interpretation of coefficient of independent variable which is measured as a % of GDP

[Sanjana Afroze]

I am doing a ols regression analysis using Gini index as the dependent variable and remittance measured as a percentage of GDP as the independent variable. How do I interpret the coefficient of my independent variable? for example, is it correct to say "when remittance increases by 1% of GDP per capita, the gini index increases by 0.351%"?

[Clyde Schechter]

The interpretation would be that a 1 percentage point difference in remittances (as percent of GDP) is associated with 0.35 difference in the GINI coefficient. The GINI coefficient is not, itself, a percentage.

[Sanjana Afroze]

Thank you!

[Jeff Wooldridge]

Just to check: Is the remittance variable a proportion or a true percent? I suspect a percent, but many researchers refer to proportions as percents.

Also, how has Gini been defined? Sometimes it is defined to be between zero and one, sometimes it is multiplied by 100. Showing summary statistics would help.

[Nick Cox]

I agree with these comments but add that you seem to use remittance and also its square as predictors. If so, the only interpretation defensible is of their joint effect, conditional on the other predictors.

[Clyde Schechter]

Hmm, I did not notice that remittancesq variable. If that really is the square of the remittanceGDP variable, then what I said in #2 is incorrect. If that's the case, it's more complicated to answer to the question. For one thing, you can't even speak any longer of "the" effect of a 1 percentage point increase in remittances (as percent of GDP). That effect will differ depending on what level of remittances you are starting from. And the calculation would be much easier if you re-did your regression using factor variable notation instead of a homebrew quadratic term.

regress GINI c.RemittanceinGDP##c.RemittanceinGDP inflation gdppercapitacurrentus literacyrate liquidliability

Then pick the starting value(s) of RemittanceinGDP you are interested in. Let's say, for the sake of illustration, that you want this when remittances are at 0.01%, 0.5%, 1%, and 2% of GDP.

margins, dydx(RemittanceinGDP) at(RemittanceinGDP = (0.0001 0.005 0.01 0.02))

and you will get the correct marginal effects. These results are then the ones that you would interpret along the lines I set out in #2..

[Sanjana Afroze]

Just to check: Is the remittance variable a proportion or a true percent? I suspect a percent, but many researchers refer to proportions as percents.

Also, how has Gini been defined? Sometimes it is defined to be between zero and one, sometimes it is multiplied by 100. Showing summary statistics would help.

I am so sorry for the late reply! Yes, the remittance is a true percent actually since it has been multiplied by 100. the summary statistics is given below!

[Jeff Wooldridge]

Sanjana: I suspected as much. Then you'll want to follow Clyde's advice but evaluate the marginal effects at values such as 1, 3, 6, 10, 15, 20, or something like that. To obtain a single number, drop the "at" option, and that will give you the average partial effect. "A one percentage point increase in the Remittance variable changes Gini by xxx on average."

[Sanjana Afroze]

Hmm, I did not notice that remittancesq variable. If that really is the square of the remittanceGDP variable, then what I said in #2 is incorrect. If that's the case, it's more complicated to answer to the question. For one thing, you can't even speak any longer of "the" effect of a 1 percentage point increase in remittances (as percent of GDP). That effect will differ depending on what level of remittances you are starting from. And the calculation would be much easier if you re-did your regression using factor variable notation instead of a homebrew quadratic term.

regress GINI c.RemittanceinGDP##c.RemittanceinGDP inflation gdppercapitacurrentus literacyrate liquidliability

Then pick the starting value(s) of RemittanceinGDP you are interested in. Let's say, for the sake of illustration, that you want this when remittances are at 0.01%, 0.5%, 1%, and 2% of GDP.

margins, dydx(RemittanceinGDP) at(RemittanceinGDP = (0.0001 0.005 0.01 0.02))

and you will get the correct marginal effects. These results are then the ones that you would interpret along the lines I set out in #2..

So instead of using squared of remittance i'll have to use "c.RemittanceinGDP##c." And then for a 1% point difference in remittance, there is a 0.322% point difference in GINI index. the result i got is given below. Thank you once again!

[Sanjana Afroze]

Sanjana: I suspected as much. Then you'll want to follow Clyde's advice but evaluate the marginal effects at values such as 1, 3, 6, 10, 15, 20, or something like that. To obtain a single number, drop the "at" option, and that will give you the average partial effect. "A one percentage point increase in the Remittance variable changes Gini by xxx on average."

OK so for an average partial effect this is the command I'll have to use : margins, dydx(RemittanceinGDP) ?

[Clyde Schechter]

So instead of using squared of remittance i'll have to use "c.RemittanceinGDP##c."

No, you use c.RemittanceinGDP##c.RemittanceinGDP. And it replaces not just your original quadratic term but also your original linear term for remittance. If the model you showed in #1 is your real model, then use the code I showed in #6 exactly as I wrote it--it's a translation of your model into the necessary factor variable notation.

And then for a 1% point difference in remittance, there is a 0.322% point difference in GINI index. the result i got is given below.

Maybe. I can't tell from the information you posted because:

1. You have not actually stated (or if you did I can't find it) whether your Gini outcome is a percentage (01-100) or a proportion (0-1). I didn't raise that issue originally because I have only seen 0-1 for Gini coefficients in the literature I follow, but since Jeff Wooldridge points out that some people use a 0-100 version, then the interpretation is going to depend on which of these you are using.

2. You don't show the regression equation you ran: the margins output cannot be interpreted in isolation--only if I can confirm that the regression is the correct model would I be able to confirm an interpretation of the -margins- results.

[Sanjana Afroze]

No, you use c.RemittanceinGDP##c.RemittanceinGDP. And it replaces not just your original quadratic term but also your original linear term for remittance. If the model you showed in #1 is your real model, then use the code I showed in #6 exactly as I wrote it--it's a translation of your model into the necessary factor variable notation.


Maybe. I can't tell from the information you posted because:

1. You have not actually stated (or if you did I can't find it) whether your Gini outcome is a percentage (01-100) or a proportion (0-1). I didn't raise that issue originally because I have only seen 0-1 for Gini coefficients in the literature I follow, but since Jeff Wooldridge points out that some people use a 0-100 version, then the interpretation is going to depend on which of these you are using.

2. You don't show the regression equation you ran: the margins output cannot be interpreted in isolation--only if I can confirm that the regression is the correct model would I be able to confirm an interpretation of the -margins- results.

Sorry, I was not clear before.
I did use the exact code you showed in #6. The regression is given below.
The GINI index is a percentage (01-100). As Mr. Wooldridge mentioned, for the average partial effect I dropped the at option.

Thank you for your help!

[Clyde Schechter]

So, on average, a 1 percentage point difference in remittances as a percentage of GDP is associated with a difference of 0.15 percentage points in the Gini coefficient.

[Sanjana Afroze]

Thank you!

[Michael Schuster]

If I may hook up here without opening another thread.

I have as dependent variable a delta (i.e. a change from t-1 to t) and as independent variable a prevalence of a disease (i.e. what is the percentage of the population in a region that has this disease). What is the interpretation then?