Country level efficiency and national systems of entrepreneurship: a data envelopment analysis approach

Abstract

This paper tests the efficiency hypothesis of the knowledge spillover theory of entrepreneurship. Using a comprehensive database for 63 countries for 2012, we employ data envelopment analysis to directly test how countries capitalize on their available entrepreneurial resources. Results support the efficiency hypothesis of knowledge spillover entrepreneurship. We find that innovation-driven economies make a more efficient use of their resources, and that the accumulation of market potential by existing incumbent businesses explains country-level inefficiency. Regardless of the stage of development, knowledge formation is a response to market opportunities and a healthy national system of entrepreneurship is associated with knowledge spillovers that are a prerequisite for higher levels of efficiency. Public policies promoting economic growth should consider national systems of entrepreneurship as a critical priority, so that entrepreneurs can effectively allocate resources in the economy.

Appendices

Appendix 1

See Table 5.

Table 5 Inefficiency score of the analyzed countries

Appendix 2: Global Entrepreneurship and Development Index (GEDI)

See Tables 6, 7 and 8.

Table 6 Structure of the GEDI index

Table 7 Description of the individual variables used to create the GEDI index

Table 8 Description and source of the GEDI applied institutional variables

Estimation of the GEDI index

The GEDI scores for all the countries are calculated according to the following eight points.

• 1 The selection of variables We start with the variables that come directly from the original sources for each country involved in the analysis. The variables can be at the individual level (personal or business) that are coming from the GEM Adult Population Survey or the institutional/environmental level that are coming from various other sources. Individual variables for a particular year is calculated as the two year moving average if a country has two consecutive years individual data, or single year variable if a country participated only in the particular year in the survey. Institutional variables reflect to most recent available data in that particular year. Altogether we use 16 individual and 15 institutional variables (for details see Appendix 1).

• 2 The construction of the pillars We calculate all pillars from the variables using the interaction variable method; that is, by multiplying the individual variable with the proper institutional variable.

  $$ z_{i,j} = ind_{i,j} x ins_{i,j} $$

  (6)

  for all j = 1, …, k, the number of pillars, individual and institutional variables, where $z_{i,j}$ is the original pillar value for the ith country and pillar j, $ind_{i,j}$ is the original score for the ith country and individual variable j, $ins_{i,j}$ is the original score for the ith country and institutional variable j.

• 3 Normalization pillars values were first normalized to a range from 0 to 1:

  $$ x_{i,j} = \frac{{z_{i,j} }}{{\hbox{max} z_{i,j} }} $$

  (7)

  for all j = 1, …, k, the number of pillars, where $x_{i,j}$ is the normalized score value for the ith country and pillar j, $z_{i,j}$ is the original pillar value for the ith country and pillar j, $max z_{i,j}$ is the maximum value for pillar j.

• 4 Capping All index building is based on a benchmarking principle. In our case we selected the 95 percentile score adjustment meaning that any observed values higher than the 95 percentile is lowered to the 95 percentile. While we used only 63 country values, the benchmarking calculation is based on all the 425 data points in the whole 2006–2013 time period.

• 5 Average pillar adjustment: The different averages of the normalized values of the pillars imply that reaching the same pillar values require different effort and resources. Since we want to apply GEDI for public policy purposes, the additional resources for the same marginal improvement of the indicator values should be the same for all indicators. Therefore, we need a transformation to equate the average values of the components. Equation 8 shows the calculation of the average value of pillar $j$:

  $$ \overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\leftharpoonup}$}} {x}_{j} = \frac{{\sum\nolimits_{i = 1}^{n} {x_{i,j} } }}{n}. $$

  (8)

  We want to transform the $x_{i,j}$ values such that the potential minimum value is 0 and the maximum value is 1:

  $$ y_{i,j} = x_{i,j}^{k} $$

  (9)

  where $k$ is the “strength of adjustment”, the $k$-th moment of $X_{j}$ is exactly the needed average, $\bar{y}_{j}$. We have to find the root of the following equation for $k$

  $$ \sum\limits_{i = 1}^{n} {x_{i,j}^{k} } - n\bar{y}_{j} = 0. $$

  (10)

  It is easy to see based on previous conditions and derivatives that the function is decreasing and convex which means it can be quickly solved using the well-known Newton–Raphson method with an initial guess of 0. After obtaining $k$ the computations are straightforward. Note that if

  $$ \begin{array}{*{20}c} {\bar{x}_{j} < \bar{y}_{j} } & {k < 1} \\ {\bar{x}_{j} = \bar{y}_{j} } & {k = 1} \\ {\bar{x}_{j} > \bar{y}_{j} } & {k > 1} \\ \end{array} $$

  that is $k$ be thought of as the strength (and direction) of adjustment.

• 6 Penalizing After these transformations, the PFB methodology was used to create indicator-adjusted PFB values. We define our penalty function following as:

  $$ h_{\left( i \right),j} = min y_{\left( i \right),j} + {\text{a}}\left( {1 - e^{{ - {\text{b}}\left( {y_{\left( i \right)j} - min y_{\left( i \right),j} } \right)}} } \right) $$

  (11)

  where $h_{i,j}$ is the modified, post-penalty value of pillar j in country i, $y_{i,j}$ is the normalized value of index component j in country i, $y_{min}$ is the lowest value of $y_{i,j}$ for country i, i = 1, 2, … n = the number of countries, j = 1, 2, …, m = the number of pillars, 0 ≤ a, b ≤ 1 are the penalty parameters, the basic setup is a = b = 1.

• 7 The pillars are the basic building blocks of the sub-index: entrepreneurial attitudes, entrepreneurial abilities, and entrepreneurial aspirations. The value of a sub-index for any country is the arithmetic average of its PFB-adjusted pillars for that sub-index multiplied by a 100. The maximum value of the sub-indices is 100 and the potential minimum is 0, both of which reflect the relative position of a country in a particular sub-index.

  $$ ATT_{i} = 100\mathop \sum \limits_{j = 1}^{5} h_{j} $$

  (12a)
  $$ ABT_{i} = 100\mathop \sum \limits_{j = 6}^{9} h_{j} $$

  (12b)
  $$ ASP_{i} = 100\mathop \sum \limits_{j = 10}^{14} h_{j} $$

  (12c)

  where $h_{i,j}$ is the modified, post-penalty value of the jth pillar in country i, i = 1, 2, …, n = the number of countries, j = 1, 2, …, 14 = the number of pillars.

• 8. The super-index, the Global Entrepreneurship and Development Index, is simply the average of the three sub-indices. Since 100 represents the theoretically available limit the GEDI points can also be interpreted as a measure of efficiency of the entrepreneurship resources

  $$ GEDI_{i} = \frac{1}{3}\left( {ATT_{i} + ABT_{i} + ASP_{i} } \right) $$

  (13)

  where i = 1, 2, …, n = the number of countries.