Panel regression & Goodness-of-fit

[Hailey Lee]

Hi all!
I've been thinking about the below two questions for several days but I couldn't get any answers.
I'm using Stata14 and trying to analyze the QUARTERLY panel data. (10 years, around 10,000 firms)


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[1] The first question is related to the correlation of ROA and ROE. ROA is defined as net income over average asset, whereas ROE is the ratio of net income to average equity.

As the numerator(net income) is same in both ratio (ROA and ROE) and the correlation of average asset and equity is high (0.9793) <see the code below>, I expect that ROA and ROE will show high correlation; however, it wasn't (0.0048). What is wrong with this? Is this a problem of code? or data? Actually, I don't think this is a problem of data.

cor avg_assets avg_equity
cor roa roe

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[2] This brings me to the second question.

When I run the panel regression on ROA with the independent variables(IVs) and control variables(CVs) <see the code below>, Stata gives me that all the variables are significant, which means F value is less than 0.05. On the other hand, when I run the regression on ROE with same IVs and CVs, it gives me all the variables are NOT significant and F value is way above than 0.05 (0.9497).

If the regression on ROE told me that just some of the variables are not significant, then I can accept that. In this case, however, it is telling me the whole model is insignificant, which mean R^2 = 0.

I think roe is definitely related to some of the CVs and IVs included in the model; therefore, the model should have explanatory power. However, the result I got is totally different from what I expected. Is this a problem of code? or Am I missing something important in statistics?


xtset id year
xtreg roa IV1 IV2 CV1 CV2 CV3 CV4 CV5, fe
xtreg roe IV1 IV2 CV1 CV2 CV3 CV4 CV5, fe

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PLEASE help me and thanks for the help in advance
The file size is too big to upload...

[Carlo Lazzaro]

Hailey:
please do not attach screenshots, as they are difficult to read. Use CODE delimiters to share what you typed and what Stata gave you back, instead (see the FAQ). Thanks.
That said:
1) if you take a look at the correlation formula, you can see that it is mainly an issue of covariance and standard deviation of the variables under investigation (https://en.wikipedia.org/wiki/Correl...and_dependence).
Hence, having the same denominator does not automatically imply a high correlation, as you can see from the following toy-example:

. use "C:\Program Files (x86)\Stata15\ado\base\a\auto.dta"
(1978 Automobile Data)

. g mpg_price=mpg/price

. g trunk_price=trunk/price

. corr mpg_price trunk_price
(obs=74)

             | mpg_pr~e trunk_~e
-------------+------------------
   mpg_price |   1.0000
 trunk_price |   0.2813   1.0000

2) your regression models seem poorly specified (the within R-sq, which is a relevant indicator when it comes to -fe- specification) is very low in your first model and null in the last one.
I would check whether you have omitted variable bias. Moreover, in both models the coefficients of IV1 and IV2 seem pretty negligible; I would check whether their scale is correct and/or something went wrong in entrying those data.