[sabeer vc]

Ok Thank you very much, Dear Professor Joao.

[sabeer vc]

Hi Professor Joao Santos Silva , Why should we take explanatory variables in log form and dependent variables in level form when the gravity model is estimated with PPML?

[Joao Santos Silva]

Dear sabeer vc,

The dependent variable is not in logs because the dependent variable should be the variable you care about and not a transformation of it. Whether the regressors are logged, depends on the specification you choose.

Best wishes,

Joao

[sabeer vc]

Thank you. I understood the reason for not logging the dependent variable. But how can we decide when to use logged regressors and when not to use them? (In which types of specifications we can use logged regressors?) It would be greatly appreciated If you could refer to any paper/portal that contains a detailed discussion on it.

[Joao Santos Silva]

Dear sabeer vc,

Remember that you are estimating a multiplicative model in exponential form, so all regressors go inside the exponential function. So, in general, continuous explanatory variables are in logs, but some times people decide not to log some of them. So, it it really up to you.

Best wishes,

Joao

[sabeer vc]

Thank you for reminding me that we are estimating a 'multiplicative model in exponential form.' So, basically, we are transforming Y=X^b into Y=e^{𝑏ln⁡𝑋}. Now my problem regarding logging seems solved.

[Ali Niazi]

Dear arthur hughes,

With reghdfe you estimate a linear regression (presumably of the log of the variable of interest) on your regressors. With ppmlhdfe you estimate an exponential model of the dependent variable on the regressors. The advantages of this approach are that, because you do not have to take logs of the dependent variable, you can use observations in which the dependent variable is zero, and you do not introduce "Jensen's inequality bias" (this comes from the fact that the expected value of log of y is not the log of the expected value of y). For further details, see here.

Best wishes,

Joao

Is there a framework to test if a coefficient from the ppmlhdfe is different from reghdfe, using the same sample?

[Joao Santos Silva]

Bootstrap is probably the best option.