.778 |
0 1 2 |
With intercept and trend |
|
Also, table
(1) shows the calculated t values of the first differences. These results prove
that the hypothesis of unit root can be rejected or to say that the variables
in their first difference are stationary time series. So the variables of the
equilibrium import demand relation are cointegrated of order one, I (1).
Having
obtained the above result of non-stationarty of the time series, we then run the
cointegrating regression for the aggregate import demand function, and obtain
the following result:
It is clear
that the equilibrium price elasticity of import demand is very low (-0.074)
where the equilibrium income elasticity of import demand is equal to (0.867).
The lowest price elasticity may result of the high multicolinearity between
price and income, where the correlation coefficient between these two variables
is about 0.75.
The CRDW is
the cointegrating Durbin-Watson Statistics, the values of t statistics are not
reported or other statistics since these estimates may be biased (Engle and
Granger, 1987), while the estimated parameters are not affected (Stock, 1985).
Engle and Granger (1987) calculated the critical values of CRDW, and they are
1%= 0.511, 5%= 0.386, and 10%= 0.322. It is clear that the aggregate import
demand function is cointegrated at the one-percent level.
Since the CRDW statistics alone is not enough to ensure the
existence of cointegration, we can run ADF and PP to test for the unit root.
The calculated values of ADF and PP are as follow:
Table (2)
Testing the
Residuals for Unit Root
|
|
Specifications |
Lags |
||
|
0 |
1 |
2 |
||
|
ADF |
With intercept |
-3.177 |
-2.141 |
-2.256 |
No intercept |
-3.251 |
-2.203 |
-2.277 |
|
|
P-P |
With intercept |
-3.177 |
-3.140 |
-3.191 |
|
No intercept |
-3.251 |
-3.216 |
-3.264 |
|
It is clear from table (2) that the obtained residuals of
the aggregate import demand function regression are stationary at five percent
significance level since ADF calculated values exceed the critical values.[4] In other words,
the contained variables in the import demand function are cointegrated.
Given that all variables on import demand equation are
cointegrated, we can proceed to the second stage of Engle-Granger cointegration approach which is to present an
Error Correction Mechanism (ECM). This model can be presented in its simple
form:
After experimenting with
different dynamic structures, we get to the following estimation:[5]
In
this representation, the t statistics of the error term 
obtained from the cointegrating regression is
significant at the 1 percent level. This is yet more piece of evidence, which
indicates that the variables contained in the import demand function are
cointegrated. Along with these results, we report the adjusted coefficient of
determination (
), the Breusch-Godfrey statistic for first order serial
correlation, and autoregressive conditional heteroscedasticity (ARCH). These
diagnostic statistics are significant at the one percent level. These results
are indication of credibility of the estimated model as well passing the
required statistical tests.
Since the estimated error term has a significant negative sign, it can be interpreted as that it measured the disequilibrium percentage in the dependent variable that can be corrected from period to another.[6] Therefore, the error correction parameter indicates that about 86% of the disequilibrium in the import demand in Syria would be adjusted from period to another. For the other two equations, the speeds of adjustment in the short run are estimated to be 0.546 and.-0.644, which are related to VAR specification.
III. The Import Demand and
Johansen Method for Cointegration
It is widely recognizable that Engle and Granger
test for cointegration would be enough if we want to examine the effect of
error correction mechanism on import demand for two sequences periods such as t and
t-1. However, since our concern is concentrated on the whole structure of the
import demand function, it is more useful to apply Johansen multivariate cointegration analysis.
The Maximum Likelihood procedure
(Johansen’s test), suggested by Johansen (1988 and 1991) and Johansen and
Juselius (1990), is preferable when the number of variables in the study
exceeds two variables due to the possibility of existence of multiple
cointegtating vectors. The advantage of Johansen’s test is not only limited to
multivariate case, but it is preferable than Engle-Granger approach even with a
two-variable-model (Gonzalo,1990).
To determine the number of
cointegrating vectors, Johansen (1988 and 1991) and Johansen and Juselius
(1990) suggested two statistic tests. The first one is the trace test
. It tests
the null hypothesis that the number of distinct cointegrating vectors is less
than or equal to q against a general unrestricted alternative q = r. This test
is calculated as follow:
where 
are the smallest value eigenvectos p-r. The
null hypothesis stated that the number of cointegrating vectors is equal to at
most to r. In other words, the number of cointegrating vectors is equal to or
less than r (where r=0,1,2,3 in our study). The second statistical test is the
maximal eigenvalue test 
that is calculated according the following formula:
This test concerns a test of
the null hypothesis that there is r of cointegrating vectors against the
alternative that r+1 cointegrating vectors.
The
results of trace and maximal value tests summerized in table 3 indicate the
possibility of rejecting the null hypothesis that says of no cointegrating
vectors at the 5 percent significant level.[7]
This means that the whole structure of the import demand is cointegrated with
import relative prices and gross domestic product. In addition, it means that
there is stationary linear combination between the import demand, relative
prices of imports and gross domestic product despite that each variable is
nonstationary. Finally, this result confirmed the existing of long run
equilibrium relationship between these variables, which means that they do not
diverge away from each other where it shows similar behavior. The number
of lags is selected by using the Akiake Information Criterion (AIC).[8]
Table (3)
Cointegrating Test
|
Null
Hypothesis |
Critical
Value 5% for Trace test |
Critical
Value 5% for Maximal Value test |
Trace
|
Maximal Value
|
|
|
|
62.99 |
31.46 |
77.34364 |
30.60464 |
0.720623 |
|
|
42.44 |
25.54 |
46.73900 |
20.931529 |
0581947 |
|
|
25.32 |
18.96 |
25.80747 |
15.81556 |
0.482622 |
|
|
12.25 |
12.25 |
9.99191 |
9.99191 |
0.340537 |
Critical
values are taken from Osterwald-Lenum (1992).
Since the calculated value
of trace test (77.34) exceeds the critical value (62.99) at the 5 percent level
of significance, it is possible to reject the null hypothesis that there is not
any cointegrating vector. The reported results of the Johansen procedure shown
in Table 3 reject the hypothesis that there are at most more than three
cointegrating vectors.[9]
The first one seems to be reasonable in terms of the magnitude of the
coefficients that they do compare with the cointegrating regression. The
normalized cointegrating regressions that resulted from these vectors are :
Table (4)
Normalized Cointegrating Vectors
|
lnM |
lnP |
lnY |
Dummy |
trend |
constant |
Log likelihood |
|
|||||||
|
1 |
0.249 (0.050) |
-1.692 (0.091) |
0.348 (0.022) |
0.036 (0.004) |
8.510 |
142.42 |
|||||||
|
1 |
-0.759 |
-0.406 |
0.107 |
-0.0004 |
|
|
|
|||||||
|
1 |
0.660 |
-0.870 |
0.542 |
0.005 |
|
|
|
|||||||
(One lag is used in the VAR; values in parenthesis are standard errors)
The
second vector was rejected because of the price coefficient sign. The first
vector was prefered over the third one due to the limited price role in
explaining imports level. This means that the long run import demand elasticity
with respect to price is equal to –0.249 while the income elasticity is about
1.69. In the relation 
, the first term in a (0.074) represents the speed at which 
, the dependent variable in the first equation of VECM,
adjusts towards the single long-run cointegration relationship, while 
represent respectively, the speeds at which 
respond to the
desequilibrium changes represented by the cointegration vector.
We can conclude
that, the cointegration analysis confirms the existence of a long run
relationship between import demand, price and income in Syria. The low value of
the price elasticity is an indication of the pricing deformation and
administrative rigidity. The income seems to be the more important variable in
the import demand function. The coefficient of the error term in the ECM
reveals a high speed of adjustment in
the short run.
Summary
This
paper has estimated import demand functions for Syria based on annual data for
the period 1970-1995. The gross domestic product has a significant effect on
explaining the change in the import demand where the equilibrium estimated
import demand elasticity with respect to income and price are 0.867 and –0.074; respectively. The price
elasticity is low, perhaps because of the deformation of the import structure
pricing and the multicolinearity effect.
This
study shows using two stages Engel-Granger approach for cointegration that the
variables of import, income and prices are non-stationary time series. The
result of error term with negatively significant sign in the second stage is an
indication of the fact that the variables in the import demand function are
cointegrated. The disequilibrium of the demand imports is corrected from period
to another by 0.86 percent.
The Johansen’s test rejects the null
hypothesis that there are no cointegrating vectors and accepting the hypothesis
of at least three cointegrating vectors is existed. This means that the whole structure
of demand is cointegrated during the studying period. The long run income
elasticity is about 1.692 where the price elasticity is - 0.249.
The
estimated results confirm the significance and limited role of the relative
prices in explaining the changes in import demand. This is because of the
differentiation in the exchange rates, tariff variations, interrelated import
availability with export revenues in artificial way, and increasing smuggling
activities. This would justify the necessary recommendation of unifying
exchange rates and removing the organizational and administrative obstacles
from legal imports to limit illegal imports as represented by smuggling
activities.
Regarding the income, the estimated results showed the
positive relationship with import demand. This means that the economic
development that occurred in Syria during the last twenty-five years did not
success in substituting domestic output for imports that kept raising as the
income increases. It is notable from the increasing in income elasticity that
the economic development in Syria would be joint by increasing in the import
levels. This is true especially if it is accompanied by the IMF recommendation
of unifying the exchange rates and removing the structure disturbances in the
Syrian economy that resulted from the organizational, administrative and
pricing obstacles.
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