Do Structural Holes and Network Connectivity Really Affect Entrepreneurial Performance?

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2012 21: 253Journal of EntrepreneurshipJarle Aarstad

Entrepreneurial Performance?Do Structural Holes and Network Connectivity Really Affect

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Editor’s Introduction 253Article

Do Structural Holes and Network Connectivity Really Affect Entrepreneurial Performance?

Jarle Aarstad

AbstractResearch shows that structural holes and network connectivity are associated with entrepreneurial performance. Yet the explanatory vari-ables will tend to be correlated, and multicollinearity may skew the results. The use of instrumental variables can nevertheless generate reliable estimates. The methodology can also identify possible reverse causal orders. Here a network of rural entrepreneurs building their own hydroelectric micro-power plants is studied. The use of instrumen-tal variables shows that structural holes and network connectivity have strong and additive effects on performance, and with a particular focus on rural entrepreneurs in developing countries, the findings’ implica-tions are discussed.

Keywordscausality, hydroelectric micro-power, instrumental variables, network connectivity, performance, rural entrepreneurs, structural holes

Actors in a position to brokerage and connect otherwise disconnected parts of a social network are rich in structural holes (Burt, 1992, 2000).

The Journal of Entrepreneurship 21(2) 253–268

© 2012 Entrepreneurship Development Institute of India

SAGE PublicationsLos Angeles, London,

New Delhi, Singapore, Washington DC

DOI: 10.1177/0971355712449788http://joe.sagepub.com

Jarle Aarstad is Associate Professor at Bergen University College, Faculty of Engineering, Bergen, Norway.



254 Jarle Aarstad

The Journal of Entrepreneurship, 21, 2 (2012): 253–268

Burt (2004: 349–350) argues that ‘opinion and behaviour are more homogenous within than between groups, so people connected across groups are more familiar with alternative ways of thinking and behav-ing…’. He finds that managers rich in structural holes get better job evaluations, are promoted more frequently and are more likely to have their ideas evaluated as valuable. In a recent study, Rodan (2010) finds that structural holes are linked to creativity and innovativeness, and other studies in a similar vein relate structural holes to performance (Burt, Hogarth & Michaud, 2000; Shipilov, 2006; Vissa & Chacar, 2009; Zaheer & Bell, 2005; Zaheer & Soda, 2009).

Thus, there seems to be ample empirical evidence for structural holes to be associated with different facet of performance. But is it for sure that one really is dealing with genuine and not merely spurious relations between the concepts? It will be shown later that graph theory proposes a strong correlation between the concepts of structural holes and network connectivity. High connectivity in a social network implies that the focal actor is related to numerous other nodes. It is a measure of network activ-ity or being in the midst of things (Freeman, 1979; Nieminen, 1974). Having multiple network ties can accumulate a rich and a broad portfolio of resources, and studies show that connectivity is related to entrepre-neurial performance (e.g., Baum, Calabrese & Silverman, 2000; Bruderl, Preisendorfer & Ziegler, 1992; Shan, Walker & Kogut, 1994; Stuart, Hoang & Hybels, 1999; Zhao, Frese & Giardini, 2010; Zheng, Liu & George, 2010). So with the aim of identifying structural holes’ and net-work connectivity’s unique contribution to entrepreneurial performance, multicollinearity problems may skew the results and generate question-able estimates (for a review and assessment of the concept of multicol-linearity, see O’Brien, 2007). Said differently, it is not clear-cut to decide whether structural holes, network connectivity or both concepts are gen-uinely associated with entrepreneurial performance, and this article will address these challenges.

Numerous network studies are also cross-sectional in nature, so in spite of robust empirical results, possible reverse causal orders between the dependent and the independent variables cannot be ruled out. For instance, it is not unlikely to assume that high performing entrepre-neurs are in a better shape to position themselves and to span structural holes or connect to numerous other nodes. Research also shows that node characteristics can be indicative on the formation of network ties



Structural Holes and Network Connectivity 255


(e.g., Powell, Koput & SmithDoerr, 1996; Powell, White, Koput & Owen-Smith, 2005).

It will be argued that the appropriate use of instrumental variables can enable scholars to deal with the challenges that are sketched out earlier. Instrumental variables have the properties that they are correlated with the explanatory variable and uncorrelated with the error term (for further details about the concept, see for instance Wooldridge, 2010). The article will assess how instrumental variable can generate consistent estimates when studying structural holes and network connectivity as possible predictors of entrepreneurial performance. Recently there has been an increased interest in the use of instrumental variables in entre-preneurial research (Berkowitz & DeJong, 2005; Bitler, Moskowitz & Vissing-Jorgensen, 2005; De Mel, McKenzie & Woodruff, 2008; Garcia-Mainar & Montuenga-Gomez, 2005; Garmaise, 2008; Grilo & Thurik, 2008; Jordahl, Poutvaara & Tuomala, 2009; Nastav & Bojnec, 2008; Oosterbeek, van Praag & Ijsselstein, 2010; Parker & Van Praag, 2006; Rodriiguez-Gutieerrez, 2007; Samila & Sorenson, 2010, 2011; Spohr, 2003; Waguespack & Fleming, 2009), but an explicit application on the topics covered in this article has not been found.

The empirical context is a network of entrepreneurs—mostly farmers —building their own hydroelectric micro-power plants in rural Norway. Although the data for this study is gathered from a (so-called) developed country, it has nevertheless been argued that the potential for micro-power particularly in rural parts of developing countries is substantial (Dunn, 2000; The Economist, 2000, 2001). The article will therefore argue that the study’s empirical context is applicable for potential rural entrepreneurs in India and in other similar places. But before turning to methods and data analyses, the article will first elaborate why the con-cepts of structural holes and network connectivity are likely to be highly correlated (thus possibly causing multicollinearity problems and skewed estimates in multiple regressions).

If one assumes that i, j and k are members of a network and that i is collaborating with both j and k, it increases the probability of a collabora-tive link between j and k, according to classical graph theory. Said differ-ently, if j and k were not collaborating, the i-j-k triplet would be a so called ‘forbidden’, unbalanced or intransitive triad (Cartwright & Harary, 1956; Davis & Leinhardt, 1972; Heider, 1946; Holland & Leinhardt, 1971). This may cause cognitive dissonance (Festinger, 1957). Member i can



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also refer to j about k (and to k about j) and accordingly facilitate a con-nection between the nodes. Unsurprisingly, therefore, research shows that triplets tend to be balanced or transitive, and that social networks tend to be clustered (for reviews, see Davis, 1979; Newman, 2003; Uzzi, Amaral & Reed-Tsochas, 2007). Gulati and Gargiulo (1999) also find that com-mon third-party ties increase the probability for firms to collaborate. The argument furthermore fits well into Granovetter’s (1985) notion of struc-tural embeddedness in that that existing relationships both enable and restrict with whom an actor can collaborate.

Yet if it is furthermore assumed that i does not only collaborate with j and k, but with a total number of n nodes, this requires n(n – 1)/2 collabo-rating ties between the n nodes to achieve complete clustering (Watts, 1999; Watts & Strogatz, 1998). Said differently, due to this exponential relationship, it is reasonable to assume that highly connected nodes are more likely to be rich in structural holes since they statistically have a larger tendency to brokerage and connect otherwise disconnected parts of a social network. This theorising might not be strikingly new, but it nevertheless illustrates why the concepts of network connectivity and the spanning of structural holes are likely to be strongly associated. As a consequence, it asserts the need to compare and assess the concepts’ pos-sible genuine effect on entrepreneurial performance. In the following empirical section, the article will further address these issues. With a particular focus on rural entrepreneurs in developing countries the article will then briefly discuss the findings, address the study’s limitations and suggest avenues for future research.

Method

As noted, the article studies a network of entrepreneurs building their own hydroelectric micro-power plants. Details about the empirical context, sampling procedure, the modelling of the network ties and entrepreneur-ial performance can be found elsewhere (Aarstad, Haugland & Greve, 2010), so the article will not go much into details here. The number of entrepreneurs from whom complete data was accessed is 20 out of 25 relevant candidates, which implies a response rate of 80 per cent.

Briefly, the dependent variable, entrepreneurial performance, is yearly electricity production divided by financial capital invested, adjusted for





inflation. Average yearly production is used in cases with more than 1 year of production.

The article applies Burt’s (1992: 54–65) measure of network con-straint at year of start-up to model structural holes as independent varia-ble. The network constraint is high if a node’s ties reach other nodes that to a large extent are connected to each other, or if they share information indirectly via a central contact. Thus, the more constrained a node’s net-work is, the fewer structural holes it spans, and vice versa (for further details, see Burt, 1992: 55, 2004: 362).

To model network connectivity as independent variable, the article applies Freeman’s (1979) concept of normalised degree centrality at year of start-up. A normalised score is used since the entrepreneurial network varies in size over the studied time period (for further details on the net-work dynamics, see Aarstad et al., 2010).

All network analyses are performed in Ucinet 6.135 (Borgatti, Everett & Freeman, 2002). The concepts of entrepreneurial performance and structural holes deviate from normal distributions, so the article corrects for this by applying Van der Waerden’s (1953) method to generate nor-mal quantile values (for further details, see Conover, 1999).

Results

Descriptive Statistics and Ordinary Regressions

Table 1 reports the correlates of entrepreneurial performance, network connectivity and structural holes. (Later the article will discuss the con-cepts of the size of the plant and mean deviation in precipitations that are also included in Table 1.) It is observed that network connectivity is strongly correlated with entrepreneurial performance. The spanning of structural holes is also correlated with the dependent variable, but the effect is modest. Finally it is observed that network connectivity and the spanning of structural holes are strongly correlated, which is in accord-ance with previous argument.

In Table 2 entrepreneurial performance is regressed on network con-nectivity and the spanning of structural holes. Since the spanning of structural holes was only modestly correlated with entrepreneurial per-formance (Table 1), it might be reasonable to assume that it is a spurious



258 Jarle Aarstad


correlation reflecting a more ‘genuine’ association between network connectivity and entrepreneurial performance. However, it is observed in Model 3 (Table 2) that when both the independent variables are included, the adjusted R-square increases by almost 10 per cent as com-pared to Model 1 (which includes only network connectivity as inde-pendent variable). This indicates that both the concepts are independently and genuinely related to entrepreneurial performance in one or another way.1

But if one takes a look at the regression estimates in Table 2, they reveal a somewhat mixed picture. It is observed in Model 3 that the

Table 1. Correlation Matrix

Mean SD EP NC SH SP

0 .891 Entrepreneurial performance (EP)

10.75 5.45 Network connectivity (NC)

.717***

–.003 .880 Structural holes (SH) –.398† –.822***41.53 30.64 Size of the plant (SP) .381† .480* –.607**92.39 10.11 Mean deviation in

precipitation–.238 –.390† .606** –.389†

Notes: † p < .10, * p < .05, ** p < .01,*** p < .001. N = 20. Two-tailed tests.

Table 2. Ordinary Least Regressions

Model 1 Model 2 Model 3 VIF

Network connectivity .717*** 1.202*** 3.082(.027) (.043)

Structural holes –.398† .591* 3.082(.219) (.263)

R-square .514 .158 .627Adj. R-square .487 .111 .583F-value 19.03*** 3.38† 14.30***

Notes: † p < .10, * p < .05, ** p < .01,*** p < .001. Dependent variable: Entrepreneurial performance. Standardised coefficients

with standard error in parentheses. Two-tailed tests. N = 20.





estimate of network connectivity has improved strongly as compared to Model 1, but a standardised estimate larger than 1 should induce some cautiousness when interpreting the result. Moreover, the standardised estimate of structural holes has, in fact, turned from a negative result in Model 2 to a positive in Model 3. In isolation this may imply that the network closures (due to, for instance, referral knowledge sharing and trust, cf. Coleman, 1988) and not the spanning of structural holes is asso-ciated with performance. The research literature gives some support to this finding (Ahuja, 2000; Ingram & Roberts, 2000), but observing large fluctuations in regression estimates may nevertheless indicate that we are dealing with multicollinearity problems.

The variance inflation factors (VIFs) reported in relation to Model 3 are lower than suggested critical values varying between 4 and 10 (for a discussion of these values, see O’Brien, 2007). But taken together with instability in the estimates, the overall interpretation of the results is nev-ertheless indicative of unreliable results. In line with this reasoning O’Brien (2007) argues that VIF values alone can be very misleading to evaluate multicollinearity, and he points out that the sample size—which is low in this study—is also of critical importance.

Regressions with Instrumental Variables

It has been stated previously that the appropriate use of instrumental variables can generate consistent estimates (cf. Wooldridge, 2010). Thus, since the simultaneous modelling of structural holes and network con-nectivity as independent variables resulted in susceptible estimates, instrumental variables can generate consistent estimates by modelling each parameter in the absence of the other. This approach eliminates pos-sible multicollinearity problems and ditto unreliable estimates. The method also takes into account possible reverse causal orders between the independent and the dependent variable.

Returning to Table 1, it is observed that network connectivity is cor-related with the concepts ‘size of the plant’ and ‘mean deviation in pre-cipitation’. This indicates that the variables fulfil one of the criteria of an instrumental variable as being correlated with the explanatory variable (this issue will be addressed in more detail later). The positive correla-tion between size of the plant and network connectivity indicates that



260 Jarle Aarstad


entrepreneurs building larger micro-power plants have had a tendency to have more network connections than entrepreneurs building smaller plants.2 The explanation of this correlation is fairly intuitive in that the larger the plant is, the more money is normally invested and the more is accordingly at stake in relation to the entrepreneurial undertaking. Entrepreneurs building relatively large plants, thus, appear to mitigate the increased risk by higher network connectivity. Larger plants may also be complex and complicated to build, which furthermore necessi-tates access to resources and advice from a rich pool of resources.

Table 1 also shows that network connectivity is negatively correlated with mean deviation in precipitation. The Norwegian Institute of Meteorology (MET) provided data on yearly precipitation from a number of weather stations in the Western Norway. The percentage deviation in yearly precipitation from the most geographically approximate weather station to each micro-power plant in the region was modelled (and from which sufficient data was also gained). Average deviation in electricity production was studied for more than a year for the plants the study had access to. The year 1999 and in particular 2000 and 2001 were unusually dry years in parts of Western Norway, and 50 per cent of the sampled entrepreneurial undertakings started electricity production during these years. Thus, several entrepreneurs were also constructing their plants during this time period. This may explain why entrepreneurs experienc-ing negative deviations in precipitations have aimed to mitigate this challenge by increasing their connectivity in the network.

If one takes a look at the concept of structural holes, Table 1 reports stronger correlations with size of the plant and deviation in precipitations than we observe for the concept of network connectivity. This may indi-cate that entrepreneurs building large plants, and possibly also experi-encing low rainfall, have aimed at not only increasing their connectivity but in particular at gaining access to non-redundant information and resources.

Taken together, size of the plant and deviation in precipitation are candidates as instrumental variables in that they are correlated with each of the explanatory variables. In particular this is the case for the concept of structural holes. However, for the time being the possibility that the candidates as instruments are correlated with the error terms cannot be ruled out. For instance, it is not unlikely to assume that large plants in general can be more efficient in terms of scale of economics, which may





induce a genuine association with entrepreneurial performance. In addi-tion, low rainfall may also decrease the electricity production, but it will be shown later that the candidates as instrumental variables are unlikely to be correlated with the error terms.

The generalised method of moments (GMM) estimator, developed by Hansen (1982), is well adapted to estimate instrumental variables, and can report standard errors that are robust to possible heteroskedasticity. In Model 1 (Table 3) network connectivity is instrumented and size of the plant and deviation in precipitation are instruments. It is observed that the regressed estimate is robust and significant. The first-stage par-tial R-square regression reported in the lower part of Model 1 (Table 3) returns a significant F-value, but Stock, Wright and Yogo (2002) suggest that the F-value should exceed 10 to be a robust instrument. In other words, partial effect of the size of the plant and mean deviation in preci-pitation on network connectivity indicates that they are weak instru-ments. To address this challenge Model 1 is replicated, but it applies instead of GMM the limited-information maximum likelihood (LIML) estimator. Scholars have suggested that the LIML estimator per- forms better than the GMM estimator when the instruments are weak

Table 3. Generalised Method of Moments (GMM) Estimates

Model 1 Model 2

Network connectivity .731***(.034)

Structural holes –.529**(.207)

Wald Chi-square 12.61*** 6.74**

First-stage partial R-square regression .279 .529 F-value 4.58* 12.23***

Hansen’s J Chi-square .085 .209(p-values in parentheses) (.770) (.648)

Notes: † p < .10, * p < .05, ** p < .01, *** p < .001. Dependent variable: Entrepreneurial performance. Standardised coefficients

with standard error in parentheses. Two-tailed tests. N = 20. In Model 1, size of the plant and deviation in precipitation are instruments and network connectivity is instrumented. In Model 2, size of the plant and deviation in precipitation are instruments and structural holes is instrumented.



262 Jarle Aarstad


(Poi, 2006; Stock et al., 2002). The replicated model returns a standard-ised parameter value of .733, which is very similar with the result reported in Model 1. Both estimates are furthermore similar with the estimate reported in the ordinary least square regression in Table 2 (Model 1).

Hansen’s (1982) J-statistic is reported at the bottom of Model 1 (Table 3) and tests if the instruments are associated with the error term (i.e., testing for over-identifying restrictions). The returning of an insig-nificant p-value shows that the applied instruments are uncorrelated with the error term and they are accordingly valid (in fact, a p-value as high as 0.770 is a robust measure).

In Model 2 (Table 3) the spanning of structural holes is instrumented and size of the plant and deviation in precipitation are instruments. It is observed that the regressed estimate is negative and significant, which is in accordance with what is reported in Table 2 (Model 2). The use of instrumental variables furthermore gives a stronger and a more signifi-cant result than before. It has been suggested earlier that multicollinear-ity generates inconsistent estimates in Table 2 (Model 3), and the finding reported in Table 3 (Model 2) strengthens this assumption.

The first-stage partial R-square regression reported in the lower part of Model 2 (Table 3) gives a robust and significant F-value taking a value larger than 10. This implies that the instruments are strong. Hansen’s (1982) J-statistic is reported at the bottom of Model 2 (Table 3) and gives an insignificant p-value. This shows that the instruments are also uncor-related with the error term. Altogether it is concluded that the use of instrumental variables shows that network connectivity and the spanning of structural holes have strong and additive effects on entrepreneurial performance.

Discussion

Research shows that both structural holes and network connectivity are related to performance (Baum et al., 2000; Bruderl et al., 1992; Burt, 2004; Burt et al., 2000; Rodan, 2010; Shan et al., 1994; Shipilov, 2006; Stuart et al., 1999; Vissa & Chacar, 2009; Zaheer & Bell, 2005; Zaheer & Soda, 2009; Zhao et al., 2010; Zheng et al., 2010). In this research note





it has been argued that the concepts are closely related, so how is it then possible to obtain consistent estimates? Multicollinearity may skew the results, yet the use of instrumental variables can generate reliable esti-mates. The methodology can also identify possible reverse causal orders. Instrumental variables have the properties that they are correlated with the explanatory variable and are uncorrelated with the error term (Wooldridge, 2010).

In this article a network of entrepreneurs building their own hydroe-lectric micro-power plants was studied. The study found that the span-ning of structural holes and network connectivity were strongly correlated. Ordinary least square regressions furthermore indicated that the simultaneous modelling of the concepts as explanatory variables generated susceptible and possibly unreliable estimates on entrepreneur-ial performance (cf. Table 2). However, modelling each of the explana-tory variables in the absence of the other—and applying instrumental variables—showed that both the spanning of structural holes and net-work connectivity have strong and additive effects on entrepreneurial performance.

An implication of these findings is that both concepts can have a gen-uine effect on performance. Thus, the spanning of structural holes is not merely reflecting a spurious correlation of a ‘genuine’ association between network connectivity and performance, or the other way round. Instrumental variables can also identify possible reverse causal orders, and the robustness of the findings reported in Table 3 accordingly shows that structural holes and network connectivity are causes, and not effects, of entrepreneurial performance.

The findings from this study add validity to other studies reporting that structural holes and network connectivity are having an effect on performance. The study moreover has methodological implications in that it illustrates how it is possible to assess highly correlated explana-tory variables’ genuine effect on one or more effect variables.

The study has also shown practical implications for rural entrepre-neurs by illustrating that structural holes and network connectivity have strong and additive effects on performance. This is not the first study indicating that this is the case, but the use of instrumental variables increases the internal validity. Since the plants are small, they do not compete against each other (Aarstad et al., 2010). Thus, rural entrepre-neurs have clear incentives—and should accordingly be encouraged—to



264 Jarle Aarstad


build networks rich in structural holes (e.g., by sharing information with distant living colleagues) and exchange as much information as possible with each other. As a result of market liberation, environmental concern and demand for reliable power, there is an increased interest in micro-power plants worldwide. Decentralised micro-power plants reduce the dependence on the grid, which is particularly critical in rural parts of the developing world (The Economist, 2000, 2001).

A limitation of this study is that the sample size is relatively small. However, the response rate is high, and the strength of the results adds validity to the findings. As noted, the entrepreneurs do not compete against each other (due to their smallness, they do not affect the price of electricity). To assess the external validity, future research should accord-ingly aim at replicating a similar methodology in other more competitive empirical contexts.

Notes

1. Unreported models have also tested if closeness centrality (Freeman, 1979) or flow-betweeness (Freeman, Borgatti & White, 1991) are related to the entrepreneurial performance, but network connectivity and structural holes yield the best model fit.

2. The Norwegian Water Resource and Energy Directorate define a micro-plant as having a maximum capacity of 100 kilowatts per hour (kWh). The size of the plants in my sample varies between 7 and 99 kWh.

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