A new perspective to explore the technology transfer efficiencies in US universities

Abstract

Universities play a critical role in the complex technology transfer process that facilitates technology transformation from pure research activities to commercialization. The literature has recently focused on whether universities are efficient in this process. With a two-stage perspective, this study explores the required capabilities for universities to be efficient in technology transfer process. To explore the efficiencies in different stages of technology transfer, we apply a 2-stage process DEA method. The model considers 2 inputs, 2 intermediate variables, and 3 output variables from the Association of University Technology Management database. These variables represent funding resource, patenting activities, and licensing and entrepreneurships. Technology transfer in the 2-stage perspective includes the research innovation stage and the value creation stage. The results show that achieving efficiency in the 2 technology-transfer stages requires many different innovation capabilities; thus, most efficient universities only perform efficiently in one of the two stages. When mapping the relative site of universities in the reference network, we found that efficient universities in the research innovation stage are in a more centralized location than those in the value creation stage. By contrast, in the value creation stage, efficient universities can be identified as different reference groups for specific inefficient universities. The network visualization also helps to explain that universities must consider their relative advantages and capabilities to reach efficiency goals in different stages. The comparison between the large-scale group and the small-scale group also showed that a resource scale is critical for universities to accumulate different required capabilities for efficiencies in both stages.

Appendix

1.1 Linear programming formulation of the two-stage DEA model

This Appendix presents the two-stage DEA model proposed by Chen et al. (2009), in both the multiplier model and dual model form. The dual model form is required for the network-based ranking method since it generates the needed peer referencing information. Assume one wants to examine the efficiencies of n decision making units whereby the production process of each unit is split into two sub-processes. For a unit j, m inputs $(x_{ij} ,i = 1, \ldots ,m)$ are utilized to produce d outputs $(z_{pj} ,p = 1, \ldots ,d)$ in the first stage; these d outputs are in turn used as inputs in the second stage to produce s outputs $(y_{rj} ,r = 1, \ldots ,s)$. The efficiency measures $TE_{k}^{1}$ and $TE_{k}^{2}$ for each sub-process under variable returns to scale (VRS) assumption for an observed unit k are defined as:

$$ TE_{k}^{1} = {{\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } + \gamma_{A} } \right)} \mathord{\left/ {\vphantom {{\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } + \gamma_{A} } \right)} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } } \right)}}} \right. \kern-0pt} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } } \right)}}, $$

(1)

$$ TE_{k}^{2} = {{\left( {\sum\nolimits_{r = 1}^{s} {u_{r} y_{rk} } + \gamma_{B} } \right)} \mathord{\left/ {\vphantom {{\left( {\sum\nolimits_{r = 1}^{s} {u_{r} y_{rk} } + \gamma_{B} } \right)} {\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}} \right. \kern-0pt} {\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}, $$

(2)

where v _i , η _p , and u _r are multipliers for ith input, pth intermediate, and rth output, respectively; γ _A and γ _B are free variables for each sub-process. The overall efficiency measure of the two-stage process can reasonably be represented as a convex linear combination of the two stage-level measures as follows:

$$ \theta_{k} = w_{1} TE_{k}^{1} + w_{2} TE_{k}^{2} \; {\text{where}}\; w_{1} + w_{2} = 1. $$

The weights (w ₁ and w ₂) are intended to represent the relative importance or contribution of the performances of individual stages to the overall performance of the two-stage process. They are determined based on the relative size of that stage. To be more specific, $\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)$ represents the total size of or total amount of resources consumed by the two-stage process. One targets w ₁ and w ₂ as the proportion of the total input used at each stage, and then:

$$ w_{1} = {{\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } } \right)} \mathord{\left/ {\vphantom {{\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } } \right)} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}} \right. \kern-0pt} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}, $$

and

$$ w_{2} = {{\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)} \mathord{\left/ {\vphantom {{\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}} \right. \kern-0pt} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}. $$

The overall efficiency θ _k becomes:

$$ \theta_{k} = {{\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} + \sum\nolimits_{r = 1}^{s} {u_{r} y_{rk} } } + \gamma_{A} + \gamma_{B} } \right)} \mathord{\left/ {\vphantom {{\left( {\sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} + \sum\nolimits_{r = 1}^{s} {u_{r} y_{rk} } } + \gamma_{A} + \gamma_{B} } \right)} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}} \right. \kern-0pt} {\left( {\sum\nolimits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\nolimits_{p = 1}^{d} {\eta_{p} z_{pk} } } \right)}}. $$

(3)

The overall efficiency θ _k of the two-stage process can be optimized, subject to the restrictions that the individual efficiency measures ($TE_{k}^{1}$ and $TE_{k}^{2}$) not exceed unity in the linear programming format. After making the usual Charnes and Cooper transformation (Charnes and Cooper 1962), the linear programming problem of additive efficiency decomposition in two-stage DEA under the VRS assumption is as follows:

$$ \begin{aligned} & \theta_{k} = Max\sum\limits_{p = 1}^{d} {\eta_{p} z_{pk} } + \sum\limits_{r = 1}^{s} {u_{r} y_{rk} } + \gamma_{A} + \gamma_{{_{B} }} \\ & \quad {\text{subject to}} \\ & \quad \, \sum\limits_{i = 1}^{m} {v_{i} x_{ik} } + \sum\limits_{p = 1}^{d} {\eta_{p} z_{pk} } = 1 \\ & \quad \sum\limits_{i = 1}^{m} {v_{i} x_{ik} \left( {\alpha - 1} \right)} + \sum\limits_{p = 1}^{d} {\eta_{p} z_{pk} \alpha < 0} \\ & \quad \sum\limits_{i = 1}^{m} {v_{i} x_{ik} \alpha } + \sum\limits_{p = 1}^{d} {\eta_{p} z_{pk} \left( {\alpha - 1} \right) < 0} \\ & \quad \sum\limits_{p = 1}^{d} {\eta_{p} z_{pj} } + \gamma_{A} - \sum\limits_{i = 1}^{m} {v_{i} x_{ij} \le 0} \\ & \quad \sum\limits_{r = 1}^{s} {u_{r} y_{rj} } + \gamma_{{_{B} }} - \sum\limits_{p = 1}^{d} {\eta_{p} z_{pj} \le 0} \\ & \quad v_{i} ,\eta_{p} ,u_{r} \ge 0;\;\alpha \in {\text{constant}};\;\gamma_{A} ,\gamma_{{_{B} }} {\text{ free}}\,{\text{in}}\,{\text{sign;}}\quad \, j = 1,2, \ldots ,n. \\ \end{aligned} $$

(4)

By virtue of the optimization process, it turns out that either w ₁ = 1 and w ₂ = 0 or w ₁ = 0 and w ₂ = 1 at optimality. To overcome this problem, w ₁ ≥ α and w ₂ ≥ α are required in Eq. (4), where α is a selected constant and 0 % < α ≥ 50 %. If γ _A = γ _B = 0 in Eq. (4), then the technology is said to exhibit constant returns to scale (CRS).The dual model form of Eq. (4) under the VRS assumption is as follows:

$$ \begin{aligned} & Min\;\;\theta_{k} \\ & \quad {\text{subject to}} \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{jk} x_{ij} \le \left( {\theta_{k} + \tau \alpha - \tau + \pi \alpha } \right)x_{ik} ,} \quad i = 1, \ldots ,m, \, \\ & \quad \sum\limits_{j = 1}^{n} {\mu_{jk} z_{pj} } - \sum\limits_{j = 1}^{n} {\lambda_{jk} z_{pj} } \le \left( {\theta_{k} - 1 + \tau \alpha + \pi \alpha - \pi } \right)z_{pk} ,\quad p = 1, \ldots ,d, \\ & \quad \sum\limits_{j = 1}^{n} {\mu_{jk} y_{rj} \ge y_{rk} ,\quad r = 1, \ldots ,s} , \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{jk} = 1,} \\ & \quad \sum\limits_{j = 1}^{n} {\mu_{jk} = 1,} \\ & \quad \tau , { }\lambda_{jk} \ge 0;\quad \, j = 1,2, \ldots ,n, \\ & \quad \pi , { }\mu_{jk} \ge 0;\quad \, j = 1,2, \ldots ,n, \\ & \quad \alpha \in {\text{constant}} .\\ \end{aligned} $$

(5)

In the solution of formula (5), λ _jk can be utilized to make a judgment on whether the unit j is a peer of the observed unit k in the first stage. If it is zero, then the unit j is not a peer, otherwise, λ _jk serves as an indication of how much the unit j is to be learned by the observed unit k. The larger λ _jk is, the stronger the unit j is related to the observed unit. Here, μ _jk plays the same role in the second stage.

Once we have obtained the overall efficiency, models similar to (4) can be developed to determine the efficiency of individual stages. Specifically, assuming pre-emptive priority for Stage One, the following model determines that stage’s efficiency $TE_{k}^{1}$, while maintaining the overall efficiency score at θ _k calculated from Eq. (5):

$$ \begin{aligned} & TE_{k}^{1} = \sum\limits_{d = 1}^{D} {\pi_{d} z_{dk} + \gamma_{A} } \\ & \quad s.t. \\ & \quad \sum\limits_{d = 1}^{D} {\pi_{d} z_{dj} + \gamma_{A} } - \sum\limits_{i = 1}^{m} {w_{i} x_{ij} \le 0,} \\ & \quad \sum\limits_{r = 1}^{s} {\mu_{r} y_{rj} + \gamma_{B} } - \sum\limits_{d = 1}^{D} {\pi_{d} z_{dj} \le 0,} \\ & \quad \left( {1 - \theta_{k} } \right)\sum\limits_{d = 1}^{D} {\pi_{d} z_{dk} } + \sum\limits_{r = 1}^{s} {\mu_{r} y_{rk} + \gamma_{A} + \gamma_{B} = \theta_{k} ,} \\ & \quad \sum\limits_{i = 1}^{m} {w_{i} x_{ik} = 1,} \\ & \quad \pi_{d} ,\mu_{r} ,w_{i} \ge 0,\quad j = 1, \ldots ,n, \\ & \quad \gamma_{A} ,\gamma_{B} \;{\text{free}}\,{\text{in}}\,{\text{sign}} .\\ \end{aligned} $$

(6)

Similarly, if Stage Two is to be give pre-emptive priority, the following model determines the efficiency $TE_{k}^{2}$ for that stage:

$$ \begin{aligned} & TE_{k}^{2} = \sum\nolimits_{r = 1}^{s} {\mu_{r} y_{rk} + } \gamma_{B} \\ & \quad s.t. \\ & \quad \sum\limits_{d = 1}^{D} {\pi_{d} z_{dj} + \gamma_{A} } - \sum\limits_{i = 1}^{m} {w_{i} x_{ij} \le 0,} \\ & \quad \sum\limits_{r = 1}^{s} {\mu_{r} y_{rj} + \gamma_{B} } - \sum\limits_{d = 1}^{D} {\pi_{d} z_{dj} \le 0,} \\ & \quad \sum\limits_{d = 1}^{D} {\pi_{d} z_{dk} } { + }\sum\limits_{r = 1}^{s} {\mu_{r} y_{rk} - \theta_{o} } \sum\limits_{i = 1}^{m} {w_{i} x_{ik} + \gamma_{A} + \gamma_{B} = \theta_{k} ,} \\ & \quad \sum\limits_{d = 1}^{D} {\pi_{d} z_{dk} = 1,} \\ & \quad \pi_{d} ,\mu_{r} ,w_{i} \ge 0,\quad j = 1, \ldots ,n, \\ & \quad \gamma_{A} ,\gamma_{B} \;{\text{free}}\,{\text{in}}\,{\text{sign}} .\\ \end{aligned} $$

(7)

The dual model form of (6) under the VRS assumption is as follows:

$$ \begin{aligned} & TE_{k}^{1} = Min \, \beta \theta_{k} + \alpha \\ & \quad s.t. \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j} x_{ij} \le \alpha x_{ik} ,\quad i = 1, \ldots ,m,} \\ & \quad \sum\limits_{j = 1}^{n} {\eta_{j} z_{dj} } - \sum\limits_{j = 1}^{n} {\lambda_{j} z_{dj} - \beta \left( {1 - \theta_{k} } \right)z_{dk} \le - z_{dk} \quad d = 1, \ldots ,D,} \\ & \quad - \sum\limits_{j = 1}^{n} {\eta_{j} Y_{rj} \le \beta y_{rk} \quad r = 1, \ldots ,s,} \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j} + \beta = 1,} \\ & \quad \sum\limits_{j = 1}^{n} {\eta_{j} + \beta = 0,} \\ & \quad \lambda_{j} \ge 0; \, j = 1,2, \ldots ,n, \\ & \quad \eta_{j} \ge 0; \, j = 1,2, \ldots ,n, \\ & \quad \alpha ,\beta \;{\text{free}}\,{\text{in}}\,{\text{sign}} .\\ \end{aligned} $$

(8)

The dual model form of (7) under the VRS assumption is as follows:

$$ \begin{aligned} & TE_{k}^{2} = Min \, \beta \theta_{k} + \alpha \\ & \quad s.t. \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j} x_{ij} \le - \beta \theta_{k} x_{ik} ,\quad i = 1, \ldots ,m,} \\ & \quad \sum\limits_{j = 1}^{n} {\eta_{j} z_{dj} } - \sum\limits_{j = 1}^{n} {\lambda_{j} z_{dj} - \beta z_{dk} - \alpha z_{dk} \le 0\quad d = 1, \ldots ,D,} \\ & \quad - \sum\limits_{j = 1}^{n} {\eta_{j} Y_{rj} - \beta y_{rk} \le - y_{rk} ,\quad \, r = 1, \ldots ,s,} \\ & \quad \sum\limits_{j = 1}^{n} {\lambda_{j} + \beta = 0,} \\ & \quad \sum\limits_{j = 1}^{n} {\eta_{j} + \beta = 1,} \\ & \quad \lambda_{j} \ge 0;\quad \, j = 1,2, \ldots ,n, \\ & \quad \eta_{j} \ge 0;\quad \, j = 1,2, \ldots ,n, \\ & \quad \alpha ,\beta {\text{ free in sign}} .\\ \end{aligned} $$

(9)

See Figs. 4, 5.