Not able to get inverted parabola for data (though theory says so)

Indu gupta

Join Date: Feb 2019
Posts: 2

Not able to get inverted parabola for data (though theory says so)

02 Feb 2019, 00:48

Hi all, can someone please help me understand the nature of the data and the unexpected results I have pertaining to my research question. Theory says that government support (tariff - FIT) for wind should increase initially but decrease later once the technology becomes market competitive. So on running the model FIT vs SGEN I should get inverted parabola but I am getting opposite signs for SGENSQ (getting positive sign in place of positive). Though data also matches theory (on a quick glance - FIT increasing first and then decreasing with increasing SGEN).

ps: Please pardon my limited knowledge of stata and econometrics which I learnt only last year in college.

Code:

* Example generated by -dataex-. To install: ssc install dataex
clear
input byte(COUNTRIES year) double(FIT SGEN) float(year06 year07 year08 year09 year10 year11 year12 year13 year14 year15 year16 year17 FIT1 t SGENSQ SCAPSQ EP1 LGD)
1  6                .068  .1030657647921458 1 0 0 0 0 0 0 0 0 0 0 0       6.8  1 .010622552 .10913751  7.174281 1.1214511         .         .         .         .        .        .         .         .
1  7                 .07  .1833960311811863 0 1 0 0 0 0 0 0 0 0 0 0         7  2 .033634104   .341685   7.27279 1.2492843  .3303597 .10913751       6.8 .10306577     2.07      2.8  908.6755  7.174281
1  8               .0828 .34571949230182764 0 0 1 0 0 0 0 0 0 0 0 0      8.28  3  .11952197 1.1153826  7.664484 1.3363228  .5845383   .341685         7 .18339603      4.2      5.7  859.5363   7.27279
1  9  .08369627042152661  .7059139714833435 0 0 0 1 0 0 0 0 0 0 0 0  8.369627  4   .4983145 4.0102744  7.854073  1.421188 1.0561167 1.1153824      8.28  .3457195   8.3877     11.4   810.397  7.664484
1 10  .08271458602683496  1.231698251526181 0 0 0 0 1 0 0 0 0 0 0 0  8.271459  5  1.5170805  9.337914  7.828656  1.517435  2.002567  4.010275  8.369627   .705914  17.5994     24.9  882.1503  7.854073
1 11   .0822274205572615  1.605950526697121 0 0 0 0 0 1 0 0 0 0 0 0  8.222742  6   2.579077 18.898586  7.771446 1.6037307    3.0558  9.337914  8.271459 1.2316983  29.6335  49.0711       644  7.828656
1 12  .08201715320940489 2.1753109914363833 0 0 0 0 0 0 1 0 0 0 0 0  8.201715  7   4.731978  28.61519  7.605576 1.6744876 4.3472505 18.898586  8.222742 1.6059505  46.3546  71.6528  574.5655  7.771446
1 13  .08142128912326714 2.6797004534055593 0 0 0 0 0 0 0 1 0 0 0 0  8.142129  8   7.180795 36.786377  7.695268  1.744265  5.349317  28.61519  8.201715  2.175311  61.5969 103.0128 564.89197  7.605576
1 14  .08050715767495024   2.97342537920674 0 0 0 0 0 0 0 0 1 0 0 0  8.050715  9   8.841258  49.44025  7.615321 1.8096385  6.065177 36.786377  8.142129 2.6797004  76.7305 138.5582 595.84717  7.695268
1 15                .078  3.337814035924643 0 0 0 0 0 0 0 0 0 1 0 0       7.8 10  11.141003  75.33122  7.406165 1.8712827  7.031376  49.44025  8.050715 2.9734254  96.8191 160.2055  569.0015  7.615321
1 16                .075  4.120177226790112 0 0 0 0 0 0 0 0 0 0 1 0       7.5 11   16.97586  81.21066  6.805224  1.930719  8.679357  75.33123       7.8  3.337814 131.5977 185.6651  466.4218  7.406165
1 17                .071  3.720850249589043 0 0 0 0 0 0 0 0 0 0 0 1       7.1 12  13.844727  93.80511  6.584537 1.9918512  9.011696  81.21066       7.5 4.1201773 148.9827 242.3877  417.2825  6.805224
2  6 .056461731493099125 5.1743944475765264 1 0 0 0 0 0 0 0 0 0 0 0  5.646173  1   26.77436 239.85153  21.16058  3.700236         .         .         .         .        .        .         .         .
2  7  .06265389876880985  6.643709596632992 0 1 0 0 0 0 0 0 0 0 0 0   6.26539  2   44.13888  262.3459  22.66835  3.733658  15.48714 239.85153  5.646173  5.174395   20.474    30.71 1815.6436  21.16058
2  8  .06720351390922401  6.770107673645236 0 0 1 0 0 0 0 0 0 0 0 0  6.720351  3   45.83436 252.52277  20.48422  3.746325 16.197096 262.34592   6.26539   6.64371   22.116   39.713  1746.071  22.66835
2  9  .06388888888888888  6.934366813794093 0 0 0 1 0 0 0 0 0 0 0 0  6.388889  4   48.08544 286.62698 17.457754   3.69103 15.890965 252.52275  6.720351  6.770108   22.794   40.574 1676.4988  20.48422
2 10 .061059602649006624  6.387213769761452 0 0 0 0 1 0 0 0 0 0 0 0   6.10596  5    40.7965  272.7566 18.230679  3.732551 16.930061 286.62698  6.388889  6.934367   25.732   38.648  1609.067 17.457754
2 11  .06318497913769124  8.505996544015918 0 0 0 0 0 1 0 0 0 0 0 0  6.318498  6  72.351974  291.9905 17.712183  3.787034 16.515345 272.75662   6.10596  6.387214   26.903   37.795  1538.625 18.230679
2 12  .07974293059125964   8.56896276071248 0 0 0 0 0 0 1 0 0 0 0 0  7.974293  7  73.427124  301.5401 17.677946 3.7900646  17.08773 291.99054  6.318498  8.505997   28.712   48.891 1469.8903 17.712183
2 13  .08715803452855245  8.606012358141232 0 0 0 0 0 0 0 1 0 0 0 0  8.715803  8  74.063446  326.3659 18.734407 3.7922194  17.36491  301.5401  7.974293  8.568963   30.979   50.681  1390.063 17.677946
2 14    .091657824933687   9.71233847327774 0 0 0 0 0 0 0 0 1 0 0 0  9.165783  9   94.32952  382.2531 17.846724  3.807164   18.0656  326.3659  8.715803  8.606012   33.477   51.721 1322.8143 18.734407
2 15  .07629711751662971 12.980954645423568 0 0 0 0 0 0 0 0 0 1 0 0  7.629712 10   168.5052  480.2829  14.81371  3.815789 19.551294  382.2531  9.165783  9.712338   38.614   57.379  1267.512 17.846724
2 16  .07627212389380532 12.826215179366617 0 0 0 0 0 0 0 0 0 0 1 0  7.627213 11   164.5118  565.7325 14.262878  3.826966  21.91536  480.2829  7.629712 12.980954    44.58   79.206 1189.4918  14.81371
2 17  .07295377677564825 12.731585736211967 0 0 0 0 0 0 0 0 0 0 0 1  7.295378 12  162.09328  653.5629 14.288498  3.844754  23.78513  565.7325  7.627213 12.826215   49.592   78.598 1119.9194 14.262878
3  6  .09410288582183186  8.311555502421346 1 0 0 0 0 0 0 0 0 0 0 0  9.410289  1  69.081955  207.7364 16.319778   3.46152         .         .         .         .        .        .         .         .
3  7  .10690834473324214  9.612474794189376 0 1 0 0 0 0 0 0 0 0 0 0 10.690834  2   92.39967 278.50394 18.748457  3.480006 14.413063  207.7364  9.410289  8.311556   11.722   23.297 1628.7825 16.319778
3  8   .0629575402635432 11.132416009999641 0 0 1 0 0 0 0 0 0 0 0 0  6.295754  3  123.93069  311.9084 17.886976 3.4751675 16.688437  278.5039 10.690834  9.612474    14.82   27.568 1523.5084 18.748457
3  9  .05913888888888889  13.68125998672397 0 0 0 1 0 0 0 0 0 0 0 0  5.913889  4   187.1769  393.5623 16.330366 3.4299185 17.660927  311.9083  6.295754 11.132416   16.555   32.946 1418.2343 17.886976
3 10 .060331125827814566 15.577675566325622 0 0 0 0 1 0 0 0 0 0 0 0  6.033113  5  242.66397  411.0326 19.903315  3.425455 19.838404  393.5623  5.913889  13.68126   19.176   38.117 1340.7026 16.330366
3 11  .05694019471488178  15.46240435884307 0 0 0 0 0 1 0 0 0 0 0 0  5.694019  6  239.08595  437.5426 18.206596  3.411864  20.27394  411.0325  6.033113 15.577676   20.693   44.271 1221.8467 19.903315
3 12  .05460154241645244 17.719845065973043 0 0 0 0 0 0 1 0 0 0 0 0  5.460154  7   313.9929  468.5415 18.584127    3.3815  20.91752  437.5426  5.694019 15.462404   21.529   42.918 1028.2157 18.206596
3 13  .05840637450199203 20.694142207054103 0 0 0 0 0 0 0 1 0 0 0 0  5.840638  8   428.2475   467.895  19.16419  3.367572  21.64582  468.5415  5.460154 17.719845   22.789   49.472  997.3483 18.584127
3 14  .04428381962864721 19.773298014884507 0 0 0 0 0 0 0 0 1 0 0 0  4.428382  9   390.9833  467.9355 21.298264 3.3842676  21.63088   467.895  5.840638  20.69414   22.958   55.646  918.6774  19.16419
3 15  .04004434589800443 18.654239835472065 0 0 0 0 0 0 0 0 0 1 0 0 4.0044346 10  347.98065  463.0162  15.70312   3.41879 21.631815  467.9354  4.428382   19.7733   22.975   52.013  791.8588 21.298264
3 16  .03969026548672567  18.91261109892534 0 0 0 0 0 0 0 0 0 0 1 0 3.9690266 11   357.6869  471.7557 19.894176  3.450166  21.51781  463.0162 4.0044346  18.65424   22.943   49.325  681.3156  15.70312
3 17  .03489289740698985  22.91862645010617 0 0 0 0 0 0 0 0 0 0 0 1   3.48929 12   525.2634 410.59155  21.24259  3.478336  21.71994  471.7557 3.9690266 18.912611   23.003   48.906 576.04144 19.894176
4  6  .08235112908219146  .9449411001332102 1 0 0 0 0 0 0 0 0 0 0 0  8.235113  1   .8929137 16.480648  8.235113 .04391539         .         .         .         .        .        .         .         .
4  7  .09971811862280476 1.2098317680401809 0 1 0 0 0 0 0 0 0 0 0 0  9.971812  2   1.463693  21.52787  9.971812 .12229734 4.0596366  16.48065  8.235113  .9449411    6.315   6.8737 1242.8097  8.235113
4  8  .09298178843540637  1.472655622983437 0 0 1 0 0 0 0 0 0 0 0 0  9.298179  3  2.1687145 33.452515  9.298179 .14577213 4.6398134  21.52787  9.971812 1.2098317   7.8445    9.387 1185.5687  9.971812
4  9  .09461832455324863 1.6853251424645357 0 0 0 1 0 0 0 0 0 0 0 0  9.461832  4   2.840321 33.215816  7.556883 .21296374  5.783815 33.452515  9.298179 1.4726557  10.2425  11.8351 1128.3276  9.298179
4 10  .08157284695796702  1.757603167125818 0 0 0 0 1 0 0 0 0 0 0 0  8.157285  5   3.089169  40.26548  8.029348 .29696646  5.763316 33.215813  9.461832  1.685325   10.925   14.595  1002.891  7.556883
4 11  .08442254124705378 1.9419094408972226 0 0 0 0 0 1 0 0 0 0 0 0  8.442254  6   3.771012  46.50406  7.623583  .3481208  6.345509  40.26548  8.157285  1.757603   13.184   16.104      1095  8.029348
4 12  .09113535565245055 2.1899104979976007 0 0 0 0 0 0 1 0 0 0 0 0  9.113536  7   4.795708  43.72822  6.903216  .3886361  6.819389  46.50406  8.442254 1.9419094   16.179  19.5281  978.3401  7.623583
4 13   .0895935014846923  2.206171508722172 0 0 0 0 0 0 0 1 0 0 0 0  8.959351  8   4.867193  42.08582    6.2047  .4383467  6.612732  43.72822  9.113536 2.1899104  17.2997  23.0692  869.7832  6.903216
4 14  .08913649025069638 2.2440186596124247 0 0 0 0 0 0 0 0 1 0 0 0  8.913649  9    5.03562  51.41434  5.735734  .4979386  6.487359  42.08582  8.959351 2.2061715  18.4204    24.64  852.4359    6.2047
4 15  .08323980546202768 2.4757535327077873 0 0 0 0 0 0 0 0 0 1 0 0   8.32398 10   6.129355  52.70134   5.45635  .5646532  7.170379  51.41434  8.913649 2.2440186  22.4653  27.2354  769.4536  5.735734
4 16  .07976783986903789  2.616282973870522 0 0 0 0 0 0 0 0 0 0 1 0  7.976784 11   6.844936  60.90283  5.239104  .6218823  7.259569  52.70134   8.32398 2.4757535  25.0882  31.8729  727.6403   5.45635
4 17  .06142317496391388 2.6328483180182287 0 0 0 0 0 0 0 0 0 0 0 1  6.142317 12    6.93189 75.461784  5.551477  .6752862  7.804027  60.90283  7.976784  2.616283  28.7004  36.2731  670.3992  5.239104
5  6   .0847145488029466 1.1468509995980456 1 0 0 0 0 0 0 0 0 0 0 0  8.471455  1  1.3152672  5.464934 18.298199 3.6992936         .         .         .         .        .        .         .         .
5  7              .09358  1.434723351931599 0 1 0 0 0 0 0 0 0 0 0 0     9.358  2  2.0584311  8.792028  20.74162  3.714801 2.3377197  5.464933  8.471455  1.146851    1.955    4.225  1570.385 18.298199
5  8  .09191176470588236 1.9753606752383936 0 0 1 0 0 0 0 0 0 0 0 0  9.191176  3    3.90205 16.490583  19.59899  3.702194  2.965135  8.792027     9.358 1.4347234    2.477    5.274 1500.4738  20.74162
5  9  .09155763239875389 2.6599463598019435 0 0 0 1 0 0 0 0 0 0 0 0  9.155764  4   7.075315 25.966637 17.271255   3.65185 4.0608597 16.490582  9.191176 1.9753606    3.447    7.124 1430.5626  19.59899
5 10  .10761978361669242  2.895885022272075 0 0 0 0 1 0 0 0 0 0 0 0 10.761978  5    8.38615 34.015644 17.448223  3.660815  5.095747 25.966637  9.155764 2.6599464     4.42    9.283 1439.2864 17.271255
5 11  .11652243589743588 4.6642139927237904 0 0 0 0 0 1 0 0 0 0 0 0 11.652244  6   21.75489   50.2189 18.594858   3.66742  5.832294 34.015648 10.761978  2.895885    5.421   10.286    1300.5 17.448223
5 12  .09369668246445498  5.861470132432545 0 0 0 0 0 0 1 0 0 0 0 0  9.369668  7   34.35683  89.71994 19.410496  3.675171   7.08653   50.2189 11.652244  4.664214    6.596   15.963 1000.5692 18.594858
5 13           .09253125  8.500219652117503 0 0 0 0 0 0 0 1 0 0 0 0  9.253125  8   72.25373 147.30177 20.098736  3.688792  9.472061  89.71994  9.369668   5.86147     9.03   19.847  1266.975 19.410496
5 14  .10412828947368422 10.112021031636873 0 0 0 0 0 0 0 0 1 0 0 0  10.41283  9  102.25297 185.24644 22.051596  3.711344 12.136794 147.30177  9.253125  8.500219   11.282   28.397 1077.4592 20.098736
5 15  .11032061068702291 12.678974111646296 0 0 0 0 0 0 0 0 0 1 0 0  11.03206 10   160.7564 219.03877  19.72275  3.726583 13.610527 185.24644  10.41283 10.112021   13.074   31.959 1030.4518 22.051596
5 16  .07354925775978408 11.744827429268586 0 0 0 0 0 0 0 0 0 0 1 0  7.354926 11  137.94096 279.15317 17.319893  3.738615 14.799958 219.03876  11.03206 12.678974   14.316   40.317  941.1846  19.72275
5 17  .06661518661518662 13.774238815898649 0 0 0 0 0 0 0 0 0 0 0 1  6.661519 12  189.72966  390.7142 17.035942  3.749845 16.707878  279.1532  7.354926 11.744827   16.217   37.367  871.2734 17.319893
6  6  .15056461731493098 1.0254074639999493 1 0 0 0 0 0 0 0 0 0 0 0  15.05646  1  1.0514605  4.517632 19.228575 3.6342165         .         .         .         .        .        .         .         .
6  7   .4103967168262654 1.3889386222720475 0 1 0 0 0 0 0 0 0 0 0 0  41.03967  2  1.9291505  8.329422   21.2351  3.643798  2.125472 4.5176315  15.05646 1.0254074    1.902    2.971 2002.7805 19.228575
6  8  .17862371888726208 1.6426067523741767 0 0 1 0 0 0 0 0 0 0 0 0 17.862371  3   2.698157 12.761048 19.532835  3.626614  2.886074  8.329422  41.03967 1.3889387    2.702    4.034 1918.4713   21.2351
6  9  .16805555555555557  2.393645918198989 0 0 0 1 0 0 0 0 0 0 0 0 16.805555  4   5.729541  23.07487 16.968405 3.5656774  3.572261  12.76105 17.862371 1.6426067    3.525    4.861  1834.162 19.532835
6 10  .15894039735099338 3.2198444595671365 0 0 0 0 1 0 0 0 0 0 0 0  15.89404  5  10.367398  29.53664  19.47654  3.579326  4.803631  23.07487 16.805555  2.393646    4.879    6.543 1825.6873 16.968405
6 11  .14325452016689846 3.4453505735096446 0 0 0 0 0 1 0 0 0 0 0 0 14.325452  6   11.87044 33.909462    17.804  3.583356  5.434762  29.53664  15.89404  3.219844    5.794    9.126      1592  19.47654
6 12  .13110539845758354  4.733683603087744 0 0 0 0 0 0 1 0 0 0 0 0  13.11054  7   22.40776  42.28199  18.86473 3.5520654  5.823184 33.909466 14.325452  3.445351    6.918    9.856  1511.367    17.804
6 13  .13280212483399734  5.406278352386137 0 0 0 0 0 0 0 1 0 0 0 0 13.280212  8  29.227846  47.06259  18.96135   3.52304   6.50246  42.28199  13.11054 4.7336836    8.102   13.407 1493.9615  18.86473
6 14   .1273209549071618 5.6921151491868205 0 0 0 0 0 0 0 0 1 0 0 0 12.732096  9  32.400173  50.86547 18.140472  3.515001  6.860218  47.06258 13.280212  5.406278    8.542   14.897 1543.1458  18.96135
6 15   .1057760532150776 5.5071791444862095 0 0 0 0 0 0 0 0 0 1 0 0 10.577605 10   30.32902   61.0243  16.36057   3.52544  7.132003  50.86547 12.732096  5.692115    8.683   15.178  1268.316 18.140472
6 16  .10685840707964601  6.425445651096812 0 0 0 0 0 0 0 0 0 0 1 0  10.68584 11   41.28635  67.56673 15.781237 3.5356846  7.811805   61.0243 10.577605  5.507179    9.137   14.844 1243.9972  16.36057
6 17  .10822998872604284   7.28789863287634 0 0 0 0 0 0 0 0 0 0 0 1    10.823 12   53.11347  55.66747 16.309982  3.551851  8.219898  67.56673  10.68584  6.425446    9.384   17.689 1159.6879 15.781237
7  6 .050188205771643665   .401857028845931 1 0 0 0 0 0 0 0 0 0 0 0  5.018821  1  .16148907  1.489602 12.407182   3.71167         .         .         .         .        .        .         .         .
7  7  .11447332421340631  .7558941449553874 0 1 0 0 0 0 0 0 0 0 0 0 11.447332  2  .57137597  3.639554 13.777563 3.7288234 1.2204925  1.489602  5.018821   .401857    1.412    2.182  2644.646 12.407182
7  8  .06149341142020498 1.0462247986880848 0 0 1 0 0 0 0 0 0 0 0 0  6.149341  3  1.0945864 8.3583975 12.764556  3.725186 1.9077615  3.639554 11.447332  .7558941    2.223     4.07   2445.99 13.777563
7  9 .057611111111111106  1.558528456027002 0 0 0 1 0 0 0 0 0 0 0 0  5.761111  4   2.429011 14.793272 11.185722  3.690186  2.891089  8.358397  6.149341 1.0462248    3.403    5.694 2247.3342 12.764556
7 10  .04703311258278146  1.841307816232259 0 0 0 0 1 0 0 0 0 0 0 0 4.7033114  5  3.3904145  22.70554  12.06206  3.704712 3.8462024 14.793273  5.761111 1.5585284    4.582    7.912 2063.3132 11.185722
7 11 .045952712100139084 2.2501018445532863 0 0 0 0 0 1 0 0 0 0 0 0  4.595271  6   5.062958 28.417774 11.852897 3.7204545  4.765033  22.70554 4.7033114 1.8413078    5.912    9.945 1852.5186  12.06206
7 12  .04708226221079692  2.781844414517911 0 0 0 0 0 0 1 0 0 0 0 0  4.708226  7   7.738658 34.283157  11.70344   3.71744  5.330832 28.417774  4.595271 2.2501018    6.679   12.052 1608.8114 11.852897
7 13  .05335989375830013  2.951598425028701 0 0 0 0 0 0 0 1 0 0 0 0  5.335989  8   8.711933  41.06712  12.52137  3.718038  5.855182 34.283157  4.708226 2.7818444    7.517   14.913  1411.216  11.70344
7 14  .06647214854111405 3.2222326543511834 0 0 0 0 0 0 0 0 1 0 0 0  6.647215  9  10.382783  50.36528   13.0963  3.722671  6.408363  41.06712  5.335989 2.9515984    8.202   16.033 1381.5582  12.52137
7 15 .056518847006651884  3.918709055631505 0 0 0 0 0 0 0 0 0 1 0 0  5.651885 10   15.35628  61.82552 11.144668  3.729117   7.09685  50.36528  6.647215 3.2222326    9.068   17.249  994.8186   13.0963
7 16 .053152654867256635  4.044514302404251 0 0 0 0 0 0 0 0 0 0 1 0  5.315266 11  16.358095  76.86417 10.985559  3.736931   7.86292  61.82552  5.651885  3.918709   10.217   21.249  856.7444 11.144668
7 17  .05191657271702367  4.503509277090901 0 0 0 0 0 0 0 0 0 0 0 1  5.191657 12  20.281595  96.00483  11.17286  3.751097  8.767221  76.86417  5.315266  4.044514   11.467     21.4  658.0887 10.985559
8  6  .09700176366843034  .4173353651642256 1 0 0 0 0 0 0 0 0 0 0 0  9.700176  1   .1741688 1.3138033  8.183296 3.8719306         .         .         .         .        .        .         .         .
8  7  .11173184357541899  .4906183716756404 0 1 0 0 0 0 0 0 0 0 0 0 11.173184  2   .2407064 2.1555605  9.274802   3.88265 1.1462126 1.3138033  9.700176  .4173354    1.423    2.473 1858.9625  8.183296
8  8  .11246485473289598   .616272656724091 0 0 1 0 0 0 0 0 0 0 0 0 11.246486  3    .379792  3.411914  8.842438 3.8817816 1.4681827 2.1555605 11.173184  .4906184     1.84    3.007  1824.585  9.274802
8  9   .1189851268591426  1.116040668851357 0 0 0 1 0 0 0 0 0 0 0 0 11.898513  4  1.2455468  6.221249  7.905523 3.8403935 1.8471367  3.411914 11.246486  .6162726    2.336    3.788 1790.2074  8.842438
8 10  .12815533980582525 1.4937479354807734 0 0 0 0 1 0 0 0 0 0 0 0 12.815534  5   2.231283   8.98903  8.586698 3.8596234  2.494243  6.221249 11.898513 1.1160407    3.282    6.641 1714.9403  7.905523
8 11  .13232323232323231 1.6603183299795563 0 0 0 0 0 1 0 0 0 0 0 0 13.232324  6   2.756657 15.694947  8.620475  3.880676  2.998171   8.98903 12.815534  1.493748    3.967    8.724  1666.125  8.586698
8 12  .12912912912912913  1.843958403167891 0 0 0 0 0 0 1 0 0 0 0 0 12.912913  7  3.4001825 22.515347  9.196453  3.886177  3.961685 15.694947 13.232324 1.6603184    5.265   10.187  1784.227  8.620475
8 13  .12475728155339806  2.814271022179959 0 0 0 0 0 0 0 1 0 0 0 0 12.475728  8   7.920121 34.257133  9.243593  3.899129 4.7450337 22.515345 12.912913 1.8439584    6.201    11.31  1725.845  9.196453
8 14  .11573236889692586 3.5296248249047366 0 0 0 0 0 0 0 0 1 0 0 0 11.573236  9   12.45825  50.20697  9.338509   3.91645   5.85296 34.257137 12.475728  2.814271    7.801   17.963 1606.3263  9.243593
8 15  .09929632525410477  4.074610578561731 0 0 0 0 0 0 0 0 0 1 0 0  9.929632 10  16.602451  57.69088  8.073607  3.918081  7.085688  50.20697 11.573236  3.529625    9.694   22.538 1521.8533  9.338509
8 16  .09433962264150944  4.735957879499566 0 0 0 0 0 0 0 0 0 0 1 0  9.433962 11  22.429296 69.575134  8.678102  3.920137  7.595451  57.69088  9.929632 4.0746107   11.214   26.446  1549.565  8.073607
8 17  .09553158705701079   4.65511134903212 0 0 0 0 0 0 0 0 0 0 0 1  9.553159 12   21.67006  72.00872  8.697777 3.9380004  8.341171 69.575134  9.433962  4.735958   11.973   30.766 1515.1873  8.678102
9  6 .060225846925972396     6.320891226214 1 0 0 0 0 0 0 0 0 0 0 0  6.022585  1   39.95367 135.38797  23.27946 3.1048684         .         .         .         .        .        .         .         .
9  7  .06662106703146375  9.013478465891229 0 1 0 0 0 0 0 0 0 0 0 0  6.662107  2    81.2428  215.2206 24.563055   3.12752 11.635633 135.38797  6.022585  6.320891    1.681    2.925 1554.6346  23.27946
9  8  .07174231332357248  13.25599098491299 0 0 1 0 0 0 0 0 0 0 0 0  7.174232  3   175.7213 328.38055  21.90554  3.128069   14.6704 215.22063  6.662107  9.013478    2.201    4.037 1513.3413 24.563055
9  9  .06820833333333333  16.00501210145365 0 0 0 1 0 0 0 0 0 0 0 0  6.820833  4   256.1604  365.2551  18.63167  3.096882 18.121273  328.3805  7.174232  13.25599    2.857    5.757  1472.048  21.90554
end

Code used:
xtreg FIT1 SGEN SGENSQ, fe

Fixed-effects (within) regression Number of obs = 288
Group variable: COUNTRIES Number of groups = 24

R-sq: Obs per group:
within = 0.1559 min = 12
between = 0.2608 avg = 12.0
overall = 0.2215 max = 12

F(2,262) = 24.20
corr(u_i, Xb) = 0.1054 Prob > F = 0.0000

------------------------------------------------------------------------------
FIT1 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
SGEN | -.4460316 .0833138 -5.35 0.000 -.6100815 -.2819816
SGENSQ | .0084565 .0025154 3.36 0.001 .0035035 .0134096
_cons | 9.623024 .4163931 23.11 0.000 8.803121 10.44293
-------------+----------------------------------------------------------------
sigma_u | 3.177689
sigma_e | 2.5218075
rho | .61357308 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(23, 262) = 18.81 Prob > F = 0.0000

Tags: None

Carlo Lazzaro

Join Date: Apr 2014
Posts: 17740

02 Feb 2019, 03:11

Indu:
welcome to this forum.
Some comments about your query:
- why creating squared terms by hand when -fvvarlist- notation can do them for you and provide you with a direct relationship with two wonderful Stata commands, such as -margins- and -marginsplot-?;
- why going -fe- without considering -re- specification (see -hausman-). By the way, as you can see in the example reported below and based on your data, -re- specification seems to be the way to go;
- with 100 observations only, is not surprising that your results seems to be inconsistent with the theory as far as the squared term is concerned. In the same fashion: are you sure that with two predictors onbly your regression model is correctly specified?

Code:

. xtset COUNTRIES year
       panel variable:  COUNTRIES (unbalanced)
        time variable:  year, 6 to 17
                delta:  1 unit

. xtreg FIT1 c.SGEN##c.SGEN, fe

Fixed-effects (within) regression               Number of obs     =        100
Group variable: COUNTRIES                       Number of groups  =          9

R-sq:                                           Obs per group:
     within  = 0.0867                                         min =          4
     between = 0.1462                                         avg =       11.1
     overall = 0.1002                                         max =         12

                                                F(2,89)           =       4.22
corr(u_i, Xb)  = -0.1294                        Prob > F          =     0.0177

-------------------------------------------------------------------------------
         FIT1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
--------------+----------------------------------------------------------------
         SGEN |  -.5094161   .2553741    -1.99   0.049    -1.016839   -.0019933
              |
c.SGEN#c.SGEN |   .0102478   .0119243     0.86   0.392    -.0134455    .0339411
              |
        _cons |   11.19885   .9153415    12.23   0.000     9.380085    13.01761
--------------+----------------------------------------------------------------
      sigma_u |  3.0174778
      sigma_e |  3.0513061
          rho |  .49442603   (fraction of variance due to u_i)
-------------------------------------------------------------------------------
F test that all u_i=0: F(8, 89) = 11.28                      Prob > F = 0.0000

. estimates store fe

. xtreg FIT1 SGEN SGENSQ, re

Random-effects GLS regression                   Number of obs     =        100
Group variable: COUNTRIES                       Number of groups  =          9

R-sq:                                           Obs per group:
     within  = 0.0865                                         min =          4
     between = 0.1487                                         avg =       11.1
     overall = 0.1016                                         max =         12

                                                Wald chi2(2)      =       9.56
corr(u_i, X)   = 0 (assumed)                    Prob > chi2       =     0.0084

------------------------------------------------------------------------------
        FIT1 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        SGEN |  -.4665353   .2422308    -1.93   0.054    -.9412989    .0082284
      SGENSQ |   .0086083   .0115982     0.74   0.458    -.0141237    .0313403
       _cons |   11.03193   1.384414     7.97   0.000     8.318527    13.74533
-------------+----------------------------------------------------------------
     sigma_u |  3.2068612
     sigma_e |  3.0513061
         rho |  .52484099   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. estimates store re

. hausman fe re

                 ---- Coefficients ----
             |      (b)          (B)            (b-B)     sqrt(diag(V_b-V_B))
             |       fe           re         Difference          S.E.
-------------+----------------------------------------------------------------
        SGEN |   -.5094161    -.4665353       -.0428808        .0808712
------------------------------------------------------------------------------
                           b = consistent under Ho and Ha; obtained from xtreg
            B = inconsistent under Ha, efficient under Ho; obtained from xtreg

    Test:  Ho:  difference in coefficients not systematic

                  chi2(1) = (b-B)'[(V_b-V_B)^(-1)](b-B)
                          =        0.28
                Prob>chi2 =      0.5959

Kind regards,
Carlo
(Stata 19.0)

Comment

Indu gupta

Join Date: Feb 2019

Posts: 2
#3

02 Feb 2019, 04:29

Thanks Carlo for the reply.

My model specification involves 5 more variables but could not generate data set with all variables since 'dataex' command in stata gave the following error "data width (258 chars) exceeds max linesize. Try specifying fewer variables". There are infact 288 observations in the data.

I tried various model specifications. However, all of them are giving me wrong sign for SGENSQ. Can you please help me know the reason behind it? Since the data trend shows inverted parabola but the model results do not. How do I find where the issue is?
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Carlo Lazzaro

Join Date: Apr 2014

Posts: 17740
#4

02 Feb 2019, 04:50

Indu:
it may well be that your sample does not allow to show evidence of a squared term for -SGEN-, whereas the effect exist in the population from which the sample was drawn.

Kind regards,
Carlo
(Stata 19.0)
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Not able to get inverted parabola for data (though theory says so)

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