Now my question is, under which conditions does the opposite happen?
Specifically, I am dealing with regressions in which I am trying to look at the contingent effect of direct and indirect ties in a collaboration network on the impact of inventions. I reproduce the outcomes of three regressions: In the first one, I only include direct ties dt, in the second one only indirect ties it, and in the third one I include dt and it (note both have a correlation of 0.87).
Code:
xtpoisson fwd log_assets log_breadth log_depth firm_prod degree struct team_deg team_str_hole team_size team_div team_sim team_mk claims num
> _cited_patents num_sbcls backcitation_struct lag it priv c.priv#c.priv pub c.pub#c.pub dt c.priv#c.dt c.priv#c.priv#c.dt c.pub#c.dt c.pub#c.
> pub#c.dt i.app_year i.grant i.tech_cat, fe robust
note: 10 groups (10 obs) dropped because of only one obs per group
Iteration 0: log pseudolikelihood = -263803.46
Iteration 1: log pseudolikelihood = -244586.92
Iteration 2: log pseudolikelihood = -244120.53
Iteration 3: log pseudolikelihood = -244117.75
Iteration 4: log pseudolikelihood = -244117.75
Conditional fixed-effects Poisson regression Number of obs = 39,785
Group variable: firm Number of groups = 127
Obs per group:
min = 2
avg = 313.3
max = 8,114
Wald chi2(44) = 55360.70
Log pseudolikelihood = -244117.75 Prob > chi2 = 0.0000
(Std. Err. adjusted for clustering on firm)
-------------------------------------------------------------------------------------
| Robust
fwd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
log_assets | -.0421138 .0183623 -2.29 0.022 -.0781032 -.0061243
log_breadth | -.0621538 .0740653 -0.84 0.401 -.2073191 .0830115
log_depth | -.0143182 .0451562 -0.32 0.751 -.1028227 .0741862
firm_prod | -.0001577 .0000945 -1.67 0.095 -.0003428 .0000274
degree | .0003697 .0004692 0.79 0.431 -.00055 .0012894
struct | -.0872349 .0384485 -2.27 0.023 -.1625926 -.0118771
team_degree_cent | -.0000941 .0005957 -0.16 0.875 -.0012615 .0010734
team_str_hole | .0418548 .036082 1.16 0.246 -.0288646 .1125742
team_size | .037857 .0061041 6.20 0.000 .0258932 .0498208
team_div | .0015678 .0583958 0.03 0.979 -.1128859 .1160214
team_sim | -.0420113 .0478152 -0.88 0.380 -.1357274 .0517047
team_mk | .0080637 .0122664 0.66 0.511 -.015978 .0321053
claims | .0065597 .0005373 12.21 0.000 .0055065 .0076129
num_cited_patents | .0014349 .0003425 4.19 0.000 .0007637 .0021061
num_sbcls | .0210066 .0026866 7.82 0.000 .015741 .0262721
backcitation_struct | .0046322 .0054924 0.84 0.399 -.0061328 .0153971
lag | .001186 .1057822 0.01 0.991 -.2061433 .2085153
it | -.02097 .0265965 -0.79 0.430 -.0730983 .0311582
priv | .4264326 .1077134 3.96 0.000 .2153183 .637547
|
c.priv#c.priv | -.4015753 .1140479 -3.52 0.000 -.6251051 -.1780454
|
pub | .2271145 .070996 3.20 0.001 .0879649 .3662641
|
c.pub#c.pub | -.1989517 .0592801 -3.36 0.001 -.3151385 -.0827649
|
dt | .0026489 .0044727 0.59 0.554 -.0061175 .0114153
|
c.priv#c.dt | .0065184 .0102537 0.64 0.525 -.0135786 .0266153
|
c.priv#c.priv#c.dt | -.0025707 .009038 -0.28 0.776 -.0202848 .0151434
|
c.pub#c.dt | .0055046 .0173412 0.32 0.751 -.0284835 .0394927
|
c.pub#c.pub#c.dt | -.0078393 .0186939 -0.42 0.675 -.0444787 .0288001
|
app_year |
2001 | -.0546176 .1084301 -0.50 0.614 -.2671367 .1579014
2002 | -.023543 .2147132 -0.11 0.913 -.4443732 .3972871
2003 | -.0025697 .3204385 -0.01 0.994 -.6306176 .6254782
2004 | -.1106726 .4307254 -0.26 0.797 -.9548789 .7335336
|
grant |
2001 | -.3226067 .1814502 -1.78 0.075 -.6782426 .0330293
2002 | -.4679425 .2522891 -1.85 0.064 -.96242 .026535
2003 | -.5601343 .3512596 -1.59 0.111 -1.248591 .1283218
2004 | -1.296592 .4499721 -2.88 0.004 -2.178521 -.4146625
2005 | -.9112545 .5510036 -1.65 0.098 -1.991202 .1686928
2006 | -.953167 .6529846 -1.46 0.144 -2.232993 .3266594
2007 | -1.062879 .7565935 -1.40 0.160 -2.545775 .4200173
2008 | -1.142632 .8518252 -1.34 0.180 -2.812178 .526915
|
tech_cat |
2 | .4231011 .0461803 9.16 0.000 .3325894 .5136128
3 | .2627944 .2686015 0.98 0.328 -.2636548 .7892437
4 | .3656174 .0411299 8.89 0.000 .2850043 .4462306
5 | .1058336 .0698564 1.52 0.130 -.0310824 .2427496
6 | .1518013 .0784977 1.93 0.053 -.0020514 .3056541
-------------------------------------------------------------------------------------
Code:
xtpoisson fwd log_assets log_breadth log_depth firm_prod degree struct team_deg team_str_hole team_size team_div team_sim team_mk claims num
> _cited_patents num_sbcls backcitation_struct lag ///
> priv c.priv#c.priv pub c.pub#c.pub it c.priv#c.it c.priv#c.priv#c.it c.pub#c.it c.pub#c.pub#c.it i.app_year i.grant i.tech_cat, fe robust
note: 10 groups (10 obs) dropped because of only one obs per group
Iteration 0: log pseudolikelihood = -263803.46
Iteration 1: log pseudolikelihood = -244617.71
Iteration 2: log pseudolikelihood = -244151.4
Iteration 3: log pseudolikelihood = -244148.57
Iteration 4: log pseudolikelihood = -244148.57
Conditional fixed-effects Poisson regression Number of obs = 39,785
Group variable: firm Number of groups = 127
Obs per group:
min = 2
avg = 313.3
max = 8,114
Wald chi2(43) = 43653.67
Log pseudolikelihood = -244148.57 Prob > chi2 = 0.0000
(Std. Err. adjusted for clustering on firm)
-------------------------------------------------------------------------------------
| Robust
fwd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
log_assets | -.0417972 .0184625 -2.26 0.024 -.0779831 -.0056114
log_breadth | -.0609179 .074052 -0.82 0.411 -.2060571 .0842213
log_depth | -.0139061 .0451387 -0.31 0.758 -.1023763 .0745641
firm_prod | -.0001575 .0000948 -1.66 0.097 -.0003434 .0000283
degree | .0003651 .0004677 0.78 0.435 -.0005516 .0012817
struct | -.0865138 .0385132 -2.25 0.025 -.1619983 -.0110293
team_degree_cent | -.0000917 .0006003 -0.15 0.879 -.0012682 .0010849
team_str_hole | .0408362 .0358463 1.14 0.255 -.0294212 .1110935
team_size | .0373599 .0063835 5.85 0.000 .0248486 .0498713
team_div | .0025884 .0604123 0.04 0.966 -.1158175 .1209943
team_sim | -.0415313 .0475202 -0.87 0.382 -.1346692 .0516065
team_mk | .0075196 .0118594 0.63 0.526 -.0157243 .0307636
claims | .0065466 .0005445 12.02 0.000 .0054794 .0076138
num_cited_patents | .0014235 .0003391 4.20 0.000 .0007589 .002088
num_sbcls | .0210129 .0026838 7.83 0.000 .0157527 .0262731
backcitation_struct | .0050463 .0056992 0.89 0.376 -.006124 .0162165
lag | .0015166 .1058611 0.01 0.989 -.2059674 .2090006
priv | .4084412 .1079815 3.78 0.000 .1968013 .6200812
|
c.priv#c.priv | -.3834548 .1167273 -3.29 0.001 -.6122361 -.1546735
|
pub | .2400234 .0716232 3.35 0.001 .0996444 .3804024
|
c.pub#c.pub | -.2132266 .0570253 -3.74 0.000 -.3249941 -.101459
|
it | -.0070345 .0077406 -0.91 0.363 -.0222058 .0081368
|
c.priv#c.it | -.0211951 .0935572 -0.23 0.821 -.2045638 .1621736
|
c.priv#c.priv#c.it | .0148457 .0691849 0.21 0.830 -.1207542 .1504456
|
c.pub#c.it | .1324775 .0920244 1.44 0.150 -.0478869 .312842
|
c.pub#c.pub#c.it | -.1396024 .072464 -1.93 0.054 -.2816292 .0024244
|
app_year |
2001 | -.0545978 .1084881 -0.50 0.615 -.2672305 .1580349
2002 | -.0236868 .2148361 -0.11 0.912 -.4447579 .3973842
2003 | -.0021412 .3206502 -0.01 0.995 -.6306041 .6263217
2004 | -.1102924 .4309893 -0.26 0.798 -.9550158 .734431
|
grant |
2001 | -.3217998 .1813656 -1.77 0.076 -.6772698 .0336703
2002 | -.4677767 .2523486 -1.85 0.064 -.9623709 .0268175
2003 | -.5597596 .3512835 -1.59 0.111 -1.248263 .1287434
2004 | -1.296205 .4500562 -2.88 0.004 -2.178299 -.4141108
2005 | -.9120754 .5512629 -1.65 0.098 -1.992531 .16838
2006 | -.9536463 .6532563 -1.46 0.144 -2.234005 .3267125
2007 | -1.063942 .756966 -1.41 0.160 -2.547568 .4196842
2008 | -1.143782 .8523521 -1.34 0.180 -2.814361 .5267978
|
tech_cat |
2 | .4247155 .0460621 9.22 0.000 .3344355 .5149954
3 | .2651247 .2684868 0.99 0.323 -.2610997 .7913492
4 | .3663356 .041281 8.87 0.000 .2854264 .4472449
5 | .104499 .0699651 1.49 0.135 -.0326301 .2416281
6 | .1533703 .0775916 1.98 0.048 .0012936 .305447
-------------------------------------------------------------------------------------
Code:
xtpoisson fwd log_assets log_breadth log_depth firm_prod degree struct team_deg team_str_hole team_size team_div team_sim team_mk claims num
> _cited_patents num_sbcls backcitation_struct lag ///
> priv c.priv#c.priv pub c.pub#c.pub dt it c.priv#c.dt c.priv#c.priv#c.dt c.priv#c.it c.priv#c.priv#c.it c.pub#c.dt c.pub#c.pub#c.dt c.pub#c.i
> t c.pub#c.pub#c.it ///
> i.app_year i.grant i.tech_cat, fe robust
note: 10 groups (10 obs) dropped because of only one obs per group
Iteration 0: log pseudolikelihood = -263803.46
Iteration 1: log pseudolikelihood = -244485.64
Iteration 2: log pseudolikelihood = -244016.26
Iteration 3: log pseudolikelihood = -244013.44
Iteration 4: log pseudolikelihood = -244013.44
Conditional fixed-effects Poisson regression Number of obs = 39,785
Group variable: firm Number of groups = 127
Obs per group:
min = 2
avg = 313.3
max = 8,114
Wald chi2(48) = 65473.80
Log pseudolikelihood = -244013.44 Prob > chi2 = 0.0000
(Std. Err. adjusted for clustering on firm)
-------------------------------------------------------------------------------------
| Robust
fwd | Coef. Std. Err. z P>|z| [95% Conf. Interval]
--------------------+----------------------------------------------------------------
log_assets | -.0416536 .0185879 -2.24 0.025 -.0780853 -.0052219
log_breadth | -.063431 .0738539 -0.86 0.390 -.208182 .08132
log_depth | -.0137816 .0450594 -0.31 0.760 -.1020963 .0745332
firm_prod | -.0001579 .0000946 -1.67 0.095 -.0003433 .0000275
degree | .0003798 .0004742 0.80 0.423 -.0005497 .0013093
struct | -.0864763 .0388271 -2.23 0.026 -.1625761 -.0103765
team_degree_cent | -.0001107 .0005991 -0.18 0.853 -.0012849 .0010635
team_str_hole | .0414972 .0363237 1.14 0.253 -.0296959 .1126903
team_size | .0378755 .0061385 6.17 0.000 .0258443 .0499068
team_div | .0007188 .0581518 0.01 0.990 -.1132566 .1146941
team_sim | -.0402486 .0477124 -0.84 0.399 -.1337633 .0532661
team_mk | .0073269 .012242 0.60 0.550 -.016667 .0313208
claims | .0065359 .0005381 12.15 0.000 .0054813 .0075905
num_cited_patents | .0014213 .0003433 4.14 0.000 .0007484 .0020942
num_sbcls | .0209203 .002683 7.80 0.000 .0156617 .0261789
backcitation_struct | .0062702 .0058392 1.07 0.283 -.0051744 .0177148
lag | .0012678 .1057345 0.01 0.990 -.205968 .2085035
priv | .3277654 .1057273 3.10 0.002 .1205437 .5349871
|
c.priv#c.priv | -.333851 .1163007 -2.87 0.004 -.5617962 -.1059058
|
pub | .3216886 .0734082 4.38 0.000 .1778112 .465566
|
c.pub#c.pub | -.2669564 .057914 -4.61 0.000 -.3804658 -.1534469
|
dt | .0011642 .0054724 0.21 0.832 -.0095615 .01189
it | -.0148946 .0319061 -0.47 0.641 -.0774295 .0476403
|
c.priv#c.dt | .0637551 .0240834 2.65 0.008 .0165524 .1109578
|
c.priv#c.priv#c.dt | -.0336542 .0185492 -1.81 0.070 -.0700099 .0027016
|
c.priv#c.it | -.352787 .1849786 -1.91 0.056 -.7153385 .0097644
|
c.priv#c.priv#c.it | .1721147 .1350795 1.27 0.203 -.0926363 .4368657
|
c.pub#c.dt | -.0737924 .0138189 -5.34 0.000 -.1008769 -.0467079
|
c.pub#c.pub#c.dt | .0548186 .0163733 3.35 0.001 .0227275 .0869098
|
c.pub#c.it | .5046088 .1258178 4.01 0.000 .2580105 .7512072
|
c.pub#c.pub#c.it | -.3730006 .0887886 -4.20 0.000 -.5470232 -.198978
|
app_year |
2001 | -.0545112 .1084542 -0.50 0.615 -.2670774 .1580551
2002 | -.0231496 .2147579 -0.11 0.914 -.4440673 .3977681
2003 | -.0026099 .3203355 -0.01 0.993 -.6304559 .6252361
2004 | -.1108742 .4305263 -0.26 0.797 -.9546902 .7329418
|
grant |
2001 | -.3247795 .1811756 -1.79 0.073 -.6798773 .0303182
2002 | -.4692111 .251969 -1.86 0.063 -.9630614 .0246391
2003 | -.5624661 .3507764 -1.60 0.109 -1.249975 .125043
2004 | -1.298661 .4493931 -2.89 0.004 -2.179455 -.4178663
2005 | -.9139517 .5503947 -1.66 0.097 -1.992705 .164802
2006 | -.9544268 .6524444 -1.46 0.144 -2.233194 .3243408
2007 | -1.065164 .7559497 -1.41 0.159 -2.546799 .4164698
2008 | -1.144925 .8512318 -1.35 0.179 -2.813308 .523459
|
tech_cat |
2 | .4252098 .046273 9.19 0.000 .3345164 .5159031
3 | .2677324 .2693331 0.99 0.320 -.2601507 .7956155
4 | .3684181 .0411073 8.96 0.000 .2878494 .4489868
5 | .1054494 .070141 1.50 0.133 -.0320244 .2429231
6 | .1546547 .0782129 1.98 0.048 .0013602 .3079493
-------------------------------------------------------------------------------------
Note that running a simple OLS on the log of the response variable has the same peculiar results, with only significant interactions when both direct and indirect ties are included.
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