To focus our theorizing on the construct the reviewers seem most interested in - asymmetric knowledge spillovers (Section I in Key Reviewer comments below)
To address how governance choices holistically affect not only safeguarding, but access to common and private benefits (Section II and III)
To advance arguments about when scope or equity might be preferred over the other method, and when double safeguarding might make sense
To maintain our emphasis on industry distance to the alliances as a key theoretical advance that sheds new light onto these questions
Architecture
alliances entail common and private benefits
risk of private benefits to others account at the expense of the focal firm
this is achieved through the use of safeguards manifest in two goverance choices: scope and mode
when making choices about which governance choices to make, firms would seek to determine their impact on common and private benefits to each party
we summarize these considerations in a net benefit question which considers how these benefits are a function of our DVs (scope, mode) and our IVs (distance in three flavors: interfirm distance, average distance to the alliance, distance asymmetry to the alliance) as captured by several mechanisms, namely:
common benefits of novel knowledge generation for all parties
private benefits through knowledge spillovers which accrue to each party, which are driven by:
the amount of firm and industry specific knowledge available to spillover (i.e, inbound knowledge from the counterparty into the alliance that is novel to the recipent of the spillover but not the source)
the scope of the arrangement (which serves as an “apeture” for knowledge to spill through)
the absorptive capacity of a focal party (which helps them absorb and process spillovers)
the monitoring capability of the counterparty (to mitigate the flow of information that can spillover)
we use derivatives of this net benefit equation with respect to governance mode choices to determine which is preferred as a function of our IVs
from this analysis, we can derive and justify our hypotheses
The Net Benefit Equation
note: derivations of this are in more detail below, providing the big picture summary here
The net benefit equation is firm-specific, the equation below is from the perspective of the further partner. The closer partner would have the second and third group of terms interchanged.
\[NB_f = \rho[S[\bar D+D_i]+\alpha] + S[ \Delta D + (\epsilon - D_i)][(\gamma - M(E,D_c))*AC(E,D_f)] - \tau S[ \Delta D + (\epsilon - D_i)][(\gamma - M(E,D_f))*AC(E,D_c)]\] A brief summary term by term:
Common Benefits: \(\rho[S[\bar D+D_i]+\alpha]\)
these benefits have some value relative to the private benefts \(\rho\), and comprise scale (\(\alpha\)) and scope benefits.
the scope benefits are a function of the scope of the alliance (S) and the new information from different industry contexts: this potential for knowledge synthesis is proxied by the distance from the focal alliance or distance between the partners \(\bar D , D_i\), respectively.
Private Benefits Accruing to the Focal Party: \(S[ \Delta D + (\epsilon - D_i)][(\gamma - M(E,D_c))*AC(E,D_f)]\)
these benefits are the numeraire, and thus the leading coefficient is 1
the first two sets of terms determine the amount of information available for spillover
as discussed above, the scope of the alliance increases the potential flowrate of information that can spill over (S)
the specific knowledge that can spill over is either firm specific \((\epsilon - D_i)\) or industry specific (\(\Delta D\)). The former indicates that firm-specific knowledge can spill over when the two partners are very close (interfirm distance is close to zero) and is less relevant when they are distant. The latter indicates that industry specific knowledge can spillover (i.e., there is relevant information spilling into the alliance from the close partner and spilling out to the further partner) when the distance asymmetry is large.
the second set of terms determines the efficacy in which that information is transmitted and absorbed
\([(\gamma - M(E,D_c))]\) captures the monitoring capability of the counterparty, which is taken to be a function of the closer partner’s distance to the alliance and the use of an equity contract
\(AC(E,D_f)\) captures the absoprtive capacity of the focal party, which is taken to be a function of the farther partner’s distance to the alliance and the use of an equity contract
typically, these two forces will work in opposite directions with respect to equity: equity will increase the ability to monitor but also increases absorptive capacity
but these effects are also subject to change with industry distance, the marginal effect of equity is likely not constant across the distance spectrum for either effect
Private Benefits Accruing to the Counterparty \(-\tau S[ \Delta D + (\epsilon - D_i)][(\gamma - M(E,D_c))*AC(E,D_f)]:\)
This final set of terms is very similar to the prior, but it captures the private benefits accruing to the other party, which the focal party seeks to safeguard against
Currently, my thinking is (whether by pure assumption or perhaps by appeals to something like prospect theory) that tau will be greater than 1 on average in the population, i.e., typically, partners are more sensitive to the counterparty receiving spillovers than the converse (although they may vary in their specific preference about some central tendency in this direction)
Deriving Hypotheses
The net benefit equation summarizes much of what we have already discussed in earlier versions but also wraps in concerns of the reviewers, which I paraphrase here:
What about common benefits? Why would partners ally in the first place with the threat of spillovers / future competition?
Can you drop uncertainty and focus on knowledge spillovers as an organizing concept?
We can use the net benefit equation to ask and answer questions. Importantly, many simplifications of this equation are possible in “simpler” cases (i.e., existing competitors, no asymmetry.
Note: Earlier in December, I started moving the hypotheses in the paper around but upon further consideration I think our original ordering remains appropriate and we might actually want to start our edits fresh.
Let’s take an example. When examining Hypothesis 1, we assume the partners are existing competitors.
In such a case:
\(D_i\) = 0 by definition (interfirm distance is 0)
\(\Delta D = 0\) by defintion (both firms are equidistant from the alliance)
\(D_c = D_f = \bar D\) by definition (both firms are equidistant from the alliance, coming from the same home industry)
This allows for many simplications:
The private benefit equations become identical and can be collapsed by a leading coefficient of \(1-\tau\)
The monitoring terms are with respect to average distance instead of unique distances
The interfirm distance and distance asymmetry terms drop out
\[NB_f = \rho[S[\bar D]+\alpha] + S[(1-\tau)(\epsilon)][(\gamma - M(E,\bar D))*AC(E,\bar D)]\] By taking derivatives with respect to our governance variables and making some observations, we can draw inferences that lead to our hypotheses.
For Hypothesis 1b:
Hypothesis 1b: When the two partners are existing competitors, the scope of the alliance becomes narrower. (Right direction, no support)
\[∂NB_f/dS = \rho\bar D + [(1-\tau)(\epsilon)][(\gamma - M(E,\bar D))*AC(E,\bar D )]\] Note the following:
\(\rho\bar D\) is positive and a function of average distance alone - i.e., there is only one degree of freedom that increases these common benefits
1-tau is negative on average in the population by assumption (-)
epsilon is the amount of firm-specific knowledge available to spillover from one competitor to another (no industry-specific spillovers here) and positive definite (+)
the last set of terms is positive semi-definite (either knowledge is flowing or fully restricted) (+)
thus the change in the net benefit equation is a positive contribution from common benefits less a negative contribution from the spillovers to the other party (1-t).
we can make further assumptions regarding functional form (which I did in my earlier work below), but what we can probably say with confidence is that unless the competitors are very jointly distant from the alliance and have a lot of common benefits to exploit, they will choose to narrow their scope
\[∂NB_i/∂E = (1-\tau)S\epsilon*([(\gamma- M(E,\bar D))*∂AC(E,\bar D)/dE] + [∂M(E,\bar D)/dE*AC(E,\bar D)])\] In other cases, we may need to take second derivatives with respect to one of our independent variables or perhaps even just first derivatives with respect to the IVs to see how these governance choices influence the net benefit equation (I’ve tried a few things below, but am running out of time in the near term).
Some Observations
Why do we need this elaborate machinery? We probably don’t at the end of the day (i.e., after we have figured this out). In particular, I would not start weaving the equations into the paper. I am using these tools as a means to keep track of how these different mechanisms interact and potential pitfalls - it has been too hard to keep all of the different permtuations in my head clear when bringing these extra ideas on board.
Second, by focusing on spillovers as a specific private benefit in the context of a full suite of benefits, we hew more closely to that line of work and reasoning and can move away from an uncertainty based lens
We retain our focus on TCE as a means to safeguard against an uncertain result (the possibility of spillovers) and continue our empahsis on these dual governance choices
I also am pretty confident that we will find an argument in here that asymmetric alliances may find a benefit to double safeguarding, but I don’t think I will have the time (at least for the next few weeks) to sit down and grind through the machinery to get there yet. In particular, I think there are a few nuggets to be pursued:
in H1 and H2 the partners are symmetric and thus the two safeguards will largely act as substitutes in dampening private benefits in the form of knowledge spillovers
but in H3, since the spillovers become asymmetric (the partners differ in their absoprtive capacity and monitoring capabilities) it is possible that, for example, if the farther partner seeks equity to increase their absorptive capacity the closer partner will reduce the alliance scope to mitigate leakage via another mechanism.
If we can do this, we can start to also address point V below (getting closer to the mechanisms) - which, at least in this setup, are more explicit than they have been in the past.
Concluding Comment
All of this being said, I am OK with taking the simpler way out and making more targeted changes to the paper that would keep the slate of hypotheses unchanged and focus essentially more on wordsmithing and tweaking the positioning of certain arguments and dropping some ideas or saying it is for others to figure out.
In a certain sense, this may be lower risk in terms of changing what we have already submitted and they generally seem to like. But at the same time, I am sensing that the reviewers still have fundamental reservations about our model and this would serve as a good faith effort to meet and exceed their expectations.
Key Reviewer Comments
Key theory comments
I. Shift focus towards knowledge spillovers and spillover asymmetries
E1(i): To me, while this [inconsistency] is a serious issue, I think it can largely be addressed by abandoning the opportunism construct and, instead, focus on knowledge spillovers as focal relational hazard (R3#3).
R1 3(i): . I’ll also offer a quick suggestion, in that I’m of the opinion the paper could largely sidestep opportunism and just argue firms are worried about protecting their knowledge assets and that drives collaboration patterns. Much of the theory development could largely be the same, while also acknowledging that firms may be sensitive to leakage
E1(ii): I also think that using the ‘spillover asymmetry’ construct would make a lot of sense […] allow you to tie in your core theoretical logic even more clearly with your attempted contribution (which focuses on asymmetric industry distance)
E4: As is, the paper does not really articulate why we would need to look at relative distance from alliances as another construct (above and beyond existing constructs such as relatedness) [spillover asymmetry allows us to do this]
E1(iii): we need to be satisfied that the paper offers an internally coherent and consistent explanatory logic in the next round <- this gives us license to make structural changes I think.
E2(ii): Please also carefully revise your theory background in which you conflate arguments around ‘propensity’
II. Explaining why alliances would occur even though spillovers possible
R1 3 (ii): I want to stress that there is still an embedded assumption in the hypotheses development that moving “toward” a partner means there’s a threat of future rivalry and how this creates a tautological argument. By design, an alliance is creating knowledge or exhibiting an interest in an area where the partner is now, or will be, due to the focal alliance! So, wouldn’t there always be concern over future rivalry for every alliance or form of collaboration? [yes, but it is a question of relative threat in the case of asymmetry, right?]
R3 2 [non-priority]: Even though H2a/b and H3a/b serve as this paper’s main contributions, this paper only stresses the potential transaction hazards in cross-industry alliances and proposes that the employment of equity-based alliance structure or narrower alliance scope as safeguard. Is value appropriation (or exploitation) the essential factor when firms decide to form cross-industry alliances? As a result, the asymmetric industry distance in an alliance should not be treated as exogenous, and this paper may also need to strengthen its theoretical reasoning on the formation of cross-industry alliances or at least endogenize its asymmetric distance variables empirically.
III. Governance choices could involve a double edged sword (e.g., changes in absorptive capacity) given the fact we are dealing with knowledge spillovers as the key transactional hazard
E2(i): a reasonable assumption to make that firms always have an incentive to avoid knowledge leakage; even if a partner hypothetically would not have an interest to compete with the focal firm in the future, the focal firm would still not like to share its knowledge/assets for ‘free’ with that partner
R1 1a: As noted in the prior round’s feedback, in much of the theory development the literature being cited establishes that equity governance is BETTER for knowledge transfer. The bottom of page 7 captures this point directly […] But then the hypotheses development argues that because firms are worried about knowledge leakage, they will choose equity alliances…which theory suggests improves knowledge transfer. This story doesn’t line up! […] If readers should believe that adjustments to scope are occurring specifically because equity increases knowledge transfer, then the paper is lacking consistency
R1 5b: If the sample is largely public firms, it is surprising that no variables were included that account for inducement or opportunities in collaboration. For example, fixed assets or PP&E, financial wellbeing, or most importantly R&D or patents to proxy for absorptive capacity (since the story is about knowledge leakage concerns
IV. Further to this point, in this context, are scope and mode substitutes, complements, or independent?
R1 1b: writing paints the manuscript into a corner due to inconsistency in cites and how they are used. On the one hand, readers are told “Oxley and Sampson (2004) found that firms choose a more protective alliance structure (i.e., equity governance) when alliance scope is broad and vice versa” (p. 6), but then the “a” and “b” hypotheses argue the opposite, given an independent variable equity governance will move in the same direction as narrow scope! On the other hand (and inconsistent with above), other citations in the theory development and later in the discussion suggest there is an already established relationship between the two dependent variables, i.e., “equity governance and narrow scope have both been identified as alternative safeguards that can substitute for each other (Lioukas and Reuer, 2020; Macher and Richman, 2008)” (p. 21). Then why do we need the two separate a/b hypotheses if they’re largely predictable as function of each other?
R1 1c(i): Specifically, arguments seem to suggest (in a currently de-coupled manner) that much of our literature, even from within the same TCE stream, has offsetting predictions about how/when firms limit knowledge transfer or use certain governance structures. At the same time, some literature claims scope and governance are a substitute, and some claim they are complements. There is an opportunity to lean into this nuance and better justify why your study is necessary and what your phenomenon of interest (distance to alliance) is able to uncover that earlier studies could not
R1 1c(ii): Addressing these inconsistencies in the literature may be a more powerful way to highlight the nuance and contribution being made here. If this feedback is pursued, it may also be worth some additional attention in the manuscript to offer some preliminary evidence why H3b had the opposite effect than H3a. While there is speculation in the discussion (starting on page 32), this may be something that the author(s) would be well served tackling, and claiming, as their own.
R2 5 [non-priority]: I appreciate the very clear message here but it does, in my opinion, undermine the impact of your study’s contribution. Your findings imply that the greater use of equity and narrower contractual scope is a hammer for any nail. In contrast, your discussion of the counterintuitive findings (increased use of alliance scope when both partners are more distant from an alliance industry) is very relevant, interesting, and well written.
V. Non-priority but could show going the extra mile: Can teasing out the differences between scope and equity predictions help us get closer to the mechanisms?
R1 2 [non-priority]: although the manuscript offers a number of explanations for why things are happening (p. 1: knowledge leakage and environmental uncertainty), those mechanisms are insufficiently established empirically. They are simply presumed to exist. In the prior version I suggested that subsampling according to alliance scope may be one way to isolate the mechanisms
VI. What about dependence? – not flagged explicitly by the editor but central to several of his flagged points
R2 1: In the case of asymmetric distance to the alliance industry, the farther partner might need to rely on the closer partner more, and trust this partner, which increases dependance, lowers control and, thus, increases the likelihood of opportunistic behavior.
R3 1: ). Besides, recent work (e.g., Runge, Schwens, and Schulz, 2022) suggests that the competition tension in alliances will be more intense when alliance partners are aware of their competitive relationship and are motivated and capable of competing, […] may be helpful to strengthen your theoretical argument by incorporating other (measurable) elements, such as dependence and competitive tension.
Paper Outline
Alliances create value and alliances between partners in different industries are common
Each partner brings to the table their unique attributes (benefits of industry incumbency, knowledge, specialized resources) in their respective markets to jointly generate common benefits. At the same time, both parties face the risk that the knowledge they contribute the alliance can spillover to their partners - a form of private benefit. Alliances are often constructed in a way to maximize the common benefits while controlling or mitigating such risks. (discussion of scope and equity safeguards, wait to the theory background to point out inconsistencies therein) [addresses II.] 2 to 3 transition. For example, prior research has considered the role how parties enact safeguards when forming alliances with existing competitors. These safeguards are in place to avoid the risk of firm-specific knowledge spilling over to a competitor. [consistent with I.]
But prior research has paid less attention to an important but underappreciated risk - that industry partners may engage in asymmetric alliances, and these asymmetries give rise to differential private benefits. In particular, asymmetries in industry distance between the partners and the focal context of the alliance can lead to unequal amounts of industry-specific knowledge spilling over from each firm into the alliance. Such industry-specific knowledge spillovers can threaten either partner’s incumbency status. And to the extent that these spillovers are uneven, one party faces a greater risk of future competition if their counterparty chooses to exploit these knowledge spillovers (whether intentionally extracted from the alliance or merely employing the fruits of accidental spillovers). [addresses I.]
We claim that this threat to incumbency is material (having a substantial impact on profitability if realized), foreseeable (the problem can be anticipated at the time of alliance formation), and controllable (through specifying appropriate alliance agreements).
From this basis, we anticipate that alliances between parties will employ safeguards.
The existing literature is unclear regarding whether these safeguards are used as substitutes, complements or are independent. [consistent with IV.]
IMPORTANTLY, SAFEGUARDS ARE NOT CREATED EQUAL IN THE CONTEXT OF SPILLOVERS. [addresses III.] Their intention: monitoring and controlling aspects of the transaction to mitigate opportunism – regardless if its source is accidental or purposeful behavior But governance mechanisms have implications for knowledge transfer: mode can increase tacit knowledge transfer rate while scope affects the amount of knowledge flow and governance mechanisms have implications for dependence: mode can lessen asset specificity / dependence given joint, a priori resource allocation; scope can increase dependence given the broader set of activities involved [haven’t thought through this fully yet]
build a model of governance structure in light of these points.
If we can build differential hypotheses, this would provide indirect evidence about which mechanism is at play where [addresses V.]
H1 – extant literature confirms discusses the presence of firm specific spillover risk for existing competitors – why scope and mode here? [they are already in the same industry and can’t learn the business from each other
H2 – symmetric spillovers at a distance
H3 – asymmetric industry-specific spillovers [here, there is an issue that one company can learn more than the other]
Discussion
what do we find regarding relative use of safeguards? [addresses IV.]
#Earlier Work
Intent
To model the net benefits to both parties in the presence of knowledge spillovers
Extant Theory
Common Benefits
Common benefits are contingent on the type of alliance: scale or scope.
To somewhat oversimplify, take Zaheer Castaner and Souder (2013) discussion of similarity and complementarity in acquisitions.
When the alliance merges similar resource and knowledge bases, it is likely for the purpose of exploiting scale advantages.
By contast, when the alliance brings together complementary, unique, non-overlapping resource and knowledge bases, it is to garner the benefits of scope.
Taken together, this indicates that there are two sources of common benefits, one of which is based on the new knowledge that can be created as a cooperating group of entities:
We are going to avoid discussing scale for now and treat it as a additive constant\(CB = Scope + Scale\)
\(\therefore CB = f(K^N) + \alpha\)
\(PB = f(K^t_i)\)
Common v. Private Benefits
But alliances also provide private benefits to the parties.
Sources of Private Benefits
What we are pointing out
Industry distance can increase both:
the potential for common benefits with respect to scope
as well as causing the potential for private benefits
as we discuss later, if industry distances are asymmetric, it can make it so those private benefits are not symmetric
Some inferential leaps and re-characterizations of the extant literature we have cited to date
Companies seek to increase the common benefits as well as their own private benefits
We will need to decide whether they take the expected private benefits of the other party into account or not (currently no)
Our model
Acronyms / Notation
\(NB_i\) = Net Benefits to Party i
\(CB\) = Common Benefits
\(PB_i\) = Private Benefits to party i
Knowledge Characteristics
Note: should we drop all discussion of resources or entangle them?
\(K^n\) = New Knowledge and Resources Created Through Recombination (to all parties)
\(K^t_i\) = Transferable Knowledge to party i (from other parties in the transaction)
Knowledge Transfer Characteristics
\(AC\) = Absorptive Capacity (continuous)
\(M\) = Monitoring mechanisms for the other party (continuous)
Governance Characteristics
\(E\) = Equity Usage (0/1)
\(S\) = Scope of the Alliance (continuous)
Distance Characteristics
\(D_i\) = Interfirm Distance
\(D_f\) = Distance from Alliance to Further Partner
\(D_c\) = Distance from Alliance to Closer Partner
Key assumptions / functional specifications (i.e. the mechanisms linking distance and governance choice to our theoretical mechanisms)
by assumptions, I am mostly referring to functional form, much of the directionality comes from our lit review and the comments of the reviews
relative value of private benefits
Perhaps in an appeal to behavioral theory, we assume that partners care more about the spillovers of their knowledge to others than the benefits of spillovers to themselves. In other words, the inbound spillovers need to be substantially larger than the outbound spillovers for a party to want them to occur.
Mechanisms
Absorptive capacity is a function of the party’s distance from the alliance (it is harder to understand knowledge that is more distant from your setting) and the use of equity (per R1 and our cites, equity increases tacit knowledge transfer)
\[AC_i = f(E,D_i)\]\[∂AC_i/dE \ge 0\]\[∂AC_i/dD_i \le 0\] The amonut of monitoring experienced by a focal party is facilitated by the proximity of the monitoring party (i.e., the other party) to the industry of the alliance (they know what to look for) and the presence of an equity agreement (to provide additional monitoring mechanisms)
The amount of relevant, actionable firm-specific knowledge that one party can learn from the other is a function of their distance to each other. The closer they are in terms of market and resource overlaps, the more useful and actionable this idiosyncratic information about their partner’s business would be (per the AMC model, as well as Oxley and Sampson (2004)):
\[K^t_i = f(D_i)\]\[∂K^t_i/dD_i \le 0\] The amount of firm-specific knowledge that can spillover is maximized when the firms are rivals \(D_i\) = 0. Without loss of generality, let us fix some number \(\epsilon\) to be the spillovers in this instance.
\[K^t_i = \epsilon - D_i\]
Importantly, note that \(D_i\) is symmetric, in other words, both parties are equally affected by spillover risks as interfirm distance changes.
The foregoing is covered by extant theory.
Existing theory is less clear about how industry-specific knowledge can spill over across the parties.
The amount of transferable industry-specific knowledge to party i from the other parties to the alliance (i.e., available for spillover) depends on two things:
the amount of industry knowledge that the counterparty contributes to the focal industry of the alliance (which is a function of the distance from the counterparty to the alliance)
the amount of industry knowledge the focal partner does not yet possess about the industry of the focal alliance and thus would be non-redundent information to them
In the case of the former, the closer the counterparty is to the alliance, the more useful information can “spill in” to the alliance
In the case of the latter, the further the focal party is to the alliance, the more the industry-specific information in the alliance is non-redundant and is a useful “spillover”
\[∂K^t_f/d(D_c) < 0\]\[∂K^t_f/d(D_f) > 0\] We will make the assumption that both of these effects are of similar magnitude (this can be tested by using the Edwards difference score procedure, which we do employ).
With this assumption, we can use a difference score to capture this overall effect:
\[∂K^t_i/d\Delta D \ge 0\] To further simplify, let’s argue that the industry and firm-specific effects are independent of each other, since this knowledge in a sense resides at different levels of analysis
\[K^t_i = \Delta D + (\epsilon - D_i)\]
Step-by-step model development (can determine what goes in theory backgound v. hypotheses)
Knowledge spillovers and private benefits
note which supported in the literature empirically or theoretically at a later date
In our model, private benefits accrue from (successful) knowledge spillovers. The reviewers have already bought into this, but in case the question is raised about other types of spillovers:
We can argue that (tangible) resources do not materially spillover in contracts since they remain in the control of the affected parties, and are are identified and tagged to particular parties per the pre-specified arrangements in equity agreements.
Knowledge on the other hand can spillover due to its unique properties.
Since knowledge spillovers are equivalent to private benefits in our telling, we can model them as the product of the knowledge that can flow (transferrable knowledge and the scope of the alliance) \([K^t_i]\), and the mechanisms that affect that flow as a function of bandwidth \([S]\) or enabling/ constraining conditions: \([(\gamma-M)*AC]\) (monitoring mechanisms and absorptive capacity).
note that we keep this simple and just say that there is a stock of potential knowledge that flows through different functions (the scope of the alliance)
note that M is subtracted from some maximum flow rate in the absence of monitoring such that more monitoring throttles information flow, we take \(\gamma\) - M to be ~ 0
\[PB_i = [K^t_i]*[S]*[(\gamma - M)*AC]\] The private benefits for the other firm (j) can be determined in a similar manner:
\[PB_j = [K^t_j]*[S]*[(\gamma - M)*AC]\]
Distance and knowledge creation
Distance between the parties increases the potential for complementarity due to non-overlapping knowledge bases
note we do need to think a bit about complementarity versus complete non-relatedness, but a bridge for another day
Recall that we defined common benefits as a function of scope and scale benefits, and we consider scale benefits as a constant
\[CB = f(K^n) + \alpha\]
We dig into the common scope benefits, and note that to the extent the parties are more distant from each other, the greater the opportunities for recombinant knowledge creation through knowledge pool synthesis. The relevant distances are the distances from each party to the focal alliance, and the distance of the parties from each other. Furthermore, the amount of potential knowledge created will be affected by the scope of the alliance - the broader the scope, the more potential areas for synthesis.
\[K^n = f(\bar D, D_i,S)\] For simplicity, let’s just consider this as a multiplicative expression as we have for private benefits, and substituting back into the common benefits equation we have:
\[CB = [\bar D+D_i]*S+\alpha\] We thus have an expression for common benefits that is in terms of industry distance, and note that distance asymmetry is not in this expression. Note also that scope, one of the goverance mechanisms, has an influence on the magnitude of common benefits.
Distance and knowledge available for spillover
Returning to the private benefits for party i:
\[PB_i = [K^t_i]*[S]*[M*AC]\] Recall from above the following assumptions regarding the relationship between distance and each element of this equation:
The net benefits that the parties strive to drive upwards is the summation of the following elements:
the common benefits that accrue (to both parties, since knowledge is non-rivalrous and scale-free both parties can draw upon this resource freely)
the private benefits that accrue to the focal party, less
the private benefits accruing to the other party (i.e., wanting to avoid getting screwed)
\[NB_i = \rho CB + PB_i-\tau PB_{\neg i}\]this should be equivalent to having a constraint that \(PB_{\neg i}\) does not exceed 0 and solving for the LaGrange multiplier
Important Note: We will assume that \(\tau > 1\), which implies that firms are more worried about spillovers to others than they place value on spillovers from others
Hypothesis Generation
Recall that our intent here is to make predictions about when equity and scope will be employed by the parties as safeguards against the threat of knowledge spillovers, and that the core tenet of TCE is to maximize the potential benefits of collaboration while protecting against opportunistic behavior (whether accidental or intentional in origin).
Thus, choices regarding equity and scope are made to increase benefits \(CB + PB_i\) while mitigating potential costs \(PB_{\neg i}\)
We perform a dynamics analysis to see how this net benefit function changes as a function of nudging the choice variables (and seeing how these values are a function of our core dependent variables of existing competitors, average distance, and distance asymmetry)
I’m not saying this is a maximization problem - rather just understanding the direction of gradient ascent and the tendency for decision makers to trend in that direction.
see our paper for why we consider these three IVs
To begin, we consider the analysis from the perspective of the further partner
IMPORTANT NOTE: We insert a parameter rho to account for the fact that the magnitude of common benefits and private benefits may be on different scales
Scope is a common multiple of everything, in other words, it influences common and private benefits proportionally
Average distance increases common benefits
Equity influences two mechanisms that move in opposite ways (monitoring and absorptive capacity)
The two parties have the same quasi-objective function until the monitoring and absorptive capacity terms for both sets of private benefits
Hypothesis 1: Existing Competitors
This implies:
\(D_i = 0\)
\(\Delta D = 0\)
\(D_f = D_c = \bar D\)
\[NB_i = \rho*[\bar D]*S+\alpha + [(\epsilon)]*[S]*[(\gamma - M(E,\bar D))*AC(E,\bar D)] - \tau[(\epsilon)]*[S]*[(\gamma - M(E,\bar D))*AC(E,\bar D)]\] Note that the private benefit terms are the same but for a leading term (1 and -tau, respectively).
\[NB_i = S \rho \bar D+\alpha + (1-\tau)S\epsilon[(\gamma - M(E,\bar D))*AC(E,\bar D)]\] Taking derivatives to determine dynamics:
As scope increases, the common benefit increases by rho*average distance.
As scope increases, the private benefits increase for both parties symmetrically, but since the parties (on average in the population) put a higher penalty on private gains for others than for themselves (1-t) is always negative and thus this offsets the gains from common benefits.
Scope does not affect scale benefits.
Increases in scope will increase net benefits only if the marginal gain to common benefits outweighs the net increase in private benefits to the other party (i.e., proportional to the difference in 1 - tau)
Equity
Expanding the Monitoring and Absorptive Capacity terms
\[∂NB_i/∂E = (1-\tau)S\epsilon[(\gamma*∂AC(E,\bar D)/dE - M(E,\bar D)*∂AC(E,\bar D)/dE + ∂M(E,\bar D)/dE*AC(E,\bar D)]\] What have we assumed about these derivatives?
gamma is the amount of information flow without monitoring
epsilon is the amount of firm-specific knowledge spillovers
1-t is the preference towards NOT having the counterparty receive spillovers, i.e. 1 - tau < 0. If 1 - tau > 0, then spillovers to the focal party outweigh the other direction. We assume that 1 - tau < 0.
Note that:
the first term from the product rule considers the current level knowledge flow because of monitoring * the change in absorptive capacity
the second term from the product rule considers how equity changes monitoring efficacy * the current level of absorptive capacity
epsilon is always > = 0, as is scope
as before, 1-t is negative by assumption, thus so long as the latter term remains
Key implications:
if the total change from the sum of the latter terms is negative, the overall derivative is positive
if the total change from the sum of these terms is positive, the overall derivative is negative
equity does not influence common benefits.
Worked derivatives in the case of simple AC / M Functions
Let’s take some reasonable, concrete functions as examples to see how this might play out.
Important Note: I re-used some greek letters here for this specific context, other than gamma they do not transfer back to the other setting
Here, absorptive capacity has some maximum level alpha when a party is in the same industry as the alliance. This amount is reduced with distance (-beta), but this negative effect is attenuated when equity is used. The assumption is that equity mitigates, but does not eliminate, this negative relationship, thus if E= {0,1} then abs|beta| > 1.
Here, monitoring when distance is 0 is very effective. It is enough to nearly stop all information flows (thus the coefficient here is in terms of the gamma used to indicate unrestricted flow above, modified by (|eta| < 1) to account for residual leakage. Let’s walk through the rest of the sequence term by term:
Equity has one path of influence:
By changing the rate at which monitoring decays with distance (E x Dbar), which offsets (phi x Dbar) by some amount
The phi term has one influence:
influencing the rate at which monitoring is more difficult as distance increases (phi x Dbar)
These functions imply the following interaction patterns:
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#create the lattice for the x (distance) variabled_i <-seq(0,1,.01)#input value of parameter in first argument to the rep function, the second makes n copies of that number#maximum absorptive capacity at distance = 0alpha =rep(1,101) #rate at which absorptive capacity decays as distance increases, set such that equity (=0/1) attenuates a negative relationship but does not serve to increase absorptive capacity above the maximum (i.e., this value must be greater than 1 since it is subtracted below)#the parameter chosen in initial testing was 1.5, essentially equity slows down the decline from -1.5 across the range to -.5.beta <-rep(1.5,101)#baseline level of monitoring, set to 1gamma <-rep(1,101)#efficacy of monitoring when distance = 0, irrespective of using equity or noteta <- .9#the parameter chosen in initial testing was 1.5phi <-rep(1.5,101)equity <-0ace0 <- alpha + (equity - beta)*d_imonitoringe0 <- eta*gamma + (equity - phi)*(d_i)infoflowe0 <- ace0*(gamma-monitoringe0)equity <-1ace1 <- alpha + (equity - beta)*d_imonitoringe1 <- eta*gamma + (equity - phi)*(d_i)infoflowe1 <- ace1*(gamma-monitoringe1)moderationdata <-tibble(d_i,ace0,ace1,monitoringe0,monitoringe1,infoflowe0,infoflowe1)ggplot(data=moderationdata,aes(x=d_i),) +geom_line(aes( y=infoflowe0,colour="Equity = 0"),linetype=1) +geom_line(aes( y=ace0,colour="Equity = 0"),linetype=3) +geom_line(aes( y=monitoringe0,colour="Equity = 0"),linetype=2) +geom_line(aes( y=infoflowe1,colour="Equity = 1")) +geom_line(aes( y=ace1,colour="Equity = 1"), linetype =3) +geom_line(aes( y=monitoringe1,colour="Equity = 1"),linetype=2) +scale_color_manual(name="Equity Condition",values=c("Equity = 0"="blue","Equity = 1"="red")) +annotate("text", x=.2, y=1, label="ac = dotted") +annotate("text", x=.2, y=.5, label="monitoring = dashed")
view(cbind(d_i,ace0,gamma-monitoringe0,infoflowe0,ace1,gamma-monitoringe1,infoflowe1))#the same thing is happening for both equations, it is just that the equity equation is evolving with respect to distance at about 1/4 of the rate - compare row 2 of e0 to row 4 of e1, row 3 of e0 to row 7 of e1, row 4 of e0 to row 10 of e1, etc.
This is quadratic in E, and thus there is some point of maximum or minimum information flow depending on the value of epsilon, but E can only take values {0,1}. Expanding the expression in E and simplifying:
\[\text{∂Information Flow/dE} =(\gamma(1 - \eta)-\alpha)(\bar D)+ (\phi + \beta- 2E )\bar D^2\] The change in information flow (i.e., the product rule term) depends on distance and distance squared. At D = 0:
There is no change in information flow when switching from equity to non-equity (consistent with the above graph).
But in the neighborhood where D is close to zero, the first term dominates since D^2 -> 0 faster than D -> 0. This is a comparison of alpha (the maximum absorptive capacity) versus monitoring capability (phi(1-eta)). Above, we assumed that absorptive capacity is maximized at D = 0 and equal to complete ability to transfer, whereas monitoring capacity can never completely stop information transfer. Thus, this leading term is negative and thus the derivative in the neighborhood of D = 0 (existing competitors) is negative.
What do we conclude then?
Information flow is lower with equity than non-equity.
given that 1-t is assumed to be < 0 in the population, this is a preference for lower information flow.
Thus, net benefits are higher when equity is used with existing competitors.
gamma is the amount of information flow without monitoring
epsilon is the amount of firm-specific knowledge spillovers
eta is the amount that monitoring at D=0 restricts information flow
alpha is the absorptive capacity of a focal firm at D = 0
phi is the loss in monitoring efficacy as D increases
beta is the loss of absorptive capacity as D increases
1-t is the preference towards NOT having the counterparty receive spillovers, i.e. 1 - tau < 0. If 1 - tau > 0, then spillovers to the focal party outweigh the other direction. We assume that 1 - tau < 0.
Note that:
the first term from the product rule considers the current level knowledge flow because of monitoring * the change in absorptive capacity
the second term from the product rule considers how equity changes monitoring efficacy * the current level of absorptive capacity
epsilon is always > = 0, as is scope
as before, 1-t is negative by assumption, thus so long as the latter term remains
Key implications:
if the total change from the sum of the latter terms is negative, the overall derivative is positive
if the total change from the sum of these terms is positive, the overall derivative is negative
equity does not influence common benefits
Further, consider the results from our simple models of absorptive capacity and monitoring:
Information flow is lower with equity than non-equity given our reasonable functional specifications.
As a consequence, net benefits are higher when equity is used with existing competitors since lower information flow is preferred.
Thus, we predict that:
Hypothesis 1a: When the two partners are existing competitors, the likelihood of employing an equity-based governance mode increases. (This is what we find)
Hypothesis 1b
\[∂NB_i/∂S = \rho \bar D + (1-\tau)\epsilon[(\gamma - M(E,\bar D))*AC(E,\bar D)]\] The latter half of this equation (after the \(\epsilon\)) can be consided in a specific case here.
Increases in scope will increase net benefits only if the marginal gain to common benefits outweighs the net increase in private benefits to the other party.
These common benefits are a function of average distance to the alliance.
With existing competitors, the gains for collaboration are limited to the new knowledge that can be created by fusing their knowledge bases together, with the source of novelty being the alliance context. By contrast, the firm-specific spillovers could be quite large in comparison.
It is likely that the private benefits will outweigh the common ones in this situation (support from our prior cites?)
We predict:
Hypothesis 1b: When the two partners are existing competitors, the scope of the alliance becomes narrower. (Right direction, no support)
Hypothesis 1c
Looking now at what happens when we compare the competitor to the non-competitor case (Di = 0 v. Di > 0)
Note that employing equity or scope is costly outside of the question of knowledge spillovers. It is directly apparent that reducing scope reduces common benefits, whereas equity ties up other firm resources irreversibly.
Note also that they serve interchangably, in that either one will restrict knowledge flow and reduce the private benefits of the other part. Their relative efficacy in this task depends distance and upon how sensitive absorptive capacity and monitoring are to equity as a function of their efficacy.
We have no strong basis to predict their simultaneous usage - either one or the other would suffice for the purposes of restricting knowledge flow, depending on the specific situation. In the absence of additional information, we can assume that the parties will pick the safeguarding mechanism that makes the most sense given the particulars of their contract and not bear the costs of double-safeguarding.
Hypothesis 1c: When the two partners are existing competitors, there are no more likely to simultaneously employ a narrow scope and equity-based governance mode than non-competitors. (have yet to test)
Hypothesis 2
For H2, the partners are still symmetrically distant, but not necessarily competitors anymore. Therefore
Dc = Df = Dbar
Delta D = 0
both Di and D bar are in play
we need to determine what happens when D bar increases
\[dNB_i/dS = \rho(\bar D+D_i) + (1-\tau)[ (\epsilon - D_i)][(\gamma - M(E,\bar D))*AC(E,\bar D)]\] What do we know or have assumed:
\(\gamma - M(E,\bar D)\)? It is positive semi-definite.
\(∂AC_i/d\bar D < 0\) per our assumptions
\(∂M_i/d\bar D < 0\) per our assumptions
\(AC(E,\bar D)\)? It is positive
\(\epsilon - D_i\) - Is is a positive semi-definitive value that captures the net firm-specific knowledge that can leak through.
\(D_i\) is range restricted by D_bar in this equidistant case; they can be competitors or as far apart as D_c + D_f but no more otherwise the triangle is inconsistent (and even this is not sufficiently restictive given the nature of the dataset but is the minimum consistency condition to impose. For now, treating them as independent.
With this information, what can we conclude regarding scope decisions as D bar increases?
Scope increases will create larger common benefits as Dbar and Dinterfirm increase, thus is makes more sense to increase rather than decreases scope as we get further and further from a common setting
The balance between the absorptive capacity effect and the monitoring effect as a function of distance will determine whether knowledge spillovers (which are not preferred will increase or decrease)
Also, the private benefits weaken for both parties as Di increases since there are fewer firm specific spillovers that can occur. As d bar increases, so does the range for Di
Upshot, partners will broaden scope if the rate at which private benefits accrue does not exceed rho
Therefore,
Hypothesis 2b (Revised): As the average industry distance from the alliance for both partners increases, the scope of the alliance becomes BROADER (change from earlier hypothesis). (This is what we actually find)
\[∂NB_i/dE = (1-\tau)S[ (\epsilon - D_i)][(\gamma - M(E,\bar D))*∂AC(E,\bar D)/dE - ∂M(E,\bar D)/dE)*AC(E,\bar D)]\] What do we know or have assumed:
\(1 - \tau\)? is it negative on average in the population
\(S\)? It is positive semi-definite.
\(\epsilon - D_i\) - Is is a positive semi-definitive value that captures the net firm-specific knowledge that can leak through.
\(∂AC_i/d\bar D < 0\) per our assumptions
\(∂M_i/d\bar D < 0\) per our assumptions
\(AC(E,\bar D)\)? It is positive
\(\epsilon - D_i\) - Is is a positive semi-definitive value that captures the net firm-specific knowledge that can leak through.
Implications for equity:
\((1-\tau)S[ (\epsilon - D_i)]\) is always negative, and thus the sign of the net benefit differential will depend on the tradeoff between the absorptive capacity effect and the monitoring effect of equity
In general:
The change in absorptive capacity is multiplied by the current level of knowledge leakage in spite of monitoring
The change in monitoring capability is multiplied by the current level of absorptive capacity
But if we use the toy models from above (replicated here):
As discussed in the code comment above, the two curves are similar to each other, it is just that the equity condition evolves with respect to distance at a much closer rate, such that the curves cross in the relevant range.
What should be a general fact regarding this specific example irrespective of the specific parameters chosen is that there will be some region near Dbar = 0 where equity is preferred since it does a better job in slowing information flow
But after the crossover point, the loss of equity’s monitoring effect is overpowered by the boon that it confers to absorptive capacity, making it that non-equity would be preferred
This line of reasoning doesn’t really get us our original H2. It would actually be the opposite
Hypothesis 2a (Revised): As the average industry distance from the alliance for both partners increases, the likelihood of employing an equity-based governance mode DECREASES.
IMPORTANT ALTERNATIVE
If we instead:
only thought about the monitoring effect as conditional on equity and distance (which was our argument earlier, that uncertainty about monitoring developments in the alliance would drive equity use)
absorptive capacity is a constant (since we didn’t factor it in earlier)
We would get this pattern instead (arguably this is closer to our original argument, even if it was just implicit):
d_i <-seq(0,1,.01)#input value of parameter in first argument to the rep function, the second makes n copies of that number#maximum absorptive capacity at distance = 0alpha =rep(1,101) #rate at which absorptive capacity decays as distance increases, set such that equity (=0/1) attenuates a negative relationship but does not serve to increase absorptive capacity above the maximum (i.e., this value must be greater than 1 since it is subtracted below)#the parameter chosen in initial testing was 1.5, essentially equity slows down the decline from -1.5 across the range to -.5.beta <-rep(1.5,101)#baseline level of monitoring, set to 1gamma <-rep(1,101)#efficacy of monitoring when distance = 0, irrespective of using equity or noteta <- .9#the parameter chosen in initial testing was 1.5phi <-rep(1.5,101)equity <-0ace0 <- alphamonitoringe0 <- eta*gamma + (equity - phi)*(d_i)infoflowe0 <- ace0*(gamma-monitoringe0)equity <-1ace1 <- alpha monitoringe1 <- eta*gamma + (equity - phi)*(d_i)infoflowe1 <- ace1*(gamma-monitoringe1)monitoreffecte0 <- gamma - monitoringe0monitoreffecte1 <- gamma - monitoringe1moderationdata2 <-tibble(d_i,ace0,monitoringe0,monitoreffecte0,infoflowe0,ace1,monitoringe1,monitoreffecte1,infoflowe1)ggplot(data=moderationdata2,aes(x=d_i),) +geom_line(aes( y=infoflowe0,colour="Equity = 0"),linetype=1) +geom_line(aes( y=ace0,colour="Equity = 0"),linetype=3) +geom_line(aes( y=monitoringe0,colour="Equity = 0"),linetype=2) +geom_line(aes( y=infoflowe1,colour="Equity = 1")) +geom_line(aes( y=ace1,colour="Equity = 1"), linetype =3) +geom_line(aes( y=monitoringe1,colour="Equity = 1"),linetype=2) +scale_color_manual(name="Equity Condition",values=c("Equity = 0"="blue","Equity = 1"="red")) +annotate("text", x=.2, y=1, label="ac = dotted") +annotate("text", x=.2, y=.5, label="monitoring = dashed")
view(moderationdata2)
As a consquence of the foregoing, we can predict:
Hypothesis 2a (Original): As the average industry distance from the alliance for both partners increases, the likelihood of employing an equity-based governance mode increases. (This is what we find, albeit at marginal significance)
(that is, if we take the difference between the alternatives as a proxy for the likeihood of its selection).
Hypothesis 3
#everything is now in play, no simplifying assumptions can be made, including using 1 - t
#the focal firm's perspective is currently d_fd_c <-c(0,0,0,0,0)d_f <-c(0,.25,.5,.75,1)#input value of parameter in first argument to the rep function, the second makes n copies of that number#maximum absorptive capacity at distance = 0alpha =rep(1,length(d_c)) #rate at which absorptive capacity decays as distance increases, set such that equity (=0/1) attenuates a negative relationship but does not serve to increase absorptive capacity above the maximum (i.e., this value must be greater than 1 since it is subtracted below)#the parameter chosen in initial testing was 1.5, essentially equity slows down the decline from -1.5 across the range to -.5.beta <-rep(1.1,length(d_c))#baseline level of monitoring, set to 1gamma <-rep(1,length(d_c))#efficacy of monitoring when distance = 0, irrespective of using equity or noteta <- .9#the parameter chosen in initial testing was 1.5phi <-rep(1.5,length(d_c))equity <-0ace0 <- alpha + (equity - beta)*d_fmonitoringe0 <- eta*gamma + (equity - phi)*(d_c)infoflowe0 <- ace0*(gamma-monitoringe0)equity <-1ace1 <- alpha + (equity - beta)*d_fmonitoringe1 <- eta*gamma + (equity - phi)*(d_c)infoflowe1 <- ace1*(gamma-monitoringe1)monitoreffecte0 <- gamma - monitoringe0monitoreffecte1 <- gamma - monitoringe1moderationdata3 <-tibble(d_c,d_f,ace0,monitoringe0,monitoreffecte0,infoflowe0,ace1,monitoringe1,monitoreffecte1,infoflowe1)ggplot(data=moderationdata3,aes(x=d_f),) +geom_line(aes( y=infoflowe0,colour="Equity = 0"),linetype=1) +geom_line(aes( y=ace0,colour="Equity = 0"),linetype=3) +geom_line(aes( y=monitoringe0,colour="Equity = 0"),linetype=2) +geom_line(aes( y=infoflowe1,colour="Equity = 1")) +geom_line(aes( y=ace1,colour="Equity = 1"), linetype =3) +geom_line(aes( y=monitoringe1,colour="Equity = 1"),linetype=2) +scale_color_manual(name="Equity Condition",values=c("Equity = 0"="blue","Equity = 1"="red")) +annotate("text", x=.2, y=1, label="ac = dotted") +annotate("text", x=.2, y=.5, label="monitoring = dashed")
view(moderationdata3)
Stopped here, but the critical piece here is that the absorptive capacity for spillovers pertains to the focal party, while the monitoring is based on the distance of the other party
Model Implied by Extant Theory - NOTHING ELSE DONE BELOW HERE
This is provided for clarity and a sanity check versus extant models
Baseline model only considering partner distance
Extant theory does not consider the alliance as a context in its own right, and to the extent it considers overlap / relatedness / distance, it is with respect to the alliance parties. Since the parties are not distant with respect to an alliance but rather each other, the M and AC functions reduce to a function of equity alone
Here, there are no meaningful alliance scope benefits to be had, and the choice of whether to use scope or equity to control spillovers is a function of the balance between these forces.
In short, they serve a pure substitute role
We find the following insights:
Equity involves a tradeoff for both parties between absorptive capacity and monitoring ability which offset each other by some factor
Scope serves as an alternative mechanism that reduces private benefits, but common ones too
As industry distance
The two parties have the same quasi-objective function until the monitoring and absorptive capacity terms
Relationship between average distance and distance asymmetry that we need to keep in mind
