# Corporate Performance and Economic Convergence between Europe and the US: A Cluster Analysis Along Industry Lines

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review and Significance of Research

## 3. Data and Method

#### 3.1. Data

#### 3.2. Method

#### 3.2.1. Cluster Tendency

#### 3.2.2. Clustering Method

#### 3.2.3. Cluster Stability

## 4. Results

## 5. Discussions

## 6. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Aoki, M. The Contingent Governance of Teams: Analysis of Institutional Complementarity. Int. Econ. Rev.
**1994**, 35, 657. [Google Scholar] [CrossRef] - Shleifer, A.; Vishny, R.W. A Survey of Corporate Governance. J. Finance
**1997**, 52, 737–783. [Google Scholar] [CrossRef] - La Porta, R.; Lopez-de-Silanes, F.; Shleifer, A.; Vishny, R.W. Law and Finance. J. Polit. Econ.
**1998**, 106, 1113–1155. [Google Scholar] [CrossRef] - Fohlin, C. Financial Systems. In Handbook of Cliometrics; Springer: Berlin/Heidelberg, Germany, 2016; pp. 393–430. ISBN 978-3-642-40405-4. [Google Scholar]
- Blass, A.; Yafeh, Y. Vagabond shoes longing to stray: Why foreign firms list in the United States. J. Bank. Finance
**2001**, 25, 555–572. [Google Scholar] [CrossRef] - Gugler, K.; Mueller, D.C.; Burcin Yurtoglu, B. The Impact of Corporate Governance on Investment Returns in Developed and Developing Countries. Econ. J.
**2003**, 113, F511–F539. [Google Scholar] [CrossRef] [Green Version] - Pagano, M.; Volpin, P.F. The Political Economy of Corporate Governance. Am. Econ. Rev.
**2005**, 95, 1005–1030. [Google Scholar] [CrossRef] - La Porta, R.; Lopez-De-Silanes, F.; Shleifer, A.; Vishny, R.W. Legal Determinants of External Finance. J. Finance
**1997**, 52, 1131–1150. [Google Scholar] [CrossRef] - Elsner, W. The process and a simple logic of ‘meso’. Emergence and the co-evolution of institutions and group size. J. Evol. Econ.
**2010**, 20, 445–477. [Google Scholar] [CrossRef] - Williamson, J.G. Globalization, Convergence, and History. J. Econ. Hist.
**1996**, 56, 277–306. [Google Scholar] [CrossRef] [Green Version] - Khanna, T.; Kogan, J.; Palepu, K. Globalization and Similarities in Corporate Governance: A Cross-Country Analysis. Rev. Econ. Stat.
**2006**, 88, 69–90. [Google Scholar] - Ben-David, D. Equalizing Exchange: Trade Liberalization and Income Convergence. Q. J. Econ.
**1993**, 108, 653–679. [Google Scholar] [CrossRef] - Solow, R.M. A Contribution to the Theory of Economic Growth. Q. J. Econ.
**1956**, 70, 65. [Google Scholar] [CrossRef] - Baumol, W.J. Productivity Growth, Convergence, and Welfare: What the Long-Run Data Show. Am. Econ. Rev.
**1986**, 76, 1072–1085. [Google Scholar] - Romer, P.M. Increasing Returns and Long-Run Growth. J. Polit. Econ.
**1986**, 94, 1002–1037. [Google Scholar] [CrossRef] [Green Version] - Bradley, M.H.; Schipani, C.A.; Sundaram, A.K.; Walsh, J.P. The Purposes and Accountability of the Corporation in Contemporary Society: Corporate Governance at a Crossroads. SSRN Electron. J.
**2000**. [Google Scholar] [CrossRef] [Green Version] - Raghuram, R.G.; Zingales, L. The Governance of the New Enterprise. In Corporate Governance, Theoretical and Empirical Perspectives; Cambridge University Press: Cambridge, UK, 2000; pp. 201–226. ISBN 0-521-78164-7. [Google Scholar]
- Hansmann, H.; Kraakman, R. The End of History for Corporate Law. Georgetown Law J.
**2001**, 89, 439–468. [Google Scholar] - La Porta, R.; Lopez-De-Silanes, F.; Shleifer, A.; Vishny, R. Investor Protection and Corporate Valuation. J. Finance
**2002**, 57, 1147–1170. [Google Scholar] [CrossRef] - Denis, D.K.; McConnell, J.J. International Corporate Governance. J. Financ. Quant. Anal.
**2003**, 38, 1. [Google Scholar] [CrossRef] - Stulz, R.M.; Williamson, R. Culture, openness, and finance. J. Financ. Econ.
**2003**, 70, 313–349. [Google Scholar] [CrossRef] [Green Version] - Damodaran, A. Various Industry and Corporate Finance Statistics Compiled from Bloomberg, Morningstar, Capital IQ and Compustat. 2017. Available online: http://pages.stern.nyu.edu/~adamodar/ (accessed on 20 December 2017).
- Clatworthy, J.; Buick, D.; Hankins, M.; Weinman, J.; Horne, R. The use and reporting of cluster analysis in health psychology: A review. Br. J. Health Psychol.
**2005**, 10, 329–358. [Google Scholar] [CrossRef] - Brock, G.; Pihur, V.; Datta, S.; Datta, S. clValid: An R Package for Cluster Validation. J. Stat. Softw.
**2008**, 25. [Google Scholar] [CrossRef] [Green Version] - Bebchuk, L.A.; Cohen, A.; Ferrell, A. What Matters in Corporate Governance? Rev. Financ. Stud.
**2009**, 22, 783–827. [Google Scholar] [CrossRef] [Green Version] - Shamir, O.; Tishby, N. Cluster Stability for Finite Samples. In Proceedings of the Twenty-First Annual Conference on Neural Information Processing Systems; NIPS Proceedings: Vancouver, BC, Canada, 2007; pp. 1297–1304. [Google Scholar]
- Banerjee, A.; Dave, R.N. Validating clusters using the Hopkins statistic. In Proceedings of the 2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542); IEEE: Budapest, Hungary, 2004; Volume 1, pp. 149–153. [Google Scholar]
- Handl, J.; Knowles, J.; Kell, D.B. Computational cluster validation in post-genomic data analysis. Bioinformatics
**2005**, 21, 3201–3212. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Rousseeuw, P.J. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math.
**1987**, 20, 53–65. [Google Scholar] [CrossRef] [Green Version] - Dunn, J.C. Well separated clusters and fuzzy partitions. J. Cybern.
**1974**, 4, 95104. [Google Scholar] [CrossRef] - Datta, S.; Datta, S. Comparisons and validation of statistical clustering techniques for microarray gene expression data. Bioinformatics
**2003**, 19, 459–466. [Google Scholar] [CrossRef] - Yeung, K.Y.; Haynor, D.R.; Ruzzo, W.L. Validating clustering for gene expression data. Bioinformatics
**2001**, 17, 309–318. [Google Scholar] [CrossRef] - Lange, T.; Roth, V.; Braun, M.L.; Buhmann, J.M. Stability-Based Validation of Clustering Solutions. Neural Comput.
**2004**, 16, 1299–1323. [Google Scholar] [CrossRef] - Ben-David, S.; von Luxburg, U.; Pal, D. A Sober Look at Clustering Stability. In Lecture Notes in Computer Science, (Conference proceedings: Learning Theory, 19th Annual Conference on Learning Theory); COLT: Pittsburgh, PA, USA, 2006; pp. 5–19. ISBN 978-3-540-35296-9. [Google Scholar]
- Zumel, N.; Mount, J. Practical Data Science with R; Manning Publications Co: Shelter Island, NY, USA, 2014; ISBN 978-1-61729-156-2. [Google Scholar]
- Castellacci, F.; Los, B.; de Vries, G.J. Sectoral productivity trends: Convergence islands in oceans of non-convergence. J. Evol. Econ.
**2014**, 24, 983–1007. [Google Scholar] [CrossRef] - Thai, M.T.; Wu, W.; Xiong, H. (Eds.) Big Data in Complex and Social Networks; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
- Singhal, C.; De, S. (Eds.) Resource Allocation in Next-Generation Broadband Wireless Access Networks; IGI Global: Hershey, PA, USA, 2017. [Google Scholar]
- Vitali, S.; Glattfelder, J.B.; Battiston, S. The Network of Global Corporate Control. PLoS ONE
**2011**, 6, e25995. [Google Scholar] [CrossRef]

**Figure 5.**Rank aggregation used to derive the optimal list of methods and number of clusters (Europe).

Data | Europe | US |
---|---|---|

Hopkins statistic | 0.163 | 0.216 |

Measure | Rank 1 | Rank 2 | Rank 3 |

Connectivity | Hierarchical-4 | Pam-4 | Hierarchical-5 |

Dunn | Hierarchical-4 | Hierarchical-5 | Hierarchical-8 |

Silhouette | Hierarchical-5 | Hierarchical-4 | Kmeans-4 |

Measure | Rank 1 | Rank 2 | Rank 3 |
---|---|---|---|

Connectivity | Hierarchical-4 | Kmeans-4 | Pam-4 |

Dunn | Hierarchical-5 | Hierarchical-6 | Kmeans-5 |

Silhouette | Hierarchical-4 | Kmeans-4 | Pam-4 |

Measure | Rank 1 | Rank 2 | Rank 3 |

APN | Hierarchical-6 | Hierarchical-5 | Hierarchical-4 |

AD | Pam-11 | Pam-10 | Kmeans-11 |

ADM | Hierarchical-6 | Hierarchical-5 | Hierarchical-4 |

FOM | Pam-4 | Pam-7 | Pam-5 |

Measure | Rank 1 | Rank 2 | Rank 3 |

APN | Hierarchical-4 | Kmeans-4 | Hierarchical-8 |

AD | Pam-11 | Pam-10 | Kmeans-11 |

ADM | Kmeans-5 | Hierarchical-6 | Pam-8 |

FOM | Hierarchical-5 | Pam-7 | Pam-8 |

Groups | Debt Ratio | Insider Holdings | Average Tax Rate | EBITDA to Sales | PE | P/Sales | Proportion |
---|---|---|---|---|---|---|---|

E3 | 0.48 | 0.15 | 0.18 | 0.10 | 29.96 | 0.92 | 0.35 |

E1 | 0.22 | 0.25 | 0.15 | 0.13 | 54.40 | 1.31 | 0.32 |

E2 | 0.30 | 0.14 | 0.09 | 0.24 | 65.61 | 2.69 | 0.32 |

E4 | 0.33 | 0.20 | 0.13 | 0.11 | 5345.2 | 0.75 | 0.01 |

Groups | Debt Ratio | Insider Holdings | Average Tax Rate | EBITDA to Sales | PE | P/Sales | Proportion |
---|---|---|---|---|---|---|---|

US1 | 0.25 | 0.15 | 0.10 | 0.14 | 46.69 | 1.37 | 0.38 |

US2 | 0.42 | 0.13 | 0.19 | 0.13 | 44.83 | 1.31 | 0.31 |

US3 | 0.26 | 0.17 | 0.08 | 0.29 | 100.79 | 3.72 | 0.30 |

US4 | 0.26 | 0.12 | 0.16 | 0.20 | 2725.1 | 2.27 | 0.01 |

**Table 8.**Clusterwise means of the bootstrapping procedure for Europe and the US for 100, 1000, and 10,000 resampling, rounded to four digits.

Clusterwise Means | Number of Resampling | Cluster 1 | Cluster 2 | Cluster 3 | Cluster 4 |
---|---|---|---|---|---|

Europe data | 100 | 0.7153 | 0.6794 | 0.6450 | 0.5086 |

1,000 | 0.7406 | 0.6875 | 0.6951 | 0.4646 | |

10,000 | 0.7434 | 0.6966 | 0.6955 | 0.4814 | |

Decision | - | Stable with uncertainty | Stable with uncertainty | Stable with uncertainty | Unstable |

US data | 100 | 0.5347 | 0.5751 | 0.5582 | 0.5335 |

1,000 | 0.5452 | 0.5754 | 0.5460 | 0.4670 | |

10,000 | 0.5425 | 0.5700 | 0.5572 | 0.4758 | |

Decision | - | Unstable | Unstable | Unstable | Unstable |

**Table 9.**Ranking of the estimated degree of similarity between pair of groups. The dissimilarity score is calculated by aggregating the six standardized differences between the levels of the same variable for each pair of two groups, and dividing the sum by 1000. A smaller value of the dissimilarity score denotes groups that are more similar. The average number of industries per pair is the simple average of the number of industries in each pair of groups.

Pairs of Groups | Dissimilarity Score | Average Number of Industries per Pair | Number of Common Industries per Pair |
---|---|---|---|

E2-US3 | 2.99 | 29 | 18 |

E3-US2 | 2.99 | 30.5 | 17 |

E1-US1 | 7.43 | 34.5 | 17 |

E1-US2 | 11.69 | 30.5 | 6 |

E3-US1 | 18.04 | 34.5 | 9 |

E1-US3 | 19.47 | 30 | 4 |

E2-US1 | 24.05 | 33.5 | 9 |

E2-US2 | 24,05 | 29.5 | 3 |

E3-US3 | 37,82 | 30 | 5 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vâlsan, C.; Druică, E.
Corporate Performance and Economic Convergence between Europe and the US: A Cluster Analysis Along Industry Lines. *Mathematics* **2020**, *8*, 451.
https://doi.org/10.3390/math8030451

**AMA Style**

Vâlsan C, Druică E.
Corporate Performance and Economic Convergence between Europe and the US: A Cluster Analysis Along Industry Lines. *Mathematics*. 2020; 8(3):451.
https://doi.org/10.3390/math8030451

**Chicago/Turabian Style**

Vâlsan, Călin, and Elena Druică.
2020. "Corporate Performance and Economic Convergence between Europe and the US: A Cluster Analysis Along Industry Lines" *Mathematics* 8, no. 3: 451.
https://doi.org/10.3390/math8030451