Comparative Analysis of Innovation Districts to Set Up Performance Goals for Tec Innovation District

Purpose: Innovation districts represent a way to create, foster, and manage innovation. Different regions apply their strategy according to the dominant stakeholder in the region, such as academia, industry, government, or entrepreneurs. This research aims to evaluate different innovation districts from a production system point of view to determine the output goals for a Tec Innovation District. Methodology/Approach: Data Envelopment Analysis (DEA) was determined to be the best tool for this study; the variable returns to scale output-oriented model was used to determine the goals for the new district; also, the bootstrap method was employed to analyse the efficiency sensitivity in the sample of districts. Findings: The average technical efficiency of the analysed innovation districts was 0.659, with the highest technical efficiency observed in the case of the Entrepreneurial type (0.831) and Industry Cluster (0.820) districts, whereas the Local government type registered the lowest technical efficiency (0.468). Research Limitation/Implication: The projections for the Tec Innovation District’s output variables were obtained using a set of U.S. innovation districts due to the similarity of the studied region to the available group. The research allowed us to determine realistic outputs for the studied innovation district. Originality/Value of paper: The study employs an original DEA for comparing innovation districts and performs a bootstrap to study the system’s robustness; within this research, the performance level of a new district was calculated to be within a specific efficiency level, according to their peers.


INTRODUCTION
Innovation has been determined to be essential for the prosperity of regional economies (Hoffecker and Rubenstein, 2019). But how can it be triggered? In the last few decades, it has been found that the innovation process can be managed, promoted, and triggered (Ángel Álvarez, 2009). The government, universities, and industrial sectors have been looking for the best way to trigger innovation and tackle the problems within their region (Etzkowitz and Leydesdorff, 2000). Innovation Districts represent one way of creating and managing innovation; these are defined as "a specific geographic location, generally within a city, where high concentrations of people work in knowledge-intensive industries in conjunction with other related companies and institutions" (Burke and Gras, 2019). Innovation District's idea goes beyond just a place for companies to work. Innovation Districts also offer a great place to live. Within such a place, there may be pleasant housing opportunities, safe public spaces, and leisure activities (Adu-McVie et al., 2021). That is why Innovation Districts are a viable economic growth model, as their goal is to be economically, spatially, and socially attractive to people with an elevated level of knowledge capable of discussing and creating solutions that tackle regional, national, or global challenges (Esmaeilpoorarabi et al., 2020). In other words, Innovation Districts pretend to be a problem-solving society that brings prosperity to their region and the world.
According to the Global Institute of Innovation Districts (GIID) (2022), there are over one hundred Innovation Districts around the globe. GIID has been researching Innovation Districts to identify what makes a district an economic engine to its region. GIID works with twenty-three districts across different regions, such as Europe, North America, The Middle East, Australia, and Asia. In the case of Latin America, GIID has been collaborating with Innovation Districts in Mexico and Colombia, for example. In the article "New empirical evidence: how one Innovation District is advancing the regional economy," the GIID mentioned the economic impact of The Cortex Innovation Community in St. Louis in the United States, where the district generated around $2 billion in annual regional output (Tripp, 2002), exposing the benefits of innovation-based economic development.
Mexico's economy is mainly based on manufacturing activities. According to Data México (2022), the manufacturing sector registered the highest Gross Domestic Product (GDP), around $280 billion. Fernández and Alva (2018) mentioned that the country needs to move from a manufacturing economy to a knowledge-oriented economy. In this line, Christensen, Ojomo, and Dillion (2019) defined the concept of efficiency innovation as those initiatives that enable a company to do more with fewer resources. The concept is more focused on process innovation rather than on the product itself. The authors mentioned that outsourcing is one of the most popular examples of efficiency innovation. Outsourcing is prevalent among American firms as they commonly outsource part of their manufacturing processes to Mexican plants intending to reduce costs. This happens because a Mexican worker makes around a sixth of what an American worker makes (Christensen, Ojomo and Dillion, 2019). However, the benefits of those savings go mainly to the foreign companies established in a developed consumption economy. Therefore, it is worthwhile to consider economic models, such as an Innovation District, to enable Mexican companies to integrate market-creating innovation focused on solving problems of a large part of the population (Christensen, Ojomo and Dillion, 2019).
In Mexico's case, some Innovation Districts are in their early stages. One is in Guadalajara, also known as "The Silicon Valley of Mexico", with an important role in developing information technology and software (Hoffecker and Rubenstein, 2019). In Mexico City, a project called "Distrito de Innovación Tlapan" (DIT) is still developing to build an Innovation District in the Tlalpan municipality; Universidad Autonoma Metropolitana, Universidad Iberoamericana, Tecnologico de Monterrey campus in Mexico City, and Tlalpan municipality are carrying out this project. The main objective of DIT is to tackle water-related problems and improve mobility in Mexico City's south region (Medina, 2020). Similarly, another Innovation District called Distrito Tec is currently being developed, in Monterrey, Nuevo León, in the home city of Tecnologico de Monterrey (TEC). TEC is the regional leader in education, innovation, patents, and research, recently ranked as the best university in Mexico and #4 in Latin America (QS Top Universities, 2022). Distrito Tec aims to generate an innovation ecosystem for researchers, entrepreneurs, students, and the academy's community by developing urban architecture design and infrastructure planning (Solís, 2021).

Performance Evaluation
Since an Innovation District is a production system that brings wealth to a region (Hoffecker and Rubenstein, 2019), it is worth analysing its performance. In this case, the performance of an Innovation District is understood as a capability to transform their resources in research outcomes with an economic added value in a region. Many quantitative and statistical methods can be applied to evaluate efficiency and performance. Considering the benchmarking techniques, the frontier analysis has become the most noteworthy approach, with Data Envelopment Analysis (DEA) -a non-parametric modelling technique most often used for evaluating the efficiency and performance of the set of decisionmaking units (Emrouznejad and Yang, 2018) -being its best representative.
DEA has a comprehensive record of successful applications in many industries. For example, Halásková, Mikušová Meričková and Halásková (2022) used DEA to evaluate the efficiency of the services of secondary education in Slovakia. Dénes et al. (2017) applied DEA to measure the efficiency of rehabilitation departments in Hungary. Flegl and Hernández Gress (2023) constructed a DEA model to ass the technical efficiency of public security in Mexico. Avilés-Sacoto et al. (2021) used the DEA methodology to study the environmental performance of 32 states in Mexico. Hosseinzadeh et al. (2023) applied DEA to evaluate the impact of the preselected assets in different portfolio optimization strategies.
DEA has also been used to evaluate innovation performance. For example, for a cross-country comparison, Guan and Chen (2012) constructed a network DEA model to measure the innovation efficiency of the national innovation systems of 22 OECD countries, whereas Aytekin et al. (2022) examined the global innovation efficiency of European Union member countries and candidate countries. Lu, Kweh, and Huang (2014) used the network DEA to evaluate the research and development (R&D) and economic efficiency of the national innovation systems in 30 countries.
Considering regional analyses, Rudskaya et al. (2022) developed a two-stage DEA to assess the effectiveness of regional innovation systems in Russia. Similarly, Broekel, Rogge, and Brenner (2017) investigated the innovation efficiency of 150 German labor market regions through a shared-input DEA model. Dzemydaitė, Dzemyda, and Galinienė (2016) evaluated the efficiency of 40 Eastern and Central European Union regional innovation systems. Kaihua and Mingting (2014) applied DEA to assess the efficiency performance of 30 Chinese regional innovation systems, and Wei (2019) used a three-stage DEA model to measure the regional innovation efficiency of 30 Chinese provinces.
In the Mexican context, Valdez Lafarga and León Balderrama (2015) measured the relative technical efficiency of regional innovation systems in 32 Mexican states. Avilés-Sacoto et al. (2020) used a two-stage DEA analysis to model the efficiency of the regional innovation system in Monterrey.
An overview of the literature review on DEA-based innovation performance evaluation is summarized by Narayanan, Ismail and Mustafa (2022).

Objective
The objective of the analysis is to evaluate the technical efficiency of the Top 25 Innovation Districts in the United States using the DEA method. To obtain a more robust result, the Bootstrap DEA model is applied. Therefore, the analysis aims to answer the following research questions (RQ):

MATERIALS AND METHODS
DEA allows to evaluate the technical efficiency of homogeneous decisionmaking units (DMUs) with respect to their capacity to convert inputs to produce outputs with input and output values ( = 1,2, … , , = 1,2, … ) and ( = 1,2, … , , = 1,2, … ). The efficiency of the is calculated as the weighted sum of outputs divided by the weighted sum of inputs (Charnes, Cooper and Rhodes, 1978). The linearized envelopment form of the variable returns to scale output-oriented model for the is defined as follows (Toloo, Keshavarz and Hatami-Marbini, 2021): (1) subjected to ( ≥ 0, = 1,2, … , . ( where is the quantity of the input of the , $ is the quantity of the output , of the , ( ≥ 0 is an intensity variable of , and % are the slack variables.
is efficient if and only if = 1 and = $ % = 0 for all and ,, i.e., there is no other DMU that produces more outputs with the same combination of inputs.

Bootstrap-DEA Method
Bootstrap is a procedure of drawing with replacement from a sample, mimicking the data-generating process of the underlying true model and producing multiple estimates which can be used for statistical inference (Tziogkidis, 2012). The Bootstrap-DEA (B-DEA) was introduced by Simar and Wilson (1998). This method allows to analyse the sensitivity of efficiency scores which results from the distribution of (in)efficiency in the sample. The specific steps of the B-DEA are as follows (Pan, Hong and Kong, 2020): • Use the traditional DEA method to calculate the initial efficiency scores 0 ( = 1, … , ) for each DMU.
• Using the DEA model to compute the modified efficiency value 0 1 for each simulation sample. • Repeating steps ii to iv for ; times to obtain a group of efficiency scores 0 1 , 4 = 1,2, … , ;.
• By simulating the distribution of the original sample estimator, the modified efficiency scores deviation under the Bootstrap-DEA method can be estimated as follows: Bias ( 0 ) • The modified efficiency value of the Bootstrap-DEA method can be computed as follows: In this analysis, the ; value was set to 2,000 to secure the accuracy of the sampling (Hall, 1986). The BCC output-oriented envelopment smoothed B-DEA model was used for the calculations. MaxDEA Ultra 7 software was used for all calculations.

Dataset and Model
Aretian is a team of Harvard affiliates from various schools offering consultancy to address challenges in building thriving urban ecosystems. These are the authors of The Atlas of Innovation Districts (The Atlas), a developed methodology to classify the Top 25 Innovation Districts in the United States based on their performance outputs (Burke and Gras, 2019). The Atlas uses three Key Performance Indicators (KPIs): • Innovation intensity: It measures the collective effort deployed to create knowledge networks. It is calculated as a percentage of employees working on knowledge-intensive activities per geographic unit.
• Innovation performance: It measures the tangible outputs created annually by the innovation community.
• Innovation impact: It describes the benefits to the broader community that result from the development of knowledge-intensive activities.
The KPIs contain metrics that provide general information about the Innovation Districts, like the number of residents per unit area, number of employees per unit area, number of companies operating in the Innovation District, and its spatial area, among others. The selection of the variables depends on the objective of each study. In general, the variables reflect personnel/employees, such as full- Therefore, to analyse the performance of the top 25 innovation districts, as well as to determine the performance goals for the Tec Innovation District (TID), the following variables were selected: • The number of companies (I1): Number of companies established in an Innovation District.
• Employees in innovation (I2): Number of employees working on knowledge creation in each Innovation District.
• (%) Innovative employment (I3): Number of employees whose work is related to knowledge creation, considering the total employment in the area. In other words, it is the result of dividing the number of employees in innovation (I2) by the total number of employees within each Innovation District.
• (%) Sales from innovation (O1): Percentage of the total sales corresponding to innovation.
• Sales from innovation per employee (O2): How much an Innovation District earns from innovations per employee per year.
Although one may think of a high correlation between I2 and I3, each variable presents different information and are not correlated. The correlation between I2 and I3 is negligible (0.087). Fig. 1 displays the model structure.   The differences obtained could be attributed to the targets of each type of Innovation district. For example, the Entrepreneurial and Industrial Cluster types are business-oriented, and the survival of the companies established within the districts depends on sales and economic success. Whereas, in the governmental districts, business is an essential factor, and they are also concerned about solving social problems that do not necessarily have to do with economic development. Similarly, the Research & Academia Innovation Districts may be focused mainly on proposing solutions for the educational and scientific scopes.  Fig. 2).

Distrito Tec's Performance Goals
As it was mentioned, Distrito Tec is currently being developed, in Monterrey, Mexico. Tecnologico de Monterrey targets positioning the Distrito Tec among the most prestigious Innovation Districts in the region. That is why it is of high importance to project its outcomes, i.e., to set up performance goals. For obvious reasons, no available data related to % Sales from innovation (O1) and Sales from innovation per employee (O2) exist. However, the information for the inputs already exists (Appendix).
The DEA methodology and the calculated projections for the inefficient DMUs can be used to set performance goals. To do so, we laid the outputs for the Distrito Tec equal to 0.0001 (to obtain a feasible solution) and included Distrito Tec among the 25 evaluated Innovation Districts.
According to the analysis and the DMUs involved in the model, Distrito Tec must reach a % Sales from innovation (O1) of 0.567 and sales per employee (O2) of $32,582 to reach maximum efficiency. For the % Sales from innovation (O1), the projection is considerably higher than the average; meanwhile, for the sales per employee from innovation (O2), the projection is lower than the average. These projections may be unreachable during the first years of the Distrito Tec operations. Several combinations of these two variables exist to reach different efficiency levels that could be set as short or mid-term goals. Fig. 3 shows the possible combinations of the outputs to obtain the 50%, 75%, and 100% levels of efficiency score. These values were obtained by iterating the DEA process and adjusting the output variables to get the desired efficiency score. As observed in Fig. 3, the combination proposed by the software is located on the right-hand side of the 100%-score curve (See Fig. 3). This indicates a high percentage of innovation in a low volume of sales. However, as the % of sales from innovation (O1) is significantly higher than the average (0.31), it could be reduced along the curve by increasing the level of sales per employee (O2).

CONCLUSION
This study's main objective was to determine the goals that Distrito Tec must have in terms of sales from innovation to be comparable to Innovation Districts in the United States. Using DEA and the software MaxDEA the projections for these two variables, (%) of sales from innovation and sales from innovation per employee, were figured out: 0.567 and $32,582, respectively. However, since