Interpret coefficients in log-log model for x percent increase

[Noemi Seng]

Dear community,

I have estimated a gravity model with PPML. I want to interpret the coefficient on the log of bilateral distance, which is -0.63 in my model. I can interpret this coefficient as an elasticity, implying that with every 1% increase in distance, FDI decreases by 0.63%. My question is now: I would like to give an example, such as when moving from FDI between Bangladesh and Malaysia (distance: 2613) to FDI between Israel and Malaysia (distance: 7779), meaning an increase in distance by 197%, what effect would this have on FDI. How can I calculate this? Is it 197%*(-0.63), implying a decrease in FDI by 124%? This sounds very wrong to me. Unfortunately I can only find information on how to interpret the coefficient as an elasticity, not how to interpret it for more flexible x% changes.

I appreciate any help!

Best wishes
Noemi

[Joao Santos Silva]

Dear Noemi Seng,

The standard elasticity interpretation is valid only for marginal changes, for a discrete change you need to use the usual formula. If distance is multiplied by k, the effect is given by 100(exp(b*ln(k)) - 1)%. So, in your case that is 100(exp(-0.63*ln(2.977)) - 1)% = -49.7%.

Best wishes,

Joao

[Noemi Seng]

Dear Joao Santos Silva

thank you very much! And can you also tell me maybe: If I want to predict the dependent variable based on e.g. the 2613 value for distance: How do I calculate the prediction? Is it exp(beta0 - 0.63*2613)? And do I ignore the other independent variables in the prediction?

Best
Noemi

[Joao Santos Silva]

Dear Noemi Seng,

You cannot make a prediction based on a single independent variable. You have to compute exp(xb) using all variables in x, including fixed effects.

Best wishes,

Joao

[Rethabile Molapo]

Dear Joao Santos Silva

Can you please assist me with the following: I have the variables (Country Year ExportValue Tariffs ln_GDP ln_Population ln_distance PreferentialTradeAgreement language WTOMembership ln_Homecountry_GDP), my dependent variable is ExportValue, WTO membership, PreferentialTradeAgreement, Tariffs, ln_GDP, ln_Population all change overtime. Language, ln_distance are fixed overtime. The data is collected over a space pf 10 years,
Can you please assist me with what the PPMLHDFE command would look like if I ran this regression on stata. My main difficulty with running the regression lies in that I do not know how to structure exposures, offsets, nolog tolerances etc.
I will appreciate any kind of assistance.

Regards
Retha

[Rethabile Molapo]

Joao Santos Silva my main problem is regressing the dummy variables into the model namely: PreferentialTradeAgreement language and WTOMembership

[Joao Santos Silva]

Dear Rethabile Molapo,

You do not need to worry about options such as exposures, offsets, nolog, and tolerance. Just check the help file for examples.

Best wishes,

Joao

[Rethabile Molapo]

Thanks Joao Santos Silva