In most of the books and posts I have read, they always mention the use of dummy variables in standard cointegration analysis to account for issues in the time series (seasonality, breaks, outliers) However in my case, for example, I have GDP (Gross Domestic Product) and NDB which is the amount outstanding of loans of a bank which are I(1). With a dummy variable I want to represent a policy of the government that instructed the bank to provide a higher percentage of the total loans to farmers. Then I built a dummy which is 1 during the periods where the policy was applied and included it as exogenous (not restricted to the cointegration space). As you can infer, with this dummy, my thinking was to investigate the implication for GDP (and NDB) of this policy.
Is this procedure right (the inclusion of the exogenous dummy)?
I have read that this procedure is not advisable because it "yields" a broken trend in the system and the standard critical values of the Johansen cointegration tests may not be valid anymore, but other reads make me think that what I am doing may be valid.
Pd: I want to acknowledge that I only have seen this strategy in the following master thesis (where BTW I think the author used the Johansen et al (2000) methodology but I doubt the cointegration test for breaks (Johansen et al 2000) is suitable for this case)
http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=2796810&fileOId=2796812
And the author stated: "in the year 1979, China launched two crucial policies, that is, economic reform and opening-up policy and one-child policy. To capture these effects, a shift dummy variable is included in the cointegration estimations.". The author included the shift dummy as exogenous and used the critical values considering the Johansen et al (2000) determination of the critical values Thanks in advance
Hola Reynaldo,
I am not an expert in VEC theoretical framework. However, let me try to help you. I believe that there should not be a problem with breaking the trend as far as the brake is modeled - say with dummy variable in a model in levels. However, if the model is specified in growth rates, the dummy becomes a point outlier dummy, since it would be capturing the jump in the time series. If you add the dummy for all the periods in a model in growth rate terms, it would mean something different, since it would suggest (assuming a significative dummy) that the new policy has affected not only trend, but also the growth.
Regarding the the standard critical values of the Johansen cointegration test, definitively they are going to be affected in both ways: because of the brake (in case with the dummy) and because of the misspecification (in case of the dummy omission). You can read this very short summary (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.233.51&rep=rep1&type=pdf).
Thus, there is no a big problem. You just need to follow any of the alternative procedures that takes into account the presence of structural brakes (e,g,. Article Testing for Multivariate Cointegration in the Presence of St...
).I would calculate both alternatives (both references in this post), use the second one in the body of my paper and mention the first one as a robustness test for the results of the test.
Hope this helps.
Best,
Miguel
Like Miguel, I am not an expert in VEC theoretical framework; however, this might enhance his outstanding answer and suggestions.
Using a single simple dummy variable as described might capture the effect of the policy if the policy has a relatively constant impact; however, it cannot accurately model acceleration or deceleration. One possibility is to include a variable for time; let's call it TIME and have it start at zero.
Then, multiply the dummy variable times TIME to form and additional variable; let's call it ITT. This might be able to the change in the slope when the policy is in place. Including both TIME and ITT is effectively the same as running two separate regressions; one when the policy is in place and another when the policy is not binding. The advantage of including both variables (i.e., TIME and ITT), if and only if including both is appropriate, is that we can use the t- statistics to test for significant differences in the intercept and separately on the slope based on the policy with the t- statistic on each variable.
Other variations are possible, of course, and it is critical that the model be formulated based on the best judgement the author. Hopefully, this adds something things to consider.
Rob
I do agree with Rob's answer.
Just adding that the variable TIME can be with any shape. The advantage of using a linear TIME (which implies a deterministic trend) is that the interpretation of the different slopes is straight forward, while a non-linear TIME (e.g., an exponential trend) has a reading less obvious but could fit the data better. Test for the properties of the errors to ensure that there is no other issue as a consequence of this.
Very much thank you Miguel Angel and Rob. I know the papers suggested by Miguel Angel and also a post of one of the authors (professor Giles)
https://davegiles.blogspot.com/2011/05/cointegrated-at-hips.html
However, the situation Giles describes there sounds different from the one here. In my understanding, the papers Miguel Angel suggests me, relate to the situation where you want to account for the breaks in both series which impacts the dynamics of the cointegration space. In my case what I wanted is to account for the effect of a policy.
Interestingly, I wonder if at the end it is the same "idea". I think it is not, but at the same time it can be the same idea. What do you think?
Hi Reynaldo Senra
In your case, it's exactly the same. You have three options to test the effects of the effectiveness of the policy:
- No extra variables for the policy: It is supposed that the effects of the policy will be affecting the performance of the coefficients associated to the variable affected by the policy, and therefor you could test the effectiveness of the policy by doing separated estimations. The differences in the slopes, would suggest evidence about it.
- Inclusion of a dummy variable: you have a dummy with a different meaning than seasonality but that it's measuring a type of break. Thus, the slope of the dummy is going to capture the changes in the variable affected by the policy when the policy is applied. If this dummy is a constant, you assume a jump, while if the dummy has some variation, the meaning depends on how you built the policy dummy variable - exponential, polynomial, logarithmic ...
- Time-varying coefficients: this would assume that the slopes of the variable affected by the policy changes over time. With some soft assumptions (coefficients following random walks, autoregressive processes ...) you can test if the policy had actually temporary effects or permanent effects ...
In the three cases, you are assuming a rupture in the consistency of the slopes, i.e., structural instabilities. Thus, a policy can have the same side effects than a structural incontestability and you can use this approach for testing its effectiveness.
Hope this is clear!
Best,
Miguel
Hola Miguel,
Yes, I am more clear now. Very much thank you for your quick reply,
Saludos
I'm working on the effect of the adoption of IFRS on the quality of financial statements of some quoted firms. I intend to use VECM dummy variables to break the research period into pre and post adoption periods. Am I on the right part? If not what appropriate model can I use? Thanks.
in my opinion you can use dummy variable that represent the policy in the equation of OLS regression or any other regression that you want to use, but if you want to study its impact in vecm use the time series of the variable such as lending rate during your study period not as a dummy variables. you can also use this equation: GDP = b0 + b1 D1.