Hello Stata users,
I am studying the effect of innovation (both firm's and academic) on the productivity growth of non-superstar firms.
I use academic innovation (innovation_index) as an instrumental variable to explain firm's innovation (nb_cp) as well.
This is because I assume that academic innovation indirectly affect firm-level productivity growth via given firm's innovation (d_loglp).
However, I found that using just -xtreg- in my model is performing better than -xtivreg- or -ivreg2- in terms of my expectation of coefficient of firm's innovation (nb_cp).
For more information, I use Error Correction Model and Hybrid model.
Below is the outputs for all of my model (+ due to limited number of characters in post, I post more regression outputs in the below post #2):
Given the above results, I would like to hear advice on whether to use IV approach or not.
To the best of my knowledge, I was thinking that university's innovation does not directly affect firm-level productivity growth (which might be wrong).
Would it be possible to hear any advice regarding the output of these models and testing instrument variable before performing the regression in Stata, please?
Thank you in advance!
I am studying the effect of innovation (both firm's and academic) on the productivity growth of non-superstar firms.
I use academic innovation (innovation_index) as an instrumental variable to explain firm's innovation (nb_cp) as well.
This is because I assume that academic innovation indirectly affect firm-level productivity growth via given firm's innovation (d_loglp).
However, I found that using just -xtreg- in my model is performing better than -xtivreg- or -ivreg2- in terms of my expectation of coefficient of firm's innovation (nb_cp).
For more information, I use Error Correction Model and Hybrid model.
Below is the outputs for all of my model (+ due to limited number of characters in post, I post more regression outputs in the below post #2):
Code:
. xtivreg d_loglp fr_growth lag_gap log_intangible log_rd logemp firm_age ///
> i.year i.naics2 (nb_cp=innov_index) if Frontier == 0, vce(cluster gvkey)
G2SLS random-effects IV regression Number of obs = 18,045
Group variable: gvkey Number of groups = 2,172
R-squared: Obs per group:
Within = 0.0282 min = 1
Between = 0.0323 avg = 8.3
Overall = 0.0146 max = 62
Wald chi2(91) = 719.89
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000
(Std. err. adjusted for 3,430 clusters in gvkey)
--------------------------------------------------------------------------------
| Robust
d_loglp | Coefficient std. err. z P>|z| [95% conf. interval]
---------------+----------------------------------------------------------------
nb_cp | -.0183235 .0206332 -0.89 0.375 -.0587638 .0221169
fr_growth | .1106896 .0122647 9.03 0.000 .0866513 .134728
lag_gap | .2021425 .0176848 11.43 0.000 .1674809 .2368041
log_intangible | .0053826 .0045773 1.18 0.240 -.0035887 .0143538
log_rd | .0615087 .0081511 7.55 0.000 .0455329 .0774845
logemp | -.074794 .0113621 -6.58 0.000 -.0970634 -.0525246
firm_age | .0030151 .0009118 3.31 0.001 .001228 .0048022
|
year |
1952 | .0075932 .0984207 0.08 0.939 -.1853079 .2004943
1953 | .1131369 .107592 1.05 0.293 -.0977396 .3240134
1954 | -.0311501 .1089366 -0.29 0.775 -.244662 .1823617
1955 | -.0198466 .1160307 -0.17 0.864 -.2472626 .2075695
1956 | -.0589943 .0929338 -0.63 0.526 -.2411413 .1231527
1957 | -.0263302 .0903444 -0.29 0.771 -.203402 .1507415
1958 | -.0600593 .1027183 -0.58 0.559 -.2613835 .141265
1959 | -.0807842 .1154156 -0.70 0.484 -.3069947 .1454263
1960 | -.1033547 .1059654 -0.98 0.329 -.311043 .1043336
1961 | -.0781265 .1049465 -0.74 0.457 -.2838178 .1275649
1962 | -.1313381 .120659 -1.09 0.276 -.3678253 .1051491
1963 | -.1334081 .1134379 -1.18 0.240 -.3557423 .0889261
1964 | -.108942 .1191606 -0.91 0.361 -.3424926 .1246085
1965 | -.1910552 .1201511 -1.59 0.112 -.426547 .0444366
1966 | -.1513376 .1133352 -1.34 0.182 -.3734705 .0707953
1967 | -.1872244 .1172957 -1.60 0.110 -.4171198 .042671
1968 | -.1495189 .1175422 -1.27 0.203 -.3798973 .0808596
1969 | -.1697759 .1174785 -1.45 0.148 -.4000294 .0604777
1970 | -.1471852 .1157171 -1.27 0.203 -.3739866 .0796161
1971 | -.1519141 .114787 -1.32 0.186 -.3768925 .0730644
1972 | -.144976 .1151366 -1.26 0.208 -.3706396 .0806877
1973 | -.2058058 .1159198 -1.78 0.076 -.4330044 .0213928
1974 | -.260185 .1168832 -2.23 0.026 -.4892718 -.0310982
1975 | -.2749146 .116734 -2.36 0.019 -.5037091 -.0461201
1976 | -.1730036 .1161963 -1.49 0.137 -.4007442 .054737
1977 | -.1793295 .1153565 -1.55 0.120 -.4054241 .046765
1978 | -.1695945 .1159301 -1.46 0.143 -.3968132 .0576243
1979 | -.1585263 .1156452 -1.37 0.170 -.3851867 .0681342
1980 | -.2663978 .1177009 -2.26 0.024 -.4970874 -.0357083
1981 | -.2762778 .1171371 -2.36 0.018 -.5058624 -.0466933
1982 | -.2233883 .1164002 -1.92 0.055 -.4515285 .0047519
1983 | -.2162437 .1167323 -1.85 0.064 -.4450348 .0125474
1984 | -.1621432 .116725 -1.39 0.165 -.39092 .0666336
1985 | -.1887889 .1173277 -1.61 0.108 -.4187471 .0411692
1986 | -.1893198 .1183286 -1.60 0.110 -.4212395 .0425999
1987 | -.1972566 .1184689 -1.67 0.096 -.4294515 .0349382
1988 | -.2416786 .1187279 -2.04 0.042 -.4743811 -.0089761
1989 | -.3407587 .1200202 -2.84 0.005 -.5759939 -.1055235
1990 | -.2886399 .1199518 -2.41 0.016 -.5237411 -.0535387
1991 | -.2737638 .1190288 -2.30 0.021 -.5070561 -.0404716
1992 | -.2736437 .1199716 -2.28 0.023 -.5087838 -.0385037
1993 | -.2743006 .1193553 -2.30 0.022 -.5082326 -.0403686
1994 | -.2769886 .1200254 -2.31 0.021 -.512234 -.0417432
1995 | -.3241784 .1217793 -2.66 0.008 -.5628613 -.0854954
1996 | -.3209233 .1232157 -2.60 0.009 -.5624216 -.079425
1997 | -.3378189 .1218752 -2.77 0.006 -.5766898 -.098948
1998 | -.3765876 .1224761 -3.07 0.002 -.6166364 -.1365388
1999 | -.3684449 .1227139 -3.00 0.003 -.6089598 -.1279301
2000 | -.3515135 .1222893 -2.87 0.004 -.591196 -.1118309
2001 | -.3942174 .12308 -3.20 0.001 -.6354497 -.1529851
2002 | -.4161021 .1223718 -3.40 0.001 -.6559463 -.1762578
2003 | -.3845803 .1243737 -3.09 0.002 -.6283482 -.1408123
2004 | -.4208611 .1257445 -3.35 0.001 -.6673157 -.1744064
2005 | -.4245245 .1245079 -3.41 0.001 -.6685555 -.1804935
2006 | -.3782574 .1246028 -3.04 0.002 -.6224744 -.1340404
2007 | -.3389723 .1231374 -2.75 0.006 -.5803171 -.0976275
2008 | -.3495783 .1230977 -2.84 0.005 -.5908454 -.1083113
2009 | -.4103811 .1246504 -3.29 0.001 -.6546915 -.1660708
2010 | -.3419459 .1267592 -2.70 0.007 -.5903893 -.0935025
2011 | -.4806655 .1263132 -3.81 0.000 -.7282349 -.2330962
2012 | -.5817466 .1290966 -4.51 0.000 -.8347713 -.3287218
2013 | -.5416179 .1290759 -4.20 0.000 -.794602 -.2886337
2014 | -.5054038 .1272834 -3.97 0.000 -.7548748 -.2559329
2015 | -.5511463 .1274472 -4.32 0.000 -.8009383 -.3013544
2016 | -.512947 .1271212 -4.04 0.000 -.7621 -.2637939
2017 | -.4858209 .1276319 -3.81 0.000 -.7359748 -.2356669
2018 | -.5862867 .1372313 -4.27 0.000 -.8552551 -.3173182
2019 | -.674928 .1711089 -3.94 0.000 -1.010295 -.3395608
|
naics2 |
21 | -.3325314 .0949668 -3.50 0.000 -.5186629 -.1463998
22 | -.0521812 .1039988 -0.50 0.616 -.256015 .1516526
23 | .0733619 .1022456 0.72 0.473 -.1270359 .2737596
31 | -.1820533 .0938883 -1.94 0.052 -.366071 .0019643
32 | -.5436712 .0897481 -6.06 0.000 -.7195743 -.3677682
33 | -.3229373 .0814436 -3.97 0.000 -.4825638 -.1633108
42 | -.2101065 .1001019 -2.10 0.036 -.4063026 -.0139104
44 | .1224316 .1096664 1.12 0.264 -.0925107 .3373738
45 | .0975564 .1274045 0.77 0.444 -.1521518 .3472646
51 | -.2685584 .0896612 -3.00 0.003 -.4442912 -.0928257
52 | -.2307234 .0879134 -2.62 0.009 -.4030305 -.0584162
53 | -.2345138 .0937569 -2.50 0.012 -.4182739 -.0507537
54 | -.0763391 .0938583 -0.81 0.416 -.2602979 .1076197
56 | -.0418498 .1035886 -0.40 0.686 -.2448797 .1611801
62 | -.1420314 .101501 -1.40 0.162 -.3409698 .056907
71 | .072057 .1299535 0.55 0.579 -.1826472 .3267613
99 | -.0610206 .1295897 -0.47 0.638 -.3150119 .1929706
|
_cons | .1762036 .154717 1.14 0.255 -.1270363 .4794434
---------------+----------------------------------------------------------------
sigma_u | .48242357
sigma_e | .21949815
rho | .82848917 (fraction of variance due to u_i)
--------------------------------------------------------------------------------
Instrumented: nb_cp
Instruments: fr_growth lag_gap log_intangible log_rd logemp firm_age 1952.year
1953.year 1954.year 1955.year 1956.year 1957.year 1958.year
1959.year 1960.year 1961.year 1962.year 1963.year 1964.year
1965.year 1966.year 1967.year 1968.year 1969.year 1970.year
1971.year 1972.year 1973.year 1974.year 1975.year 1976.year
1977.year 1978.year 1979.year 1980.year 1981.year 1982.year
1983.year 1984.year 1985.year 1986.year 1987.year 1988.year
1989.year 1990.year 1991.year 1992.year 1993.year 1994.year
1995.year 1996.year 1997.year 1998.year 1999.year 2000.year
2001.year 2002.year 2003.year 2004.year 2005.year 2006.year
2007.year 2008.year 2009.year 2010.year 2011.year 2012.year
2013.year 2014.year 2015.year 2016.year 2017.year 2018.year
2019.year 21.naics2 22.naics2 23.naics2 31.naics2 32.naics2
33.naics2 42.naics2 44.naics2 45.naics2 51.naics2 52.naics2
53.naics2 54.naics2 56.naics2 62.naics2 71.naics2 99.naics2
innov_index
.
. ivreg2 d_loglp fr_growth lag_gap log_intangible log_rd logemp firm_age ///
> i.year i.naics2 (nb_cp=innov_index) if Frontier == 0, cluster(gvkey)
IV (2SLS) estimation
--------------------
Estimates efficient for homoskedasticity only
Statistics robust to heteroskedasticity and clustering on gvkey
Number of clusters (gvkey) = 2172 Number of obs = 18045
F( 92, 2171) = 11.12
Prob > F = 0.0000
Total (centered) SS = 1083.295632 Centered R2 = -0.0599
Total (uncentered) SS = 1108.40422 Uncentered R2 = -0.0359
Residual SS = 1148.158639 Root MSE = .2522
--------------------------------------------------------------------------------
| Robust
d_loglp | Coefficient std. err. z P>|z| [95% conf. interval]
---------------+----------------------------------------------------------------
nb_cp | -.0043337 .0028194 -1.54 0.124 -.0098597 .0011924
fr_growth | .05528 .0108574 5.09 0.000 .0339998 .0765601
lag_gap | .0943791 .0078615 12.01 0.000 .0789708 .1097875
log_intangible | .0038313 .0019486 1.97 0.049 .0000121 .0076505
log_rd | .0205121 .0029973 6.84 0.000 .0146374 .0263868
logemp | -.0167956 .0044938 -3.74 0.000 -.0256033 -.0079878
firm_age | -.0001927 .0004979 -0.39 0.699 -.0011686 .0007832
|
year |
1952 | .0128839 .0952745 0.14 0.892 -.1738506 .1996185
1953 | .0958709 .10507 0.91 0.362 -.1100626 .3018044
1954 | -.0246161 .1165839 -0.21 0.833 -.2531163 .2038842
1955 | .0098143 .1211598 0.08 0.935 -.2276546 .2472832
1956 | -.0104543 .093212 -0.11 0.911 -.1931464 .1722378
1957 | .0129183 .0924923 0.14 0.889 -.1683633 .1941999
1958 | -.0291111 .1053856 -0.28 0.782 -.2356631 .1774408
1959 | -.050061 .1178718 -0.42 0.671 -.2810854 .1809634
1960 | -.0546584 .1066312 -0.51 0.608 -.2636517 .1543348
1961 | -.0251373 .1037336 -0.24 0.809 -.2284514 .1781768
1962 | -.0625013 .1160197 -0.54 0.590 -.2898957 .1648931
1963 | -.0535668 .1080296 -0.50 0.620 -.265301 .1581674
1964 | -.0142636 .1142841 -0.12 0.901 -.2382562 .2097291
1965 | -.096433 .1148438 -0.84 0.401 -.3215227 .1286567
1966 | -.0634798 .1090455 -0.58 0.560 -.277205 .1502454
1967 | -.0995556 .1129192 -0.88 0.378 -.3208732 .1217621
1968 | -.072371 .1128219 -0.64 0.521 -.2934978 .1487557
1969 | -.0833136 .1129207 -0.74 0.461 -.3046341 .1380069
1970 | -.0387594 .1111377 -0.35 0.727 -.2565853 .1790665
1971 | -.0419807 .1102024 -0.38 0.703 -.2579735 .1740121
1972 | -.0154236 .1100865 -0.14 0.889 -.2311892 .200342
1973 | -.05089 .110314 -0.46 0.645 -.2671015 .1653215
1974 | -.0837 .1104576 -0.76 0.449 -.3001929 .132793
1975 | -.1264329 .1111489 -1.14 0.255 -.3442807 .0914149
1976 | -.0336202 .1102972 -0.30 0.761 -.2497988 .1825585
1977 | -.05166 .1099393 -0.47 0.638 -.267137 .163817
1978 | -.0417988 .1100085 -0.38 0.704 -.2574115 .173814
1979 | -.0317522 .1099878 -0.29 0.773 -.2473243 .1838199
1980 | -.0842467 .1105141 -0.76 0.446 -.3008503 .1323569
1981 | -.097152 .1104139 -0.88 0.379 -.3135593 .1192553
1982 | -.0705939 .1098683 -0.64 0.521 -.2859319 .1447441
1983 | -.0657705 .1105615 -0.59 0.552 -.2824671 .1509261
1984 | -.0063699 .1110492 -0.06 0.954 -.2240223 .2112824
1985 | -.0322631 .1113514 -0.29 0.772 -.2505079 .1859817
1986 | -.0270527 .111519 -0.24 0.808 -.245626 .1915205
1987 | -.0171148 .111581 -0.15 0.878 -.2358096 .20158
1988 | -.0441947 .1114284 -0.40 0.692 -.2625903 .1742008
1989 | -.1154639 .1117717 -1.03 0.302 -.3345324 .1036045
1990 | -.0650903 .1115886 -0.58 0.560 -.2837999 .1536192
1991 | -.0657566 .1108142 -0.59 0.553 -.2829484 .1514353
1992 | -.0596378 .1112055 -0.54 0.592 -.2775966 .1583211
1993 | -.056129 .110778 -0.51 0.612 -.2732499 .1609919
1994 | -.0451688 .1115111 -0.41 0.685 -.2637265 .1733889
1995 | -.0730855 .1119592 -0.65 0.514 -.2925214 .1463505
1996 | -.0611862 .1122911 -0.54 0.586 -.2812728 .1589004
1997 | -.0744509 .1120481 -0.66 0.506 -.2940611 .1451593
1998 | -.0956299 .1120439 -0.85 0.393 -.3152319 .1239721
1999 | -.0888379 .1121245 -0.79 0.428 -.3085979 .1309221
2000 | -.0433057 .1120501 -0.39 0.699 -.2629198 .1763084
2001 | -.1106013 .1126249 -0.98 0.326 -.3313421 .1101396
2002 | -.1306693 .1116332 -1.17 0.242 -.3494663 .0881278
2003 | -.0705411 .1124902 -0.63 0.531 -.2910177 .1499356
2004 | -.0961206 .1125033 -0.85 0.393 -.316623 .1243818
2005 | -.1165383 .1123751 -1.04 0.300 -.3367894 .1037128
2006 | -.0914046 .1124241 -0.81 0.416 -.3117517 .1289425
2007 | -.0665785 .1120089 -0.59 0.552 -.2861119 .1529548
2008 | -.0794525 .1116307 -0.71 0.477 -.2982446 .1393397
2009 | -.14715 .1129864 -1.30 0.193 -.3685993 .0742993
2010 | -.0512294 .1136283 -0.45 0.652 -.2739369 .171478
2011 | -.1507805 .1125098 -1.34 0.180 -.3712957 .0697348
2012 | -.21483 .1141982 -1.88 0.060 -.4386544 .0089944
2013 | -.1793044 .1147935 -1.56 0.118 -.4042956 .0456868
2014 | -.1481436 .1138088 -1.30 0.193 -.3712048 .0749176
2015 | -.1940603 .1137458 -1.71 0.088 -.4169979 .0288773
2016 | -.1519657 .113707 -1.34 0.181 -.3748273 .0708959
2017 | -.1121644 .1138888 -0.98 0.325 -.3353823 .1110535
2018 | -.1630929 .112947 -1.44 0.149 -.3844649 .0582791
2019 | -.1551232 .114523 -1.35 0.176 -.3795841 .0693378
|
naics2 |
21 | -.2348334 .0638334 -3.68 0.000 -.3599445 -.1097223
22 | -.0268351 .0583537 -0.46 0.646 -.1412061 .087536
23 | .0601628 .0807291 0.75 0.456 -.0980634 .218389
31 | -.154002 .0573798 -2.68 0.007 -.2664642 -.0415397
32 | -.282569 .0577642 -4.89 0.000 -.3957848 -.1693532
33 | -.1908146 .0565469 -3.37 0.001 -.3016446 -.0799847
42 | -.1428124 .0638389 -2.24 0.025 -.2679345 -.0176904
44 | -.0298656 .0727159 -0.41 0.681 -.1723862 .112655
45 | -.0347025 .0701206 -0.49 0.621 -.1721364 .1027314
51 | -.1726631 .0574031 -3.01 0.003 -.2851711 -.060155
52 | -.1394516 .0566348 -2.46 0.014 -.2504537 -.0284495
53 | -.1662955 .0579644 -2.87 0.004 -.2799037 -.0526873
54 | -.0899666 .0584149 -1.54 0.124 -.2044576 .0245245
56 | -.1523446 .0765918 -1.99 0.047 -.3024618 -.0022273
62 | -.1331588 .067334 -1.98 0.048 -.2651311 -.0011865
71 | -.1121225 .0696005 -1.61 0.107 -.2485368 .0242919
99 | -.0797737 .0608704 -1.31 0.190 -.1990775 .0395301
|
_cons | .0902494 .1228108 0.73 0.462 -.1504554 .3309541
--------------------------------------------------------------------------------
Underidentification test (Kleibergen-Paap rk LM statistic): 4.430
Chi-sq(1) P-val = 0.0353
------------------------------------------------------------------------------
Weak identification test (Cragg-Donald Wald F statistic): 27.144
(Kleibergen-Paap rk Wald F statistic): 4.429
Stock-Yogo weak ID test critical values: 10% maximal IV size 16.38
15% maximal IV size 8.96
20% maximal IV size 6.66
25% maximal IV size 5.53
Source: Stock-Yogo (2005). Reproduced by permission.
NB: Critical values are for Cragg-Donald F statistic and i.i.d. errors.
------------------------------------------------------------------------------
Warning: estimated covariance matrix of moment conditions not of full rank.
overidentification statistic not reported, and standard errors and
model tests should be interpreted with caution.
Possible causes:
number of clusters insufficient to calculate robust covariance matrix
singleton dummy variable (dummy with one 1 and N-1 0s or vice versa)
partial option may address problem.
------------------------------------------------------------------------------
Instrumented: nb_cp
Included instruments: fr_growth lag_gap log_intangible log_rd logemp firm_age
1952.year 1953.year 1954.year 1955.year 1956.year
1957.year 1958.year 1959.year 1960.year 1961.year
1962.year 1963.year 1964.year 1965.year 1966.year
1967.year 1968.year 1969.year 1970.year 1971.year
1972.year 1973.year 1974.year 1975.year 1976.year
1977.year 1978.year 1979.year 1980.year 1981.year
1982.year 1983.year 1984.year 1985.year 1986.year
1987.year 1988.year 1989.year 1990.year 1991.year
1992.year 1993.year 1994.year 1995.year 1996.year
1997.year 1998.year 1999.year 2000.year 2001.year
2002.year 2003.year 2004.year 2005.year 2006.year
2007.year 2008.year 2009.year 2010.year 2011.year
2012.year 2013.year 2014.year 2015.year 2016.year
2017.year 2018.year 2019.year 21.naics2 22.naics2
23.naics2 31.naics2 32.naics2 33.naics2 42.naics2
44.naics2 45.naics2 51.naics2 52.naics2 53.naics2
54.naics2 56.naics2 62.naics2 71.naics2 99.naics2
Excluded instruments: innov_index
------------------------------------------------------------------------------
. weakivtest
(obs=18,045)
Montiel-Pflueger robust weak instrument test
--------------------------------------------
Effective F statistic: 4.429
Confidence level alpha: 5%
--------------------------------------------
--------------------------------------------
Critical Values TSLS LIML
--------------------------------------------
% of Worst Case Bias
tau=5% 37.418 37.418
tau=10% 23.109 23.109
tau=20% 15.062 15.062
tau=30% 12.039 12.039
--------------------------------------------
Given the above results, I would like to hear advice on whether to use IV approach or not.
To the best of my knowledge, I was thinking that university's innovation does not directly affect firm-level productivity growth (which might be wrong).
Would it be possible to hear any advice regarding the output of these models and testing instrument variable before performing the regression in Stata, please?
Thank you in advance!
Comment