Elasticities for Log-Log model using instrumental variable approach

[Aisha Khan]

For a research project I am estimating the impact of subsidy on labor productivity using a farm level panel data for three time periods.
in my regression Log labor productivity is the dependent variable and subsidy is a dummy variable taking the value of 1 if the farm received a subsidy and 0 otherwise. I also have other farm level controls that are log transformed. I do not have any interactions of squared terms in the regression.
Due to endogeneity issues I use an instrumental variable approach to estimate the above regression.
My question is that as I run a log-log model will the coefficients be interpreted as elasticities. Especially for the subsidy dummy variable will i treat the coefficient as a dummy variable?

[Jeff Wooldridge]

Aisha: It's important to distinguish between the model and estimation method. If you know how to interpret the parameters in the model that you've written down -- and it seems like you do -- then that is how you interpret them, regardless of the estimation method. I could use OLS, IV, fixed effects, random effects, fixed effects IV, and so on. So, yes, if you have log(y) and log(x), the coefficient on log(x) will be an estimated elasticity. If you have a dummy variable, d, then the coefficient on d is (approximately) the proportionate effect on y. If you multiply by 100, you obtain a percentage effect. Or, use exp(b_d) - 1 and multiply by 100 if b_d is large.

[Aisha Khan]

Thank you for your reply and clarification Prof. Jeff Wooldridge .

Is it then correct to say that the coefficients of the log-log model (all continuous controls and dummy for subsidy) are interpreted as elasticities?

[Jeff Wooldridge]

The coefficient on the dummy is not an elasticity. It can be interpreted as a percentage effect after multiplying by 100. You cannot change a dummy variable by a certain percent. It goes from 0 to 1 or 1 to 0. You're estimating the percentage change in y when d goes from 0 to 1. So if the coefficient is 0.093, it's 9.3% increase in y.

I know of an introductory textbook that explains all of this .... ;-)

[Aisha Khan]

hank you for your reply Prof. Jeff Wooldridge .
I think I understand.
And you are right, I should consult said book!