Measuring Regional Innovation and Entrepreneurship Capabilities

Abstract

With the rise of internationalization and rapid industrial transformation, the maintenance of regional innovation and entrepreneurship has become an important issue, in the strategic planning of science parks. However, the measurement and prioritization of regional innovation and entrepreneurship capabilities has been largely neglected. Having reviewed four theoretical building blocks: (1) creative class, (2) intellectual capital, (3) regional innovation systems, and (4) industrial clusters, this paper develops an integrated FIEC framework, with four dimensions (financing, innovation and cluster, entrepreneurship and culture) and 15 indicators to measure regional innovation and entrepreneurship capabilities. Based on a dataset of 46 completed questionnaires, an overall 46% response rate, these dimensions and indicators were prioritized using AHP (analytic hierarchy process) analysis. The results show that: (1) the innovation and cluster dimension is the most important of the four dimensions; (2) the top three indicators “Completeness of upstream–downstream industries”, “Assistance of incubators” and “Abundance talent pools” are the most important of the 15 indicators; (3) within each dimension, “abundance of venture capital” is the most important indicator in the financing dimension, “completeness of upstream–downstream industries” is the most important indicator in the innovation and cluster dimension, “assistance of incubators” is the most important indicator in the entrepreneurship dimension and “self-employed culture” is the most important indicator in the regional culture dimension. These results show the importance of maintaining healthy regional innovation capabilities, for Science Park Administrations, on the island of Taiwan and elsewhere.

Appendix

AHP Analysis

AHP enables us to make effective decisions on complex issues by simplifying and expediting our natural decision-making processes. It also provides an effective structure for group decision making by imposing discipline on the groups’ thought processes [40].

Let C ₁, C ₂,…, C _n be the set of activities. The quantified judgments on pairs of activities C _i , C _j are represented by an n × n matrix.

$$ A = \left( {{a_{{ij}}}} \right),\left( {i,j = {1},{2}, \ldots, n} \right) $$

The entries a _ij are defined by the following entry rules.

• Rule 1. If a _ij = α, then a _ij = 1/α, α ≠ 0

• Rule 2. If C _i is judged to be of equal relative importance as C _j , then a _ij  = 1, a _ji  = 1; in particular, a _ii  = 1 for all i.

Thus, the matrix A has the form:

$$ A = \left[ {\matrix{{*{20}{c}} 1 & {{a_{{12}}}} & \cdots & {{a_{{1n}}}} \\ {1/{a_{{12}}}} & 1 & \cdots & {{a_{{2n}}}} \\ \vdots & \vdots & { \vdots \vdots \vdots } & \vdots \\ {1/{a_{{1n}}}} & {1/{a_{{2n}}}} & \cdots & 1 \\ } } \right] $$

Let us assume first that the “judgments” are merely the result of precise physical measurements. In this ideal case of exact measurement, the relations between the weights w _i and the judgments a _ij are simply given by:

$$ \frac{{{w_i}}}{{{w_j}}} = {a_{{ij}}}\quad \left( {{\text{for}}\,i,\,j = 1,2, \ldots, n} \right) $$

And

$$ A = \left[ {\matrix{{*{20}{c}} {{w_1}{/}{w_1}} & {{w_1}{/}{w_2}} & \cdots & {{w_1}{/}{w_n}} \\ {{w_2}{/}{w_1}} & {{w_2}{/}{w_2}} & \cdots & {{w_2}{/}{w_n}} \\ \vdots & \vdots & {} & \vdots \\ {{w_n}{/}{w_1}} & {{w_n}{/}{w_2}} & \cdots & {{w_n}{/}{w_n}} \\ } } \right] $$

In the ideal case relations, it appears reasonable to require that w _i should be equal to the average of these values. However, the more realistic relations for the general case take the form:

$$ {w_i} = {\text{the}}\,{\text{average}}\,{\text{of}}\,\left( {{a_{{i1}}}{w_1},\,{a_{{i2}}}{w_2}, \ldots, {a_{{in}}}{w_n}} \right) $$

More explicitly, we have

$$ {w_i} = \frac{1}{n}\sum\limits_{{j = 1}}^n {{a_{{ij}}}{w_j}} \quad i = 1,2, \ldots, n $$

Or

$$ \sum\limits_{{j = 1}}^n {{a_{{ij}}}{w_j}} = n{w_i}\quad i = 1, \ldots, n $$

Which is equivalent to

$$ Aw = nw $$

Clearly, in the consistent case, n is the largest eigenvalue of A.

Four Basic Stages of AHP

AHP was created by Thomas Saaty to structure complex judgments. The four basic stages are as follows:

• (1) Systematizing the judgments into a hierarchy or tree

  The AHP process is hierarchical and its hierarchy is structured from the top down, much like relevance trees. This stage allows a complex decision to be structured into a hierarchy descending from an overall objective to various “criteria”, “sub-criteria”, and so on until the lowest level. According to Saaty [40], a hierarchy can be constructed by creative thinking, recollection and using people’s perspectives.

• (2) Performing elemental, pairwise comparisons

  People can judge between two items more easily than they can make composite judgments of multiple items all at once. Therefore, AHP uses pairwise comparison among each relevant pair of items as the basic judgments. The preferences are quantified by using a 9-point scale and the meaning of each scale measurement is explained in Table 8.

  Table 8 The scales of preference between the two elements

• (3) Synthesizing those pairwise judgments to arrive at overall judgments

  The stage is to synthesize the judgments within a given matrix (for local priorities) and then across matrices (global priorities). The method of calculating the eigenvalue is usually used by AHP to evaluate the vectors of priorities of parameters. The vector of priorities of the parameters in the lower level in the hierarchy is first calculated and then it progresses to get the overall priority vector. There are four methods for approximating the solution:

  • (a) The NRA (normalization of row average) method sums the elements in each row and normalizes by dividing each sum by the total of all the sums. In mathematical form:

    $$ {w_i} = \sum\nolimits_{{j = 1}}^n {{a_{{ij}}}} {/}\sum\nolimits_{{i = 1}}^n {\sum\nolimits_{{j = 1}}^n {{a_{{ij}}}} } \quad i,j = 1,2, \ldots, n $$

  • (b) The NRC (normalization of the reciprocal sum of columns) method is to take the sum of the elements in each column and form the reciprocals of these sums. Then normalize by dividing each reciprocal by the sum of the reciprocals. In mathematical form:

    $$ {w_i} = \frac{{\left( {1{/}\sum\limits_{{i = 1}}^n {{a_{{ij}}}} } \right)}}{{\sum\limits_{{i = 1}}^n {\left( {1{/}\sum\limits_{{i = 1}}^n {{a_{{ij}}}} } \right)} }}\quad i,j = 1,2, \ldots, n $$

  • (c) The ANC (average of normalized columns) method is to divide the elements of each column by the sum of that column (i.e., normalize the column) and then add the elements in each resulting row and divide this sum by the number of elements in the row (n). This is a process of averaging over the normalized columns. In mathematical form, the vector of priorities can be calculated as:

    $$ {w_i} = \frac{1}{n}\sum\limits_{{j = 1}}^n {\frac{{{a_{{ij}}}}}{{\sum\limits_{{i = 1}}^n {{a_{{ij}}}} }}} \quad i,j = 1,2, \ldots, n $$

  • (d) The NGM (normalization of the geometric mean of the rows) method is to multiply the n elements in each row and take the nth root. Then normalize the resulting numbers as follows:

    $$ {w_i} = {\left( {\prod\limits_{{j = 1}}^n {{a_{{ij}}}} } \right)^{{1/n}}}/\sum\limits_{{i = 1}}^n {{{\left( {\prod\limits_{{j = 1}}^n {{a_{{ij}}}} } \right)}^{{1/n}}}} \quad i,j = 1,2, \ldots, n $$

    In practice, NGM is the most commonly applied method, which is adopted in the study. λ _max can be calculated as:

    $$ {\lambda_{{\max }}} = \frac{1}{n}\left( {\frac{{w{\prime_1}}}{{{w_1}}} + \frac{{w{\prime_2}}}{{{w_2}}} + \Lambda + \frac{{w{\prime_n}}}{{{w_n}}}} \right) $$

• (4) Checking that the judgments combined are reasonably consistent with each other

  Collections of pairwise judgments are apt to show inconsistencies. These may reflect crude scaling. Besides, raters may just be flagrantly inconsistent. AHP provides a helpful indicator to signal the degree of inconsistency in a matrix of judgments: consistency ratio (CR), defined as:

  $$ {\text{CR}} = \frac{\text{CI}}{{\text{RI}}} $$

  where CI is called the consistency index and RI is the random index.

  Furthermore, Saaty [39, 40] provided average consistencies (RI values) of randomly generated matrices. CI for a matrix of order n is defined as:

  $$ {\text{CI}} = \frac{{{\lambda_{{\max }}} - n}}{{n - 1}} $$

  Saaty [40] suggests that the acceptable value of CI should be less than or equal to 0.1. In general, Saaty suggests that CR should be 0.1 or less; sometimes up to 20% may be tolerated.