Coefficient Interpretation- Fixed Panel Model

[Sedef Sen]

Dear Stata User,

I am conducting a research which I try to explain the relationship between trade openness and social protection expenditure. Trade variable is a sum of import and export as a share of GDP. Social protection expenditure is a share of GDP as well. I run my fixed model as level-level form.

However I confused a little interpreting of coefficents.

After run xtreg social protection trade x2 x3 x4, fe

I get the following estimated coefficent for trade: -0.02243 with 0.015 p value.

I know that for level- level model we can interpret coefficient like this: “If you change x by one, we’d expect y to change by β1".

However, what "one" term refer to in my study? Does one unit change means one percentage point change in my study since my data is a share of GDP? But I do not run model log-log, that why I can not be sure about it!

How can I adapt this (“If you change x by one, we’d expect y to change by β1" ) logic to my research.

Thank you in advance any help.

[Clyde Schechter]

Well, the first question is whether by "share of GDP" you mean that these variables are percentages (i.e. they range from 0 to 100) or whether they are proportions (ranging from 0 to 1.)

Assuming that they are in fact percentages, a unit change in x does indeed mean a 1 percentage point increase in X And if the coefficient of X is -0.02243, then that will be associated with an expected decrease of 0.02243 percentage points in Y as well. It's quite simple and straightforward.

What I think is confusing you is, if you had a log-log model instead of a level-level model, you would want to talk about a 1 percent (not 1 percentage point) change in X and the corresponding percent (not percentage point) change in Y. And that involves a somewhat different calculation (although if the coefficient is small, the result is approximately the same).

Just to be clear: if X starts out at 50%, a one percentage point increase brings X up to 51%, whereas a 1 percent change brings X up to 50.5%. Percent changes are multiplicative, percentage point changes are additive.

Finally, if your "shares" are actually proportions and not percentages, a unit change means a change from none to total GDP. Working with changes like that is usually not meaningful. In that case, I would look at a change of, say, 0.01 in X, rather than a unit change in X, and that would be associated with a change of 0.01*(-0.02243) = -0.0002243 in Y.

[Sedef Sen]

Thank you so much Clyde. I turn out to be clear now.