Hello,
I'm using ARDL model to estimate the effect of macroeconomic factors on default rate. All the tests are valid including the CUSUM and ECT is negative and significant. But R-squared is too high and VIF also (my sample data is only 29 observations). I've read that the multicollinearity is not a problem in ARDL model. How can I interpret this point logically? Is there any valuable reference about that?
Thank you in advance!
Multicollinearity is not a problem in ardl. Are your variables statistically significant with the high r squared? If yes then I don't see a problem.
Yes they are statistically significant but I need a reference about that point to convince my thesis supervisor!
Hi Vanessa, I think your results may be biased, because you don't have a sufficient observations.
VIF if it exceed 5 it will give you evidence that there is a multicolinearity problem, in spite of that there is some researchs mentioned that there is no problem if you use ARDL but in my opinion it is important to check about multicolinearity.
If you could increase the number of observation I don't think you may face the problem. Try It
I agree with Rami Obeid that size of sample is an issue here. Of course, increases in the size of sample would help to overcome multicollinearity. But more important issue here is that ARDL model requires relative large sample. It is understandable, since ARDL model identifies the equilibrium condition which might need more than 30 years (not for financial markets). So if you have annual data, the minimum size should be 30 (if you have quarterly data, one might even need 120 observations). Note also that critical values for bound tests needs to be adjusted according to size of (small) sample. If one has more than 80 observations, critical values in Pesaran, Shin, and Smith (2001) can be used. Otherwise, Narayan (2005) provides critical values for small samples, down to 30. In your case, you have only 29 obs. It might not be enough to carry out bounds test based on Narayan (2005).
Multicollinearity is always a problem for econometric estimations, independent of what estimation model you want to use. If e.g. two explaining variables are correlated, it is often impossible, to diffenentiate between the effects of them. I do not understand why yqu use ARDL before thinking over how default may be dependent on macroeconomic development. This should be the first step. From that you could develope a model about the influences on the default rate (however measured). And then you can try to statistically test, if these hypothetical effects are important. Beginning with a too elaborated econometric method, will often lead to (may be good statistical) coefficients, which are difficult or even impossible to explain.
I am facing the same problem in my thesis with the use of ARDL bounds approach to cointegration. If you are using the VIF to test for multicollinearity, you will notice very high VIFs exceeding 10, pointing to the presence of multicollinearity. This happens because of the presence of lagged variables in the ARDL model. For instance you will expect a very strong correlation between GDP and GDP(-1) no matter how large the time scope is. However, a logical way of testing for multicollinearity is to use the pairwise correlation matrix to test for multicollinearity prior to running ARDL model. My humble opinion
Multicollinearity can indeed be a significant issue in ARDL (AutoRegressive Distributed Lag) modeling, just as it can be in other regression models. Multicollinearity occurs when independent variables in a regression model are highly correlated with each other, which can lead to unreliable coefficient estimates and difficulties in interpreting the model. Here's how it can affect ARDL modeling and some ways to test and address it:
1. Testing for Multicollinearity:
- Correlation Matrix: Calculate the correlation matrix among the independent variables. High correlation coefficients (close to 1 or -1) indicate multicollinearity.
VIF (Variance Inflation Factor): Compute the VIF for each independent variable. VIF measures how much the variance of an estimated regression coefficient is increased due to multicollinearity. High VIF values (usually above 10) suggest multicollinearity.
2. Addressing Multicollinearity:
Remove Redundant Variables:If two or more variables are highly correlated, consider removing one of them from the model.
-Combine Variables: Create new variables by combining highly correlated variables into a single one.
- Principal Component Analysis (PCA): PCA can help reduce multicollinearity by transforming the original variables into a set of uncorrelated variables (principal components).
- Regularization Techniques:
Ridge or Lasso regression can be used to introduce a penalty term on the coefficients, which can help reduce multicollinearity.
3. Centering and Scaling: Centering and scaling variables can sometimes help mitigate multicollinearity. Centering involves subtracting the mean from each variable, while scaling involves dividing by the standard deviation. This can make coefficients more interpretable.
4. Domain Knowledge:Prior to knowledge of the subject matter can guide you in deciding which variables to include or exclude, reducing multicollinearity.
5. Collect More Data:
Sometimes, multicollinearity is a result of a small sample size. Collecting more data can help alleviate this issue.
6. Stepwise Regression: Use stepwise regression techniques to iteratively add or remove variables from the model based on their significance and contribution to the model.
Remember that the choice of how to address multicollinearity should be based on the specific context of your ARDL analysis and the goals of your research. It's essential to strike a balance between model simplicity and explanatory power while avoiding multicollinearity issues.
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