Dear all,
I am working on panel data analysis and found a phenomenon that I cannot explain. Thus, I post my question here and see whether any experts could help me. Thank you all very much in advance.
My sample is a short unbalanced panel (8 years for each company; and 12 independent + control variables). Overall, 12250 observations for analysis.
The Hausman test suggests applying the fixed-effect model. However, the change of R squared (also the change of adjusted R squared) are very small from my base model (control only) to main model (add independent variables), namely, from 0.1938 to 0.1951. It looks like no explanatory power added when I include the independent variable into the fixed-effect regression model.
However, I use the same sample to run the OLS, the adjusted R square change from the base model to the main model is from 0.07 to 0.09, which is an acceptable rate of increment.
How can we explain this phenomenon?
The interested independent variable is significant and the overall model (F) is significant as well while applying fixed-effect panel and OLS, respectively.
Can I still use the fixed-effect panel as the main model in my study while there is almost no R squared increment for the independent variable addition?
Best wishes,
Han
R-squared is a statistic that indicates the percentage of the variance in the dependent variable that the independent variables explain collectively. R-squared measures the strength of the relationship between your model and the dependent variable on a convenient 0 – 100% scale. This is expressed as the coefficient of determination
What is NOT clear to me is why you are concerned about the increment of this coefficient for the independent variable addition with your idea of a fixed-effect
Dear Professor Samantar,
Thank you very much for your explanation. I worry about the small R-squared increment is because some management scholars tend to have a concern on this point. One comment on my study is that the addition of interest independent variable capture very little variance, and could be a big concern. They expect that I can have a good explanation to alleviate this concern. For example, any signs to address that this is possible in fixed-effect panel model? Or say, this phenomenon is not bad while applying the fixed-effect model. However, I could not find suitable econometric sources to address a good statement until now. Thus, if you or anyone could help clarify more on this, it is much appreciated. Thank you very much again for your previous comment.
Han Yang , which R2? The overall R2, the within R2 or the between R2? (There are 3 of them in panel data as you probably know).
I believe I have an explanation for your issue, but I need more information:
* How many cross-sectional units do you have?
* What is the p-value of the independent variable when added to the FE model?
Dear Dr Gonzales,
I am talking about within R2 since the fixed-effect estimator is the within estimator. I also use areg (STATA code) to get the value of adjusted R-squared, which get small increment as well.
My dataset is an unbalanced panel.
I have 11 control variables + 1 interest independent variable. While applying fixed-effect model, I also do year (8-9), industry (43), location (51) fixed-effect. That is, put i.year, i.industry, i.location in the stata code.
The p-value of the independent variable is 0.013 when added to the FE model (running xtreg, fe r in Stata).
Overall, ~12250 observations / 3000 groups in the FE analysis.
Thank you so much for your help!
Han Yang, then my theory of what is happening is the following one: you have a lot of fixed effects and controls that are capturing all the variation in the dependent variable - this is common when using FE, and this is why the contribution of the independent variable of interest is marginal (in terms of explanatory power measured by the within R2) but not irrelevant from a statistical point of view (as the variable is statistically significant at the 5% but not the 1%).
When you use OLS you need to introduce manually a FE design matrix as additional controls in order to make the results comparable (and this will increase and stabilize the R2); I argue that this why you get different results when estimating with FE compared to pooled OLS (without FE).
There is also a way to test my theory: you can estimate (only as a robustness exercise) the model with RE and controls with and without the variable of interest; you should see a more notorious difference in R2 if my theory about the impact of using FE is correct.
In any case, I would not worry too much about the difference in the R2, it does not mean that the variable of interest have no explanatory power, as the variable is statistically significant even after including controls.
Dear Rolando,
Thank you so much for providing a very clear explanation for this issue. However, may I ask do you know any relevant literature, or econometric/statistics textbooks which can support your theory? I try to search for it, however, did not find a good one until now. I will keep searching, but if you could suggest an authors' name or papers to look at, it is much appreciated.
Overall, I sincerely appreciate your time for answering my question in details. It is really helpful, which greatly disentangle my confusion. Thank you so much!
Han Yang , I believe I saw a similar discussion (more formally of course) in the excellent book of Cheng Hsiao, but it has been a long time and I do not remember exactly where:
Book Analysis of panel data: Third edition
(Of course my theory is just that: a theory, it is hard to say with certainty without actually seeing the data and making additional estimations to see what is actually happening there.)
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