Predictions using ppmlhdfe

[Steve Dago]

Dear users
I am trying to use ppmlhdfe command proposed by Sergio Correia, Paulo Guimarães and Thomas Zylkin ( 2019 ) to estimate a gravity model. I am interested in getting RTA driven predicted trade that I can use in a subsequent analysis. Suppose that after estimating the model
ppmlhdfe Xijt RTAijt, a(imp#year exp#year imp#exp) d (FE) cluster (imp#exp)
(where Xijt is the level of exports from i to j at time t, RTAijt is a dummy equal to 1 when I and j are involved in the trade agreement at period t) I got the following equation
Xijt=exp(22.54 + 0.69 RTAijt+FE)
I read that using the command predict fiited_trade, mu yields the overall predicted trade. When I rather use the predict xb,xb I don’t get 0.69*RTAijt as the fitted value as is the case after ppml_panel_sg. I get the fitted value when I add my xb to fixed effects FE and then take the exponential i.e. exp(xb+FE). So I have a couple of questions:
First, I want to use only trade driven by my RTA variable. Do I need to reestimate the model without fixed effects or s it still possible to get what I want while including the fixed effects?
Second, Does it make sense to try to get RTA-driven trade? If yes, should I consider the xb, the fitted_trade, or the 0.69*RTAijt?
Finally, as the inclusion of FE yields actual trade, what about the error term? Does it mean that the model is perfect?
Thanks

[Joao Santos Silva]

Dear Steve Dago,

There is something strange about what you say: using predict xb,xb should give you 22.54 + 0.69 RTAijt. Please check.
I guess that what you want to compute is the difference between actual trade and an estimate of the counterfactual trade in the absence of a FTA; That would be mu*(1-exp(- 0.69 RTAijt)).
Finally, the inclusion of FE does not yield actual trade and therefore the model is not perfect; no model is perfect!

Best wishes,

Joao

[Steve Dago]

Thank you Prof Joao Santos Silva for replying.
I think you are right; the predict, xb gives me exactly 22.54 + 0.69 RTAijt.
In two papers I read Frankel and Romer, Does Trade Cause Growth?, AER 1999 Vol 89, and Blanchard and Olney, Globalization and Human Capital Investment: Export Composition Drives Educational, JIE 2017 Vol 106, the authors use a linear model to estimate gravity equations with only some variables and then using these estimates they predict a particular component of trade. In Frankel and Romer (1999) it is a "geographical component" and in Blanchad and Olney (2017) it is an "importer demand component". My first concern was to know whether this idea could be used with non-linear estimates like ppml to derive a "trade policies" component of trade.
The second concern was to know if 22.54 + 0.69 RTAijt. has an economic meaning.
Finally I'm a bit confused for I get exactly the actual country-pair trade after predict,mu or after exp(22.54 + 0.69 RTAijt+FE). For instance, when I try to get fitted trade I get the actual trade. Is it normal? or should I use only exp(22.54+0.69RTA) as predicted trade? Or should I deep the idea about conterfactual trade you proposed above?

Thanks again
Regards

[Joao Santos Silva]

Dear Steve Dago,

a) Yes, you can achieve the same goal with a non-linear model. Actually, it is better to use an exponential model as you are doing.
b) 22.54 + 0.69 RTAijt is meaningless.
c) That is not possible unless you have as many parameters as observations. What you should get is that trade and predicted trade have the same mean, but are not the same.
d) I think what I suggested above is what you are trying to do, but you should check it.

Best wishes,

Joao

[Steve Dago]

Well noted Prof Joao Santos Silva. I will carefully work on it and come back if necessary.
But do you have or know any paper where the idea you proposed is addressed?
Thank you again

[Joao Santos Silva]

That is the standard interpretation of the coefficients in gravity equations.

[Steve Dago]

Well noted Prof,

Regards

[Steve Dago]

Dear Prof Joao Santos Silva sorry for the disturbance if any.

As you said above, the fitted trade obtained with predict,mu is not the actual trade value. The problem comes when I try to aggregate fitted values to get exporter-year trade instead of bilateral predicted trade (as done in the aforementioned papers). The sum of predicted trade is equivalent to the sum of actual trade. Any idea?

[Joao Santos Silva]

Dear Steve Dago,

That happens by construction and is one of the advantages of using PPML; see here.

Best wishes,

Joao

[Steve Dago]

Thank you Dear Joao Santos Silva . I will work on your proposition.

Regards