[alessandro gst]

Hello everyone,

I have a related question to the topic.

I am estimating a PPML gravity equation. One of the variables on the right-hand side indicates a share. In my case is share of children (0-100) working in the country. My question is how to interpret the coefficient for share variables? For instance, would it be correct to say that a -0.1 coefficient, means that a 1% increase in child labour leads to a decline of 0.1% in exports? Or should I treat it as a continuous variable and take the log of the variable? thanks a lot for your help

Best regards

[marco cancelli]

Joao Santos Silva Dear Joao, I am estimating a PPML model where dependent variable is originally categorial ranging from zero to four. I know that, being PPML a multiplicative model, coefficient of independent variable are semi-elasticities and, as such, they must be interpreted in terms of percentage variation of the dependent variable. But, if I want to interpret them as variation in level of the dependent variable, is there a way to calculate it? Example, as I told you before the dep. var. ranges from zero to one, coefficient associated with main independent variable is 0.02 (variable is standardized). I can now say that one standard deviation in the ind. var. increases dep. var of approx 2%. However, how can I calculate how much points are 2%? Thanks for your kind collaboration and for your help!

[Joao Santos Silva]

Dear marco cancelli,

How many points does a 2% change imply will depend on the starting value, so it is not a constant. That is why we prefer to work with (semi) elasticities. Note that PPML may not be a good choice when the data is bounded between 0 and an upper limit.

Best wishes,

Joao

[marco cancelli]

Joao Santos Silva Dear Joao, thank you very much for your prompt reply. Thus, you suggest to keep a standard OLS approach or Tobit model?

[Joao Santos Silva]

Dear marco cancelli,

You need something like a fractional logit model (after scaling your variable so that it is bounded between 0 and 1).

Best wishes,

Joao

[marco cancelli]

Joao Santos Silva Dear Joao, thanks a lot for your suggestion. Actually, my dep var is the difference is satisfaction with democracy levels among individuals, using survey data. Given that satisfaction levels range from 0 to 5, differences range from zero to five too. Just to better understand, why PPML is not consistent in such model? Is instead fractional models more accurate in such contexts? Thank you very much. Best regards

[Joao Santos Silva]

Dear marco cancelli,

PPML assumes an exponential conditional mean, so it has no upper bound. So, it will only be suitable for your data if only very few observations are close to 5. The alternative is to divide your dependent variable by 5 and treat it as bounded between 0 and 5 and use a fractional logit. (You can also use it as it is if you use the glm command to estimate a binomial model.)

Best wishes,

Joao

[marco cancelli]

Joao Santos Silva Thank you very much. Yes, but with binomial glm, interpretation of independent vars get a little confusing, isn't it? However, I have very few observations close to the upper bound 0-5- Maybe it is the case to keep PPML (actually ppmlhdfe, as I have fixed effects and standard errors clustered for each observations containing the same pair.
Best regards

[Joao Santos Silva]

Dear marco cancelli,

OK, then stick to ppml :-)

Best wishes,

Joao

[Meredith Mugler]

Dear Joao Santos Silva

I am estimating a gravity model, the independent variable are trade values and the main dependent variable of interest is an index, ranging from 0 to 100. In the OLS regression, trade values have to be logged, in the PPML estimation not- did I understand this correctly? The index remains in levels.
I ran both regressions and received the beta_OLS= 0.0005 and beta_PPML= 0.0009. Now I was wondering if the interpretation of the coefficients produced by OLS and PPML is similar, as in PPML trade values are not logged? beta_OLS can be interpreted as a semi-elasticity, a 1-point increase of the index leads to a 0.5% increase in trade. But does beta_PPML mean that a 1-point increase of the index leads to a 0.9% increase?

Thank you very much for your insight already in advance.

Best regards,
Meredith

[Joao Santos Silva]

Dear Meredith Mugler,

You are correct in saying that with PPML the dependent variable is not logged; that is the main attraction of this method. However, the interpretation of the coefficients is exactly the same because PPML estimates an exponential model whereas ols (in logs) estimates the linearized version of the same model.

Best wishes,

Joao

[Meredith Mugler]

Dear Joao Santos Silva

Thank you very much for your previous answer.

Another question has come up: How would one calculate a standardized coefficient from the PPML output, in the same manner as in the log-linearized model, which would be beta_std= beta* (SD_X/SD_log(Y))? I want to get the interpretation of "1 SD change in X is associated with a beta_std*100% change in Y" .

Thank you and best,
Meredith

[Joao Santos Silva]

Dear Meredith Mugler,

You certainly should not compute the SD of log(y) if y has zeros. Anyway, I may be missing something but I do not think the expression you provide has the interpretation you are giving it, and I do not see how you can get such interpretation from a constant elasticity model. Other will be in a better position to help you on this.

Best wishes,

Joao

[DN Jay]

Dear OA Stata,

The coefficients on logged regressors are elasticities and there is no need to transform those. For regressors not in logs, the semi-elasticity is given by 100*(exp(beta) - 1)%. This is negative for negative beta and positive for positive beta; is is also approximately equal to 100*(beta)% for beta close to zero.

About #2, note that it should be (e^(-0.4)-1)*100 = -0.33%.

Best wishes,

Joao

Dear Professor Santos Silva,

I would like to clarify how to interpret when the independent variable is not in logs. In my PPML gravity model, the dependent variable is "patents" and the independent variable is "CS" (not log transformed). The coefficient is 0.128. Since CS is not in logs, should I interpret this coefficient as 1 unit increase in CS leads to 13.6% increase in patents? Is this interpretation correct?

Thank you in adavnce.

Best,
DN Jay

[Joao Santos Silva]

That sounds correct to me.

Best wishes,

Joao