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# Cointegration and error correction model

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Error correction model and its application to agri economics research.

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• sir can you differentiate PLZ what is difference between VECM AND ECM

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### Cointegration and error correction model

1. 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. 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. Department Of Agricultural Economics, 2 Bangalore
3. 3. Concept and definitions Department Of Agricultural Economics, 3 Bangalore
4. 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. Department Of Agricultural Economics, 4 Bangalore
5. 5. Figure 1: Monthly prices of Arecanut in Mangalore from 2005 to 2011 Department Of Agricultural Economics, 5 Bangalore
6. 6. Pure Random WalkRandom Walk with Drift  Department Of Agricultural Economics, 6 Bangalore
7. 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 Department Of Agricultural Economics, 7 Bangalore
8. 8. Price series is I(1)Figure 2: 1st difference of monthly prices of Arecanut in Mangalorefrom 2005 to 2011 Department Of Agricultural Economics, 8 Bangalore
9. 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 Department Of Agricultural Economics, 9 Bangalore
10. 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 Department Of Agricultural Economics, 10 Bangalore
11. 11. Spurious Regression Suppose that Yt and Xt are two non stationary time series variables Yt = βXt + error: β significant β not significantDue to actual Due to trend Yt and Xt are independent relationship (non stationarity)Cointegration Spurious regression R2 >D.W stat Department Of Agricultural Economics, 11 Bangalore
12. 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. Department Of Agricultural Economics, 12 Bangalore
13. 13. Observe that two series follow each other closely Shho S orr t trru unndd isseq i equu ilibb ili rru i i um mFigure 3: Monthly prices of Arecanut in Mangalore and Kundapura from2005 to 2011 Department Of Agricultural Economics, 13 Bangalore
14. 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; Department Of Agricultural Economics, 14 Bangalore
15. 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 Department Of Agricultural Economics, 15 Bangalore
16. 16. Residual plot of regression Bantwala V/S kundapura Department Of Agricultural Economics, 16 Bangalore
17. 17. Johansens procedure• Johansens 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. Department Of Agricultural Economics, 17 Bangalore
18. 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 Department Of Agricultural Economics, 18 Bangalore
19. 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 Department Of Agricultural Economics, 19 Bangalore
20. 20. ECMs can be appropriate whenevertime series data Non stationary Interested in both short and long term relationshipsIntegrated of same order Cointegrated Department Of Agricultural Economics, 20 Bangalore
21. 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. Department Of Agricultural Economics, 21 Bangalore
22. 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 Department Of Agricultural Economics, 22 Bangalore
23. 23. Engle and Granger Two-Step ECM Department Of Agricultural Economics, 23 Bangalore
24. 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. Department Of Agricultural Economics, 24 Bangalore
25. 25. Department Of Agricultural Economics, 25 Bangalore
26. 26. • Market integration of Arecanut in Karnataka state: An ECM approach. (Source: Author) Department Of Agricultural Economics, 26 Bangalore
27. 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 Department Of Agricultural Economics, 27 Bangalore
28. 28. Integrated markets: Efficiency Equality Stability Maximize social welfareDepartment Of Agricultural Economics, 28 Bangalore
29. 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. Department Of Agricultural Economics, 29 Bangalore
30. 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. Department Of Agricultural Economics, 30 Bangalore
31. 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. Department Of Agricultural Economics, 31 Bangalore
32. 32. Table 1:MarkeTs selecTed for sTudy Sl no WCT RBT 1 Mangalore Shimoga 2 Bantwala Sagara 3 Kundapura Davangeree 4 Sirsi Department Of Agricultural Economics, 32 Bangalore
33. 33. Methodology Department Of Agricultural Economics, 33 Bangalore
34. 34. Unit root testingNH: Series is non stationary Department Of Agricultural Economics, 34 Bangalore
35. 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 Department Of Agricultural Economics, 35 Bangalore
36. 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) Department Of Agricultural Economics, 36 Bangalore
37. 37. Testing for cointegration Department Of Agricultural Economics, 37 Bangalore
38. 38. Engle Granger test -Decision rule• Engle Granger critical value at 1% LOS is -3.96 Ut= ΏUt-1 + e Department Of Agricultural Economics, 38 Bangalore
39. 39. Table 4. Engle Granger cointegration test for major arecanut markets in Karnataka Kundapura MangaloreBantwala -6.2580 -2.57891Kundapura -6.47711 Sagara Shimoga SirsiDavangeree -5.264 -6.16165 -5.4227Sagara -5.7895 -5.5994Shimoga -5.4529 There is cointegration among all markets under consideration except Bantwala and Mangalore Department Of Agricultural Economics, 39 Bangalore
40. 40. Johansen cointegration test Department Of Agricultural Economics, 40 Bangalore
41. 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 pSagara 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 0.122Shimoga R=0 29.09037 0.0003 18.48941 0.0171 R≤ 1 4.906882 0.0267 2.71361 0.0995Davangeree R=0 29.16382 0.0003 R≤ 1 2.9382 0.0865 Department Of Agricultural Economics, 41 Bangalore
42. 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 0.0004Davangeree R≤ 1 2.9382 0.0865 Department Of Agricultural Economics, 42 Bangalore
43. 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 Department Of Agricultural Economics, 43 Bangalore
44. 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-1Model estimated: ∆ Yt= C + Φ ∆Xt+ α Ut-1Model 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) Department Of Agricultural Economics, 44 Bangalore
45. 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. Department Of Agricultural Economics, 45 Bangalore
46. 46. Table 9: Speed of error correction Sagara Shimoga Sirsi Mangalore Kundapura Bantwala 66 72Davang 64 73 64ereeSagara 60 64Shimog 67a Department Of Agricultural Economics, 46 Bangalore
47. 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. Department Of Agricultural Economics, 47 Bangalore
48. 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. Department Of Agricultural Economics, 48 Bangalore
49. 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. Department Of Agricultural Economics, 49 Bangalore
50. 50. Department Of Agricultural Economics, 50 Bangalore