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# KNOWLEDGE SPILLOVER IN CORPORATE FINANCING NETWORKS ...

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• 9. Knowledge Spillover in Corporate Financing Networks 603 percent.3 We conducted sensitivity tests of these observing outcome i corresponds to the probabil- categories by changing the cut-off points within ity that the estimated linear function, plus random a sensible range given the distribution of the error, is within the range of the cut points estimated dependent variables and extant theory. For exam- for the outcome (Greene, 1993): ple, we divided larger ranges into multiple lev- els of magnitude and collapsed the six-category Odds (outcome more severe than i) variable into a ﬁve-, four-, and three-category Pr(Outcomej =i ) = Pr(ki−1 < B1 xij variables. Since our six-category variable mapped closely to theory and practice and these other + · · · + Bk xkj + uj ≤ ki ) changes produced no substantive differences in our ﬁndings, we report the six-category variable uj is assumed to be logistically distributed in results.4 the ordered logit. One estimates the coefﬁcients In the ordered logit model, the underlying prob- B1 , B2 , . . . , BI −1 along with the cut points ability score of how a one-unit change in an inde- k1 , k2 , . . . , kI −1 , where I is the number of possible pendent variable affects the change in probability outcomes. k0 is taken as minus ∞ and kI is of magnitude of the dependent variable is esti- taken as plus ∞. This is a generalization of mated as a linear function of the independent vari- the ordinary two-outcome logit model. Thus, a ables and set of cut points. The probability of positive coefﬁcient signiﬁes that increases in an independent variable increase the probability that 3 The ordered logit model correctly estimates the effect of a the ﬁrm takes a larger percent of trade-credit unit change in an independent variable on the probability of discounts or incurs proportionately more late- increases/decreases in magnitude of the ordinal dependent vari- payment penalties. able. In the ordered logit model, the numerical values of the dependent variable are unimportant (Greene, 1993). In ordi- nary regression, arbitrarily labeling ‘75 to 100 percent discounts taken’ as 5, ‘51 to 75 percent discounts taken’ as 4, and so on, Independent variables is problematic because different numerical values for each cate- gorical division (say 10 for ‘all’ and 8 for ‘many’) would obtain As indicated in the previous sections, we are different estimates. This is not true in an ordered logit model. interested in the effect of three measures of embed- All that is required is that larger numerical values correspond dedness: the duration of the bank–ﬁrm relation- to more intense outcomes or levels. Ordered logits also handle dependent variables with unequal frequency distributions in a ship, the multiplexity of the bank–ﬁrm relation- multicategory dependent variable in the same way that an ordi- ship, and the size of a ﬁrm’s bank network. Our nary logit model can with a two-category variable, providing methodological technique for developing quanti- additional robustness to the estimates (Long, 1997). 4 Another statistical check on the ordered logit’s speciﬁcation tative measures looked for convergence among is to run a tobit regression on the untransformed percentage theory, face validity, and discriminant validity variable. While the tobit is designed for censored variables (Miles and Huberman, 1994). In this method, (e.g., variables with categories made up of distinctions such as ‘<\$13,000 income’ or ‘>\$50,000 income’) rather than a per- validity increases if multiple sources of inde- centage variable, which is naturally bounded between zero and pendent evidence triangulate on a consistent pat- 100, it offers a check because its results should be similar. An tern.5 We looked for convergence among theory ordinary logit can also be used by dividing the percentage vari- able into a binary variable. This technique loses information on on tie strength (Granovetter, 1973; Marsden and the intensity of trade credit behavior, but should produce results Campbell, 1984; Borgatti and Feld, 1994) and the that are similar to the ordered logit. OLS regression should also accounts of RMs (face validity) by asking RMs to produce similar results even if the magnitudes of the coefﬁcients and standard errors are biased. The tobit, logit, and OLS regres- consider how relational governance could be quan- sion analyses conﬁrmed the ﬁndings of our ordered logit; all of titatively measured and distinguished from other our predicted variables were signiﬁcant and in the same direction variables (discriminant validity). For instance, we as in the ordered logit model. Finally, a very helpful reviewer noted that while the ordered logit offers many advantages, the probed RMs with inquiries such as, ‘If you want results should be carefully interpreted because a possible cor- to determine if your colleague has a close tie with relation between the two dependent variables could bias the coefﬁcients. To account for this potential issue, we followed the 5 reviewer’s suggestion and ran a seemingly unrelated regression As with psychometric methods, the value for construct validity (SUR), which models both dependent variables simultaneously is not known a priori; rather, it increases if several methods to account for any possible correlation between them. The results yield systematically similar results. Thus, although no formal indicated that the estimated standard errors were barely larger in statistical tests are involved in proving convergence, it works by the SUR model. Consequently, they did not change the levels of demonstrating that a measure accurately represents the construct statistical signiﬁcance, size, or direction of the coefﬁcients from even if some nuances are omitted in the same way that a valid those reported using the ordinary ordered logit models. econometric model does not explain all the variance. Copyright  2002 John Wiley & Sons, Ltd. Strat. Mgmt. J., 23: 595–618 (2002)
• 10. 604 B. Uzzi and J. J. Gillespie a client like the one we have been discussing, Finally, previous studies have used network size what quantitative information would you use or to operationalize the network embeddedness of a look for?’ ﬁrm’s banking relationships (Baker, Faulkner, and As documented in the hypothesis section, the Fisher, 1998; Uzzi, 1999). Consistent with this lit- degree to which a commercial attachment is em- erature, we created bank network size, a log of the bedded in social attachments has been associated count of the number of banks a ﬁrm uses. While with a relationship’s duration and multiplexity. the ﬁeld research indicated that each new rela- Seabright, Levinthal, and Fichman (1992: 135) tionship in our multiplexity measure was likely to operationalized relational attachment as the dura- be distinct, this was not true of duration or net- tion of the tie between two exchange partners: ‘the work size, which we logged to capture diminishing length of time the individual engages in activi- returns in increases in the duration of the relation- ties associated with the relationship . . . [which] ship or in the number of banks to which the ﬁrm is likely to increase with the years of tenure that is linked. have elapsed since the formation of an interor- We performed discriminant validity on these ganizational relationship.’ Given that the longest measures (Kidder, 1981) by inquiring if our above relationship is most closely related to our the- proxies also measured the costs of relationships. ory and has precedence in the literature (Petersen RMs said the above variables lowered transaction and Rajan, 1995), we instrumented the duration costs and increased client retention, but did not of the bank–ﬁrm relationship as the log of the directly affect the economic costs of managing an number of years of the longest relationship in account. For example, one RM said of duration, ‘It the ﬁrm’s network of banking ties. While we fol- doesn’t make it less expensive to manage a tie the lowed theory and focused on the length of the longer it’s around because some long-term clients main relationship (Uzzi, 1999) as an indicator of want to see the banker every month or utilize the bank’s services where that gets expensive.’ RMs embeddedness, it is worth noting that the mean also stated that network size is a measure of the duration of all ties is highly correlated with the quality of the ﬁrm’s bank–ﬁrm relationships rather longest tie (0.796), suggesting that the longest tie than of a ﬁrm’s bargaining power, which in the also empirically captures the main information of midcap market tends to be weak because banks are the mean. almost always larger than midcap ﬁrms. Typically, Seabright et al. (1992) measured attachment RMs remarked that their banks do not negotiate strength between exchange partners as the number prices with ﬁrms with large networks because large of overlapping services on which they interfaced, networks indicate that the ﬁrm is not committed to or multiplexity. Padgett and Ansell (1993) and maintaining embedded ties. One stated, ‘Do I want Uzzi (1999) also measured the embeddedness of a to be doing this term loan [for a ﬁrm with a big relationship as multiplexity. In the bank–ﬁrm rela- network] when there are other banks out there? I tionship, multiplexity is indicated by the number kind of said, “Why don’t you ask one of your other of business and personal bank services used by banks?” [So], I priced it too high, ﬁguring one of the entrepreneur at the bank. Personal bank ser- the other banks will come in with a lower bid. I vices include exchanges that focus on the banking won’t insult them by saying, “No, I don’t want and ﬁnancial planning of the entrepreneur’s per- the business,” but I know they’re not gonna give sonal ﬁnances. RMs noted that personal services me it.’ deepen social relationships and reinforce multi- plexity. Thus, we operationalized the multiplexity of the relationship as the number of business and Control variables: ﬁrm, ﬁnancial, and market personal bank services used by the entrepreneur. NSSBF data contain an inclusive set of control Business and personal services included broker- variables that permit isolation of the effects of age, capital leases, cash management services, embeddedness net of the organizational, ﬁnancial, credit card receipt processing, letters of credit, and market factors that affect trade-credit man- night depository, pension funds, personal estate agement (Mizruchi and Sterns, 1994; Angelini, Di planning, trusts, retirement planning, revolving Salvo, and Ferri, 1998; Petersen and Rajan, 1999). credit arrangements, money/coins for operations, To control for organizational size and ﬁnancial and wire transfers. competencies, we included number of employees Copyright  2002 John Wiley & Sons, Ltd. Strat. Mgmt. J., 23: 595–618 (2002)