ppml and ppmlhdfe in gravity model

[Juan Quicana]

Dear Joao Santos Silva

I am an undergraduate student who is researching for his thesis about the trade impact of non-tariff measures on Peruvian exports in 2016. For this purpose, and since I have a large number of zeros in my sample, I'm using the gravity model and PPML estimator as you recommend on your papers titled " The log of gravity" (2006) and "Further simulation evidence on the performance of the Poisson pseudo-maximum likelihood estimation" (2011). Also, I'm using the UNESCAP (2013) user guide in order to get the correct code to estimate my model using the PPML. However, I still have some questions about your estimator and its results.

1) My dataset contains 50 importer fixed-effects and 21 HS sector fixed-effects. Is it correct to include very high fixed effects into PPML estimations? Do I have to use the ppmlhdfe estimator? Is it any difference between ppml with high fixed effects and ppmlhdfe estimator?

2) The outcome table (after 11 iterations) presents a warning message which says that I need to rescale the lnPIB_reporter variable (which is in million of dollars). Does it have any consequence if I don't rescale the above variable?

3) Is it neccessary to turn on the "option strict"?

Finally, I was wondering if you can share me the stata code of your 2011 paper to observe how to estimate the ET Tobit and GPML estimator. I want to use them in my robustness check.

Best,

Juan Quicana

Pd: I attach my stata code

ppml exports lnPBI_partner lnPBI_reporter lnDistancia frontera lenguaje colonia ALC mediterraneo ln_arancel MNA_dummy exp_dum_* imp_dum_* seccion_dum_*, cluster(distancia)

[Joao Santos Silva]

Dear Juan Quicana,

1) You can use either ppml or ppmlhdfe; the results should be the same but ppmlhdfe is much faster.

2) You can ignore the warning if you get convergence, but rescaling the variables may help with convergence.

3) I am afraid I did not use Stata for that.

Best of luck,

Joao

[Juan Quicana]

Dear Joao Santos Silva ,

I have problems with ppml estimation. When I applied the RESET test for robustness check with OLS estimations, the Null Hypothesis is not rejected which is a mistake because, as Santos Silva & Tenreyro (2006) shows, only the PPML estimation should not reject this one. My data is about the Peruvian exports (only one exporter) to its 50 major trade partners (i.e. 50 importers). So, lnExportaciones is the log of Peruvian exports in 2016, lnDistancia is the log of distance between Peru and its partners, frontera is a dummy for common borders, colonia is a dummy for colonial tie, ALC is a dummy for the existence of any Free Trade Agreement, ln_arancel is the log of (1+NMF tariff), MNA_dummy is a dummy for the presence of any technical non-tariff measure at hs6 product, and the remain variables are fixed effects for exporter, importer and HS sector.

I attach my results using OLS and PPML estimations on augmented gravity model.

This is the outcome using OLS estimations and RESET test using its results.

 reg lnExportaciones lnDistancia frontera lenguaje colonia ALC mediterraneo ln_arancel MNA_dummy exp_dum_* imp_dum_* seccion_dum_*, ro
> bust cluster(distancia)
note: lenguaje omitted because of collinearity
note: exp_dum_1 omitted because of collinearity
note: imp_dum_5 omitted because of collinearity
note: imp_dum_6 omitted because of collinearity
note: imp_dum_7 omitted because of collinearity
note: imp_dum_9 omitted because of collinearity
note: imp_dum_25 omitted because of collinearity
note: imp_dum_39 omitted because of collinearity
note: seccion_dum_15 omitted because of collinearity

Linear regression Number of obs = 22,968
F(21, 49) = .
Prob > F = .
R-squared = 0.1083
Root MSE = 3.1238

(Std. Err. adjusted for 50 clusters in distancia)
--------------------------------------------------------------------------------
| Robust
lnExportacio~s | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------+----------------------------------------------------------------
lnDistancia | -.2998416 .0685826 -4.37 0.000 -.4376635 -.1620197
frontera | .6653672 .1170468 5.68 0.000 .4301529 .9005815
lenguaje | 0 (omitted)
colonia | 2.121283 .0539995 39.28 0.000 2.012767 2.229799
ALC | 1.440475 .0598281 24.08 0.000 1.320246 1.560704
mediterraneo | -1.996203 .0786285 -25.39 0.000 -2.154212 -1.838193
ln_arancel | -.0855022 .043193 -1.98 0.053 -.1723018 .0012975
MNA_dummy | .0311182 .1154152 0.27 0.789 -.2008173 .2630536
exp_dum_1 | 0 (omitted)
imp_dum_1 | .6857985 .0435804 15.74 0.000 .5982204 .7733766
imp_dum_2 | -1.615787 .1637222 -9.87 0.000 -1.944799 -1.286775
imp_dum_3 | 1.043826 .0463143 22.54 0.000 .9507542 1.136898
imp_dum_4 | .2572804 .0682895 3.77 0.000 .1200474 .3945133
imp_dum_5 | 0 (omitted)
imp_dum_6 | 0 (omitted)
imp_dum_7 | 0 (omitted)
imp_dum_8 | -.659314 .0683305 -9.65 0.000 -.7966293 -.5219986
imp_dum_9 | 0 (omitted)
imp_dum_10 | -2.074721 .0758223 -27.36 0.000 -2.227092 -1.92235
imp_dum_11 | 1.419923 .0729906 19.45 0.000 1.273243 1.566603
imp_dum_12 | -2.10325 .1012643 -20.77 0.000 -2.306749 -1.899752
imp_dum_13 | -2.478621 .091669 -27.04 0.000 -2.662837 -2.294405
imp_dum_14 | -.127389 .0653746 -1.95 0.057 -.2587642 .0039862
imp_dum_15 | .0927774 .0639727 1.45 0.153 -.0357806 .2213353
imp_dum_16 | -.5920855 .0589754 -10.04 0.000 -.710601 -.4735701
imp_dum_17 | -1.848416 .0980064 -18.86 0.000 -2.045368 -1.651465
imp_dum_18 | -2.307547 .094996 -24.29 0.000 -2.498448 -2.116645
imp_dum_19 | -1.446503 .0709078 -20.40 0.000 -1.588997 -1.304008
imp_dum_20 | -.8376343 .0534267 -15.68 0.000 -.9449993 -.7302693
imp_dum_21 | .1184033 .0528089 2.24 0.030 .0122799 .2245267
imp_dum_22 | -.7777943 .0674378 -11.53 0.000 -.9133156 -.6422731
imp_dum_23 | 1.969916 .0995804 19.78 0.000 1.769802 2.170031
imp_dum_24 | -.9649846 .0676121 -14.27 0.000 -1.100856 -.8291129
imp_dum_25 | 0 (omitted)
imp_dum_26 | 1.961194 .0752227 26.07 0.000 1.810028 2.112359
imp_dum_27 | 2.315353 .0947973 24.42 0.000 2.124851 2.505855
imp_dum_28 | -.0137991 .0524735 -0.26 0.794 -.1192486 .0916504
imp_dum_29 | -.3083044 .0402962 -7.65 0.000 -.3892826 -.2273262
imp_dum_30 | .6142792 .066835 9.19 0.000 .4799692 .7485892
imp_dum_31 | -1.346248 .0815976 -16.50 0.000 -1.510225 -1.182272
imp_dum_32 | 1.30673 .082259 15.89 0.000 1.141424 1.472035
imp_dum_33 | 7.536008 .2247036 33.54 0.000 7.08445 7.987567
imp_dum_34 | -1.113641 .0923868 -12.05 0.000 -1.299299 -.927983
imp_dum_35 | -.0711428 .0618066 -1.15 0.255 -.1953478 .0530622
imp_dum_36 | -.4017771 .0925707 -4.34 0.000 -.5878049 -.2157494
imp_dum_37 | 1.337569 .0606326 22.06 0.000 1.215723 1.459415
imp_dum_38 | -2.224083 .1017227 -21.86 0.000 -2.428502 -2.019663
imp_dum_39 | 0 (omitted)
imp_dum_40 | 2.123605 .0233982 90.76 0.000 2.076585 2.170626
imp_dum_41 | -.7301875 .0789125 -9.25 0.000 -.888768 -.571607
imp_dum_42 | -1.345195 .065103 -20.66 0.000 -1.476025 -1.214366
imp_dum_43 | -.8963577 .0734018 -12.21 0.000 -1.043864 -.7488513
imp_dum_44 | .8043817 .0740803 10.86 0.000 .6555118 .9532517
imp_dum_45 | 1.121185 .0400836 27.97 0.000 1.040634 1.201736
imp_dum_46 | -2.700035 .1230584 -21.94 0.000 -2.94733 -2.45274
imp_dum_47 | 1.082689 .0567908 19.06 0.000 .9685633 1.196814
imp_dum_48 | -1.841087 .0966188 -19.06 0.000 -2.035249 -1.646924
imp_dum_49 | 3.217984 .0720305 44.68 0.000 3.073233 3.362734
imp_dum_50 | 1.728445 .0854262 20.23 0.000 1.556775 1.900115
seccion_dum_1 | .6094123 .9347438 0.65 0.517 -1.269026 2.48785
seccion_dum_2 | .5144564 .8542967 0.60 0.550 -1.202317 2.23123
seccion_dum_3 | .7990357 .9916706 0.81 0.424 -1.193801 2.791873
seccion_dum_4 | .5795956 .8440886 0.69 0.496 -1.116664 2.275855
seccion_dum_5 | -1.204721 .8828119 -1.36 0.179 -2.978798 .569356
seccion_dum_6 | .9570452 .9967685 0.96 0.342 -1.046036 2.960126
seccion_dum_7 | -.5086988 .8826663 -0.58 0.567 -2.282483 1.265085
seccion_dum_8 | -1.020494 .8730824 -1.17 0.248 -2.775018 .7340312
seccion_dum_9 | -1.436218 .7945794 -1.81 0.077 -3.032985 .1605495
seccion_dum_10 | -2.331401 .9006834 -2.59 0.013 -4.141392 -.5214097
seccion_dum_11 | -1.002241 .8314073 -1.21 0.234 -2.673016 .6685346
seccion_dum_12 | -1.703868 .8221108 -2.07 0.043 -3.355961 -.0517743
seccion_dum_13 | -1.59006 .8393409 -1.89 0.064 -3.276779 .0966586
seccion_dum_14 | .0822513 .7290053 0.11 0.911 -1.38274 1.547242
seccion_dum_15 | 0 (omitted)
seccion_dum_16 | -1.538568 .8492565 -1.81 0.076 -3.245212 .1680773
seccion_dum_17 | -1.754125 .7792247 -2.25 0.029 -3.320036 -.1882145
seccion_dum_18 | -1.153806 .7881399 -1.46 0.150 -2.737632 .4300206
seccion_dum_19 | -2.248167 .7731533 -2.91 0.005 -3.801876 -.694457
seccion_dum_20 | -1.666725 .8304987 -2.01 0.050 -3.335674 .0022248
seccion_dum_21 | -1.14414 .9493878 -1.21 0.234 -3.052006 .7637259
_cons | -3.025892 .9701796 -3.12 0.003 -4.975541 -1.076243
--------------------------------------------------------------------------------

.
end of do-file


. predict fit, xb
(8,855 missing values generated)

. gen fit2=fit^2
(8,855 missing values generated)

. qui reg lnExportaciones lnDistancia frontera lenguaje colonia ALC mediterraneo ln_arancel MNA_dummy fit2 exp_dum_* imp_dum_* seccion_
> dum_*, robust cluster(distancia)

. test fit2=0

( 1) fit2 = 0

F( 1, 49) = 4.10
Prob > F = 0.0484

And this one is using the PPML estimator and its RESET Test.

ppml exports lnDistancia frontera lenguaje colonia ALC mediterraneo ln_arancel MNA_dummy exp_dum_* imp_dum_* seccion_dum_*, cluster(d
> istancia) nocons

note: checking the existence of the estimates

Number of regressors excluded to ensure that the estimates exist: 1
Excluded regressors: exp_dum_1
Number of observations excluded: 0

note: lenguaje omitted because of collinearity
note: imp_dum_2 omitted because of collinearity
note: imp_dum_6 omitted because of collinearity
note: imp_dum_7 omitted because of collinearity
note: imp_dum_9 omitted because of collinearity
note: imp_dum_39 omitted because of collinearity
note: seccion_dum_21 omitted because of collinearity

note: starting ppml estimation
note: exports has noninteger values

Iteration 1: deviance = 4593500
Iteration 2: deviance = 1780699
Iteration 3: deviance = 784224.2
Iteration 4: deviance = 448619.8
Iteration 5: deviance = 345239.1
Iteration 6: deviance = 317970.5
Iteration 7: deviance = 313196.8
Iteration 8: deviance = 312894.9
Iteration 9: deviance = 312892.9
Iteration 10: deviance = 312892.9
Iteration 11: deviance = 312892.9

Number of parameters: 72
Number of observations: 251391
Pseudo log-likelihood: -161567.16
R-squared: .01332209
Option strict is: off
(Std. Err. adjusted for 50 clusters in distancia)
--------------------------------------------------------------------------------
| Robust
exports | Coef. Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
lnDistancia | -.4314336 .0913318 -4.72 0.000 -.6104405 -.2524266
frontera | .0536002 .4740994 0.11 0.910 -.8756175 .982818
colonia | -2.148252 .5473999 -3.92 0.000 -3.221136 -1.075368
ALC | -.6642191 .21579 -3.08 0.002 -1.08716 -.2412786
mediterraneo | 1.386913 .2031351 6.83 0.000 .9887759 1.785051
ln_arancel | -.5273742 .4726209 -1.12 0.264 -1.453694 .3989458
MNA_dummy | .327095 .5174765 0.63 0.527 -.6871404 1.34133
imp_dum_1 | -1.114786 .7385051 -1.51 0.131 -2.562229 .3326577
imp_dum_3 | -2.287402 .1831118 -12.49 0.000 -2.646294 -1.928509
imp_dum_4 | -.7043209 .0894402 -7.87 0.000 -.8796204 -.5290213
imp_dum_5 | -1.966358 .0901732 -21.81 0.000 -2.143094 -1.789621
imp_dum_8 | -.1922745 .2714673 -0.71 0.479 -.7243406 .3397917
imp_dum_10 | 2.030261 .2649003 7.66 0.000 1.511066 2.549456
imp_dum_11 | 2.589501 .48576 5.33 0.000 1.637428 3.541573
imp_dum_12 | .8760401 1.019772 0.86 0.390 -1.122677 2.874757
imp_dum_13 | -1.116519 .2784217 -4.01 0.000 -1.662215 -.5708223
imp_dum_14 | -.3284742 .0896567 -3.66 0.000 -.5041981 -.1527503
imp_dum_15 | -2.638665 .0896506 -29.43 0.000 -2.814377 -2.462953
imp_dum_16 | -1.240777 .2715198 -4.57 0.000 -1.772946 -.7086077
imp_dum_17 | .7759496 .9283841 0.84 0.403 -1.04365 2.595549
imp_dum_18 | 2.059247 .5389441 3.82 0.000 1.002936 3.115558
imp_dum_19 | -2.749813 .0902551 -30.47 0.000 -2.92671 -2.572917
imp_dum_20 | -1.674184 .0894419 -18.72 0.000 -1.849487 -1.498881
imp_dum_21 | -.7085908 .0894534 -7.92 0.000 -.8839162 -.5332653
imp_dum_22 | -1.69295 .2719001 -6.23 0.000 -2.225865 -1.160036
imp_dum_23 | -2.964382 .2365645 -12.53 0.000 -3.42804 -2.500724
imp_dum_24 | -2.105445 .2730055 -7.71 0.000 -2.640526 -1.570364
imp_dum_25 | -3.820418 .6337192 -6.03 0.000 -5.062484 -2.578351
imp_dum_26 | -3.283073 .7815935 -4.20 0.000 -4.814968 -1.751178
imp_dum_27 | .208122 1.181887 0.18 0.860 -2.108334 2.524578
imp_dum_28 | -1.003474 .0895397 -11.21 0.000 -1.178969 -.8279792
imp_dum_29 | .1850982 .1439038 1.29 0.198 -.0969482 .4671445
imp_dum_30 | .7520112 .4614294 1.63 0.103 -.1523739 1.656396
imp_dum_31 | .9273767 .4205746 2.21 0.027 .1030656 1.751688
imp_dum_32 | -2.878425 .3426314 -8.40 0.000 -3.54997 -2.20688
imp_dum_33 | -3.682623 .5347607 -6.89 0.000 -4.730735 -2.634511
imp_dum_34 | -2.57902 .2934571 -8.79 0.000 -3.154186 -2.003855
imp_dum_35 | -.3156104 .0894486 -3.53 0.000 -.4909264 -.1402944
imp_dum_36 | -3.769253 .2506863 -15.04 0.000 -4.260589 -3.277917
imp_dum_37 | -4.74559 .2039107 -23.27 0.000 -5.145248 -4.345932
imp_dum_38 | 1.193222 .1915438 6.23 0.000 .8178035 1.568641
imp_dum_40 | -2.579854 .7342528 -3.51 0.000 -4.018963 -1.140745
imp_dum_41 | -3.460296 .0948384 -36.49 0.000 -3.646176 -3.274416
imp_dum_42 | -2.019692 .2721201 -7.42 0.000 -2.553038 -1.486346
imp_dum_43 | -3.035312 .0898989 -33.76 0.000 -3.21151 -2.859113
imp_dum_44 | -2.977139 .1058087 -28.14 0.000 -3.18452 -2.769758
imp_dum_45 | -4.105837 .3306784 -12.42 0.000 -4.753955 -3.457719
imp_dum_46 | -1.394045 .0322961 -43.16 0.000 -1.457345 -1.330746
imp_dum_47 | 1.218534 .2017521 6.04 0.000 .8231075 1.613961
imp_dum_48 | -.4187494 .132765 -3.15 0.002 -.6789641 -.1585348
imp_dum_49 | -2.626287 .5964335 -4.40 0.000 -3.795275 -1.457299
imp_dum_50 | -2.920057 .5411621 -5.40 0.000 -3.980715 -1.859399
seccion_dum_1 | 2.454451 .5466919 4.49 0.000 1.382954 3.525947
seccion_dum_2 | 4.030944 .5201629 7.75 0.000 3.011444 5.050444
seccion_dum_3 | 3.471219 .7475501 4.64 0.000 2.006047 4.93639
seccion_dum_4 | 4.332082 .9034854 4.79 0.000 2.561284 6.102881
seccion_dum_5 | 1.653574 .69767 2.37 0.018 .2861657 3.020982
seccion_dum_6 | 5.801144 .7624295 7.61 0.000 4.306809 7.295478
seccion_dum_7 | 1.339814 .7187279 1.86 0.062 -.0688673 2.748494
seccion_dum_8 | 2.553449 .8186998 3.12 0.002 .9488271 4.158071
seccion_dum_9 | 1.397105 .8936823 1.56 0.118 -.3544798 3.14869
seccion_dum_10 | 1.251831 .753649 1.66 0.097 -.2252937 2.728956
seccion_dum_11 | 2.309953 .6252397 3.69 0.000 1.084506 3.535401
seccion_dum_12 | 1.270458 .9277279 1.37 0.171 -.5478556 3.088771
seccion_dum_13 | 2.330507 .7416038 3.14 0.002 .8769899 3.784023
seccion_dum_14 | 6.331289 .7285506 8.69 0.000 4.903356 7.759222
seccion_dum_15 | 1.002838 .614894 1.63 0.103 -.2023323 2.208008
seccion_dum_16 | 3.172186 .7711696 4.11 0.000 1.660721 4.68365
seccion_dum_17 | .5115352 .5719157 0.89 0.371 -.6093991 1.632469
seccion_dum_18 | .8632077 .7256116 1.19 0.234 -.5589649 2.28538
seccion_dum_19 | -.8254245 .549203 -1.50 0.133 -1.901843 .2509937
seccion_dum_20 | 1.710909 .7958455 2.15 0.032 .1510808 3.270738
--------------------------------------------------------------------------------

predict fitt, xb
(8,855 missing values generated)

. gen fitt2=fitt^2
(8,855 missing values generated)

. qui ppml exports lnDistancia frontera lenguaje colonia ALC mediterraneo ln_arancel MNA_dummy fitt2 exp_dum_* imp_dum_* seccion_dum_*,
> cluster(distancia) nocons
WARNING: fitt2 has very large values, consider rescaling or recentering
Number of regressors excluded to ensure that the estimates exist: 1
Number of observations excluded: 0

. test fitt2=0

( 1) fitt2 = 0

chi2( 1) = 4.94
Prob > chi2 = 0.0263

Is there any problem with my code? Is it any problem with my model specification?

I'll be waiting for your reply.

[Joao Santos Silva]

Dear Juan Quicana,

I think you may have misread our paper. Whatever the results of the test, OLS should not be used in this context.

Best wishes,

Joao

[Juan Quicana]

Dear Joao Santos Silva

Thanks for your reply.
I have other questions about ppml. If my R2 is too small, am I making a mistake? is my model misspecified?. Furthermore, if the RESET test fail to check the PPML regression, is my model misspecified? I read your comment in other forum that if my data is only about one exporter country to the rest of the world (which is my case), the RESET could fail. Can you explain me that affirmation?

Gratefully,

Juan

[Joao Santos Silva]

Dear Juan Quicana,

The R2 is meaningless, so a low R2 is not an issue in itself. Having said that, gravity equations typically have high R2 values, so a low value may indicate that there is something wrong with what you are doing, or something strange about your data.

In my experience, gravity equations fit very well when we use data for a large number of countries, but often fit poorly (and fail the RESET) when using data for a small number of countries. This suggests that the standard gravity equation does a good job describing world-wide trade flows, but may struggle to describe trade between a particular set of countries, which is not surprising.

Best wishes,

Joao

[Juan Quicana]

Dear Joao Santos Silva

I have a last question about RESET test. If I use the ppmlhdfe estimator, may I use the RESET test?

Gratefully,
Juan

[Joao Santos Silva]

Sure! By the way, ppmlhdfe is not an estimator but a command that implements the PPML estimator.