Hi everyone,

I have a data set that I included here. I try to run the regression to find the effect of import volume on the tariff. The product code includes 6 digits. I include in the regression industry fix effect at 2 digits (for example, product 112345 and 114567 are in the same industry 11) and run the command:

areg tariff import_volume,a( industry_2digit) robust

My result is:

. areg tariff import_volume,a( industry_2digit) robust

Linear regression, absorbing indicators Number of obs = 94
Absorbed variable: industry_2digit No. of categories = 22
F( 1, 71) = .
Prob > F = .
R-squared = 1.0000
Adj R-squared = 1.0000
Root MSE = 0.0000

-------------------------------------------------------------------------------------------------------------
tariff | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+-------------------------------------------------------------------------------------
import_volume | 0 (omitted)
_cons | 88.26729 . . . . .
-------------------------------------------------------------------------------------------------------------

I try but can not explain why R2==1 (perfect fit) but the coefficient equal 0 and omitted Standard error. I try another command like that

reg tariff import_volume i.industry_2digit, robust

and get the result:

. reg tariff import_volume i.industry_2digit, robust

Linear regression Number of obs = 94
F(0, 71) = .
Prob > F = .
R-squared = 1.0000
Root MSE = 0

--------------------------------------------------------------------------------------------------------------------------
| Robust
tariff | Coef. Std. Err. t P>|t| [95% Conf. Interval]
---------------+---------------------------------------------------------------------------------------------------------
import_volume | 2.54e-16 3.42e-16 0.74 0.461 - 4.29e-16 9.36e-16
|
industry_2di~t |
3 | 18.23529 3.86e-15 4.7e+15 0.000 18.23529 18.23529
7 | -236.4044 4.92e-14 -4.8e+15 0.000 -236.4044 -236.4044
8 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
9 | 38.23529 3.85e-15 9.9e+15 0.000 38.23529 38.23529
13 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
15 | 38.23529 3.97e-15 9.6e+15 0.000 38.23529 38.23529
17 | 38.23529 6.10e-15 6.3e+15 0.000 38.23529 38.23529
24 | 38.23529 9.04e-15 4.2e+15 0.000 38.23529 38.23529
25 | 38.23529 1.62e-14 2.4e+15 0.000 38.23529 38.23529
30 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
41 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
44 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
52 | 38.23529 7.30e-15 5.2e+15 0.000 38.23529 38.23529
57 | 38.23529 9.04e-15 4.2e+15 0.000 38.23529 38.23529
61 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
62 | 38.23529 3.86e-15 9.9e+15 0.000 38.23529 38.23529
64 | 38.23529 1.68e-14 2.3e+15 0.000 38.23529 38.23529
71 | 38.23529 4.94e-15 7.7e+15 0.000 38.23529 38.23529
72 | 38.23529 4.03e-15 9.5e+15 0.000 38.23529 38.23529
74 | 38.23529 3.94e-15 9.7e+15 0.000 38.23529 38.23529
80 | 38.23529 6.09e-15 6.3e+15 0.000 38.23529 38.23529
|
_cons | 61.76471 3.86e-15 1.6e+16 0.000 61.76471 61.76471
---------------------------------------------------------------------------------------------------------------------


Could anyone help me to explain why two results of coefficient of import volume are different? Which one is correct? Thanks in advance!