Dear readers of Statalist,

I have an unbalanced panel data of companies in a country and their corresponding regional/ industrial variables including population, industry employment share in the region, the number of industry (diversity), competition and two control variables (1 at company level, 1 at regional level).
The variables of interest is two first one.
I'm trying to regress company's productivity (measured as company's total factor productivity) on regional/ industrial variables.
I prepared for the regression like this:
HTML Code:
xtset    id year, yearly
    panel variable:    id (unbalanced)
    time variable:    year, 2011 to 2016,    but    with    gaps
    delta:    1 year
Because the information from the command xtsum for exlanatory variables shows that within-variation is much smaller than between-variation, and in fact, regional/ industrial variables are slowly changing over time, which makes standard error of fixed-effects (FE) estimation very high. Hence, besides FE estimation, I also conduct random-effects (RE) estimation to see the outcome from between-variation though results from the command xtoverid in favor of FE over RE. As Tom S. Clark et al. (2012) at the link "https://datajobs.com/data-science-repo/Fixed-Effects-Models-[Clark-and-Linzer].pdf" point out that, in the case of big N and small T with slow-changing explanatory variables, RE model is even better than FE model, as long as Fixed-effects factor is low correlated with explanatory variables. I believe that my case is valid for that argument.
The basic results for RE model using GLS technique with Stata 15.1 is as follows: (I removed results for year dummies for the sake of space).
HTML Code:
xtreg lnProductivity lnPopulation IndustryShare Diversity Competition Control1 Control2    i.year,    re    vce(cluster    Region_Industry)

Random-effects GLS regression                   Number of obs     =     82,557
Group variable: id                              Number of groups  =     28,722

R-sq:                                           Obs per group:
within  = 0.0507                                         min =          1
between = 0.0404                                         avg =        2.9
overall = 0.0449                                         max =          6

Wald chi2(11)     =     694.47
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

(Std. Err. adjusted for 978 clusters in Region_Industry)

Robust
lnProductiv~y       Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

lnPopulation     .1219238    .027064     4.51   0.000     .0688793    .1749683
IndustryShare     .060369   .0277869     2.17   0.030     .0059078    .1148302
Diversity        .0668951   .0376893     1.77   0.076    -.0069745    .1407647
Competition     -.0721706   .0303292    -2.38   0.017    -.1316148   -.0127265
Control1         .0002489   .0001706     1.46   0.145    -.0000855    .0005833
Control2        -.0003625   .0003653    -0.99   0.321    -.0010785    .0003536
To control industrial fixed-effect, I add the industry variable (classification of industry for companies) to the command, I yield:
HTML Code:
xtreg lnProductivity lnPopulation IndustryShare Diversity Competition Control1 Control2    i.Industry    i.year,    re    vce(cluster    Region_Industry)

Random-effects GLS regression                   Number of obs     =     82,557
Group variable: id                              Number of groups  =     28,722

R-sq:                                           Obs per group:
within  = 0.0515                                         min =          1
between = 0.5351                                         avg =        2.9
overall = 0.5430                                         max =          6

Wald chi2(69)     =   15884.90
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0000

(Std. Err. adjusted for 978 clusters in Region_Industry)

Robust
lnProductiv~y       Coef.   Std. Err.      z    P>z     [95% Conf. Interval]

lnPopulation      .1224042   .0080391    15.23   0.000     .1066478    .1381606
IndustryShare    .0442533   .0140208     3.16   0.002     .0167729    .0717336
Diversity       .0323125   .0091825     3.52   0.000     .0143152    .0503098
Competition     -.0450796   .0103554    -4.35   0.000    -.0653757   -.0247835
Control1         .0003052   .0001753     1.74   0.082    -.0000384    .0006488
Control2        -.0007511   .0005478    -1.37   0.170    -.0018248    .0003225

Industry
102         .1498892   .0985636     1.52   0.128    -.0432918    .3430703
103         .1355773   .1181954     1.15   0.251    -.0960815     .367236
104         .3746264   .1751559     2.14   0.032     .0313272    .7179256
105         .4152645   .2612369     1.59   0.112    -.0967504    .9272794
106         .1885796   .1911881     0.99   0.324    -.1861422    .5633014
107         .0894018   .1089424     0.82   0.412    -.1241214    .3029251
108         .5530862   .1164927     4.75   0.000     .3247646    .7814078
110         -1.04191   .1067401    -9.76   0.000    -1.251117   -.8327036
There are about 60 industries, but I cut it down to keep the results table short.
As you can see, the overall R-squared goes up to above 0.5, much bigger than 0.05 in the previous regression.
So, I'm quite confused the reason behind this jump and wondering whether I should put industry fixed-effect into the RE model?

Thank you very much in advance for your time and advice!