Theoretical Framework

In the present chapter, we try to infer how the characteristics of the invention re‡ect these two dimensions of the research leading to that invention: the institutional dimension, and the process of research (itself).

From the institutional perspective, we can identify two main settings involved in re-search activities: one directed mainly to augment the current stock of knowledge, and another oriented to research with the goal of obtaining concrete answers to practical questions. Let us call Academia the …rst setting, and Corporate the second. Following what is common in the literature (OECD, 2002), we de…ne the activities of research linked with the …rst goal (advancement of knowledge) asbasic research, and the ones linked with the second goal (achievement of answers to practical questions) as applied research.

For the sake of simplicity, in this theoretical exposition, we refer to one university (the University), and to one …rm (the Firm), as representative members of each institutional setting, Academia and Corporate, respectively. Both organizations, University and Firm, may develop research projects. Since research projects can have both basic and applied features, we identify a project byx, wherexdenotes the importance of the basic research component in that project, that is, its degree ofbasicness.

A research project can end either in a successful outcome or in a failure. In the case of a success, the project ends in a discovery, yielding a revenue V_i for organization i (i = U; F), when i is involved in the research leading to that discovery. Given the goals that each party has for research, the type of project a¤ects the revenues,V_U(x)andV_F(x).

Following a normalization procedure similar to the one developed in the previous chapter, we considerx2[0;1]; VU(x) increasing inx, and VF(x) decreasing inx.⁴

In the case of ending in a failure, the project brings no value to any of the parties.

With probabilityp 2 (0;1) there is a successful outcome, where p depends positively on the e¤ort e_i that party i exerts during the research process, such that _@e^@p

i >0; ^@_@e^2p2 i

0:

From exerting an e¤ort, partyi bears a cost C_i(e_i); where we assume ^@C_@eⁱ

i 0; ^@_@e^2C2ⁱ

i 0,

and Ci does not depend on ej. Three alternative cases are then possible:

1. complementarity of e¤orts in the probability of success, _@e^@2p

i@ej >0;

2. substitutability of e¤orts, _@e^@2p

i@ej <0;

3. independence of e¤orts, _@e^@2p

i@ej = 0:

As far as the research process is concerned, we may consider two alternative situa-tions: the research is conducted under a partnership of the two organizations, or each one conducts it individually and separately.

4The theoretical model in this section follows closely the analysis in the previous chapter of this disser-tation. We consider that a successful project ends in a discovery, which yields di¤erent (and independent) payo¤s for the two organizations. Nevertheless, here, we introduce some additional simpli…cations. We just analyze one successful outcome of research (patented invention), from which both University and Firm bene…t.

In case of individual research, and for simplicity, we assume that there is no interaction between the two organizations, neither at the level of the research process (itself), nor at the level of the outcomes. Under this scenario, party i chooses the amount of e¤ort e_i; and the type of projectx to develop, solving the following problem:

max

fx;eigE _i(e_i; x) = p(e_i)V_i(x) C_i(e_i)

s:t: E _i u_i; (3.3.1)

whereu_i is the (general) payo¤ ofiin its outside option to research. Lete_i;alone andx_i;alone be the optimal solutions to this problem.

In the alternative case of a partnership, the e¤ort of both parties contributes to the success of the project, and the expected gain ofi comes:

E _i(e_f; e_u; x) =p(e_f; e_u)V_i(x) C_i(e_i): (3.3.2) Comparing (3.3.2) with the objective function in (3.3.1), it is clear that the decision of having a partner in research allowsi to bene…t from the e¤ort of its partner j (higher probability of success, for the same e_i), but the type of project x may not be the same.

In fact, given that the two organizations have di¤erent goals for research, the choice of x becomes a source of problems in the partnership. For the sake of simplicity, suppose that party i promotes the relationship. Denote this situation by decentralized structure of governance from party i:⁵ In this context, party i chooses e_i as well as the project to be jointly developed, and presents it to the other party. For simpli…cation, we assume that e_i is always veri…able: Regarding the e¤ort of the other party, e_j; two (extreme) scenarios are possible: either it is veri…able (hence contractible), or it is non-veri…able (hence non-contractible).

Whene_j is veri…able,i⁰s decision is given by:

max

f^x;ef;eugE _i(e_f; e_u; x) s:t: E _i(e_f; e_u; x) u_i;

E _j(e_f; e_u; x) u_j;

i 6= j; i; j =F; U; (3.3.3)

where u_j is the (general) payo¤ of j in its outside option. Let e_f;i+j; e_u;i+j, and x_i+j be the optimal solutions to this problem. Under a partnership situation as in (3.3.3), it can be shown that partyj earns as much as in its outside option, u_j: Furthermore,e_i;i+j and x_i+j are not necessary equal toe_i;alone and x_i;alone, respectively. When the contribution of

5This situation is one of the possibles structures of governance analyzed in the previous Chapter 2. As shown there, the qualitative results here described can be extended for di¤erent structures of governance.

e_j to the success of the project is relatively high, to secure thatj is willing to participate in the partnership, partyimay choose a project closer to the preferences of j, rather than x_i;alone (i⁰s most preferred project).⁶ Another tool that i has available to guarantee the participation of j (for a certain level of ej) is the level of e¤ort ei. It is then possible to check that: e_i;i+j > e_i;alone, when e_i and e_j are complementary; e_i;i+j < e_i;alone, when e_i and e_j are substitute; and e_i;i+j = e_i;alone, whene_i and e_j are independent.

Whene_j is non-veri…able (j⁰s moral-hazard), i⁰s decision is given by:

max

fx;eigE _i(e_f; e_u; x) s:t:

8>

<

>:

E i(ef; eu; x) ui; E _j(e_f; e_u; x) u_j; e_j : arg max

f^e0jgE _j(e_i; e⁰_j; x);

i 6= j; i; j =F; U: (3.3.4)

Let e^Aj_i;i+j; e^Aj_j;i+j, and x^Aj_i+j be the optimal solution to this problem. On top of the participation constraint ofj; the governing partyifaces now an additional restriction: to give incentives fore_j: In this case, the distortions of e_i and x, in comparison with e_i;alone and x_i;alone, respectively, are expected to be even higher than in problem (3.3.3). This happens whenj⁰s contribution for the success of the project is su¢ ciently important, and a success brings a su¢ ciently high revenue to i:⁷

In other words, from the theoretical framework, we expect that when (say) a …rm is governing a research partnership in which a university participates, the …rm chooses a project less applied than it would individually choose. Moreover, this distortion is reinforced when the e¤ort of the university is non-veri…able. If we consider a reverse situation where a university is governing a research partnership, and a …rm participates on it, we expect a distortion of the type of project that the university would individually prefer, towards a less basic research project.

Up to now, we focused in two (extremes) scenarios of veri…ability of e_j, yes or no.

However, we also would like to analyze more intermediate (and realistic) situations. For such, instead of referring to veri…ability of e_j, we shift the discussion to the capacity of party j to commit on a certain level of e¤ort e_j. Furthermore, we believe that the capacity of commitment is positively related with theinteraction of the partners during the research process. Denote by 2[0;1]the degree of interaction between the partners, when developing a common project. Under a decentralized structure of governance, we expect that: as approaches 1 (maximum interaction), the design of the relationship becomes closer to the formalization in problem (3.3.3), while as decreases towards 0 (minimum interaction), the problem becomes similar to (3.3.4). Under a decentralized governance of i, suppose that e_j can be decomposed in two parts, one in which j can

6This result corresponds to Proposition 2.3.4.

7This result is shown in Propositions 2.3.5 and 2.3.6.

commit for the partnership, e^C_j ; and another in which j cannot commit, e^{N C}_j : Since the capacity of commitment is assumed to be related with interaction of the partners: e_j =

e^C_j + (1 )e^{N C}_j : With this formalization, the decisions in the partnership follow:

max f^x;ei;eCjg

E _i(e_i; e^C_j ; e^{N C}_j ; ; x) = p e_i; e^C_j ;(1 )e^{N C}_j V_i(x) C_i(e_i)

s:t:

8>

<

>:

E _i(e_i; e^C_j ; e^{N C}_j ; ; x) u_i; E _j(e_i; e^C_j ; e^{N C}_j ; ; x) u_j; e^{N C}_j : arg max

f^e0jgE j(ei; e^C_j ; e⁰_j; ; x);

i 6= j; i; j =F; U: (3.3.5)

In practical terms, this conjecture means that:

- when a …rm undertakes a research project, if it does so in partnership with a university, we expect the outcome to be more basic than when it develops the research alone.

The distortion towards a more basic research project is higher, the weaker the interaction between the partners;

- when a university undertakes a research project, a similar (and symmetric) outcome is expected: a more applied research than when university makes research alone, and the weaker the interaction, the more applied is the project.