1. NGUYEN THI HANG NGA
    2 years & 3 months ago

    Dear Divya Dhuria,
    Can you tell me when to use Var and VECM models?
    Thank you sincerely
    Best regards

    Reply
  2. Victor Lumumba
    2 years & 7 months ago

    What should I do if the system tells me that “the parameters of the cointegrating equations are not identified by the sample, check your sample and the number of lags specified”
    Kindly assist me

    Reply
  3. Ellis
    3 years & 4 months ago

    Hi, thanks for this article. In Stata VECM output, there is a table at the bottom called ‘Johansen normalization restriction imposed’. That table seems to be missing in your article. I understand it contains the long-run relationship. Could you please explain?

    Reply
  4. Degefa Heyi
    3 years & 8 months ago

    I am a MA student in deveploment economics at AUWC, while i doing my thesis data analysis i some chalenge questions
    Two of my variables are I(0) and the rest are I(1) will proceed to Johnson co-integration?

    Reply
  5. Cheng TONGYANG
    4 years & 9 months ago

    Thank you. Your lesson is very important and very good for all researchers.

    Reply
  6. Belay Zewude
    5 years & 1 month ago

    No answer for this question ? the economist please say something

    Reply
  7. Belay Zewude
    5 years & 1 month ago

    I thank you very much for your response but I have attempted to do stability test and I have got the result of it. Also please the following result and see whether it has long term and short term relationship and also normality.

    AIC = 2.399748
    Log likelihood = -30.39534 HQIC = 2.614638
    Det(Sigma_ml) = 3.56e-06 SBIC = 3.009285

    Equation Parms RMSE R-sq chi2 P>chi2
    —————————————————————-
    D_LCDT 2 .164031 0.4397 27.46918 0.0000
    D_LEpnd 2 .120953 0.6194 56.94922 0.0000
    D_LGrant 2 .378515 0.1601 6.672735 0.0356
    D_LRGDP 2 .128568 0.2534 11.88228 0.0026
    D_Lopns 2 3.11808 0.1337 5.400241 0.0672
    —————————————————————-

    ——————————————————————————
    | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    D_LCDT |
    _ce1 |
    L1. | .0677391 .0586611 1.15 0.248 -.0472345 .1827128
    |
    _cons | .134283 .0271441 4.95 0.000 .0810815 .1874844
    ————-+—————————————————————-
    D_LEpnd |
    _ce1 |
    L1. | .1363515 .0432553 3.15 0.002 .0515727 .2211303
    |
    _cons | .1291361 .0200154 6.45 0.000 .0899067 .1683656
    ————-+—————————————————————-
    D_LGrant |
    _ce1 |
    L1. | -.2432827 .1353649 -1.80 0.072 -.508593 .0220275
    |
    _cons | .1283122 .062637 2.05 0.041 .0055459 .2510785
    ————-+—————————————————————-
    D_LRGDP |
    _ce1 |
    L1. | -.0068975 .0459785 -0.15 0.881 -.0970137 .0832187
    |
    _cons | .0731539 .0212755 3.44 0.001 .0314547 .1148531
    ————-+—————————————————————-
    D_Lopns |
    _ce1 |
    L1. | 2.57387 1.115092 2.31 0.021 .388329 4.75941
    |
    _cons | .0019491 .5159836 0.00 0.997 -1.00936 1.013258
    ——————————————————————————

    Cointegrating equations

    Equation Parms chi2 P>chi2
    ——————————————-
    _ce1 4 346.3087 0.0000
    ——————————————-

    Identification: beta is exactly identified

    Johansen normalization restriction imposed
    ——————————————————————————
    beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    _ce1 |
    LCDT | 1 . . . . .
    LEpnd | -2.482578 .4359987 -5.69 0.000 -3.33712 -1.628036
    LGrant | 1.178082 .2423768 4.86 0.000 .7030325 1.653132
    LRGDP | 1.110874 .6505622 1.71 0.088 -.1642045 2.385953
    Lopns | -.056375 .0174486 -3.23 0.001 -.0905737 -.0221763
    _cons | -3.983634 . . . . .
    ——————————————————————————

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vec LCDT LEpnd LGrant LRGDP Lopns,lags(1)rank (1) noetable

    Vector error-correction model

    Sample: 2 – 38 Number of obs = 37
    AIC = 2.399748
    Log likelihood = -30.39534 HQIC = 2.614638
    Det(Sigma_ml) = 3.56e-06 SBIC = 3.009285

    Cointegrating equations

    Equation Parms chi2 P>chi2
    ——————————————-
    _ce1 4 346.3087 0.0000
    ——————————————-

    Identification: beta is exactly identified

    Johansen normalization restriction imposed
    ——————————————————————————
    beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    _ce1 |
    LCDT | 1 . . . . .
    LEpnd | -2.482578 .4359987 -5.69 0.000 -3.33712 -1.628036
    LGrant | 1.178082 .2423768 4.86 0.000 .7030325 1.653132
    LRGDP | 1.110874 .6505622 1.71 0.088 -.1642045 2.385953
    Lopns | -.056375 .0174486 -3.23 0.001 -.0905737 -.0221763
    _cons | -3.983634 . . . . .
    ——————————————————————————

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vec LCDT LEpnd LGrant LRGDP Lopns,lags(1)rank (1) noetable

    Vector error-correction model

    Sample: 2 – 38 Number of obs = 37
    AIC = 2.399748
    Log likelihood = -30.39534 HQIC = 2.614638
    Det(Sigma_ml) = 3.56e-06 SBIC = 3.009285

    Cointegrating equations

    Equation Parms chi2 P>chi2
    ——————————————-
    _ce1 4 346.3087 0.0000
    ——————————————-

    Identification: beta is exactly identified

    Johansen normalization restriction imposed
    ——————————————————————————
    beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    _ce1 |
    LCDT | 1 . . . . .
    LEpnd | -2.482578 .4359987 -5.69 0.000 -3.33712 -1.628036
    LGrant | 1.178082 .2423768 4.86 0.000 .7030325 1.653132
    LRGDP | 1.110874 .6505622 1.71 0.088 -.1642045 2.385953
    Lopns | -.056375 .0174486 -3.23 0.001 -.0905737 -.0221763
    _cons | -3.983634 . . . . .
    ——————————————————————————

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vec LCDT LEpnd LGrant LRGDP Lopns,lags(1)rank (1) nobtable

    Vector error-correction model

    Sample: 2 – 38 Number of obs = 37
    AIC = 2.399748
    Log likelihood = -30.39534 HQIC = 2.614638
    Det(Sigma_ml) = 3.56e-06 SBIC = 3.009285

    Equation Parms RMSE R-sq chi2 P>chi2
    —————————————————————-
    D_LCDT 2 .164031 0.4397 27.46918 0.0000
    D_LEpnd 2 .120953 0.6194 56.94922 0.0000
    D_LGrant 2 .378515 0.1601 6.672735 0.0356
    D_LRGDP 2 .128568 0.2534 11.88228 0.0026
    D_Lopns 2 3.11808 0.1337 5.400241 0.0672
    —————————————————————-

    ——————————————————————————
    | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    D_LCDT |
    _ce1 |
    L1. | .0677391 .0586611 1.15 0.248 -.0472345 .1827128
    |
    _cons | .134283 .0271441 4.95 0.000 .0810815 .1874844
    ————-+—————————————————————-
    D_LEpnd |
    _ce1 |
    L1. | .1363515 .0432553 3.15 0.002 .0515727 .2211303
    |
    _cons | .1291361 .0200154 6.45 0.000 .0899067 .1683656
    ————-+—————————————————————-
    D_LGrant |
    _ce1 |
    L1. | -.2432827 .1353649 -1.80 0.072 -.508593 .0220275
    |
    _cons | .1283122 .062637 2.05 0.041 .0055459 .2510785
    ————-+—————————————————————-
    D_LRGDP |
    _ce1 |
    L1. | -.0068975 .0459785 -0.15 0.881 -.0970137 .0832187
    |
    _cons | .0731539 .0212755 3.44 0.001 .0314547 .1148531
    ————-+—————————————————————-
    D_Lopns |
    _ce1 |
    L1. | 2.57387 1.115092 2.31 0.021 .388329 4.75941
    |
    _cons | .0019491 .5159836 0.00 0.997 -1.00936 1.013258
    ——————————————————————————

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vec LCDT LEpnd LGrant LRGDP Lopns,lag(2)rank (1)

    Vector error-correction model

    Sample: 3 – 38 Number of obs = 36
    AIC = 2.804347
    Log likelihood = -11.47824 HQIC = 3.403095
    Det(Sigma_ml) = 1.30e-06 SBIC = 4.519826

    Equation Parms RMSE R-sq chi2 P>chi2
    —————————————————————-
    D_LCDT 7 .178226 0.4397 22.7582 0.0019
    D_LEpnd 7 .112423 0.7265 77.01659 0.0000
    D_LGrant 7 .354822 0.3877 18.36007 0.0104
    D_LRGDP 7 .129923 0.3683 16.90535 0.0180
    D_Lopns 7 3.16823 0.2577 10.06795 0.1848
    —————————————————————-

    ——————————————————————————
    | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    D_LCDT |
    _ce1 |
    L1. | -.0564224 .0707425 -0.80 0.425 -.1950752 .0822304
    |
    LCDT |
    LD. | .0698024 .2275522 0.31 0.759 -.3761916 .5157965
    |
    LEpnd |
    LD. | .0972834 .2407466 0.40 0.686 -.3745712 .5691381
    |
    LGrant |
    LD. | -.0251761 .0802288 -0.31 0.754 -.1824217 .1320694
    |
    LRGDP |
    LD. | .328565 .4310464 0.76 0.446 -.5162705 1.1734
    |
    Lopns |
    LD. | .0047569 .0107492 0.44 0.658 -.0163112 .025825
    |
    _cons | .1235277 .0483707 2.55 0.011 .0287228 .2183326
    ————-+—————————————————————-
    D_LEpnd |
    _ce1 |
    L1. | .1734465 .0446235 3.89 0.000 .0859862 .2609069
    |
    LCDT |
    LD. | -.044177 .1435369 -0.31 0.758 -.3255042 .2371501
    |
    LEpnd |
    LD. | .076646 .1518598 0.50 0.614 -.2209937 .3742856
    |
    LGrant |
    LD. | .1050035 .0506073 2.07 0.038 .005815 .2041919
    |
    LRGDP |
    LD. | -.665257 .2718984 -2.45 0.014 -1.198168 -.132346
    |
    Lopns |
    LD. | .0063684 .0067805 0.94 0.348 -.0069211 .0196578
    |
    _cons | .0693701 .0305116 2.27 0.023 .0095685 .1291718
    ————-+—————————————————————-
    D_LGrant |
    _ce1 |
    L1. | .2509111 .1408383 1.78 0.075 -.0251269 .526949
    |
    LCDT |
    LD. | .6066396 .4530238 1.34 0.181 -.2812708 1.49455
    |
    LEpnd |
    LD. | -.1620136 .4792921 -0.34 0.735 -1.101409 .7773816
    |
    LGrant |
    LD. | -.3765547 .1597241 -2.36 0.018 -.6896081 -.0635013
    |
    LRGDP |
    LD. | -1.844968 .8581518 -2.15 0.032 -3.526915 -.1630213
    |
    Lopns |
    LD. | -.001615 .0214001 -0.08 0.940 -.0435585 .0403285
    |
    _cons | .0891856 .0962992 0.93 0.354 -.0995574 .2779285
    ————-+—————————————————————-
    D_LRGDP |
    _ce1 |
    L1. | .0764743 .0515697 1.48 0.138 -.0246005 .177549
    |
    LCDT |
    LD. | -.1907902 .1658804 -1.15 0.250 -.5159098 .1343293
    |
    LEpnd |
    LD. | .2469228 .1754988 1.41 0.159 -.0970486 .5908941
    |
    LGrant |
    LD. | .0269571 .058485 0.46 0.645 -.0876713 .1415856
    |
    LRGDP |
    LD. | -.2205035 .3142231 -0.70 0.483 -.8363694 .3953624
    |
    Lopns |
    LD. | .0035621 .0078359 0.45 0.649 -.0117961 .0189202
    |
    _cons | .036443 .0352612 1.03 0.301 -.0326677 .1055536
    ————-+—————————————————————-
    D_Lopns |
    _ce1 |
    L1. | -2.250422 1.257553 -1.79 0.074 -4.715181 .2143374
    |
    LCDT |
    LD. | 5.360883 4.045077 1.33 0.185 -2.567323 13.28909
    |
    LEpnd |
    LD. | -.5193796 4.279628 -0.12 0.903 -8.907296 7.868537
    |
    LGrant |
    LD. | 2.92722 1.426186 2.05 0.040 .131947 5.722493
    |
    LRGDP |
    LD. | 5.600819 7.66249 0.73 0.465 -9.417385 20.61902
    |
    Lopns |
    LD. | -.041468 .1910831 -0.22 0.828 -.4159839 .333048
    |
    _cons | .0134316 .8598615 0.02 0.988 -1.671866 1.698729
    ——————————————————————————

    Cointegrating equations

    Equation Parms chi2 P>chi2
    ——————————————-
    _ce1 4 197.9077 0.0000
    ——————————————-

    Identification: beta is exactly identified

    Johansen normalization restriction imposed
    ——————————————————————————
    beta | Coef. Std. Err. z P>|z| [95% Conf. Interval]
    ————-+—————————————————————-
    _ce1 |
    LCDT | 1 . . . . .
    LEpnd | -2.495936 .5687129 -4.39 0.000 -3.610593 -1.38128
    LGrant | -.223748 .2883544 -0.78 0.438 -.7889123 .3414163
    LRGDP | 4.119485 1.050475 3.92 0.000 2.060591 6.178379
    Lopns | .0162884 .0183115 0.89 0.374 -.0196014 .0521782
    _cons | -31.60329 . . . . .
    ——————————————————————————

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vecstable

    Eigenvalue stability condition
    +—————————————-+
    | Eigenvalue | Modulus |
    |————————–+————-|
    | 1 | 1 |
    | 1 | 1 |
    | 1 | 1 |
    | 1 | 1 |
    | .9951696 | .99517 |
    | -.1939456 + .5329696i | .567161 |
    | -.1939456 – .5329696i | .567161 |
    | -.4558523 | .455852 |
    | .2549587 | .254959 |
    | -.1655585 | .165558 |
    +—————————————-+
    The VECM specification imposes 4 unit moduli.

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vecstable, graph

    Eigenvalue stability condition
    +—————————————-+
    | Eigenvalue | Modulus |
    |————————–+————-|
    | 1 | 1 |
    | 1 | 1 |
    | 1 | 1 |
    | 1 | 1 |
    | .9951696 | .99517 |
    | -.1939456 + .5329696i | .567161 |
    | -.1939456 – .5329696i | .567161 |
    | -.4558523 | .455852 |
    | .2549587 | .254959 |
    | -.1655585 | .165558 |
    +—————————————-+
    The VECM specification imposes 4 unit moduli.

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . veclmar, mlag(1)

    Lagrange-multiplier test
    +————————————–+
    | lag | chi2 df Prob > chi2 |
    |——+——————————-|
    | 1 | 12.9130 25 0.97755 |
    +————————————–+
    H0: no autocorrelation at lag order

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . veclmar, mlag(2)

    Lagrange-multiplier test
    +————————————–+
    | lag | chi2 df Prob > chi2 |
    |——+——————————-|
    | 1 | 12.9130 25 0.97755 |
    | 2 | 10.0484 25 0.99652 |
    +————————————–+
    H0: no autocorrelation at lag order

    .
    end of do-file

    . do “C:\Users\belayz\AppData\Local\Temp\STD07000000.tmp”

    . vecnorm

    Jarque-Bera test
    +——————————————————–+
    | Equation | chi2 df Prob > chi2 |
    |——————–+———————————–|
    | D_LCDT | 3.189 2 0.20304 |
    | D_LEpnd | 0.047 2 0.97694 |
    | D_LGrant | 0.935 2 0.62654 |
    | D_LRGDP | 524.794 2 0.00000 |
    | D_Lopns | 1.167 2 0.55799 |
    | ALL | 530.131 10 0.00000 |
    +——————————————————–+

    Skewness test
    +——————————————————–+
    | Equation | Skewness chi2 df Prob > chi2 |
    |——————–+———————————–|
    | D_LCDT | .7012 2.950 1 0.08587 |
    | D_LEpnd | .07336 0.032 1 0.85738 |
    | D_LGrant | .39395 0.931 1 0.33456 |
    | D_LRGDP | 3.7208 83.068 1 0.00000 |
    | D_Lopns | -.43828 1.153 1 0.28302 |
    | ALL | 88.134 5 0.00000 |
    +——————————————————–+

    Kurtosis test
    +——————————————————–+
    | Equation | Kurtosis chi2 df Prob > chi2 |
    |——————–+———————————–|
    | D_LCDT | 3.3988 0.239 1 0.62523 |
    | D_LEpnd | 2.9022 0.014 1 0.90462 |
    | D_LGrant | 3.0511 0.004 1 0.95013 |
    | D_LRGDP | 20.161 441.726 1 0.00000 |
    | D_Lopns | 2.9025 0.014 1 0.90490 |
    | ALL | 441.997 5 0.00000

    Reply
  8. Belay Zewude
    5 years & 1 month ago

    Johansen tests for cointegration
    Trend: constant Number of obs = 34
    Sample: 5 – 38 Lags = 4
    ——————————————————————————-
    5%
    maximum trace critical
    rank parms LL eigenvalue statistic value
    0 114 -65.153897 . 207.3882 94.15
    1 125 -13.512973 0.95206 104.1063 68.52
    2 134 9.1839255 0.73687 58.7125 47.21
    3 141 24.124265 0.58474 28.8318* 29.68
    4 146 32.964474 0.40549 11.1514 15.41
    5 149 38.016635 0.25709 1.0471 3.76
    6 150 38.540188 0.03033
    ————————————————————————
    can I say there cointigration? when I have tested stability it is not stable and not normal so what can I do to have stable out put

    Reply
  9. HP
    5 years & 1 month ago

    Thank you.

    Reply
  10. Saptarshi Basu Roy Choudhury
    5 years & 2 months ago

    Hi HP,

    Thanks for your comment. We have already published articles on how to do unit root test, lag selection, cointegration, and vecm test. Each of those articles also includes the output as produced by STATA. If you need to summarize results, either you can copy the output tables first to excel and then import them to a word document. But it often does not give you the right alignment or formatting. For a better way to summarize results, you can use the command “outreg2”. For that, first, install the comment in STATA, then copy and paste your output tables in a word document and finally run the command. Refer to this link for how to use this command.

    https://www.princeton.edu/~otorres/Outreg2.pdf

    Hope it helps.

    Reply