PPML Gravity Model: interacting continuous variables

[Max Chupilkin]

Good afternoon! I am estimating a PPML gravity model of trade adding an index of ethnic fractionalisation for each country as independent variables. Ethnic fractionalisation is a continuous variable from 0 to 1 which is a probability that two random individuals in a country are from different ethnic groups.

I had two basic questions regarding the model. First, should I log-transform ethnic fractionalisation or keep it in the standard form (all other variables besides dependent variable and dummies are logged)? Second, If I want to study the interaction between ethnic diversities in two countries, can I add ethnic1 * ethnic2 in the model or it may bias the estimates? Thank you for your help!

[Joao Santos Silva]

Dear Max Chupilkin,

Whether or not to log a variable bounded between 0 and 1 is an empirical question; check which one works better. You can also include the product you mention.

Best wishes,

Joao

[Shikha Gupta]

Dear Joao Santos Silva
I am very new to gravity model , your kind suggestion on the model and results would help me a lot

ppml Xijt gi gj logpij lognij exchange linder3 Cost RTA contig lang Landlocked

note: checking the existence of the estimates
WARNING: Xijt has very large values, consider rescaling
WARNING: gi has very large values, consider rescaling or recentering
WARNING: gj has very large values, consider rescaling or recentering
WARNING: exchange has very large values, consider rescaling or recentering
WARNING: Cost has very large values, consider rescaling or recentering
note: starting ppml estimation
note: Xijt has noninteger values

Iteration 1: deviance = 3.93e+09
Iteration 2: deviance = 3.12e+09
Iteration 3: deviance = 3.03e+09
Iteration 4: deviance = 3.00e+09
Iteration 5: deviance = 2.91e+09
Iteration 6: deviance = 2.86e+09
Iteration 7: deviance = 2.86e+09
Iteration 8: deviance = 2.86e+09
Iteration 9: deviance = 2.86e+09
Iteration 10: deviance = 2.86e+09
Iteration 11: deviance = 2.86e+09
Iteration 12: deviance = 2.86e+09
Iteration 13: deviance = 2.86e+09
Iteration 14: deviance = 2.86e+09
Iteration 15: deviance = 2.86e+09
Iteration 16: deviance = 2.86e+09
Iteration 17: deviance = 2.86e+09
Iteration 18: deviance = 2.86e+09
Iteration 19: deviance = 2.86e+09
Iteration 20: deviance = 2.86e+09

Number of parameters: 12
Number of observations: 3922
Number of observations dropped: 0
Pseudo log-likelihood: -1.449e+09
R-squared: .58449951
------------------------------------------------------------------------------
| Robust
Xijt | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
gi | .0452378 .0037543 12.05 0.000 .0378794 .0525962
gj | -.0087716 .0037564 -2.34 0.020 -.016134 -.0014093
logpij | -.7586275 .1582948 -4.79 0.000 -1.06888 -.4483754
lognij | 1.95404 .13085 14.93 0.000 1.697579 2.210502
exchange | .0006345 .0004417 1.44 0.151 -.0002312 .0015003
linder3 | -.2784518 .1139317 -2.44 0.015 -.5017539 -.0551497
Cost | -.4860289 .1373231 -3.54 0.000 -.7551772 -.2168805
RTA | .5449323 .0897372 6.07 0.000 .3690506 .7208139
contig | .6506576 .1505984 4.32 0.000 .3554902 .945825
lang | .1742402 .0724501 2.40 0.016 .0322406 .3162399
Landlocked | -.6947127 .1333741 -5.21 0.000 -.9561212 -.4333043
_cons | -2.561144 .5722439 -4.48 0.000 -3.682722 -1.439567
------------------------------------------------------------------------------
Number of regressors dropped to ensure that the estimates exist: 0
Option strict is off

[Max Chupilkin]

Dear Joao Santos Silva thank you for your answer! What should be the criterion for checking which one works better? In my models logged variables are always significant, while not logged are sometimes not. Thank you for your help!

[Joao Santos Silva]

That depends on what you want to do, but for example you can include both variables and see if only one of them is significant.

[Max Chupilkin]

Dear Joao Santos Silva, thank you for your help!