Interpretation of coefficients linear log model, dependent variable in %

[Thai Curry]

Hi,

I have a very simple question. I have the following equation. My dependent variable is CRES which is the share of renewables in a country's energy supply. My independent variables are log transformed, besides Kyoto which is a dummy variable.

CRES= β0 + β1lnGDP + β2Kyoto+ β3ln_oil_price

For my OLS regression I obtained a statistically significant effect for GDP which is 2,73***.
However, I dont know to interpret the coefficient. I know that usually having a linear-log model, an increase in x (GDP) by one percent is associated with an increase in y by (β1/100) units which would be for CRES (2,73/100).= 0,0273.

Does this interpretation still hold if CRES is in %?
Then, the economic significance of my effects would be rather small.

Thank you,Rex

[Marcos Almeida]

Hello "Thai Curry",


Welcome to the Stata Forum.

As recommended in the FAQ, I kndly ask you to present the commands and output under CODE delimiters.

If this is not your real name, please re-register with full name, just by clicking on the "contact us" button, as recommended in the FAQ.

With regards to the model, considering the dependent variable is presented in percentages, you may find insightful discussions on this among previous messages.

That said, a generalized linear model with a logit link under a binomial family may be an appropriate solution.

You may wish to read this text on the matter :http://www.ats.ucla.edu/stat/stata/faq/proportion.htm

Best,

Marcos

[Nick Cox]

Marcos gives very good advice.

See also

help fracreg 
help betareg

[Emad Shehata]

dear Thai Curry
Simply this is the functional form of your Linear-Log model:

Y = B0 + B1 ln(X)

- Marginal Effect = B1 / X
- Elasticity = B1 / Y

Interpretation of (B1) coefficient in (Lin-Log) model is:

(1) Marginal Effect:
an increase in (X) by one UNIT leads to an increase in (Y) by (B1/X) UNITS,
with all other things being equal

(2) Elasticity:
an increase in (X) by (1%) one Percent leads to an increase in (Y) by (B1/Y) %,
with all other things being equal

So, your Interpretation above is not correct, because it is related to the elasticity of double log or (Log-Log) Model, not for semi-log or (Lin-Log) Model.

Also I want to know additional information about Interpretation of (Lin-Log) Model:

** If B1 > 0 (+)
an increase in (X) by one UNIT leads to an increase in (Y) by (B/X) UNITS, but at a decreasing rate.

** If B1 < 0 (-)
an increase in (X) by one UNIT leads to a decrease in (Y) by (B/X) UNITS, but at a decreasing rate.

with my best wishes

[Thai Curry]

Hi Emad,

thank you for your response.
However, I still have problems understanding the interpretation of the coefficients.

I have a semi-log model as you said, but the main problem I am facing is that my dependent variable is in shares and not logged transformed.
Do I interpret my coefficients in units then? That does not sound reasonable to me, as my independent variable is logged-transformed.

Could you maybe clarify your answer by using the example I gave above?

CRES (in %) = B0 + B1 ln (GDP)

For my OLS regression I obtained a statistically significant effect for GDP which is 2,73***.

Thank you!