Any workaround for the problem of panel regression' coefficient become insignificant

[Jurat Shahidin]

Dear Statalist:

This is my very first time to post my question in this forum, so let me go straight my problem. In my research project, I am examining the impact of temperature and precipitation on growths of per capita GDP and also in it's components, namely, agricultural value-added, industrial value-added and other three sectors' value added at NUTS 3 level from a panel dataset in which contains 427 districts being observed from 1980 to 2008. I used two-way fixed effects model for regression plus I added non-linear (square) terms of temperature and precipitation as my independent variables, and when my dependent variable was growth in per capita GDP(Natural log of GDP per capita), the output was significant. . However, I am wondering why my estimate' results of Gross Value Added in each sector are not significant. Here is the stata scripts down below:

 xi: xtreg ln_gva_agr_per_worker temp temp_sq prec100 prec100_sq i.year, fe
i.year            _Iyear_1980-2008    (naturally coded; _Iyear_1980 omitted)

Fixed-effects (within) regression               Number of obs     =     11,261
Group variable: nuts_id                         Number of groups  =        427

R-sq:                                           Obs per group:
     within  = 0.5303                                         min =         18
     between = 0.0258                                         avg =       26.4
     overall = 0.3304                                         max =         29

                                                F(32,10802)       =     381.11
corr(u_i, Xb)  = -0.0289                        Prob > F          =     0.0000

------------------------------------------------------------------------------
ln_gva_agr~r |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        temp |  -.0559938    .047335    -1.18   0.237    -.1487791    .0367915
     temp_sq |   .0045938   .0024318     1.89   0.059    -.0001729    .0093605
     prec100 |   .0007092   .0008371     0.85   0.397    -.0009317      .00235
  prec100_sq |  -.0000154   .0000129    -1.20   0.231    -.0000406    9.83e-06
 _Iyear_1981 |  -.0151681   .0284041    -0.53   0.593    -.0708455    .0405092
 _Iyear_1982 |   .1471999   .0333447     4.41   0.000     .0818381    .2125617
 _Iyear_1983 |   .0818918   .0348414     2.35   0.019     .0135962    .1501874
 _Iyear_1984 |   .2337834   .0271073     8.62   0.000     .1806481    .2869188
 _Iyear_1985 |   .2562463   .0271715     9.43   0.000     .2029852    .3095074
 _Iyear_1986 |   .3309238   .0274023    12.08   0.000     .2772104    .3846373
 _Iyear_1987 |   .2720868   .0268266    10.14   0.000     .2195018    .3246719
 _Iyear_1988 |   .3156214   .0355192     8.89   0.000     .2459973    .3852455
 _Iyear_1989 |    .359082   .0390624     9.19   0.000     .2825124    .4356515
 _Iyear_1990 |   .4374567   .0391526    11.17   0.000     .3607104    .5142031
 _Iyear_1991 |   .6351093   .0280698    22.63   0.000     .5800874    .6901312
 _Iyear_1992 |   .6159567   .0376376    16.37   0.000     .5421801    .6897333
 _Iyear_1993 |   .7228997   .0291412    24.81   0.000     .6657775    .7800218
 _Iyear_1994 |   .6126641   .0434097    14.11   0.000     .5275731     .697755
 _Iyear_1995 |   .7491805   .0327843    22.85   0.000     .6849173    .8134438
 _Iyear_1996 |   .8209237   .0268705    30.55   0.000     .7682525     .873595
 _Iyear_1997 |   .8423416   .0323935    26.00   0.000     .7788443    .9058388
 _Iyear_1998 |   .8338915   .0344429    24.21   0.000      .766377    .9014059
 _Iyear_1999 |   .9639368   .0396041    24.34   0.000     .8863055    1.041568
 _Iyear_2000 |    .927599   .0442933    20.94   0.000      .840776    1.014422
 _Iyear_2001 |    1.00045   .0346132    28.90   0.000     .9326015    1.068298
 _Iyear_2002 |    .967341   .0408675    23.67   0.000     .8872333    1.047449
 _Iyear_2003 |    .953381    .039245    24.29   0.000     .8764537    1.030308
 _Iyear_2004 |   1.196531   .0327579    36.53   0.000     1.132319    1.260743
 _Iyear_2005 |   1.137292   .0338471    33.60   0.000     1.070946    1.203639
 _Iyear_2006 |   1.085869   .0403975    26.88   0.000     1.006682    1.165055
 _Iyear_2007 |   1.051976   .0442739    23.76   0.000     .9651912    1.138761
 _Iyear_2008 |   1.095157   .0386327    28.35   0.000      1.01943    1.170884
       _cons |   2.320279   .2365243     9.81   0.000     1.856648     2.78391
-------------+----------------------------------------------------------------
     sigma_u |  .38561429
     sigma_e |  .34084369
         rho |  .56139543   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(426, 10802) = 32.86                 Prob > F = 0.0000

I am wondering why my regression coefficient become insignificant. Why does this happen? Any idea please? Thanks in advance!

[Carlo Lazzaro]

Jurat:
welcome to this forum.
Some comment about your query:
- -xi.- prefix is redundant; use -fvvarlist- instead (as you are recommended to for creating squared terms:

c.temp##c.temp
c.prec100##.prec100

;
by the way, there's no evidfence of squared terms-related turning points: hence you can keep the linear term only for those variables;
- it is not clear to me how you tested two-way fixed effect with -xtreg, fe-;
- if -ln_gva_agr~r- is your dependent variable, I fail to get how you investigated its staistical significance, nor I'm clear with phrasing like "the output was significant";
- the only relevant predictor in your model is -i.year-;
- anyway, your within R-sq is remerkable (this is the indicator we usually look at when dealing with -xtreg, fe-).

All that said: what are you complaining about?

[Jurat Shahidin]

Dear Carlos:

Thanks for your hit on my post. I tried what you suggested to me but nothing changed. I want to figure out the source of the problem and want to optimize the output as robust and significant as possible. Do you think is there any possibility to improve regression output? Any possible suggestion or approach would be appreciated. Thank you


PS: I ran two-way fixed effects (fixed by district, and fixed by time), here is the stata command:

testparm  i.year

[Carlo Lazzaro]

Jurat:
again, I do not see your problem:
- you have a quite remakable within R-sq, which is a good results for -fe- specification;
- I would get rid of squared terms for -temp- and -prec100-, as they do not add anything informative to your regression model;
- i would explicitly test the joint siignificance of -i-year- via -testparm-.

[Jurat Shahidin]

Dear Carlo:
Thanks for your in time reply, let me explain why I did what I did in this panel analysis:
I used two-way fixed effects instead of only entity-fixed effect because first my professor suggested to do it by his experience and the related literature recommended to do so and to verify if there's need in including the time fixed effects, I used the command testparm, and it turned out that the F-test is very significant, as you can see below:

xtreg ln_gva_agr_per_worker temp prec100 c.temp##c.temp c.prec100##c.prec100 i.year, fe
note: temp omitted because of collinearity
note: prec100 omitted because of collinearity

Fixed-effects (within) regression Number of obs = 11,261
Group variable: nuts_id Number of groups = 427

R-sq: Obs per group:
within = 0.5303 min = 18
between = 0.0258 avg = 26.4
overall = 0.3304 max = 29

F(32,10802) = 381.11
corr(u_i, Xb) = -0.0289 Prob > F = 0.0000


ln_gva_agr_per_wo~r Coef. Std. Err. t P>t [95% Conf. Interval]

temp -.0559938 .047335 -1.18 0.237 -.1487791 .0367915
prec100 .0007092 .0008371 0.85 0.397 -.0009317 .00235
temp 0 (omitted)

c.temp#c.temp .0045938 .0024318 1.89 0.059 -.0001729 .0093605

prec100 0 (omitted)

c.prec100#c.prec100 -.0000154 .0000129 -1.20 0.231 -.0000406 9.83e-06

year
1981 -.0151681 .0284041 -0.53 0.593 -.0708455 .0405092
1982 .1471999 .0333447 4.41 0.000 .0818381 .2125617
1983 .0818918 .0348414 2.35 0.019 .0135962 .1501874
1984 .2337834 .0271073 8.62 0.000 .1806481 .2869188
1985 .2562463 .0271715 9.43 0.000 .2029852 .3095074
1986 .3309238 .0274023 12.08 0.000 .2772104 .3846373
1987 .2720868 .0268266 10.14 0.000 .2195018 .3246719
1988 .3156214 .0355192 8.89 0.000 .2459973 .3852455
1989 .359082 .0390624 9.19 0.000 .2825124 .4356515
1990 .4374567 .0391526 11.17 0.000 .3607104 .5142031
1991 .6351093 .0280698 22.63 0.000 .5800874 .6901312
1992 .6159567 .0376376 16.37 0.000 .5421801 .6897333
1993 .7228997 .0291412 24.81 0.000 .6657775 .7800218
1994 .6126641 .0434097 14.11 0.000 .5275731 .697755
1995 .7491805 .0327843 22.85 0.000 .6849173 .8134438
1996 .8209237 .0268705 30.55 0.000 .7682525 .8735949
1997 .8423416 .0323935 26.00 0.000 .7788443 .9058388
1998 .8338915 .0344429 24.21 0.000 .766377 .9014059
1999 .9639368 .0396041 24.34 0.000 .8863055 1.041568
2000 .927599 .0442933 20.94 0.000 .840776 1.014422
2001 1.00045 .0346132 28.90 0.000 .9326015 1.068298
2002 .967341 .0408675 23.67 0.000 .8872333 1.047449
2003 .953381 .039245 24.29 0.000 .8764537 1.030308
2004 1.196531 .0327579 36.53 0.000 1.132319 1.260743
2005 1.137292 .0338471 33.60 0.000 1.070946 1.203639
2006 1.085869 .0403975 26.88 0.000 1.006682 1.165055
2007 1.051976 .0442739 23.76 0.000 .9651912 1.138761
2008 1.095157 .0386327 28.35 0.000 1.01943 1.170884

_cons 2.320279 .2365243 9.81 0.000 1.856648 2.78391

sigma_u .38561429
sigma_e .34084369
rho .56139543 (fraction of variance due to u_i)

F test that all u_i=0: F(426, 10802) = 32.86 Prob > F = 0.0000

. testparm i.year

( 1) 1981.year = 0
( 2) 1982.year = 0
( 3) 1983.year = 0
( 4) 1984.year = 0
( 5) 1985.year = 0
( 6) 1986.year = 0
( 7) 1987.year = 0
( 8) 1988.year = 0
( 9) 1989.year = 0
(10) 1990.year = 0
(11) 1991.year = 0
(12) 1992.year = 0
(13) 1993.year = 0
(14) 1994.year = 0
(15) 1995.year = 0
(16) 1996.year = 0
(17) 1997.year = 0
(18) 1998.year = 0
(19) 1999.year = 0
(20) 2000.year = 0
(21) 2001.year = 0
(22) 2002.year = 0
(23) 2003.year = 0
(24) 2004.year = 0
(25) 2005.year = 0
(26) 2006.year = 0
(27) 2007.year = 0
(28) 2008.year = 0

F( 28, 10802) = 309.45
Prob > F = 0.0000

At the very beginning of the post, I mentioned my significance problem and more specifically, why each of my independent variables turned out to be insignificant: t-value and P value didn't show any significance in my case, that's why I was wondering about what should I do to make them statistically significant. The quadratic terms entered my equation, first, because it was theory based: I wish to get an inverse-U shape; secondly, for my GDP per capita, which is another dependent variable, I got very good result, that's why I put the quadratic terms also in other applications.

encode index, gen(nuts_id)

.
. xtset nuts_id year
panel variable: nuts_id (strongly balanced)
time variable: year, 1980 to 2008
delta: 1 unit

. xtreg ln_gdp_per_capita temp c.temp##c.temp prec100 c.prec100##c.prec i.year, fe
note: temp omitted because of collinearity
note: prec100 omitted because of collinearity
note: prec omitted because of collinearity

Fixed-effects (within) regression Number of obs = 11,261
Group variable: nuts_id Number of groups = 427

R-sq: Obs per group:
within = 0.6451 min = 18
between = 0.2590 avg = 26.4
overall = 0.0474 max = 29

F(32,10802) = 613.49
corr(u_i, Xb) = -0.1513 Prob > F = 0.0000


ln_gdp_per_cap~a Coef. Std. Err. t P>t [95% Conf. Interval]

temp .1022121 .0134009 7.63 0.000 .0759438 .1284803
temp 0 (omitted)

c.temp#c.temp -.0062924 .0006885 -9.14 0.000 -.0076419 -.0049429

prec100 .0008333 .000237 3.52 0.000 .0003687 .0012978
prec100 0 (omitted)
prec 0 (omitted)

c.prec100#c.prec -2.05e-08 3.65e-08 -0.56 0.574 -9.19e-08 5.10e-08

year
1981 -.0036072 .0080414 -0.45 0.654 -.0193699 .0121555
1982 -.0054267 .0094402 -0.57 0.565 -.0239311 .0130778
1983 .0171475 .0098639 1.74 0.082 -.0021876 .0364825
1984 .0403212 .0076743 5.25 0.000 .0252781 .0553642
1985 .0593237 .0076925 7.71 0.000 .044245 .0744023
1986 .0709681 .0077578 9.15 0.000 .0557614 .0861748
1987 .0954401 .0075948 12.57 0.000 .0805529 .1103274
1988 .1447036 .0100558 14.39 0.000 .1249925 .1644148
1989 .1810437 .0110589 16.37 0.000 .1593663 .2027212
1990 .2376349 .0110844 21.44 0.000 .2159074 .2593624
1991 .1321853 .0079468 16.63 0.000 .1166081 .1477624
1992 .1900665 .0106555 17.84 0.000 .1691797 .2109532
1993 .1824098 .0082501 22.11 0.000 .166238 .1985815
1994 .2327552 .0122896 18.94 0.000 .2086652 .2568451
1995 .2346346 .0092815 25.28 0.000 .2164412 .2528281
1996 .2459972 .0076073 32.34 0.000 .2310856 .2609089
1997 .2620937 .0091709 28.58 0.000 .2441171 .2800703
1998 .2817502 .0097511 28.89 0.000 .2626363 .3008641
1999 .3142071 .0112122 28.02 0.000 .2922291 .3361852
2000 .3501229 .0125398 27.92 0.000 .3255426 .3747032
2001 .3440763 .0097993 35.11 0.000 .3248679 .3632847
2002 .3531459 .0115699 30.52 0.000 .3304667 .375825
2003 .3541495 .0111106 31.88 0.000 .3323708 .3759283
2004 .3576885 .009274 38.57 0.000 .3395097 .3758673
2005 .3679752 .0095824 38.40 0.000 .3491919 .3867584
2006 .4060625 .0114369 35.50 0.000 .3836442 .4284809
2007 .4390167 .0125343 35.03 0.000 .4144472 .4635862
2008 .4428533 .0109372 40.49 0.000 .4214143 .4642923

_cons 2.366575 .0669619 35.34 0.000 2.235318 2.497833

sigma_u .35743588
sigma_e .09649559
rho .93206919 (fraction of variance due to u_i)

F test that all u_i=0: F(426, 10802) = 304.42 Prob > F = 0.0000

Maybe my way thinking is incorrect, please don't hesitate to pointing out any problem.

[Carlo Lazzaro]

Jurat:
a minor amendment should be included in both the regression models, where codes should have been (but this amendment concerns the efficiency of your codes only):

xtreg ln_gva_agr_per_worker  c.temp##c.temp c.prec100##c.prec100 i.year, fe

You actually included -temp- and -prec100- in excess: that's why Stata omitted them due to collinearity with

c.temp##c.temp

and

c.prec100##c.prec100

respectively.

Again, I do not find anything wrong with your approach/code.

As an aside, please always use CODE delimiters to share what you typed and what Stata gave you back. Thanks.