This document provides an overview of an upcoming presentation on error correction models and their application to agricultural economics research. It outlines the major topics to be covered, including concepts and definitions related to cointegration and error correction models, Johansen's cointegration test, the Engle-Granger two-step error correction model, and a case study on market integration of arecanut in Karnataka state using an error correction model approach. Tables and figures are included to illustrate key concepts like order of integration, cointegration, and the residual-based test for cointegration.

1. 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

2. 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.
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3. Concept and definitions
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4. 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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5. Figure 1: Monthly prices of Arecanut in Mangalore from 2005 to 2011
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6. Pure Random Walk
Random Walk with Drift
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7. 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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8. Price series
is I(1)
Figure 2: 1st difference of monthly prices of Arecanut in Mangalore
from 2005 to 2011
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9. 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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10. 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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11. 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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12. 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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13. 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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14. 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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15. • 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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16. Residual plot of regression
Bantwala V/S kundapura
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17. 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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18. 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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19. 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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20. 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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21. • 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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22. • 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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23. Engle and Granger Two-Step
ECM
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24. • 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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25. Department Of Agricultural Economics, 25
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26. • Market integration of Arecanut in
Karnataka state: An ECM approach.
(Source: Author)
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27. 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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28. Integrated markets:
Efficiency
Equality
Stability
Maximize social welfare
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29. • 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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30. • 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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31. 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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32. 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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33. Methodology
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34. Unit root testing
NH: Series is non stationary
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35. 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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36. 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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37. Testing for cointegration
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38. Engle Granger test -Decision
rule
• Engle Granger critical value at 1% LOS is -3.96
Ut= ΏUt-1 + e
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39. 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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40. Johansen cointegration test
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41. 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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42. 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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43. 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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44. 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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45. 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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46. 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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47. 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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48. 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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49. • 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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50. Department Of Agricultural Economics, 50
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