Hi , I am using ARDL bound test approach for a data set which contains 29 period. I am facing two issues. Please direct me how to solve these issues. 1. The two ARDL bound test statistics (F-test and t-test) comes up with dissimilar decision. What could be the reason behind this? 2. I have four regressors in my model. But two of the variable dropped by the Stata because of collinearity. How to address this problem?
Thanks'
Alauddin
The problem is p-value selection is very poor, See the introduction in the attached and for a solution see: https://www.google.com/search?ei=CoDcXuq9OpPNtQbtt74Q&q=adaptive+lasso+and+its+oracle+properties&oq=adaptive+lasso&gs_lcp=CgZwc3ktYWIQARgJMgIIADICCAAyAggAMgIIADICCAAyAggAMgIIADICCAAyAggAMgIIADoECAAQQzoOCAAQ6gIQtAIQmgEQ5QI6BQgAEJECOgUIABCDAToFCAAQsQM6BwgAEIMBEEM6BwgAELEDEEM6BwgAELEDEAo6BAgAEApQ3KQ6WPP9OmDF2jtoAXAAeAOAAWeIAesZkgEEMzguMpgBAKABAaoBB2d3cy13aXqwAQY&sclient=psy-ab
Best, D. Booth
1. the problem is with your variable detected colinearity. 2 of 4 variable colinearity is the situation. its depend on your goal research, how important is your variable.
2. change your methods
See David and Bramastyo's answers on the collinearity issue. Regarding the apparently different conclusions drawn by the t and F test you should read the papers below. Essentially you need to consider whether the dependent variable is forming a cointegrating equation with the explanatory variables (both t and F test reject the null) or whether the explanatory variables form a stationary linear combination without cointegrating with the dependent variable (the degenerate lagged dependent variable case where the F-test rejects the null and the t-test does not). For cointegration BOTH the t and F test need to reject the null.
McNown, R., Sam, C.Y., Goh, S.K. (2018). “Bootstrapping the Autoregressive Distributed Lag Test for Cointegration”, Applied Economics, 50, 1509-1521.
Sam, C. Y., McNown, R. and Goh, S. K. (2019). “An augmented autoregressive distributed lag bounds test for cointegration”, Economic Modelling, 80, 130 – 141.
I agree with Bramastyo Bontas Prastowo . In general I agree with David Eugene Booth's remarks but this time I saw no immediate relation of the question with the reference (an adaptative Lasso test in the case of a GARCH model) and the introduction of the attached paper on stepwise logistic regression. Perhaps because I don't know well the techniques behind the ADRL test.
It appears that you have 29 observations. If you are using 4 lags of each variable you are estimating 26 coefficients. Even with 3 lags of the first differences you have more than 20 coefficients in your ARDL model. You do not have enough data.
The ARDL F bounds test is a joint test that the coefficients of the error correction terms are not all zero.
The ARDL bounds t-test is a test that the coefficient on the lagged dependent variable is zero.
These are two different hypotheses and therefore may give rise to different results. The interpretation of an econometric analysis should've done within the terms of the economic model that you are examining. Without knowledge of that model one can not give advice on how you can interpret your results. You need to reconsider your model and, given your limited data set, to adopt some a simpler model and a less demanding econometric procedure.
The initial problem started from your number of observations. Because 30-80 observations are regarded as small sample size. But your own is 29.
29 = 30 - 1. As John C Frain pointed out, the problem is with the number of degrees of freedom.
Sule Akkoyunlu There are 29 observations. If you allow 4 lags in the first differences, 5 observations are lost and there are 24 observations left for estimation. There are 25 coefficients for the first differences of all variable 5 for the lagged terms and a constant. That gives you 31 coefficients to be estimated. Even if only 4 initial terms and three lagged first differences you will be estimating 21 coefficients. You can not get sensible results with a sample of 29 and a model as complex as this. Also, there is no way to look at the stability of the model with such a small sample. In such a situation almost any test of a hypothesis will pass because the test will have very small power.
Your 29 issues if it implies 29 obsevations then please considerthe decision with the t statistic since the observation is below 30 as a rule of thumb. But you can seek further views. Rememder, however, that if the ARDL model involved lags then you may loss some data points which implies your may not even have 29 observation in the final model, the more reason you sholud consider a small sample statistic like t.
I have faced a similar problem, where, F stat < I(1) but t stat >I(1), that gives no clear guideline about the cointegration. But Augmented ARDL Aporoach by Sam, C.Y., McNown, R. and Goh, S.K., (2019) extended ARDL approach and noted, "... we gain a complete picture of the cointegration status of the system. If all the three tests (overall F-test on lagged level variables, t-test on the lagged level of the dependent variable, and F-test on the lagged levels of the independent variable(s)) are found to be significant, we can conclude that there is cointegration. If the overall F-test and the t-test on the lagged dependent variable are found to be significant but not the test on the lagged independent variable(s), this indicates that it is a degenerate lagged independent variable(s) case. Another possibility is when the overall F-test and the test on the lagged level of the independent variable(s) are found to be significant but not for the t-test on the lagged level of the dependent variable. This falls into the case of a degenerate lagged dependent variable. Either of the degenerate cases will imply a case of no cointegration; therefore all three tests must be applied to reach a valid conclusion.
Your F-stat is in the dubious range and you can make no conclusion on the basis of the F-test. Your t-test is in the dubious range at the 5% and !% levels. I see no contradiction. Perhaps I have not understood.
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