Keeping it within bounds: Regression analysis of proportions in international business

Abstract

International business researchers commonly estimate proportions, percentages, rates, or fractions – so-called “proportional dependent variables”. In this paper, we posit that two regression strategies are particularly pertinent to the international business field: Tobit and fractional regression. Reviewing recent international business research, we find that, while fractional regression is rarely used, analyses from Tobit regression are often incomplete or erroneously interpreted with consequences for the validity of the reported results. Accordingly, we clarify how researchers should choose between Tobit and fractional regression and interpret their results. We present insights based on simple simulations and data examples with associated Stata code and a decision tree for choosing between types of models for use with proportional dependent variables.

French

Les chercheurs en international business estiment généralement des proportions, des pourcentages, des taux ou des fractions, appelés « variables dépendantes proportionnelles ». Dans cet article, nous postulons que deux stratégies de régression sont particulièrement pertinentes dans le domaine de l’international business: la régression Tobit et la régression fractionnelle. En examinant des recherches récentes en international business, nous constatons que, bien que la régression fractionnelle soit rarement utilisée, les analyses de la régression Tobit sont souvent incomplètes ou interprétées de façon erronée, avec des conséquences sur la validité des résultats rapportés. En conséquence, nous clarifions la manière dont les chercheurs devraient choisir entre la régression Tobit et la régression fractionnelle et interprétons leurs résultats. Nous présentons des éclairages fondés sur des simulations simples et des exemples de données avec le code Stata associé et un arbre de décision pour choisir entre les types de modèles à utiliser avec des variables dépendantes proportionnelles.

Spanish

Los investigadores de negocios internacionales comúnmente estiman proporciones, porcentajes, tasas, o fracciones, las llamadas “variables dependientes proporcionales”. En este articulo, planteamos que dos estrategias de regresión son particularmente relevantes para el campo de negocios internacionales: Tobit y la regresión fraccional. Revisando la investigación reciente en negocios internacionales, encontramos que, mientras que la regresión fraccional es raramente usada, los análisis de modelos de regresión Tobit son con frecuencia incompletos o interpretados erróneamente con consecuencias para la validez de los estudios reportados. Por consiguiente, clarificamos como los investigadores deben escoger entre Tobit y la regresión fraccional e interpretar sus resultados. Presentamos aportes basados en simulaciones simples y ejemplos de datos con el código Stata asociado y un árbol de decisión para escoger entre tipos de modelos para usar con variables dependientes proporcionales.

Portuguese

Pesquisadores de negócios internacionais geralmente estimam proporções, porcentagens, taxas ou frações - as chamadas “variáveis dependentes proporcionais”. Neste artigo, postulamos que duas estratégias de regressão são particularmente pertinentes ao campo de negócios internacionais: Tobit e regressão fracionária. Revendo pesquisas recentes de negócios internacionais, descobrimos que, embora a regressão fracionária raramente seja usada, análises da regressão Tobit são muitas vezes incompletas ou erroneamente interpretadas com consequências para a validade dos resultados relatados. Assim, esclarecemos como pesquisadores devem escolher entre Tobit e regressão fracionária e interpretar seus resultados. Apresentamos insights com base em simulações simples e exemplos de dados com o código Stata associado e uma árvore de decisão para escolher entre os tipos de modelos para uso com variáveis dependentes proporcionais.

Chinese

国际商务研究人员通常会估算比例、百分比、比率或分数,即所谓的“比例因变量”。在本文中, 我们假设两种回归策略与国际商务领域特别相关:Tobit和分数回归。综述最近的国际商务研究, 我们发现, 虽然分数回归很少被使用, 但Tobit回归分析通常被不完整地或被错误地解释, 从而影响了所报告结果的有效性。因此, 我们阐明了研究人员应如何在Tobit和分数回归之间进行选择并解读其结果。基于简单的仿真和带有关联Stata代码的数据示例以及用于在与比例因变量一起使用的模型类型之间进行选择的决策树, 我们提出了洞解。

This is a preview of subscription content, access via your institution.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5

REFERENCES

  1. Agnihotri, A., & Bhattacharya, S. 2015. Determinants of export intensity in emerging markets: An upper echelon perspective. Journal of World Business, 50(4): 687–695.

    Google Scholar 

  2. Aguinis, H., Cascio, W. F., & Ramani, R. S. 2017. Science’s reproducibility and replicability crisis: International business is not immune. Journal of International Business Studies, 48(6): 653–663.

    Google Scholar 

  3. Arikan, I., & Shenkar, O. 2013. National animosity and cross-border alliances. Academy of Management Journal, 56(6): 1516–1544.

    Google Scholar 

  4. Bailey, W., Kumar, A., & Ng, D. 2008. Foreign investments of U.S. individual investors: Causes and consequences. Management Science, 54(3): 443–459.

    Google Scholar 

  5. Barbosa, N., & Faria, A. P. 2011. Innovation across Europe: How important are institutional differences? Research Policy, 40(9): 1157–1169.

    Google Scholar 

  6. Baum, C. F. 2008. Stata tip 63: Modeling proportions. Stata Journal, 8(2): 299–303.

    Google Scholar 

  7. Boubakri, N., Guedhami, O., Kwok, C. C. Y., & Saffar, W. 2016. National culture and privatization: The relationship between collectivism and residual state ownership. Journal of International Business Studies, 47(2): 170–190.

    Google Scholar 

  8. Bowen, H. P., & De Clercq, D. 2008. Institutional context and the allocation of entrepreneurial effort. Journal of International Business Studies, 39(4): 747–768.

    Google Scholar 

  9. Cameron, A. C., & Trivedi, P. K. 2010. Microeconometrics using Stata. College Station, TX: Stata Press.

    Google Scholar 

  10. Chang, S.-J., Chung, J., & Moon, J. J. 2013. When do wholly owned subsidiaries perform better than joint ventures? Strategic Management Journal, 34(3): 317–337.

    Google Scholar 

  11. Chi, T., Li, J., Trigeorgis, L. G., & Tsekrekos, A. E. 2019. Real options theory in international business. Journal of International Business Studies, 50(4): 525–553.

    Google Scholar 

  12. Cook, D. O., Kieschnick, R., & McCullough, B. D. 2008. Regression analysis of proportions in finance with self selection. Journal of Empirical Finance, 15(5): 860–867.

    Google Scholar 

  13. Cragg, J. 1971. Some statistical models for limited dependent variables with application to the demand for durable goods. Econometrica, 39(5): 829–844.

    Google Scholar 

  14. Cuervo-Cazurra, A., & Genc, M. 2008. Transforming disadvantages into advantages: Developing-country MNEs in the least developed countries. Journal of International Business Studies, 39(6): 957–979.

    Google Scholar 

  15. Cui, L., & Jiang, F. 2012. State ownership effect on firms’ FDI ownership decisions under institutional pressure: A study of Chinese outward-investing firms. Journal of International Business Studies, 43(3): 264–284.

    Google Scholar 

  16. Cuypers, I. R. P., & Martin, X. 2010. What makes and what does not make a real option? A study of equity shares in international joint ventures. Journal of International Business Studies, 41(1): 47–69.

    Google Scholar 

  17. Estrin, S., Meyer, K. E., Nielsen, B. B., & Nielsen, S. 2016. Home country institutions and the internationalization of state owned enterprises: A cross-country analysis. Journal of World Business, 51(2): 294–307.

    Google Scholar 

  18. Fernández, Z., & Nieto, M. J. 2006. Impact of ownership on the international involvement of SMEs. Journal of International Business Studies, 37(3): 340–351.

    Google Scholar 

  19. Ganotakis, P., & Love, J. H. 2012. Export propensity, export intensity and firm performance: The role of the entrepreneurial founding team. Journal of International Business Studies, 43(8): 693–718.

    Google Scholar 

  20. Gao, G. Y., Murray, J. Y., Kotabe, M., & Lu, J. 2010. A “strategy tripod” perspective on export behaviors: Evidence from domestic and foreign firms based in an emerging economy. Journal of International Business Studies, 41(3): 377–396.

    Google Scholar 

  21. Hoetker, G. 2007. The use of logit and probit models in strategic management research: Critical issues. Strategic Management Journal, 28(4): 331–343.

    Google Scholar 

  22. Hoff, A. 2007. Second stage DEA: Comparison of approaches for modelling the DEA score. European Journal of Operational Research, 181(1): 425–435.

    Google Scholar 

  23. Hottenrott, H., & Lopes-Bento, C. 2014. (International) R&D collaboration and SMEs: The effectiveness of targeted public R&D support schemes. Research Policy, 43(6): 1055–1066.

    Google Scholar 

  24. Laursen, K., Masciarelli, F., & Prencipe, A. 2012. Trapped or spurred by the home region the effects of potential social capital on involvement in foreign markets for goods and technology. Journal of International Business Studies, 43(9): 783–807.

    Google Scholar 

  25. Li, J., & Li, Y. 2010. Flexibility versus commitment: MNEs’ ownership strategy in China. Journal of International Business Studies, 41(9): 1550–1571.

    Google Scholar 

  26. Liang, H., Ren, B., & Sun, S. L. 2015. An anatomy of state control in the globalization of state-owned enterprises. Journal of International Business Studies, 46(2): 223–240.

    Google Scholar 

  27. Liou, R. S., Chao, M. C. H., & Yang, M. 2016. Emerging economies and institutional quality: Assessing the differential effects of institutional distances on ownership strategy. Journal of World Business, 51(4): 600–611.

    Google Scholar 

  28. Maddala, G. S. 1991. A perspective on the use of limited-dependent and qualitative variables models in accounting research. Accounting Review, 66(4): 788–807.

    Google Scholar 

  29. Malhotra, S., & Gaur, A. S. 2014. Spatial geography and control in foreign acquisitions. Journal of International Business Studies, 45(2): 191–210.

    Google Scholar 

  30. Mariotti, S., & Marzano, R. 2019. Varieties of capitalism and the internationalization of state-owned enterprises. Journal of International Business Studies, 50(5): 669–691.

    Google Scholar 

  31. McDonald, J. F., & Moffitt, R. A. 1980. The uses of Tobit analysis. The Review of Economics and Statistics, 62(2): 318.

    Google Scholar 

  32. Messner, J., Mayr, G., & Zeileis, A. 2016. Heteroscedastic censored and truncated regression with crch. The R Journal, 3(1): 173–181.

    Google Scholar 

  33. Nell, P. C., Ambos, B., & Schlegelmilch, B. B. 2011. The MNC as an externally embedded organization: An investigation of embeddedness overlap in local subsidiary networks. Journal of World Business, 46(4): 497–505.

    Google Scholar 

  34. Newey, W. K. 1987. Specification tests for distributional assumptions in the Tobit model. Journal of Econometrics, 34(1–2): 125–145.

    Google Scholar 

  35. Oxelheim, L., Gregorič, A., Randøy, T., & Thomsen, S. 2013. On the internationalization of corporate boards: The case of Nordic firms. Journal of International Business Studies, 44(3): 173–194.

    Google Scholar 

  36. Pan, Y. 2002. Equity ownership in international joint ventures: The impact of source country factors. Journal of International Business Studies, 33(2): 375–384.

    Google Scholar 

  37. Pan, Y., Teng, L., Supapol, A. B., Lu, X., Huang, D., & Wang, Z. 2014. Firms’ FDI ownership: The influence of government ownership and legislative connections. Journal of International Business Studies, 45(8): 1029–1043.

    Google Scholar 

  38. Papke, L. E., & Wooldridge, J. M. 1996. Econometric methods for fractional response variables with an application to 401(k) plan participation rates. Journal of Applied Econometrics, 11(6): 619–632.

    Google Scholar 

  39. Petrou, A. P., & Thanos, I. C. 2014. The “grabbing hand” or the “helping hand” view of corruption: Evidence from bank foreign market entries. Journal of World Business, 49(3): 444–454.

    Google Scholar 

  40. Piening, E. P., Salge, T. O., & Schäfer, S. 2016. Innovating across boundaries: A portfolio perspective on innovation partnerships of multinational corporations. Journal of World Business, 51(3): 474–485.

    Google Scholar 

  41. Ramalho, J. J. S., & da Silva, J. V. 2009. A two-part fractional regression model for the financial leverage decisions of micro, small, medium and large firms. Quantitative Finance, 9(5): 621–636.

    Google Scholar 

  42. Ramalho, J. J. S., & da Silva, J. V. 2013. Functional form issues in the regression analysis of financial leverage ratios. Empirical Economics, 44(2): 799–831.

    Google Scholar 

  43. Tobin, J. 1958. Estimation of relationships for limited dependent variables. Econometrica, 26(1): 24.

    Google Scholar 

  44. Villadsen, A. R., & Wulff, J. N. 2019. Are you 110% sure? Modeling of fractions and proportions in strategy and management research. Strategic Organization (in press).

  45. Wagner, J. 2001. A note on the firm size-export relationship. Small Business Economics, 17(4): 229–237.

    Google Scholar 

  46. Wang, S. L., & Li, D. 2019. Responding to public disclosure of corporate social irresponsibility in host countries: Information control and ownership control. Journal of International Business Studies, 50(8): 1283–1309.

    Google Scholar 

  47. Wiersema, M. F., & Bowen, H. P. 2008. Corporate diversification: The impact of foreign competition, industry globalization, and product diversification. Strategic Management Journal, 29(2): 115–132.

    Google Scholar 

  48. Wiersema, M. F., & Bowen, H. P. 2009. The use of limited dependent variable techniques in strategy research: Issues and methods. Strategic Management Journal, 30(6): 679–692.

    Google Scholar 

  49. Wilhelm, M. O. 2008. Practitioners’ corner: Practical considerations for choosing between Tobit and SCLS or CLAD estimators for censored regression models with an application to charitable giving. Oxford Bulletin of Economics and Statistics, 70(4): 559–582.

    Google Scholar 

  50. Wooldridge, J. M. 2010. Econometric analysis of cross section and panel data. Cambridge, MA: The MIT Press.

    Google Scholar 

  51. Wulff, J. N. 2015. Interpreting results from the multinomial logit model: Demonstrated by foreign market entry. Organizational Research Methods, 18(2): 300–325.

    Google Scholar 

  52. Wulff, J. N. 2019. Generalized two-part fractional regression with cmp. The Stata Journal, 19(2): 375–389.

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Jesper N Wulff.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Accepted by Tailan Chi, Area Editor, 30 September 2019. This article has been with the authors for four revisions.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 20 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Wulff, J.N., Villadsen, A.R. Keeping it within bounds: Regression analysis of proportions in international business. J Int Bus Stud 51, 244–262 (2020). https://doi.org/10.1057/s41267-019-00278-w

Download citation

Keywords:

  • econometrics < research methods
  • Tobit
  • fractional regression
  • proportional dependent variable
  • multiple regression analysis < research methods