Understanding of coefficients

[Nick Wijst]

Dear members of the forum,

I had a question regarding the understanding of coefficients. So basically I am using a fixed effects model to estimate the relationship between CEO compensation and firm performance.
The compensation data that I gathered is in 1,000's of euro's. And I kind of blindly put that into stata. After noticing the rather low coefficients I multiplied the compensation with 1000 to get the actual amount of compensation. However, the coefficient has become even lower. How does that work?

See regression results below. Unfortunately, I cannot give you the data, since it is confidential.

Before multiplying with 1000


After multiplying with 1000


Thanks in advance and I am looking forward to your replies!

With kind regards,

Nick Wijst

[Clyde Schechter]

The FAQ asks people not to post screenshots. There are two reasons for this. One is that it isn't then possible to copy and paste information into Stata to work with. That doesn't matter here, but the second one does bite: screenshots are often unreadable. On my computer, what shows up is too small to read.

That said, I don't need to see the output to answer your question. What you should have done is divide the compensation by 1000.

Think of it like this. Let's pretend you just had a very simple model: outcome = b0 + b1*compensation. Then the units of coefficient b1 are outcome units per compensation unit. By multiplying the compensation numbers by 1000 you changed the unit of currency from dollars to milli-dollars (or Euros to milliEuros, or Yen to milliYen, or whatever). Well if b1 needed to be a small number to start with so that b1*dollars came out in the order of magnitude to match the outcome values, then by replacing the compensation by a variable that is 1,000 times larger and in smaller units, the value of b1 needs to be even smaller still to scale down these new, larger numbers. In terms of units, b1 is now in outcome units per milli-dollar, which must be a smaller number than the original b1.

1 outcome unit per dollar = 1 outcome unit per dollar * 1
= 1 outcome unit per dollar * 0.001 dollar per milli-dollar
= 0.001 outcome unit per milli-dollar

Had you divided the compensation values by 1,000, everything would go the opposite way, and the value of b1 would have gone up by a factor of 1,000.

[Nick Wijst]

Hey Clyde,

Thanks for the quick response. Sorry about the screenshots, I didn't read through the whole FAQ.
Also thanks for the explanation. I now understand how this works.

With kind regards,

Nick Wijst