Rescaling variables in PPML

[Anne Wanyonyi]

I re scaled my dependent variable and main covariate by dividing by 1 million.

Should I divide my estimated coefficients by 1 million before interpretation since the ppml is a multiplicative model. Or how else can I interpret the results for the re scaled covaraite?

[Joao Santos Silva]

If you rescaled the covariate and then took logs, there is no need to change anything else.

[Anne Wanyonyi]

Thank you so much Joao, that has helped. Initially, I was re scaling the already logged covariate.

Last question if you do not mind. I have introduced exporter and importer time fixed effects and the bilateral country-pair fixed effects to address the multilateral resistance effects and endogeneity respectively. However, once I ran the PPML model, my time-invariant covariates (distance, language, common colonizer, common boundary) are not absorbed as posited in various papers (I still get the coefficients of this variables, though they are very different from the coefficients before I include the bilateral country-pair fixed effects.
Should I just go ahead and omit these variables before I ran the PPML model as I am already aware of the collinearity between such variables and the country-pair fixed effects? Or does the fact these time invariant variables are not absorbed point to a problem with the model?

[Joao Santos Silva]

To be on the safe side, please use ppmlhdfe.

[Anne Wanyonyi]

I have used ppmlhfde, but the time invariant variables still appear.

[Joao Santos Silva]

Pair-specific time invariant variables such as distance should not be dropped if you use time-varying origin and destination dummies; they will be dropped if you use pair-fixed effects. If you include pair fixed effects and still see the coefficient for distance when estimating by ppmlhdfe, there there is probably something wrong with your data or with how you are interpreting it.

[Anne Wanyonyi]

The coefficient of the time invariant variables (contig, comlang_off, comcol and distw) are still appearing, even after including the pair fixed effects and using ppmlhdfe. Kindly have a look at some of my data, to see if something is a miss.

 
iso3_d
iso3_o
Year
Exports
Covariate 1
contig
comlang_off
comcol
distw
RTA

BEN
AGO
2006
84709
10880
0
0
0
2340.251
0

BEN
AGO
2007
10759
10921
0
0
0
2340.251
0

BEN
AGO
2008
7817
3504
0
0
0
2340.251
0

BEN
AGO
2009
24029
609
0
0
0
2340.251
0

BEN
AGO
2010
0
11410
0
0
0
2340.251
0

BEN
AGO
2011
129317
9872
0
0
0
2340.251
0

BEN
AGO
2012
26634
473
0
0
0
2340.251
0

BEN
AGO
2013
0
625
0
0
0
2340.251
0

BEN
AGO
2014
0
546
0
0
0
2340.251
0

BEN
AGO
2015
64420
497
0
0
0
2340.251
0

BWA
AGO
2006
6109148
525
0
0
0
2013.847
1

BWA
AGO
2007
1257595
426
0
0
0
2013.847
1

BWA
AGO
2008
3259288
600
0
0
0
2013.847
1

BWA
AGO
2009
856470
0
0
0
0
2013.847
1

BWA
AGO
2010
364812
0
0
0
0
2013.847
1

BWA
AGO
2011
1465002
0
0
0
0
2013.847
1

BWA
AGO
2012
761803
0
0
0
0
2013.847
1

BWA
AGO
2013
1972258
1265
0
0
0
2013.847
1

BWA
AGO
2014
2029540
2430
0
0
0
2013.847
1

BWA
AGO
2015
2492606
1185
0
0
0
2013.847
1

COG
AGO
2006
0
3382
0
0
0
681.5906
1

COG
AGO
2007
3.32E+08
2837
0
0
0
681.5906
1

COG
AGO
2008
1.51E+08
2134
0
0
0
681.5906
1

COG
AGO
2009
9.53E+08
3193
0
0
0
681.5906
1

COG
AGO
2010
9.03E+08
3352
0
0
0
681.5906
1

COG
AGO
2011
1.20E+09
9661
0
0
0
681.5906
1

COG
AGO
2012
3.70E+08
7896
0
0
0
681.5906
1

COG
AGO
2013
8.91E+08
14750
0
0
0
681.5906
1

COG
AGO
2014
3.33E+08
7242
0
0
0
681.5906
1

COG
AGO
2015
0
4000
0
0
0
681.5906
1

EGY
AGO
2006
2636251
1010
0
0
0
2403.401
1

EGY
AGO
2007
2942020
560
0
0
0
4814.249
0

EGY
AGO
2008
25367570
576
0
0
0
4814.249
0

EGY
AGO
2009
43027364
678
0
0
0
4814.249
0

EGY
AGO
2010
17855384
547
0
0
0
4814.249
0

EGY
AGO
2011
24557504
303
0
0
0
4814.249
0

EGY
AGO
2012
25382537
354
0
0
0
4814.249
0

EGY
AGO
2013
29214075
209
0
0
0
4814.249
0

EGY
AGO
2014
38566264
410
0
0
0
4814.249
0

EGY
AGO
2015
33402048
301
0
0
0
4814.249
0

ETH
AGO
2006
39421
0
0
0
0
3510.41
0

ETH
AGO
2007
137303
0
0
0
0
3510.41
0

ETH
AGO
2008
458768
0
0
0
0
3510.41
0

ETH
AGO
2009
79082
0
0
0
0
3510.41
0

ETH
AGO
2010
1107526
0
0
0
0
3510.41
0

ETH
AGO
2011
4083630
0
0
0
0
3510.41
0

ETH
AGO
2012
3297537
0
0
0
0
3510.41
0

ETH
AGO
2013
1303131
0
0
0
0
3510.41
0

ETH
AGO
2014
814669
0
0
0
0
3510.41
0

ETH
AGO
2015
284349
0
0
0
0
3510.41
0

LSO
AGO
2006
0
0
0
0
0
2617.787
1

LSO
AGO
2007
0
0
0
0
0
2617.787
1

LSO
AGO
2008
0
0
0
0
0
2617.787
1

LSO
AGO
2009
0
0
0
0
0
2617.787
1

LSO
AGO
2010
0
0
0
0
0
2617.787
1

LSO
AGO
2011
777781
0
0
0
0
2617.787
1

LSO
AGO
2012
10112
0
0
0
0
2617.787
1

LSO
AGO
2013
0
0
0
0
0
2617.787
1

LSO
AGO
2014
0
0
0
0
0
2617.787
1

LSO
AGO
2015
0
0
0
0
0
2617.787
1

MAR
AGO
2006
20341233
474
0
0
0
5301.951
0

MAR
AGO
2007
20995860
506
0
0
0
5301.951
0

MAR
AGO
2008
32684108
834
0
0
0
5301.951
0

MAR
AGO
2009
28872086
1426
0
0
0
5301.951
0

MAR
AGO
2010
35355366
2926
0
0
0
5301.951
0

MAR
AGO
2011
33144410
4231
0
0
0
5301.951
0

MAR
AGO
2012
46404670
2378
0
0
0
5301.951
0

MAR
AGO
2013
66104593
1015
0
0
0
5301.951
0

MAR
AGO
2014
82424996
1435
0
0
0
5301.951
0

MAR
AGO
2015
45534865
1055
0
0
0
5301.951
0

MDG
AGO
2006
105923
0
0
0
0
3785.104
1

MDG
AGO
2007
13809
0
0
0
0
3785.104
1

MDG
AGO
2008
13880
0
0
0
0
3785.104
1

MDG
AGO
2009
9985
0
0
0
0
3785.104
1

MDG
AGO
2010
20726
0
0
0
0
3785.104
1

MDG
AGO
2011
101433
0
0
0
0
3785.104
1

MDG
AGO
2012
0
0
0
0
0
3785.104
1

MDG
AGO
2013
0
13
0
0
0
3785.104
1

MDG
AGO
2014
14073
49
0
0
0
3785.104
1

MDG
AGO
2015
145230
65
0
0
0
3785.104
1

MUS
AGO
2006
2855433
118
0
0
0
4828.119
1

MUS
AGO
2007
2306880
90
0
0
0
4828.119
1

MUS
AGO
2008
589661
185
0
0
0
4828.119
1

MUS
AGO
2009
2318799
123
0
0
0
4828.119
1

MUS
AGO
2010
1916575
155
0
0
0
4828.119
1

MUS
AGO
2011
833784
208
0
0
0
4828.119
1

MUS
AGO
2012
24312
330
0
0
0
4828.119
1

MUS
AGO
2013
39748
505
0
0
0
4828.119
1

MUS
AGO
2014
138857
570
0
0
0
4828.119
1

MUS
AGO
2015
34276
434
0
0
0
4828.119
1

NGA
AGO
2006
17734695
6722
0
0
0
2209.762
0

NGA
AGO
2007
6981292
11515
0
0
0
2209.762
0

NGA
AGO
2008
18758163
12795
0
0
0
2209.762
0

NGA
AGO
2009
5346578
13385
0
0
0
2209.762
0

NGA
AGO
2010
59207992
13496
0
0
0
2209.762
0

NGA
AGO
2011
1.05E+08
0
0
0
0
2209.762
0

NGA
AGO
2012
55553659
24324
0
0
0
2209.762
0

NGA
AGO
2013
14801503
372
0
0
0
2209.762
0

NGA
AGO
2014
6500832
3600
0
0
0
2209.762
0

NGA
AGO
2015
0
7550
0
0
0
2209.762
0

RWA
AGO
2006
7602
0
0
0
0
1996.589
1

RWA
AGO
2007
9824
93
0
0
0
1996.589
0

RWA
AGO
2008
3815
127
0
0
0
1996.589
0

RWA
AGO
2009
1807496
146
0
0
0
1996.589
0

RWA
AGO
2010
0
268
0
0
0
1996.589
0

RWA
AGO
2011
26418
173
0
0
0
1996.589
0

RWA
AGO
2012
4424
154
0
0
0
1996.589
0

RWA
AGO
2013
0
153
0
0
0
1996.589
0

RWA
AGO
2014
5641
194
0
0
0
1996.589
0

RWA
AGO
2015
0
280
0
0
0
1996.589
0

SWZ
AGO
2006
0
0
0
0
0
2623.159
1

SWZ
AGO
2007
0
0
0
0
0
2623.159
1

SWZ
AGO
2008
0
0
0
0
0
2623.159
1

SWZ
AGO
2009
0
0
0
0
0
2623.159
1

SWZ
AGO
2010
0
0
0
0
0
2623.159
1

SWZ
AGO
2011
0
0
0
0
0
2623.159
1

SWZ
AGO
2012
0
0
0
0
0
2623.159
1

SWZ
AGO
2013
33278313
0
0
0
0
2623.159
1

SWZ
AGO
2014
42363223
0
0
0
0
2623.159
1

SWZ
AGO
2015
37188003
0
0
0
0
2623.159
1

TZA
AGO
2006
2799575
286
0
0
0
2596.974
1

TZA
AGO
2007
2124561
435
0
0
0
2596.974
1

TZA
AGO
2008
1260003
377
0
0
0
2596.974
1

TZA
AGO
2009
669243
270
0
0
0
2596.974
1

TZA
AGO
2010
3207946
517
0
0
0
2596.974
1

TZA
AGO
2011
28965421
656
0
0
0
2596.974
1

TZA
AGO
2012
2618196
609
0
0
0
2596.974
1

TZA
AGO
2013
29040644
811
0
0
0
2596.974
1

TZA
AGO
2014
2452740
1710
0
0
0
2596.974
1

TZA
AGO
2015
3812585
661
0
0
0
2596.974
1

UGA
AGO
2006
481160
0
0
0
0
2384.524
1

UGA
AGO
2007
42836
0
0
0
0
2384.524
0

UGA
AGO
2008
464686
0
0
0
0
2384.524
0

UGA
AGO
2009
0
0
0
0
0
2384.524
0

UGA
AGO
2010
1007280
0
0
0
0
2384.524
0

UGA
AGO
2011
775280
0
0
0
0
2384.524
0

UGA
AGO
2012
343416
0
0
0
0
2384.524
0

UGA
AGO
2013
2700
333
0
0
0
2384.524
0

UGA
AGO
2014
87500
155
0
0
0
2384.524
0

UGA
AGO
2015
2611892
134
0
0
0
2384.524
0

ZAF
AGO
2006
6.87E+08
28349
0
0
0
2579.672
1

ZAF
AGO
2007
7.72E+08
31227
0
0
0
2579.672
1

ZAF
AGO
2008
8.98E+08
35993
0
0
0
2579.672
1

ZAF
AGO
2009
6.82E+08
37254
0
0
0
2579.672
1

ZAF
AGO
2010
7.15E+08
38543
0
0
0
2579.672
1

ZAF
AGO
2011
8.90E+08
39217
0
0
0
2579.672
1

ZAF
AGO
2012
1.00E+09
47714
0
0
0
2579.672
1

ZAF
AGO
2013
1.01E+09
57041
0
0
0
2579.672
1

ZAF
AGO
2014
1.05E+09
53592
0
0
0
2579.672
1

ZAF
AGO
2015
6.76E+08
48416
0
0
0
2579.672
1

ZWE
AGO
2006
370404
5056
0
0
0
2048.661
1

ZWE
AGO
2007
1367388
23478
0
0
0
2048.661
1

ZWE
AGO
2008
2273703
10439
0
0
0
2048.661
1

ZWE
AGO
2009
3145390
8131
0
0
0
2048.661
1

ZWE
AGO
2010
4187246
2285
0
0
0
2048.661
1

ZWE
AGO
2011
8866088
3297
0
0
0
2048.661
1

ZWE
AGO
2012
0
1437
0
0
0
2048.661
1

ZWE
AGO
2013
0
1796
0
0
0
2048.661
1

ZWE
AGO
2014
0
854
0
0
0
2048.661
1

ZWE
AGO
2015
6468
1308
0
0
0
2048.661
1

AGO
BDI
2006
0
31
0
0
0
1905.42
1

AGO
BDI
2007
0
23
0
0
0
1905.42
0

AGO
BDI
2008
0
58
0
0
0
1905.42
0

AGO
BDI
2009
0
21
0
0
0
1905.42
0

AGO
BDI
2010
0
34
0
0
0
1905.42
0

AGO
BDI
2011
0
37
0
0
0
1905.42
0

AGO
BDI
2012
0
40
0
0
0
1905.42
0

AGO
BDI
2013
0
33
0
0
0
1905.42
0

AGO
BDI
2014
0
56
0
0
0
1905.42
0

AGO
BDI
2015
1881
49
0
0
0
1905.42
0

BEN
BDI
2006
0
2036
0
1
0
3278.666
0

BEN
BDI
2007
0
1240
0
1
0
3278.666
0

BEN
BDI
2008
0
74
0
1
0
3278.666
0

BEN
BDI
2009
29577
31
0
1
0
3278.666
0

BEN
BDI
2010
38330
1035
0
1
0
3278.666
0

BEN
BDI
2011
124731
611
0
1
0
3278.666
0

BEN
BDI
2012
0
512
0
1
0
3278.666
0

BEN
BDI
2013
37348
345
0
1
0
3278.666
0

BEN
BDI
2014
12175
220
0
1
0
3278.666
0

BEN
BDI
2015
0
219
0
1
0
3278.666
0

BWA
BDI
2006
0
0
0
0
0
2265.744
0

BWA
BDI
2007
0
0
0
0
0
2265.744
0

BWA
BDI
2008
129023
0
0
0
0
2265.744
0

BWA
BDI
2009
0
0
0
0
0
2265.744
0

BWA
BDI
2010
87989
0
0
0
0
2265.744
0

BWA
BDI
2011
47611
0
0
0
0
2265.744
0

BWA
BDI
2012
8919
0
0
0
0
2265.744
0

BWA
BDI
2013
8678
123
0
0
0
2265.744
0

BWA
BDI
2014
28800
28
0
0
0
2265.744
0

BWA
BDI
2015
994
32
0
0
0
2265.744
0

CAF
BDI
2006
0
0
0
1
0
1554.957
0

CAF
BDI
2007
0
0
0
1
0
1554.957
0

CAF
BDI
2008
0
0
0
1
0
1554.957
0

CAF
BDI
2009
0
0
0
1
0
1554.957
0

CAF
BDI
2010
0
0
0
1
0
1554.957
0

CAF
BDI
2011
0
0
0
1
0
1554.957
0

CAF
BDI
2012
301424
0
0
1
0
1554.957
0

CAF
BDI
2013
22922
0
0
1
0
1554.957
0

CAF
BDI
2014
1527
0
0
1
0
1554.957
0

CAF
BDI
2015
128842
0
0
1
0
1554.957
0

COG
BDI
2006
0
0
0
1
0
1727.978
0

COG
BDI
2007
52601
0
0
1
0
1727.978
0

COG
BDI
2008
1526741
0
0
1
0
1727.978
0

COG
BDI
2009
0
0
0
1
0
1727.978
0

COG
BDI
2010
0
0
0
1
0
1727.978
0

COG
BDI
2011
0
443
0
1
0
1727.978
0

COG
BDI
2012
0
332
0
1
0
1727.978
0

COG
BDI
2013
0
1524
0
1
0
1727.978
0

COG
BDI
2014
0
466
0
1
0
1727.978
0

COG
BDI
2015
0
371
0
1
0
1727.978
0

EGY
BDI
2006
105393
582
0
0
0
3720.649
1

EGY
BDI
2007
82210
639
0
0
0
3720.649
1

EGY
BDI
2008
3229449
503
0
0
0
3720.649
1

EGY
BDI
2009
12902133
574
0
0
0
3720.649
1

EGY
BDI
2010
15727714
467
0
0
0
3720.649
1

EGY
BDI
2011
14029855
304
0
0
0
3720.649
1

EGY
BDI
2012
11421614
312
0
0
0
3720.649
1

EGY
BDI
2013
11994310
243
0
0
0
3720.649
1

EGY
BDI
2014
10153781
317
0
0
0
3720.649
1

EGY
BDI
2015
6672556
342
0
0
0
3720.649
1

ETH
BDI
2006
0
0
0
0
0
1748.314
0

ETH
BDI
2007
135963
0
0
0
0
1748.314
0

ETH
BDI
2008
38225
0
0
0
0
1748.314
0

ETH
BDI
2009
49136
0
0
0
0
1748.314
0

ETH
BDI
2010
30620
0
0
0
0
1748.314
0

ETH
BDI
2011
174409
0
0
0
0
1748.314
0

ETH
BDI
2012
13585
0
0
0
0
1748.314
0

ETH
BDI
2013
28377
0
0
0
0
1748.314
0

ETH
BDI
2014
75017
0
0
0
0
1748.314
0

ETH
BDI
2015
27804
0
0
0
0
1748.314
0

MAR
BDI
2006
60244
92
0
1
0
5612.109
0

MAR
BDI
2007
113734
164
0
1
0
5612.109
0

MAR
BDI
2008
13082
286
0
1
0
5612.109
0

MAR
BDI
2009
25314
137
0
1
0
5612.109
0

MAR
BDI
2010
519618
193
0
1
0
5612.109
0

MAR
BDI
2011
175064
189
0
1
0
5612.109
0

MAR
BDI
2012
170486
314
0
1
0
5612.109
0

MAR
BDI
2013
206083
217
0
1
0
5612.109
0

MAR
BDI
2014
392644
222
0
1
0
5612.109
0

MAR
BDI
2015
462098
221
0
1
0
5612.109
0

MDG
BDI
2006
0
0
0
1
0
2637.587
1

MDG
BDI
2007
4300473
0
0
1
0
2637.587
1

MDG
BDI
2008
14544
0
0
1
0
2637.587
1

MDG
BDI
2009
10659
0
0
1
0
2637.587
1

MDG
BDI
2010
9529
0
0
1
0
2637.587
1

MDG
BDI
2011
848
0
0
1
0
2637.587
1

MDG
BDI
2012
10521
0
0
1
0
2637.587
1

MDG
BDI
2013
167
48
0
1
0
2637.587
1

MDG
BDI
2014
11416
82
0
1
0
2637.587
1

MDG
BDI
2015
0
0
0
1
0
2637.587
1

MUS
BDI
2006
182744
57
0
1
0
3563.77
1

MUS
BDI
2007
230425
71
0
1
0
3563.77
1

MUS
BDI
2008
356845
43
0
1
0
3563.77
1

MUS
BDI
2009
51869
63
0
1
0
3563.77
1

MUS
BDI
2010
1469706
76
0
1
0
3563.77
1

MUS
BDI
2011
1633676
80
0
1
0
3563.77
1

MUS
BDI
2012
1642131
69
0
1
0
3563.77
1

MUS
BDI
2013
1120892
80
0
1
0
3563.77
1

MUS
BDI
2014
790383
100
0
1
0
3563.77
1

MUS
BDI
2015
285031
115
0
1
0
3563.77
1

RWA
BDI
2006
1818643
0
1
1
1
162.1818
1

RWA
BDI
2007
2549385
102134
1
1
1
162.1818
1

RWA
BDI
2008
5666753
74686
1
1
1
162.1818
1

RWA
BDI
2009
5020317
97154
1
1
1
162.1818
1

RWA
BDI
2010
3938631
72316
1
1
1
162.1818
1

RWA
BDI
2011
5564224
75824
1
1
1
162.1818
1

RWA
BDI
2012
9556095
77600
1
1
1
162.1818
1

RWA
BDI
2013
12698754
101735
1
1
1
162.1818
1

[Joao Santos Silva]

Looks OK to me; make sure you are defining the pairs correctly.

Best wishes,

Joao

[Anne Wanyonyi]

This is how I defined the pairs. I hope I defined them correctly.

[/CODE]egen pairID=group(importer exporter)
xtset pairID Year

tabulate pairID, gen(PAIR_FE)[/CODE]