[Deborah Cipi]

Deborah:
you should get yourself more familiar with the Statalist rules.
That said, elaborating on your .dta file (please, learn how to share data example/excerpt via -dataex- with no risk of downloading active contencts at the repliers' side), you can go as follows:

. gen ln_DiffMeanHourlyPercent=ln( DiffMeanHourlyPercent)

. regress ln_DiffMeanHourlyPercent i.RegionCode i.IndustrySectorCode i.EmployerSizecode, robust

Linear regression Number of obs = 6,256
F(34, 6221) = 26.05
Prob > F = 0.0000
R-squared = 0.1204
Root MSE = .92171

------------------------------------------------------------------------------------
| Robust
ln_DiffMeanHourl~t | Coefficient std. err. t P>|t| [95% conf. interval]
-------------------+----------------------------------------------------------------
RegionCode |
2 | .1719134 .0718272 2.39 0.017 .0311073 .3127196
3 | .2133954 .0610139 3.50 0.000 .093787 .3330037
4 | .0436778 .0749884 0.58 0.560 -.1033254 .1906811
5 | .1382207 .0667634 2.07 0.038 .0073414 .2690999
6 | -.0827402 .1919834 -0.43 0.667 -.4590941 .2936136
7 | .0892374 .078761 1.13 0.257 -.0651614 .2436362
8 | .2251707 .0653417 3.45 0.001 .0970784 .353263
9 | .1172461 .0738838 1.59 0.113 -.0275916 .2620838
10 | .0058935 .0905899 0.07 0.948 -.171694 .183481
11 | .0947933 .0704681 1.35 0.179 -.0433486 .2329352
|
IndustrySectorCode |
2 | .3597039 .2165566 1.66 0.097 -.0648219 .7842297
3 | -.0439148 .1833722 -0.24 0.811 -.4033876 .315558
4 | .298753 .2023624 1.48 0.140 -.0979472 .6954532
5 | -.2177145 .235142 -0.93 0.355 -.678674 .243245
6 | .5294608 .1857151 2.85 0.004 .165395 .8935266
7 | .1806306 .1840547 0.98 0.326 -.1801801 .5414413
8 | -.1691013 .1900056 -0.89 0.374 -.5415779 .2033753
9 | -.6617052 .1918709 -3.45 0.001 -1.037838 -.285572
10 | .2723101 .1849734 1.47 0.141 -.0903016 .6349219
11 | .6965266 .1845571 3.77 0.000 .3347309 1.058322
12 | .3836583 .2072682 1.85 0.064 -.0226589 .7899755
13 | .3344334 .1844582 1.81 0.070 -.0271683 .6960351
14 | .0391356 .1850471 0.21 0.833 -.3236205 .4018917
15 | -.3197152 .2994744 -1.07 0.286 -.9067885 .267358
16 | .0697266 .1901965 0.37 0.714 -.3031243 .4425775
17 | -.3545895 .1944688 -1.82 0.068 -.7358154 .0266364
18 | .6443213 .2082458 3.09 0.002 .2360877 1.052555
19 | .0026552 .1959132 0.01 0.989 -.3814023 .3867127
20 | -.055708 .2865058 -0.19 0.846 -.6173583 .5059423
|
EmployerSizecode |
2 | -.0706938 .0715729 -0.99 0.323 -.2110015 .0696138
3 | -.0769075 .0727363 -1.06 0.290 -.2194957 .0656808
4 | -.1846449 .0736806 -2.51 0.012 -.3290842 -.0402055
5 | -.218186 .090523 -2.41 0.016 -.3956423 -.0407296
6 | -.2457864 .1263792 -1.94 0.052 -.4935333 .0019605
|
_cons | 2.297391 .1989316 11.55 0.000 1.907416 2.687366
------------------------------------------------------------------------------------

. estat ovtest

Ramsey RESET test for omitted variables
Omitted: Powers of fitted values of ln_DiffMeanHourlyPercent

H0: Model has no omitted variables

F(3, 6218) = 2.35
Prob > F = 0.0706

. linktest

Source | SS df MS Number of obs = 6,256
-------------+---------------------------------- F(2, 6253) = 428.27
Model | 723.908211 2 361.954106 Prob > F = 0.0000
Residual | 5284.73535 6,253 .845151984 R-squared = 0.1205
-------------+---------------------------------- Adj R-squared = 0.1202
Total | 6008.64357 6,255 .960614479 Root MSE = .91932

------------------------------------------------------------------------------
ln_DiffMea~t | Coefficient Std. err. t P>|t| [95% conf. interval]
-------------+----------------------------------------------------------------
_hat | 1.210942 .3420908 3.54 0.000 .540327 1.881558
_hatsq | -.0437125 .0705351 -0.62 0.535 -.1819856 .0945605
_cons | -.2493378 .4111786 -0.61 0.544 -1.055389 .5567135
------------------------------------------------------------------------------

Once ln-transformed, while the number of your observations drops (those <0 cannot be logged), your regression looks technically speaking fine (heteroskedasticity was accounted for via -robust- standard errors).
That said, please note that:
- now you have a log-linear regression (see coefficients intepretation in any decent econometrics textbook);
- your R-sq is not that sky-rocketing. This might be due to the lack of non-categorical predictors in the right-hand side of your regression equation;
- get yourself familiar with -estat hettest-; -estat ovtest- and -linktest- postestimation commands by reading the related Stata .pdf manual entries.

just one more doubt: Is it ok to log the dependent variable when is already expressed in percentage in the dataset?

[Maarten Buis]

Don't take the log of the variable. Zero and negative numbers are real here and ignoring those will seriously bias your estimates.

[Deborah Cipi]

Don't take the log of the variable. Zero and negative numbers are real here and ignoring those will seriously bias your estimates.

Should I follow the procedure without loging the dependent variable first?

[Maarten Buis]

yes