Cointegration and error correction model

Error Correction Model And Its
Application To Agricultural
Economics Research.
Presenter
Aditya K.S., PALB (1094)
Sr. M.Sc. (Agricultural Economics)

Major Adviser: Dr. T.N. Prakash Kammardi

Flow of presentation
Concepts and definitions.
Cointegration.
Residual based test for cointegration.
Johansen’s cointegration test.
Introduction to ECM.
Engle – Granger two step ECM.
Market integration of Arecanut in Karnataka state: An ECM approach.
Final outcome.
Concluding remarks.
References.

Department Of Agricultural Economics, 2
Bangalore

Concept and definitions

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Stationary v/s non stationary
• If a time series is stationary, its mean and
variance remain the same no matter at what
point we measure them;
That is, they are time invariant.

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Figure 1: Monthly prices of Arecanut in Mangalore from 2005 to 2011

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Pure Random Walk

Random Walk with Drift

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Order of Integration
 Differencing is a way to convert non stationary data into stationary.
 If the data has to be differenced d times to make it stationary then series
said to be integrated of order (d) and represented as I(d)
 I(1) processes are fairly common in economic time series data

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Price series
is I(1)

Figure 2: 1st difference of monthly prices of Arecanut in Mangalore
from 2005 to 2011

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UNIT ROOT
Yt = ρYt −1 + ut
• If ρ = 1 it becomes a pure random walk.
• If ρ is in fact 1, we face what is known as the unit root
problem, that is, a situation of nonstationary;
• The name unit root is due to the fact that ρ = 1.

Synonymous

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Testing for unit roots
Augmented dickey fuller test(ADF) – Include the lagged terms.

Phillip Perron tests (PP) – Non parametric method.

NH: Series contains unit root

AH : Series does not contain unit roots

Decision rule: Reject NH if P<0.05

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Spurious Regression
Suppose that Yt and Xt are two non stationary time series variables

Yt = βXt + error:

β significant β not significant

Due to actual Due to trend Yt and Xt are independent
relationship (non stationarity)

Cointegration Spurious regression R2 >D.W stat

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Cointegration
• Economic theory often suggests that certain
subset of variables should be linked by a long-
run equilibrium relationship.
• Although the variables under consideration
may drift away from equilibrium for a while,
economic forces or government actions may
be expected to restore equilibrium.

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Observe that two
series follow each
other closely

Shho
S orr
t trru
unndd
isseq
i equu
ilibb
ili rru
i i um
m

Figure 3: Monthly prices of Arecanut in Mangalore and Kundapura from
2005 to 2011

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Residual-based Test for
Cointegration
• One of most popular tests for (a single) co
integration has been suggested by Engle and
Granger (1987, Econometrica).

Consider the multiple regression: Yt = βXt + ut;

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• for yt and xt to be cointegrated, ut must be I(0).
• Otherwise it is spurious. Thus, a basic idea
behind is to test whether ut is I(0) or I(1).

Cointegration
Ut is stationary

Ut is not stationary Spurious
regression

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Residual plot of regression
Bantwala V/S kundapura
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Johansen's procedure

• Johansen's procedure builds cointegrated variables
directly on maximum likelihood estimation
• Tests for determining the number of cointegrating
vectors.
• Multivariate generalization of the Dickey-Fuller test.
• Two different likelihood ratio tests namely the Trace
test and the Maximum Eigen value test.

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Two time series are cointegrated
if
Both are integrated of the same order.

There is a linear combination of the two time series that is I(0) - i.e. - stationary.

Cointegrated data are never drift too far away from each other

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An Introduction to ECMs
• Error Correction Models (ECMs) multiple time
series models that estimate the speed at which a
dependent variable - Y - returns to equilibrium
after a change in an independent variable - X. i.e
SPEED OF ADJUSTMENT

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ECMs can be appropriate
whenever

time series data Non stationary

Interested in
both short and
long term
relationships

Integrated of
same order Cointegrated

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• Yt = βXt + Ut
• Here, Ut represents the portion of Y (in levels)
that is not attributable to X.
• In short, Ut will capture the error correction
relationship by capturing the degree to which
Y and X are out of equilibrium.

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• Ut-1 = Yt-1 - Xt-1
• When Ut-1 = 0 the system is in its equilibrium
state.
• So ECM can be built as
∆Yt = C + Φ ∆Xt + αUt-1

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Engle and Granger Two-Step
ECM

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• Engle and Granger (1987) suggested an
appropriate model for Y, based two or more
time series that are cointegrated.
• First, we can obtain an estimate of Ut by
regressing Y on X.
• Second, we can regress ∆ Yt on Ut-1 plus any
relevant short term effects as ∆ X t.

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Bangalore

• Market integration of Arecanut in
Karnataka state: An ECM approach.
(Source: Author)

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Market Integration

• Spatial market integration refers to co-
movements or a long run relationship of
prices.
• It is defined as the smooth transmission of
price signals and information across spatially
separated markets

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Integrated markets:
Efficiency
Equality
Stability
Maximize social welfare

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• Study of market integration is very important
though neglected.
• Knowledge of market integration would be
vital to know the market efficiency, and to
device measures to overcome imperfections.

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• Traditional method of study employs
correlation matrix to study the market
integrations.
• Since the data are non stationary results may
not be accurate and hence criticized.

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Data and Methodology
• For the purpose of analyzing the integration of
arecanut markets, monthly prices of arecanut
from 2005 to 2011 in 7 major arecanut
markets in Karnataka was used.
• Data was collected from Agmarknet.

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Table 1:MarkeTs selecTed for sTudy

Sl no WCT RBT
1 Mangalore Shimoga
2 Bantwala Sagara
3 Kundapura Davangeree
4 Sirsi

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Methodology

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Unit root testing
NH: Series is non stationary

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Table 2: Results of Unit root test for arecanut price in major RBT
markets from 2005 to 2011
At level
PP P value ADF P value
Sagara -1.90949 0.3259 -1.53207 0.5105
Shimoga -2.59777 0.0991 -2.69163 0.0815

Davangeree -2.39903 0.1464 -1.59475 0.4787

Sirsi -2.14473 0.2285 -1.13264 0.6969
After first difference
PP P value ADF P value
Sagara -10.8727 0 -10.1247 0
Shimoga -14.8105 0 -6.57014 0

Davangeree -11.1522 0 -8.09634 0

Sirsi -11.37 0 -8.307 0

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Table 3: Results of Unit root test for arecanut price in
major WCT markets from 2005 to 2011
At level
ADF P PP p

Mangalore -1.75041 0.4024 -1.75041 0.4024

Kundapura -2.09198 0.2484 -2.13241 0.2328

Bantwala -0.56366 0.8719 -0.64773 0.8531

At 1st difference
ADF P PP p

Mangalore -7.89198 0 -7.94013 0

Kundapura -7.02788 0 -8.49619 0

Bantwala -12.1208 0.0001 -12.3691 0.0001

Both tests indicate that prices are integrated of order (1)

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Testing for cointegration

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Engle Granger test -Decision
rule
• Engle Granger critical value at 1% LOS is -3.96
Ut= ΏUt-1 + e

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Table 4. Engle Granger cointegration test
for major arecanut markets in Karnataka

Kundapura Mangalore
Bantwala -6.2580 -2.57891
Kundapura -6.47711

Sagara Shimoga Sirsi
Davangeree -5.264 -6.16165 -5.4227
Sagara -5.7895 -5.5994
Shimoga -5.4529

There is cointegration among all markets under
consideration except Bantwala and Mangalore

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Johansen cointegration test

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Table 5. Johansen’s cointegration test for RBT
arecanut markets

Shimoga Davangeree Sirsi

No of coint
equations trace stat p trace stat p trace stat p

Sagara R=0 20.68967 0.0075 26.24133 0.0008 22.90293 0.0032

R≤1 2.148919 0.1427 2.197354 0.1382 2.391261 0.122

Shimoga R=0 29.09037 0.0003 18.48941 0.0171

R≤ 1 4.906882 0.0267 2.71361 0.0995

Davangeree R=0 29.16382 0.0003

R≤ 1 2.9382 0.0865

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Contd…………….

Shimoga Davangere Sirsi
Number of Max Max
Max eigen
coint p eigen p eigen p
value
equations value value

R=0 18.54075 0.0099 24.04398 0.0011 20.51167 0.0045

Sagara
R≤ 1 2.148919 0.1427 2.197354 0.1382 2.391261 0.122

R=0 24.18349 0.001 15.7758 0.0286

Shimoga
R≤ 1 4.906882 0.0267 2.71361 0.0995

R=0 26.22562 0.0004
Davangeree
R≤ 1 2.9382 0.0865

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Table :6 Johansen’s cointegration test for WCT arecanut markets

trace stat Max eigen value

No. of coint
Dependent Independent value P value P
equation

Bantwala Mangalore R=0 10.29579 0.3888 7.901239 0.255

R≤1 2.394551 0.1218 2.394551 0.1218

Kundapura Bantwala R=0 23.32457 0.0027 23.26433 0.0015

R≤1 0.060234 0.8061 0.060234 0.8061

Kundapura Mangalore R=0 16.93599 0.0301 13.84253 0.05

R≤1 3.093461 0.0786 3.093461 0.0786

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Table 7 : Error correction models for RBT arecanut markets
Error Correction model results for RBT.

∆ Dav = -9.73171+0.8484∆ sag – 0.64371 et-1

Model estimated: ∆ Yt= C + Φ ∆Xt+ α Ut-1
Model estimated: ∆ Yt= C + Φ ∆Xt+ α Ut-1 (0.90) (0) (0)

∆ Dav = -12.3961 + 0.8104 ∆ sir – 0.64273 et-1

(0.8967) (0) (0)

∆ Dav = -6.92457 + 0.7822 ∆ shiv – 0.73867 et-1

(0.9249) (0) (0)

∆ Sag = - 2.2253 + 0.65523 ∆ shiv – 0.6073 et-1

(0.98) (0) (0)

Figures in parenthesis indicate the ∆ Sag = - 3.9302 + 0.8762 ∆ shir– 0.6453 et-1
probability values.
(0.95) (0) (0)

∆ shiv = - 7.6146 + 1.007 ∆ shir– 0.6719 et-1

(0.93) (0) (0)
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Table 8 : Error correction models for RBT arecanut markets

Error Correction model results for WCT.

∆ kund = 3.79 + 0.83 ∆mang -0.66 et-1
( 0.98) ( 0.001) (0)

∆ bant = 22.75 +0.75 ∆kund -0.72 et-1
(0.97) (0.002) (0)

Figures in parenthesis indicate the probability values.

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Table 9: Speed of error correction
Sagara Shimoga Sirsi Mangalore Kundapura

Bantwala 66 72
Davang 64 73 64
eree
Sagara 60 64
Shimog 67
a

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Final outcome
• Arecanut markets are highly cointegrated may be
because of better marketing infrastructure, existence
of cooperatives, easy flow of market information and
non perishability.
• Price volatility observed during last few years has
nothing to do with the inefficiency of domestic
markets.
• If the government wants to stabilize the prices of
arecanut, then it can be done by stabilizing the prices
in one important market.
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Concluding remarks
• Most valuable contribution of concept of cointegration is to
force us to test for Stationarity of the residuals.
• Cointegration can be thought as pre test to avoid spurious
regression situation.
• Cointegrated variables will always have a built in error
correction mechanism, estimation of which will be helpful to
know short run dynamics of the system.

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• Though theoretically appealing, practically
simple, ECM cannot be used in complex
situations involving more number of non
stationary variables.
• In such situations one can go for vector error
correction models (VECM) which are nothing
but multivariate specification of ECM.

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Cointegration and error correction model

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