Download error correction model of gdp and inflation based on one long

Transnational Journal of Science and Technology
January 2013 edition vol.3, No.1
ERROR CORRECTION MODEL OF GDP AND INFLATION
BASED ON ONE LONG-RUN EQUILIBRUM RELATIONSHIP
IN NIGERIA ECONOMY
Agboluaje,A.A. Mr
Ibrahim Badamasi Babangida University, Mathematics And Computer Science Department,
Lapai, Niger State, Nigeria
Olaleye, I. O. Mr
Federal Polytechnic, Mathematics Department, Bida, Niger State, Nigeria
Abstract:
This research is for the development of Error Correction Model of GDP and Inflation rate for
Nigeria economy. The basic idea is the use of one long-run equilibrium relation. When the
variables are Cointegrated, the model used is Vector Error Correction. The cointegration
VAR (3) model is appropriate and the VEC (2) model has exactly one cointegrating relation.
The analysis reveals that; per capital GDP is positively correlation with nominal GDP and
negatively correlation with inflation rate. Nominal GDP is positively correlation with per
capital GDP and positively correlation with inflation rate. Inflation rate is negatively
correlation with per capital GDP and positively correlation with nominal GDP. The evidence
suggests that Nominal GDP is positively correlation with both per capital GDP and inflation
rate.
Key Words: VAR, VEC, per capital GDP, Nominal GDP and Inflation
1.
Introduction:
Inflation is an important concept in the history of economic thought and can be
defined as a sustained rise in the general level of prices i.e. a persistent rise in the price levels
of commodities and services, leading to a fall in the currency’s purchasing power. High
inflation is bad for the economy and it adversely affects economic performance. Even
moderate levels of inflation can distort investment and consumption decisions. Reducing
inflation also has costs associated with the including lost output and higher rates of
unemployment. The problem of inflation used to be confined to national boundaries, and was
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caused by domestic money supply and price rises. In this era of globalization, the effect of
economic inflation crosses borders and percolates to both developing and developed nations.
Nigeria has experienced all manner of inflationary episodes – from creeping to
moderate and from high to galloping .Average inflation during the period 1960–1972 was
relatively low, the historical average rate being 5.01%. When assessed on an annual basis,
however, rising prices became a cause for concern for the then military government when in
1969 the inflation rate hit double digits at 10.36%. Government’s concern seems to have been
justified by the fact that Nigeria was experiencing double-digit inflation for the first time, in
the face of a raging civil war whose end was not then in sight. In reaction, government
imposed a general wage freeze for a period of one year. Apparently aware of possible
opposition by labour unions, price control measures were introduced with the official
promulgation of the Price Control Decree, early in 1970 .Inflationary pressures continued
unabated, however, even with price controls.
As inflationary pressure continued to mount in 1974, government put several
measures in place, including reduction in import duties on a relatively wide range of goods
and raw materials. Monetary policy measures that encouraged banks to lend more to the
productive sectors of the economy were put in place.
On a comparative scale, the period 1986–1995 represents a time of greater
inflationary pressures than the preceding periods, as indicated by a historical average rate of
31.50%. When the inflation experience is taken on a year-by-year basis, however, it is found
that 1986 and 1987 recorded relatively low rates of 5.4 and 10.2%, respectively. The change
is attributed largely to the improved food supply situation, particularly during the year 1986.
In 1988, domestic prices went up sharply to 38.3%, reaching an all-time high of 40.9% in
1989. Inflationary pressures eased relatively in 1990, with an inflation rate of 7.5% – again
because of rising output growth in the staple food subsection. From 1991, the trajectory of
domestic prices was upward trending, with inflation rates of 44.6%, 57.2%, 57.0% and 72.8%
recorded in 1992, 1993, 1994 and 1995, respectively. The inflation rate declined significantly
from 72.8% in 1995 to 29.3% in 1996. This reflected the salutary effect of sustained
implementation of stabilization measures during the period, including disciplined fiscal and
restrained monetary policies. The fight against inflation was highly successful in 1997, when
for the first time since 1990 the rate dropped to a single digit of 8.5%, against the 53%
average rate in the previous three years. The major factors that influenced the moderation in
the inflation rate were the relatively good harvest of staples (brought about by favorable
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rainfall conditions) and the associated fall in food prices, exchange rate stability, sustained
fiscal discipline, and non-accommodating monetary policy.
Historically, from 2005 until 2012, Nigeria GDP Growth Rate averaged 6.8 Percent
reaching an all time high of 8.6 Percent in December of 2010 and a record low of 4.5 Percent
in March of 2009. The Gross Domestic Product (GDP) growth rate provides an aggregated
measure of changes in value of the goods and services produced by an economy. Nigeria is
one of the most developed economies in Africa. The petroleum industry provides 95% of
foreign trade earnings and about 80% of budget revenues. Yet, agriculture is the main source
of revenue for two-thirds of the population. Still, more than 50% of Nigerians live in poverty
with corruption and poor infrastructure as the main obstacles for future sustainable
development.-accommodating monetary policy. It is significant to note that the low inflation
rate was achieved in spite of the adverse effect of the rise in the costs of production and
marketing stemming from frequent shortages of petroleum products and disruptions in power
supply among other structural bottlenecks. The inflation rate increased from 8.5% in 1997 to
10% in 1998, thus slipping back to the double-digit level, but remained subdued until the last
quarter of the year when domestic and external imbalances mounted. The major factor that
influenced the resurgence was the rising cost of production (goods and services) induced by
continued scarcity of petroleum products, frequent power outages, deteriorating infrastructure
and equipment, and the announcement effect of the upward review of the salary structure of
the public sector. However, the economy recorded a mixed performance in 2002.
The real gross domestic product (GDP) increased by 3.3% relative to the preceding
year’s 4.2%. Inflation declined from 18.9% in 2001 to 12.9% at the end of the year. The food
index, a dominant component, rose by 13.1% compared with 28.0% in the preceding year.
Core inflation, which excludes the impact of food, was 12.5%. The Gross Domestic Product
(GDP) in Nigeria expanded 6.5 percent in the third quarter of 2012
The Gross Domestic Product growth rate measures the increase in value of the goods
and services produced by an economy. Economic growth is usually calculated in real terms or
inflation-adjusted terms, in order to net out the effect of changes on the price of the goods and
services produced. The Gross Domestic Product can be determined using three different
approaches, which should give the same result. These different methods are the product
technique, the income technique, and the expenditure technique. In sum, the product
technique sums the outputs of every class of enterprise to arrive at the total. The expenditure
technique works on the principle that every product must be bought by somebody, therefore
the value of the total product must be equal to people's total expenditures in buying products
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and services. The income technique works on the principle that the incomes of the productive
factors must be equal to the value of their product, and determines GDP by finding the sum of
all producers' incomes. The real GDP per capita of an economy is often used as an indicator
of the average standard of living of individuals in that country, and economic growth is
therefore often seen as indicating an increase in the average standard of living. However,
there are some problems in using growth in GDP per capita to measure the general well-being
of a country´s population. In fact, GDP was first developed by Simon Kuznets for a US
Congress report in 1934, who immediately said not to use it as a measure for welfare. First,
GDP per capita does not provide much information relevant to the distribution of income in a
country. Second, GDP per capita does not take into account negative externalities such as
pollution consequent to economic growth. Third, GDP per capita does not take into account
positive externalities that may result from services such as education and health. Finally,
GDP per capita excludes the value of all the activities that take place outside of the market
place such as free leisure activities or less positive activities like organized crime.
The notion of an ‘Error Correction Model’ (ECM) is considered to be a very
powerful, organsing principle in applied econometrics and has been applied widely,
especially since the appearance of the seminal paper by Davidson et al.(1978).It has also
prompted a range of statistical developments, most notably the concept of cointegration
Engle and Granger( 1987). In fact, in a recent paper Hylleberg and Mizon (1989) suggest that
‘when estimating structural models it is our experience from practical applications that the
error correction formulation provides an excellent framework within which it is possible to
apply both the data information and the information obtainable from economic theory’
2.
Literature Review:
Understanding the relationship between inflation and real growth has all along been a
key concern in macro-economic research. According to Rangarajan (1998), the question, in
essence, presupposes a possible trade-off between price stability and growth either in the long
or short run. The new endogenous growth theories, for instance, surmised that inflation has
an adverse impact on growth because of its harmful effects on productivity and efficiency.
Others such as Choi, Smith and Boyd (1996) echoed a similar view and argued that inflation,
in the presence of information asymmetry can harm growth by accentuating financial markets
frictions and thereby adversely affecting the provision and allocation of investment. The
rational expectations revolution inter alia, criticised the non-neutrality proposition of
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Keynesians by arguing that, under flexible markets, 8 inflation in the long run [Rangarajan
1998].
Bruno and Easterly (1998) conclude that there was no evidence of a growth-inflation
trade-off in a sample which excluded discrete high inflationary crisis. On the other hand,
there was ample evidence to show that growth turned sharply negative when inflation crossed
past a high threshold rate of 40 % per annum. They also argue that the failure of investigators
in detecting a meaningful relationship between inflation and growth can be attributed to a
stylized rapid recovery of output after inflation which, on an average, renders the overall
statistical relationship insignificant. On the other hand, Sarel (1996) attempts an alternative
empirical investigation of the problem and also concludes that inflation affects growth only if
it breaches a specific 'threshold' rate of inflation but not otherwise. He concludes that an
inflation threshold of about 8 % for a pooled sample of a large number of countries, including
India, serves as a good common benchmark for the sample as a whole. Since the common
threshold is an estimate from a pooled sample, it may not be exactly suitable for particular
country if taken in isolation. There is, therefore, a need to have yet another empirical
assessment of the problem of finding the level at which inflation actually begins to erode
economic growth in given economy.
A more recent work involving 70 countries (of which 48 are developing economies)
for the period 1960-1989 found no causal relationship between inflation and economic
growth in 40 % of the countries; they reported bidirectional causality in about 20 % of
countries and a unidirectional (either inflation to growth or vice versa) relationship in the rest.
More interestingly, the relationship was found to be positive in some cases, but negative in
others. Recent cross-country studies, found that inflation affecting economic growth
negatively, includes Fischer (1993), Barro (1996) and Bruno and Easterly (1998). Fischer
(1993) and Barro (1996) found a very small negative impact of inflation on growth. Yet
Fischer (1993: 281) concluded ―however weak the evidence, one strong conclusion can be
drawn: inflation is not good for longer-term growth‖. Barro (1996) also preferred price
stability because he believed it to be good for economic growth.
Bruno and Easterly‘s (1998) work is interesting. They note that the ratio of people
who believe inflation is harmful to economic growth to tangible evidence is unusually high.
Thus, Bruno and Easterly (1998) examined only cases of discrete high-inflation (40 % and
above) crises and found a robust empirical result that growth falls sharply during highinflation crises, then recovers rapidly and strongly after inflation falls.
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3.
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Vector Error Correction Modeling:
The cointegrated series can be represented by a vector error correction model
according to the Granger representation theorem (Engle and Granger 1987). Consider the
vector autoregressive process with Gaussian errors defined by
or
where the initial values, y-p+1, ... ,y0, are fixed and
. Since the AR operator
can be re-expressed as
where
with
the vector error correction model is
or
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where ,
One motivation for the VECM(p) form is to consider the relation as defining the
underlying economic relations and assume that the agents react to the disequilibrium error
through the adjustment coefficient
to restore equilibrium; that is, they satisfy
the economic relations. The cointegrating vector, is sometimes called the long-run
parameters. You can consider a vector error correction model with a deterministic term. The
deterministic term Dt can contain a constant, a linear trend, seasonal dummy variables, or
nonstochastic regressors.
where
.
The alternative vector error correction representation considers the error correction
term at lag t-p and is written as
If the matrix
has a full rank (r=k), all components of yt are I(0). On the other hand, yt are
stationary in difference if
.When the rank of the matrix
is r<k, there are k-r
linear combinations that are nonstationary and r stationary cointegrating relations.Note
thatthe linearly independent vector
is stationary and this transformation is
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notunique unless r=1. There does not exist a unique cointegrating matrix
coefficient matrix
since the
can also be decomposed as
where M is an r×r nonsingular matrix.
3.1 Test for the Cointegration
The cointegration rank test determines the linearly independent columns of
.
Johansen (1988, 1995) and proposed the cointegration rank test using the reduced rank
regression.
Different Specifications of Deterministic Trends
When you construct the VECM (p) form from the VAR(p) model, the deterministic
terms in the VECM (p) form can differ from those in the VAR(p) model. When there are
deterministic cointegrated relationships among variables, deterministic terms in the VAR (p)
model will not be present in the VECM (p) form. On the other hand, if there are stochastic
cointegrated relationships, deterministic terms appear in the VECM (p) form via the error
correction term or as an independent term in the VECM (p) form.
Case 1: There is no separate drift in the VECM (p) form.
Case 2: There is no separate drift in the VECM (p) form, but a constant enters only
via the error correction term.
Case 3: There is a separate drift and no separate linear trend in the VECM (p) form.
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Case 4: There is a separate drift and no separate linear trend in the VECM (p) form,
but a linear trend enters only via the error correction term.
Case 5: There is a separate linear trend in the VECM (p) form.
First, focus on cases 1, 3, and 5 to test the null hypothesis that there are at most r
cointegrating vectors. Let
where Dt can be empty for Case 1; 1 for Case 3; (1,t) for Case 5. Let
parameters consisting of
be the matrix of
and A, where parameters A corresponds to regressors
Dt. Then the VECM (p) form is rewritten in these variables as
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The log-likelihood function is given by
The residuals, R0t and R1t, are obtained by regressing Z0t and Z1t on Z2t, respectively.
The regression equation in residuals is
The cross products matrices are computed
Then the maximum likelihood estimator for
is obtained from the eigenvectors
corresponding to the r largest eigenvalues of the following equation:
The eigenvalues of the preceding equation are squared canonical correlations between
R0t and R1t, and the eigenvectors corresponding to the r largest eigenvalues are the r linear
combinations of yt-1which have the largest squared partial correlations with the stationary
process as
after correcting for lags and deterministic terms. Such an analysis calls for a
reduced rank regression of on yt-1 corrected for
. Johansen
(1988) suggested two test statistics to test the null hypothesis that there are at most r
cointegrating vectors
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3.2 Trace Test
The asymptotic distribution of this statistic is given by
where tr(A) is the trace of a matrix A, W is the k-r dimensional Brownian motion, and
is
the Brownian motion itself, or the demeaned or detrended Brownian motion according to the
different specifications of deterministic trends in the vector error correction model.
Maximum Eigenvalue Test
The asymptotic distribution of this statistic is given by
where max(A) is the maximum eigenvalue of a matrix A.
In case 2, consider that Z1t = (yt',1)' and
.In case 4, Z1t = (yt',t)' and
.
3.3. Estimation of Vector Error Correction Model
Now consider cases 1, 3, and 5 for the vector error correction model. The preceding
log-likelihood function is maximized for
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The estimators of the orthogonal complements of
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and
are
and
The ML estimators have the following asymptotic properties:
where
and
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4.
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VAR Representation
The method of estimation of the parameters in equation (4.1) is ordinary least square.
Below is the VAR representation of the estimated VEC Model.
Pt
Nt
0,596
=
28.224
0.004 1.269
0.005 0.368
It
46.553
Pt
1
0.443
Nt
1
0.394
It
+
73.671
247 .210
12.413
1.354
29.280 4.163
1
const
Trend (t )
+
U 1(t )
...4. 1
U 2(t )
U 2(t )
4.1. VECM Representation
The VECM representation of the VAR (3) model is given in equation (4.2) Using the
method of maximum likelihood (ML) estimation on the sample.
VECM has one long-run relation from the above representation. The model is
presented in the table below.
Pt
Nt
It
0.404
=
Pt
0.004 1.00 69.947 115.368 Nt
It
0.005
1
1
1
+
73.671
247 .210
12.413
1.354
29.280 4.163
const
Trend (t )
+
U 1(t )
…4. 2
U 2(t )
U 3(t )
4.2. VECM Model Checking
To assess the adequacy the VECM (3) following the tests are applied to the residuals
(i) the Portmanteau LB tests, Godfrey LM tests for autocorrelation (ii) autoregressive
conditional heteroskedastic-Lagrange Multiplier tests for heteroskedastic-Lagrange Multiplier
test for heteroskedasticity (iii) Jarque-Bera tests for normality. See tables below.
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Table 1: Results for VECM Serial Correlation & Heteroskedicity Test
Residual Test
p-value
Portmanteau test LB
0.9489
Breusch – Godfrey LM test
0.0934
ARCH – LM test
0.3608
From the table the p-values for the tests are greater than the significant values 0.05 and 0.01.
There are no serial correlations or conditional heteroskedasticity in the residuals.
Table 2: Result of VECM Jarque-Bera Normality Test for individual Residual
Variables
2
p-value
Skewness
Kurtosis
U1
0.6750
-0.3788
3.1859
U2
0.5664
-0.4018
3.4843
U3
0.7511
-0.0492
3.3416
Table 3: Result of VECM Normality Test for Joint Residual
Reference: Doornik & Hansen (1994)
Joint statistic
3.3636
p-value
0.7620
The VECM Normality Tests for both individual and joint Residuals are normally distributed,
since p-values are greater than significant values 0.05.
4.3. Macroeconomic Implications
If all lagged differences of equation (4.2) are equal to zero, the long-run relation is
0.404
Pt
0.004 1.00 69.947 115.368 Nt
It
0.005
1
1
=0
…4.3
1
It implies
-0.404Pt-1 + 0.280Nt-1 – 0.577It-1 = 0
…4.4
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Therefore, from equations (4.3 & 4.4), there is one long-run relation for the past
observation, and it is possible to analyze the behavior of the past observations of per capital
GDP regarding the changes in past observations and vice versa.
Pt-1 = 0.693Nt-1 - 1.428It-1
…4.5
From equation 4.5 the past observation of per capital GDP is expected to increase at
the rate of 0.693 percent of the past observation of nominal GDP and decrease at the rate of 1.428 percent of the past observation of inflation rate.
More so, if the past observation of nominal GDP is independent on the other past
observation, equation 4.4 can be written as;
Nt-1 = 1.443Pt-1 + 2.061I t-1 …4.6
From equation 4.6, the past observation of nominal GDP is expected to increase at the
rate of 1.443 percent of the past observation of per capital GDP and at the rate of 2.061
percent of past observation of inflation rate.
Finally, if the past observation of inflation rate is dependent on past observations of
the other variables, equation 4.4 can be written as;
It-1 = - 0.700Pt-1 + 0.485Nt-1
…4.7
In equation 4.7 the past observation of inflation rate is expected to decrease at the rate
of -0.700 percent of the past observation of per capital GDP and increase at the rate of 0.485
percent of the past observation of nominal GDP.
5. Conclusion:
This study employs a cointegration VEC analysis of GDP and Inflation rate based on
one long-run equilibrium relationship in Nigeria economy. The annual datasets from 1970 to
2004 are: per capital GDP, nominal GDP, and Inflation Rate; and each datum represented in
the model as P, N and I respectively. When the variables are Cointegrated, the model used is
Vector Error Correction. The cointegration VAR (3) model is appropriate and the VEC (2)
model has exactly one cointegrating relation.
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The analysis also shows that per capital GDP is positively correlation with nominal
GDP and negatively correlation with inflation rate. Nominal GDP is positively correlation
with per capital GDP and positively correlation with inflation rate. Inflation rate is negatively
correlation with per capital GDP and positively correlation with nominal GDP.
5.1. Recommendations
Below are the recommendations based on the research work?
The government should encourage the citizen to rely mostly on home made goods and
encourage exportation of local goods for better economy.
Government should always plan for budget surplus and make sure it comes to pass.
In international trade, there should be balance of payment or surplus to promote economic
growth.
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Rangarajan, C. 'Development, Inflation and Monetary Policy' in I S Ahluwalia and IMD
Little (eds), India's Economic Reforms and Development, Oxford
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