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I have been trying to create a regression model for my master thesis for the last week and I am stuck with the following issue. Currently seeking any help I can get, so greatful for any input you might have. :)

My goal is to find the effect of the EU emissions allowances price on the free cashflow to firm with several firm and macro economic control variables. The data set I am using for this covers around 500 firms and data from 2005 till 2022.

I have set up in R a one-way fixed effects model (within) and have tried to estimate the model with that. It leads to the following results, which are ok, but in my opinion do not make sense, as I am sure that some variables should have a significant effect such as GDP growth.

Is there anything that I could do/look into, to see if there is an error in the way I estimate the model? Do I need to transform the variables in a certain way (have tried some things like log, standardizing, differencing)?

Thanks a lot for your help! Greatly appreciated.

R Output:

Oneway (individual) effect Within Model

Call: plm(formula = FCFF ~ GDP_Growth + INTANGIBLE_ASSETS + REVENUE + DEPRECIATION + TOTAL_ASSETS + Patents_Filed + Exchange_Rate_EUR.CNY + Inflation + Oil_Price + Lead_Spot + EU_ETS_Future + EU_ETS_Spot, data = data, model = "within")

Balanced Panel: n = 511, T = 18, N = 9198

Residuals: Min. 1st Qu. Median 3rd Qu. Max. -5609351.5 -5784.3 -676.8 3676.6 7938700.2

enter image description here

Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares: 3.5016e+14

Residual Sum of Squares: 2.8466e+14

R-Squared: 0.18705

Adj. R-Squared: 0.13814

F-statistic: 166.339 on 12 and 8675 DF

p-value: < 2.22e-16

EDIT/UPDATE:

Not sure if I need to make a new question or just edit the post, so just trying to edit first.

I have made some changes to the model, including using a new, better dataset and standardizing the variables. I have also changed the variables within the boundaries not creating colinearity among slightly. This has lead to the following updated results. However, still the R squared is surprisingly low. Also the p values seem a bit too good to be true.

Not sure if I can use such results now.

Updated Data Output:

enter image description here

And thank you all for helping me on this one. :)

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  • $\begingroup$ Greetings and welcome to CV! Please format your code so that people can read it :) $\endgroup$
    – Shawn Hemelstrand
    Commented May 27 at 12:39
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    $\begingroup$ Have you considered collinearity? Variance Inflation Factors and other regression diagnostics? $\endgroup$
    – user78229
    Commented May 27 at 12:52
  • $\begingroup$ Yes, I have excluded due to collinearity several variables, leading to the current selection. $\endgroup$
    – DataScience-Student
    Commented May 28 at 12:27
  • $\begingroup$ Do variable clustering on the predictors e.g. Hmisc::varclus(…) and plot the dendrogram. $\endgroup$
    – Frank Harrell
    Commented May 29 at 11:29
  • $\begingroup$ Sure, I have done that: ibb.co/BjRTV6X However, it basically just splits that into micro and macro variables. Will try to choose a cut-off point for it and then see if it helpts the model. Thanks. Related question: Is standardized data a problem for clustering the predictors? $\endgroup$
    – DataScience-Student
    Commented May 29 at 13:29

1 Answer 1

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GDP_Growth may not be significant because it is strongly correlated with some or more other variables that share the same information about the response. Note that the test for which the p-value is given assumes that all other variables are in the model, i.e., you test whether GDP_Growth has an impact beyond the information in all other variables.

In order to explore this visually I'd recommend first to look at a scatterplot GDP_Growth vs. FCFF (if things are as you think they are, you should see a clear relation there; if not, this already puts into question your beliefs), and then run a regression of FCFF against all variables other than GDP_Growth, and plot the residuals of that against GDP_Growth. If your p-value is correct, you shouldn't see a relation there, meaning that GDP_Growth doesn't do anything to explain whatever remains of FCFF having taken into account the other variables before.

Looking at other plots and regression diagnostics (potentially including Variance Inflation Factor as said in a comment) may also help. I would certainly look at a scatterplot matrix of every variable against every other one, which can also show you what's correlated with GDP_Growth. These (including residual plots) should also hint at whether a transformation may be much better for a linear model - but note that the theory behind these p-values does not allow you to change the model dependent on the data, meaning that if you try out stuff until, say, GDP_Growth becomes significant, that significance is invalid and not reliable. (In practice people may do it anyway if diagnostics show that the first model is clearly inappropriate and a model with a certain transformation clearly better, because then it may be even worse to use the first model than to formally invalidate your tests by changing the model, however it is problematic in any case, and particularly if you do it because a certain p-value doesn't match your expectations.)

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  • $\begingroup$ Thanks a lot for your answer. Looking into that! $\endgroup$
    – DataScience-Student
    Commented May 29 at 13:33

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