Regressions and the coefficient of the constant

[Patrick van Dam]

Hi everyone,

I am currently performing crossectional regression on CARs (as a result of an event study).
The regression I am currently performing is as follows:
reg CAR Time Size Leverage ROA Environment Governance Social
However, the constant (alfa) gives me a value of -521.7961 which makes no sense and is highly insignificant.
When I exclude my time variable, which measures in which year the event happened, the constant becomes -7.85 (measured in percentage points) and is significant. This makes much more sense, therefore I suspect that I should use some limitations for this variable.
For instance, a value of 0 would be unrealistic for the time variable since an event cannot happen when the year is equal to zero.
Therefore, my question is whether you have any suggestions for my Time variable. My hypothesis for this variable would be to see if the effect is bigger recently compared to several years ago.

Thanks in advance,

Kind regards

Patrick van Dam

[Rich Goldstein]

you need to re-scale or transform your variables so that the constant is meaningful; you do that by ensuring that 0 is a meaningful value for each and every predictor in the model; e.g., for year you might want to subtract the minimum value from all other values - or you might prefer to subtract the mean or some other other value

[Carlo Lazzaro]

Patrick:
as an aside to Rich's helpful advice, if, as it seems, you consider time as a continuous variable, it may be worth testing whether there's a non-linear relationship between time and the regressand.
See -c.- prefix in -fvvarlist- notation.

[Richard Williams]

The constant is the predicted value when all the Xs equal 0. It may be impossible for all the Xs to equal zero, so it is often not worth paying much attention to.

This handout talks about how you can make the intercept more meaningful. It emphasizes interactions but it is still relevant if you don't have interactions.

https://www3.nd.edu/~rwilliam/stats2/l53.pdf

But again, it may not be worth paying much attention to. I've rarely if ever seen a paper that made a big deal about what the constant term is. It is mostly worth paying attention to if it is possible for all the Xs to equal zero, and it is substantively interesting to look at that situation.

[Rich Goldstein]

Richard Williams I'm going to, in a sense, disagree with what you say - for many people who do not have sufficient substantive expertise, a way to determine how "important" a coefficient is is to compare its value to a meaningful constant - this is true in linear regression, logistic regression, poisson regression and many others; thus, I do think that the data should be re-scaled (or changed in some other way) to make the constant meaningful

[Richard Williams]

Rich Goldstein I certainly agree results should be understandable! Re-scaling is one way to do that, like my handout says, but you can also use things like margins and graphs.

The main thing I was reacting to: Patrick said

However, the constant (alfa) gives me a value of -521.7961 which makes no sense and is highly insignificant.
When I exclude my time variable, which measures in which year the event happened, the constant becomes -7.85 (measured in percentage points) and is significant. This makes much more sense, therefore I suspect that I should use some limitations for this variable.

That statement to me implies there must be something wrong with the model. Nothing is wrong; you just have to understand how to interpret the constant. (I wouldn't want some reviewer to look at Patrick's analyis and say "What??? The constant is -521.8??? That's absurd! Obviously the authors totally screwed this up! Reject!!!)

So, to be clear, a constant like -521.8 doesn't mean that you must have screwed up the model somehow and need to fix it. The model may be perfectly fine, but you may want to find ways to express results in a more intuitive and meaningful way.