Stata Tutorial: Cointegration and Error Correction

A basic application of the Engle-Granger residual based co-integration test for two variables.
Link to "Gentle Introduction to Stata"
www.amazon.com/gp/product/159...
Link to the excellent Introduction to Econometrics Textbook by AH Studenmund:
www.amazon.com/gp/product/933...
Link to Jeffrey Wooldridge Introductory Econometrics Textbook:
www.amazon.com/gp/product/813...
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[@tombic6373]

This video provides a clear, concise explanation on how to apply the Engle-Granger test. It's clear--he shows you the files to download to replicate his results; it's concise--he covers a great deal in 13 minutes; and, as a bonus--he shows you how to download a time-saving command. Awesome. Mike, fine presentation!

[@egecant]

You explain it very calmly and simple manner. I appreciate your effort. Thank you for creating these videos, we owe you so much.

[@versystudio822]

Thank you indeed for your help! Most of tutorials throw a pile of greeks on you without any practical step-by-step palpable explanation what they mean. After just one video like that and after fingers did the job on the keyboard, many of those greeks turn into something meaningful.

[@muhammadmuazubala8361]

Actually anytime I have computational or pedagogical problems your short but very illustrastrative videos cleared my all douubts in no time. Thank you truly.

[@thordlandrolone6569]

This guy is a hero.

[@1johnydeluxe]

i love you bold guy you just saved my exam

[@amaimask8685]

Thanks for your your very good explanation. I want to conduct time series model but i am confuse whether to use ecm or vecm, which model is better?

[@kkxio935]

Hi Mr Jonas. thanks for your explanation. Do you know how can we get the chart after regress this equation(i.e. plot a line pic) and get the chart of actual and fitted price values from the equation? And how can we use standard robustness tests after the regress?

[@syedatasfiatasneem9579]

Thanks for the great video! If I have two variables that are I(2) instead of I(1), how can I check whether they have a cointegrating relationship?

[@raifatou1]

thank you very much for this video. What will happen if the test statistic is smaller than the critical value on the table? Does it mean our model is not good?

[@MAX-ho6wg]

Thanks Mr. Jonas for the lessons. Could you kindly share with me the link about your teachings on extracting data from yahoo finance and how to use it in stata.

[@devran6112]

Is it necessary to find lag order from varsoc and use it on ADF? When I use lag for my data from suggested criterias I find my data have unit root for 1. and 2. differences.

[@thetruth4712]

Hi Mr. Jonas, sorry for disturbing and thank you for the video. I have a question that really need an answer. How do I interprete the stata output of "parms and LL" of johansen cointegration? Your help is highly appreciated. Best regards.

[@varunmiglani110]

i also have the same question , when i run the vec command, what is parms and p-value associated with it

[@ribico1]

Hello thanks again for this video, was very helpfull, can i ask, how can I prove that is valid to use idex like S&P 500, IPSA, Nikkei, etc, as independent variables in my study?? if you could refer me to a book to study i will appreciate ir so much!

[@mahirlabib4512]

Hi, great video! I have a question, that is if both my variables had been stationary at level to begin with, I(0), then would I have repeated the same things you did? For cointegration, the order of integration has to be the same right? In my case both are zero for level terms, so I should be able to run the steps you just outlined? Appreciate any response.

[@mikejonaseconometrics1886]

Hi Mahir; in order for two variables to be cointegrated, they must each individually be non-stationary, and have the same order of integration (both I(1), typically). Therefore, the two variables you mention are not candidates to be cointegrated, and an error correction model would not be appropriate.

[@crazymonkey11231]

Thank you so much for the help on STATA. Can I put your name on my acknowledgement page for my dissertation?

[@mikejonaseconometrics1886]

Very glad to know I was helpful, Justin, - I would be honored!

[@crazymonkey11231]

@@mikejonaseconometrics1886 Sure Mr Jonas. Just wanted to ask something about the egragner command. When I was using the command to reestimate the MacKinnon critical value shown when I run a ADF test on the dynamic equation residual, I am not sure is it because the fact that my equation is a dynamic equation instead of a static one shown in the video. The test statistic changed as well as the critical value when I use the egragner command to compute whether my residual is a stationary one. Is there any reason behind so or am I doing it wrongly?

[@minhnghiatran6879]

Hello Mr. Jonas ! I'm having 3 variables that are all I(1) and cointegrated, say X, Y, Z. I've run a regression of Y on X and Z. Now, how can I build a correction model for these 3 variables using 12 lags on each of them ?

[@officialmintt]

Thank you! Is it that the hypothesis of Stata's egranger command is that there is no cointegration?

[@mikejonaseconometrics1886]

Right, like the dfuller test, the null is a “unit root” or a non-stationary series. In this case it applies to the linear combination of variables: if we reject the null, we conclude the series are cointegrated.

[@ribico1]

Hello and thanks for the video! I've got a question about cointegration, what happens if i do the Engle and granger 2 steps method and my variables do not cointegrate but if i do the ECM the coeficient is negative, lower than 1 and significant? what model can i use?? Thank you very much for your answer

[@mikejonaseconometrics1886]

The problem with using the error correction term when the variables are not cointegrated is that you are including a non-stationary level term in the regression. This can lead to the problem of spurious regression results and non-stable coefficients, and should be avoided when causal effects are the desired interpretation.

[@casparvieira6667]

I love you

[@seanh19954]

Hi Mr Jonas! I have a couple of questions regarding the ECM Model and was wondering whether I could get your help?

[@mikejonaseconometrics1886]

I can try-how can I help?

[@seanh19954]

@@mikejonaseconometrics1886 Im using an ardl model, an my data has shown that there is heteroskedascity, how do i get around this?

[@mikejonaseconometrics1886]

@@seanh19954 A good option would be to use a robust standard error option, which adjusts the calculation of variance, standard errors and t-statistics for the presence of het. Simply append the regress command with ",robust" to control for het. If you have both het and autocorrelation in the error, you can use the Newey-West robust option. These can be done in the context of an error correction model, as with any regress command.

[@mn-rj4fq]

Thank you very much. I have one quastion. I am using ardl model with one dependent and 3 independent variables. There is cointegration among variables and optimal structure of ardl model is (3 0 1 1). After estimate long-run coefficients I want to use ecm model to estimate short-run coefficients...I know I need to use first difference of variables in ecm model, but I dont know how to write command in Stata with (3 0 1 1) lag lenghts. Can you please help me and write commad for ecm model that includes lags (3 0 1 1)? Thank you in advance🙏

[@boniphace1]

Very informative..kindly improve the quality of Mic/audio

[@XPxp2012xpXP]

I have one confusion here. The return is not the first difference. It is the first difference divided by the previous period price. Can I still say the price is I(1) based on that?

[@mikejonaseconometrics1886]

Technically, yes, you are correct and the difference should be tested as well. However, if the return is stationary, then the difference will be as well (but not always the other way around). Good question!

[@therpope]

why do you first difference and divide by lagged?

[@JMRG2992]

I kinda lost myself in point 1. didn't you say that non-stationary variables must be cointegrated at the same order ? then why procceed when some variables are I(0) and others I(1)

[@mikejonaseconometrics1886]

In the case of the example here, the two variables of interest are stock price (p_bac) and index level (sp), both are non-stationary in levels, but stationary in differences (returns), so both are I(1) and therefore candidates for possible co-integration. The variables that would be considered I(0) or stationary are the returns, which in essence are the differences. Basically, 4 dfuller tests are required to check this condition: one on the level and difference (return) on each of the two variables. Hope that helps!

[@JMRG2992]

Oh I see, Yeah it really helped the clarification. I'd really like to thank you for making this kind of videos. It's kind of hard to understand some interpretation of stata outputs of the commands. Btw, maybe you can help with another doubt. I've used Johansen Test to see if two non-stationary series are cointegrated, and the result according to stata is that they're cointegrated. I want to check out the causality of granger, and for that i've seen some people use VAR models to test the causality. however i've found opinions that differs a lot. some say VAR needs stationary variables, some other say they don't. (the regresion of the long term relationship didn't had stationary residuals in my case) ... so what do you think of using VAR in non stationary series to test the granger causality ?

[@mikejonaseconometrics1886]

Any time the goal is to determine causal inference, stationary variables should be used. This is to avoid the problem of "spurious" correlations due to shared trends of non-stationary variables giving a "false positive" to a test (in particular, Granger causality). Granger-causality testing, however, is a great application of a well specified stationary VAR model.

[@JMRG2992]

Hey it's me again, thank you for your help, I've just read about an interesting feature you might want to explain in Stata, the Toda & Yamamoto test for causality which is, as i'm reading an Augmented Granger Causality test. No need of stationary variables, may Integrated at different orders and no need of cointegration.

[@mikejonaseconometrics1886]

I will check that out, thanks for the suggestion!