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 innovationdriven economies make a more efficient use of their resources, and that the accumulation of market potential by existing incumbent businesses explains countrylevel 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.
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Notes
 1.
Data were obtained from the World Bank (http://data.worldbank.org/indicator/IT.CEL.SETS.P2).
 2.
Also see Plummer and Acs (2014) who test the localization hypothesis and localized competition at the local level for US counties.
 3.
According to the World Bank, gross capital formation consists of outlays on additions to the fixed assets of the economy plus net changes in the level of inventories. Fixed assets include land improvements (fences, ditches, drains, and so on); plant, machinery, and equipment purchases; and the construction of roads, railways, and the like, including schools, offices, hospitals, private residential dwellings, and commercial and industrial buildings. Inventories are stocks of goods held by firms to meet temporary or unexpected fluctuations in production or sales, and ‘work in progress.’
 4.
The result of the Kruskal–Wallis test confirms that the GEDI index for countries in Group 5 is significantly lower at the 1 % level than the value reported for countries in the rest of Groups.
References
Abdih, Y., & Joutz, F. (2006). Relating the knowledge production function to total factor productivity: An endogenous growth puzzle. IMF Staff Papers, 53(2), 242–271.
Acs, Z. J., Autio, E., & Szerb, L. (2014). National systems of entrepreneurship: Measurement issues and policy implications. Research Policy, 43, 476–494.
Acs, Z. J., Braunerhjelm, P., Audretsch, D. B., & Carlsson, B. (2009). A knowledge spillover theory of entrepreneurship. Small Business Economics, 32, 15–30.
Aghion, P., & Howitt, P. A. (1992). Model of growth through creative destruction. Econometrica, 60(2), 323–351.
Anderberg, M. R. (1973). Cluster analysis for applications. New York: Academic Press.
Anselin, L., Varga, A., & Acs, Z. J. (1997). Local geographic spillovers between university research and high technology innovations. Journal of Urban Economics, 42, 422–448.
Audretsch, D. B., Keilbach, M. C., & Lehmann, E. E. (2006). Entrepreneurship and economic growth. USA: Oxford University Press.
Barro, R. J. (1991). Economic growth in a cross section of countries, Quarterly Journal of Economics, 106(2), 407–444.
Boussemart, J.P., Briec, W., Kerstens, K., & Poutineau, J.C. (2003). Luenberger and Malmquist productivity indices: Theoretical comparisons and empirical illustration. Bulletin of Economic Research, 55(4), 391–405.
Braunerhjelm, P., Acs, Z. J., Audretsch, D., & Carlsson, B. (2010). The missing link: Knowledge diffusion and entrepreneurship in endogenous growth. Small Business Economics, 34(2), 105–125.
Calinski, R. B., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3(1), 1–27.
Chambers, R. G., & Pope, R. D. (1996). Aggregate productivity measures. American Journal of Agricultural Economics, 78(5), 1360–1365.
Cooper, W. W., Seiford, L. M., & Zhu, J. (2011). Handbook on data envelopment analysis (2nd ed.). New York: Springer.
Debreu, G. (1951). The coefficient of resource utilization. Econometrica, 19, 273–292.
Dreher, A., Gaston, N., & Martens, P. (2008). Measuring Globalisation—gauging its consequences. New York: Springer.
Epure, M., & Lafuente, E. (2015). Monitoring bank performance in the presence of risk. Journal of Productivity Analysis. doi:10.1007/s111230140413z.
Everitt, B. S. (1980). Cluster analysis (2nd ed.). London: Heineman.
Färe, R., Grosskopf, S., Norris, M., & Zhang, Z. (1994). Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review, 84(1), 66–81.
Farrell, M. J. (1957). The measurement of productive efficiency. Journal of the Royal Statistical Society, 120, 253–281.
Greene, W. (2003). Econometric analysis (5th ed.). New Jersey: Upper Saddler River.
GrifellTatjé, E., & Lovell, C. A. K. (1999). Profits and productivity. Management Science, 45(9), 1177–1193.
Groh, A., Liechtenstein, H., & Lieser, K., (2012). The Global Venture Capital and Private Equity Country Attractiveness Index 2012 Annual. http://blog.iese.edu/vcpeindex/about/
Mahlberg, B., & Sahoo, B. K. (2011). Radial and nonradial decompositions of Luenberger productivity indicator with an illustrative application. International Journal of Production Economics, 131(2), 721–726.
Miller, D. (1986). Configurations of strategy and structure: Towards a synthesis. Strategic Management Journal, 7, 233–249.
Miller, D. (1996). Configurations revisited. Strategic Management Journal, 17, 505–512.
Morck, R., Wolfenzon, D., & Yeung, D. (2004). Corporate governance, economic entrenchment and growth. National Bureau of Economic Research, Working paper 10692, August 2004.
Nataraja, N. R., & Johnson, A. L. (2011). Guidelines for using variable selection techniques in data envelopment analysis. European Journal of Operational Research, 215(3), 662–669.
Pekka, S., Acs, Z. J., & Weubker, R. (2013). Exploring country level institutional arrangements on the rate and type of entrepreneurial activity. Journal of Business Venturing, 28(1), 176–193.
Plummer, L. A., Acs, Z. J. (2014). Localized competition in the knowledge spillover theory of entrepreneurship. Journal of Business Venturing, 29(1), 121–136.
Romer, P. (1990). Endogenous technological change. Journal of Political Economy, 98(October), 71–102.
Ruggiero, J. (2005). Impact assessment of input omission on DEA. International Journal of Information Technology & Decision Making, 4(3), 359–368.
Sanandaji, T., & Leson, P. T. (2013). Billionairs. Industrial and Corporate Change, 22(1), 313–337.
Sengupta, J. K. (1987). Efficiency measurement in nonmarket systems through data envelopment analysis. International Journal of Systems Science, 18(12), 2279–2304.
Tone, K., & Sahoo, B. (2003). Scale, indivisibilities and production function in data envelopment analysis. International Journal of Production Economics, 84(2), 165–192.
World Economic Forum. (2013). The Global Competitiveness Report 2013–2014. Geneva, Switzerland
Acknowledgments
László Szerb benefited from the financial support of the European Union (TÁMOP Project: No. 4.2.2 A–11/1/KONV20120058). Esteban Lafuente acknowledges financial support by the Spanish Ministry of Science and Innovation (ECO201348496C44R).
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Appendices
Appendix 1
See Table 5.
Appendix 2: Global Entrepreneurship and Development Index (GEDI)
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 wellknown 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 indicatoradjusted 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, postpenalty 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 subindex: entrepreneurial attitudes, entrepreneurial abilities, and entrepreneurial aspirations. The value of a subindex for any country is the arithmetic average of its PFBadjusted pillars for that subindex multiplied by a 100. The maximum value of the subindices is 100 and the potential minimum is 0, both of which reflect the relative position of a country in a particular subindex.
$$ ATT_{i} = 100\mathop \sum \limits_{j = 1}^{5} h_{j} $$(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, postpenalty 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 superindex, the Global Entrepreneurship and Development Index, is simply the average of the three subindices. 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.
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Lafuente, E., Szerb, L. & Acs, Z.J. Country level efficiency and national systems of entrepreneurship: a data envelopment analysis approach. J Technol Transf 41, 1260–1283 (2016). https://doi.org/10.1007/s1096101594409
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Keywords
 Knowledge spillover theory
 GEDI
 GEM
 Efficiency
 Data envelopment analysis
 Clusters
JEL Classification
 C4
 O10
 L26
 M13