Complementarity in alliance portfolios and firm innovation

Figures & data

Figure 1. Portfolio dimensions.

Table 1. Descriptive statistics and correlations (n = 1300).

Variable	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
1. Patents	1
2. Functional	−0.05	1
3. Relational	−0.05	−0.05	1
4. Structural	−0.01	−0.03	−0.01	1
5. Attribute	−0.25	−0.21	−0.08	−0.06	1
6. Functional & relational	0.01	−0.10	−0.04	−0.03	−0.17	1
7. Functional & structural	0.04	−0.10	−0.04	−0.03	−0.18	−0.08	1
8. Functional & attribute	0.01	−0.11	−0.04	−0.03	−0.19	−0.09	−0.09	1
9. Relational & structural	−0.00	−0.04	−0.02	−0.01	−0.07	−0.03	−0.03	−0.04	1
10. Structural & attribute	−0.02	−0.05	−0.02	−0.01	−0.08	−0.04	−0.04	−0.05	−0.02	1
11. Relational & attribute	−0.03	−0.05	−0.02	−0.02	−0.09	−0.04	−0.05	−0.05	−0.02	−0.02	1
12. Functional & relational & structural	0.32	−0.12	−0.05	−0.03	−0.21	−0.09	−0.10	−0.11	−0.04	−0.05	−0.05	1
13. Functional & relational & attribute	0.11	−0.08	−0.03	−0.02	−0.14	−0.07	−0.07	−0.08	−0.03	−0.03	−0.04	−0.08	1
14. Relational & structural & attribute	−0.01	−0.03	−0.01	−0.01	−0.05	−0.02	−0.02	−0.03	−0.01	−0.01	−0.01	−0.03	−0.02	1
15. Functional & structural & attribute	0.01	−0.06	−0.02	−0.02	−0.11	−0.05	−0.05	−0.06	−0.02	−0.02	−0.03	−0.06	−0.04	−0.01	1
16. Functional & relational & structural & attribute	0.13	−0.07	−0.03	−0.02	−0.12	−0.05	−0.06	−0.06	−0.02	−0.03	−0.03	−0.07	−0.05	−0.02	−0.03	1
17. Firm size	0.65	−0.06	0.00	−0.01	−0.22	0.04	0.01	0.00	0.05	−0.05	0.02	0.24	0.10	−0.02	−0.03	0.16	1
18. Log (R&D)	0.66	−0.03	−0.10	−0.02	−0.22	0.02	0.10	0.05	−0.01	−0.03	−0.07	0.23	0.08	−0.03	−0.00	0.13	0.83	1
19. Patents/R&D	−0.03	−0.04	0.02	0.01	−0.03	0.03	−0.03	0.05	0.01	−0.01	0.00	0.00	0.02	−0.01	0.13	−0.02	−0.20	−0.34	1
20. Portfolio size	0.60	−0.07	−0.06	−0.02	−0.38	0.04	0.18	−0.05	−0.04	−0.06	−0.09	0.53	0.01	−0.03	0.08	0.20	0.48	0.51	−0.07	1
21. Log (Firm age)	0.46	−0.07	0.04	0.02	−0.09	0.04	0.01	−0.09	0.05	−0.02	0.03	0.12	0.09	−0.01	−0.02	0.14	0.80	0.62	−0.22	0.31	1
22. Experience alliances	0.50	0.02	−0.10	−0.01	−0.43	0.11	0.23	0.04	−0.05	−0.06	−0.15	0.37	0.04	−0.04	0.08	0.18	0.44	0.60	0.12	0.69	0.26	1
23. Cultural distance	0.34	0.08	0.04	0.02	−0.56	0.10	0.18	0.06	−0.02	0.00	−0.05	0.28	0.08	−0.01	0.13	0.16	0.23	0.22	0.04	0.53	−0.04	0.39	1
Mean	58.77	0.11	0.02	0.01	0.27	0.07	0.08	0.09	0.01	0.02	0.02	0.1	0.05	0.01	0.03	0.04	0.45	5.94	0.1	6.65	3.39	2.35	0.65
Std. dev.	93.93	0.31	0.13	0.1	0.44	0.26	0.27	0.29	0.11	0.14	0.15	0.31	0.22	0.08	0.17	0.18	2.15	1.82	0.18	8.56	1.14	1.04	0.3
Min	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	−4.51	0.74	0	0	0	0	0
Max	825	1	1	1	1	1	1	1	1	1	1	1	1	1	1	1	4.81	10.65	3.46	58	5.67	4.92	1

Table 2. Contingency of portfolio dimensions (n = 1300).

Dimensions	Number of cases
None	88
Functional	142
Relational	23
Structural	12
Attribute	345
Functional & relational	92
Functional & structural	104
Functional & attribute	122
Relational & structural	16
Structural & attribute	25
Relational & attribute	31
Functional & relational & structural	136
Functional & relational & attribute	69
Relational & structural & attribute only	9
Functional & structural & attribute	40
Functional & relational & structural & attribute	46

Note: The categories are exclusive (combinations of) portfolio dimensions with co-occurrence of exploration- and exploitation-related alliances.

Table 3. Estimates of Equation (1): firm innovation and alliance portfolio dimensions.

	Model 1	Model 2	Model 3
Intercept	0.208 (0.441)	0.171 (0.451)	0.511 (0.927)
Log(R&D)	0.347*** (0.041)	0.343*** (0.041)	0.664*** (0.032)
Patents/R&D	0.509*** (0.079)	0.503*** (0.079)	2.878*** (0.151)
Firm size	−0.053 (0.039)	−0.034 (0.039)	0.064** (0.030)
Portfolio size	0.010*** (0.003)	0.011*** (0.003)	0.001 (0.005)
Experience alliances	−0.101** (0.048)	−0.140*** (0.051)	0.155*** (0.043)
Log(Firm age)	−0.065 (0.065)	−0.066 (0.066)	−0.056 (0.038)
Cultural distance	0.101 (0.078)	0.027 (0.086)	−0.254** (0.115)
Functional		0.337*** (0.094)	0.222* (0.123)
Relational		0.142 (0.157)	0.275 (0.212)
Structural		0.383** (0.176)	0.198 (0.277)
Attribute		0.186** (0.086)	0.170 (0.109)
Functional & relational		0.189* (0.101)	0.438*** (0.139)
Functional & structural		0.265** (0.103)	0.255* (0.140)
Functional & attribute		0.322*** (0.095)	0.465*** (0.128)
Relational & structural		−0.238 (0.156)	0.333 (0.244)
Structural & attribute		0.504*** (0.145)	0.588*** (0.206)
Relational & attribute		−0.007 (0.136)	0.061 (0.189)
Functional & relational & structural		0.291*** (0.100)	0.511*** (0.147)
Functional & relational & attribute		0.356*** (0.098)	0.574*** (0.148)
Relational & structural & attribute		0.275 (0.204)	0.055 (0.314)
Functional & structural & attribute		0.152 (0.123)	0.223 (0.178)
Functional & relational & structural & attribute		0.321*** (0.108)	0.530*** (0.175)
Log-likelihood	−4333.878	−4310.811	−1656.137

Notes:

n = 1300; year dummies are not shown; numbers in parentheses are standard errors; R²= 0.71 in model 3.

^* p < 0.1

^** p < 0.05

^*** p < 0.01.

Table 4. Summary of tests for complementarity and sub-additivity between portfolio dimensions.

	Functional & relational	Functional & structural	Functional & attribute	Relational & structural	Relational & attribute	Structural & attribute
Complementarity
TP1: H0: Rβ ≥ 0 vs. H1:	0.06	11.44	4.81	1.27	0.11	2.56
TP2: H0: Rβ = 0 vs. H1: Rβ ≥ 0	13.79	5.66	2.95	4.30	6.31	5.04
Subadditivity
TP1: H0: Rβ ≤ 0 vs. H1:	13.79	5.19	2.79	4.23	6.17	4.92
TP2: H0: Rβ = 0 vs. H1: Rβ ≤ 0	0.06	11.90	4.97	1.33	0.24	2.68

Note:

The reported LR statistics is in TP1 for the test of the null hypothesis of complementarity and in TP2 for the null of the absence of complementarity (sub-additivity) for a given pair of dimensions. The upper bound critical value at a 10% significance level is 7.09 (critical values given in Kodde and Palm, 1986), which implies that the null hypothesis is rejected when the statistic is above 7.09.

Table A1. Inequality constrained estimates of Equation (1) testing for complementarity or sub-additivity in alliance portfolio.

Independent variables	Model 4	Model 5	Model 6	Model 7	Model 8	Model 9	Model 10	Model 11	Model 12	Model 13	Model 14	Model 15
Intercept	0.150 (0.451)	0.272* (0.156)	0.167 (0.452)	0.390** (0.168)	0.117 (0.450)	0.190 (0.453)	0.190 (0.454)	0.587*** (0.227)	0.089 (0.452)	0.307* (0.170)	0.069 (0.185)	0.136 (0.451)
Log(R&D)	0.352*** (0.041)	0.339*** (0.038)	0.344*** (0.041)	0.336*** (0.038)	0.345*** (0.041)	0.345*** (0.041)	0.344*** (0.041)	0.327*** (0.038)	0.345*** (0.041)	0.338*** (0.038)	0.350*** (0.039)	0.341*** (0.041)
Patents/R&D	0.492*** (0.078)	0.501*** (0.078)	0.496*** (0.079)	0.497*** (0.079)	0.500*** (0.079)	0.501*** (0.079)	0.504*** (0.079)	0.494*** (0.078)	0.495*** (0.078)	0.501*** (0.078)	0.501***(0.078)	0.507*** (0.079)
Firm size	–0.042 (0.039)	–0.030 (0.035)	–0.038 (0.039)	–0.030 (0.035)	–0.039 (0.039)	–0.036 (0.039)	–0.034 (0.039)	–0.017 (0.036)	–0.038 (0.039)	–0.029 (0.035)	–0.043 (0.035)	–0.035 (0.039)
Portfolio size	0.012*** (0.003)	0.011*** (0.003)	0.012*** (0.003)	0.010*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.012*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.011*** (0.003)	0.011*** (0.003)
Experience alliances	–0.140*** (0.051)	–0.138*** (0.050)	–0.135*** (0.051)	–0.131*** (0.050)	–0.139*** (0.050)	–0.143*** (0.051)	–0.144*** (0.051)	–0.129*** (0.050)	–0.150*** (0.050)	–0.137*** (0.050)	–0.138*** (0.050)	–0.146***(0.051)
Log(Firm age)	–0.065 (0.066)	–0.074 (0.059)	–0.067 (0.067)	–0.084 (0.058)	–0.059 (0.066)	–0.072 (0.066)	–0.076 (0.066)	–0.098 (0.059)	–0.054 (0.066)	–0.076 (0.059)	–0.061 (0.060)	–0.059 (0.066)
Cultural distance	0.029 (0.086)	0.022 (0.084)	0.047 (0.086)	0.018 (0.084)	0.043 (0.086)	0.022 (0.087)	0.006 (0.086)	0.011 (0.085)	0.031 (0.086)	0.021 (0.084)	0.044 (0.084)	0.025 (0.086)
Functional	0.319*** (0.094)	0.329*** (0.088)	0.314*** (0.093)	0.306*** (0.088)	0.336*** (0.094)	0.325*** (0.094)	0.299*** (0.093)	0.303*** (0.088)	0.296*** (0.093)	0.328*** (0.090)	0.331*** (0.091)	0.356*** (0.092)
Relational	0.124 (0.157)	0.127 (0.145)	–0.107 (0.127)	0.130 (0.155)	–0.032 (0.128)	0.134 (0.157)	0.152 (0.158)	0.070 (0.146)	0.139 (0.157)	0.123 (0.146)	–0.003 (0.153)	0.145 (0.157)
Structural	–0.027 (0.135)	0.377** (0.175)	0.359** (0.176)	0.334** (0.165)	0.382** (0.176)	0.486*** (0.134)	0.406** (0.176)	0.299* (0.165)	0.273* (0.163)	0.376** (0.175)	0.379** (0.163)	0.391** (0.176)
Attribute	0.154* (0.086)	0.178** (0.079)	0.172** (0.086)	0.183** (0.079)	0.188** (0.086)	0.174** (0.086)	0.188** (0.086)	0.150* (0.078)	0.184** (0.086)	0.175** (0.078)	0.185** (0.080)	0.189** (0.086)
Functional & relational	0.172* (0.100)	0.184* (0.098)	0.197** (0.100)	0.171* (0.097)	0.213** (0.099)	0.180* (0.101)	0.252* (0.094)	0.154 (0.095)	0.238** (0.095)	0.180* (0.097)	0.182* (0.097)	0.229** (0.096)
Functional & structural	0.263** (0.103)	0.259*** (0.100)	0.235** (0.102)	0.250** (0.101)	0.262** (0.103)	0.243** (0.103)	0.318** (0.099)	0.231** (0.098)	0.242** (0.102)	0.257** (0.100)	0.255*** (0.101)	0.248** (0.102)
Functional & attribute	0.340*** (0.091)	0.315*** (0.090)	0.304*** (0.094)	0.254*** (0.089)	0.321*** (0.095)	0.312*** (0.094)	0.312*** (0.093)	0.289*** (0.089)	0.363*** (0.091)	0.313*** (0.090)	0.317*** (0.091)	0.310*** (0.093)
Relational & structural	–0.036 (0.127)	–0.243 (0.155)	–0.057 (0.123)	–0.266* (0.156)	–0.237 (0.156)	–0.116 (0.134)	–0.240 (0.157)	–0.218 (0.151)	–0.159 (0.139)	–0.245 (0.155)	–0.107 (0.135)	–0.244 (0.156)
Structural & attribute	0.389*** (0.134)	0.498*** (0.143)	0.487*** (0.145)	0.171 (0.110)	0.506*** (0.145)	0.416*** (0.130)	0.510*** (0.146)	0.465*** (0.129)	0.558*** (0.138)	0.496*** (0.143)	0.495*** (0.146)	0.509*** (0.146)
Relational & attribute	0.122 (0.101)	–0.015 (0.132)	–0.027 (0.136)	0.031 (0.123)	0.087 (0.120)	–0.022 (0.136)	0.004 (0.136)	–0.051 (0.122)	–0.012 (0.136)	–0.009 (0.135)	0.064 (0.126)	–0.005 (0.136)
Functional & relational & structural	0.254*** (0.099)	0.285*** (0.096)	0.246** (0.098)	0.283*** (0.096)	0.289*** (0.100)	0.270*** (0.099)	0.271*** (0.099)	0.260*** (0.094)	0.307 (0.098)	0.284*** (0.096)	0.281*** (0.097)	0.274*** (0.099)
Functional & relational & attribute	0.309*** (0.097)	0.351*** (0.095)	0.336*** (0.097)	0.333*** (0.096)	0.332*** (0.097)	0.350*** (0.098)	0.392*** (0.094)	0.329*** (0.094)	0.305*** (0.095)	0.350*** (0.095)	0.351*** (0.096)	0.324*** (0.095)
Relational & structural & attribute	0.482*** (0.139)	0.270 (0.203)	0.260 (0.204)	0.028 (0.136)	0.284 (0.204)	–0.050 (0.142)	0.278 (0.205)	0.264* (0.148)	0.126 (0.175)	0.268 (0.203)	–0.040 (0.178)	0.279 (0.204)
Functional & structural & attribute	0.176 (0.118)	0.145 (0.120)	0.119 (0.122)	0.243** (0.112)	0.149 (0.123)	0.173 (0.117)	0.218** (0.109)	0.118 (0.118)	0.218** (0.108)	0.144 (0.120)	0.141 (0.121)	0.202* (0.109)
Functional & relational & structural & attribute	0.269** (0.107)	0.315*** (0.105)	0.291*** (0.107)	0.330*** (0.104)	0.318*** (0.108)	0.336*** (0.107)	0.298*** (0.106)	0.291*** (0.104)	0.282*** (0.105)	0.314*** (0.105)	0.309*** (0.106)	0.369*** (0.102)
Pair of dimensions tested
Imposed constraints	Functional & Relational		Functional & Structural		Functional and Attribute		Relational & Structural		Relational & Attribute		Structural & Attribute
Constraint1	–β fun – β rel + β con + β fun,rel > 0	–β fun – β rel + β con + β fun,rel < 0	–β fun – β str + β con + β fun,str > 0	–β fun – β str + β con + β fun,str < 0	–β fun – β atr + β con + β fun,atr > 0	–β fun – β atr + β con + β fun,atr < 0	–β rel – β str + β con + β rel,str < 0	–β rel – β str + β con + β rel,str > 0	–β rel – β atr + β con + β rel,atr < 0	–β rel – β atr + β con + β rel,atr > 0	–β str – β atr + β con + β str,atr < 0	–β str – β atr + β con + β str,atr > 0
Constraint2	–β fun,atr – β rel,atr + β atr + β fun,rel,atr > 0	–β fun,atr – β rel,atr + β atr + β fun,rel,atr < 0	–β fun,atr – β str,atr + β atr + β fun,str,atr > 0	–β fun,atr – β str,atr + β atr + β fun,str,atr < 0	–β str,atr – β fun,str + β str + β fun,str,atr > 0	–β str,atr – β fun,str + β str + β fun,str,atr < 0	–β fun,rel – β fun,str + β fun + β fun,rel,atr < 0	–β fun,rel – β fun,str + β fun + β fun,rel,atr > 0	–β fun,rel – β fun,atr + β fun + β fun,rel,atr < 0	–β fun,rel – β fun,atr + β fun + β fun,rel,atr > 0	–β fun,str – β fun,atr + β fun + β fun,rel,atr < 0	–β fun,str – β fun,atr + β fun + β fun,rel,atr > 0
Constraint3	–β fun,str – β rel,str + β str + β fun,rel,str > 0	–β fun,str – β– + β str + β fun,rel,str < 0	–β fun,rel – β rel,str + β rel + β fun,rel,str > 0	–β fun,rel – β rel,str + β rel + β fun,rel,str < 0	–β fun,rel – β rel,atr + β rel + β fun,rel,atr > 0	–β fun,rel – β rel,atr + β rel + β fun,rel,atr < 0	–β str,atr – β rel,atr + β atr + β rel,str,atr < 0	–β str,atr – β rel,atr + β atr + β rel,str,atr > 0	–β rel,str – β str,atr + β str + β rel,str,atr < 0	–β rel,str – β str,atr + β str + β rel,str,atr > 0	–β rel,str – β rel,atr + β rel + β rel,str,atr < 0	–β rel,str – β rel,atr + β rel + β rel,str,atr > 0
Constraint4	–β fun,str,atr – β rel,str,atr + β str,atr + β fun,rel,str,atr > 0	–β fun,str,atr – β rel,str,atr + β str,atr + β fun,rel,str,atr < 0	– β fun,rel,atr – β rel,str,atr + β rel,atr + β fun,rel,str,atr > 0	–β fun,rel,atr – β rel,str,atr + β rel,atr + β fun,rel,str,atr < 0	–β fun,rel,str – β rel,str,atr + β rel,str + β fun,rel,st,atr > 0	–β fun,rel,str – β rel,str,atr + β rel,str + β fun,rel,st,atr < 0	–β fun,rel,atr – β fun,str,atr + β fun,atr + β fun,rel,str,atr < 0	–β fun,rel,atr – β fun,str,atr + β fun,atr + β fun,rel,str,atr > 0	–β fun,rel,str – β fun,str,atr + β fun,str + β fun,rel,str,atr < 0	–β fun,rel,str – β fun,str,atr + β fun,str + β fun,rel,str,atr > 0	–β fun,rel,atr – β fun,rel,atr + β fun,rel + β fun,rel,str,atr < 0	–β fun,rel,atr – β fun,rel,atr + β fun,rel + β fun,rel,str,atr > 0
AIC	8711.681	8721.411	8719.058	8716.815	8714.432	8714.409	8710.891	8713.854	8711.731	8713.793	8712.179	8714.543
SBC	8944.337	8943.726	8941.373	8949.470	8941.917	8947.064	8938.376	8941.340	8944.386	8936.108	8939.664	8942.028
Log–Likelihood	–4310.841	–4317.705	–4316.529	–4313.407	–4313.216	–4312.204	–4311.446	–4312.927	–4310.865	–4313.897	–4312.089	–4313.271
Log–Likelihood^‡	–4317.736	–4317.736	–4319.358	–4319.358	–4314.691	–4314.691	–4313.594	–4313.594	–4314.018	–4314.018	–4314.611	–4314.611

Notes:

n = 1300; year dummies are not shown; numbers in parentheses are standard errors;

^* p < 0.1

^** p < 0.05

^*** p < 0.01

^‡ from a model imposing the corresponding constraints as equalities.