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Exponential Regression of Fractional-Response Fixed-Effects Models with an Application to Firm Capital Structure

  • Esmeralda A. Ramalho ORCID logo , Joaquim J.S. Ramalho ORCID logo EMAIL logo and Luís M.S. Coelho

Abstract

New fixed-effects estimators are proposed for logit and complementary loglog fractional regression models. The standard specifications of these models are transformed into a form of exponential regression with multiplicative individual effects and time-variant heterogeneity, from which four alternative estimators that do not require assumptions on the distribution of the unobservables are proposed. All new estimators are robust to both time-variant and time-invariant heterogeneity and can accomodate fractional responses with observations at the boundary value of zero. Additionally, some of these estimators can be applied to dynamic panel data models and can accommodate endogenous explanatory variables without requiring the specification of a reduced form model. A Monte Carlo study and an application to firm capital structure choices illustrate the usefulness of the suggested estimators.

JEL Classification: C25; C23

Acknowledgments

The authors thank the Editor for his valuable suggestions and remarks that substantially improved the paper. Financial support from Fundacao para a Ciencia e a Tecnologia (grants PTDC/EGE-ECO/119148/2010 and UID/ECO/04007/2013) is also gratefully acknowledged. Aspects of this research were presented at the 2nd Annual Conference of the International Association for Applied Econometrics (IAAE) and the 11th Econometric Society World Congress.

References

Alti, A. 2006. “How Persistent is the Impact of Market Timing on Capital Structure.” Journal of Finance 61: 1681–1710.10.1111/j.1540-6261.2006.00886.xSearch in Google Scholar

Baker, M., and J. Wurgler. 2002. “Market Timing and Capital Structure.” Journal of Finance 57: 1–32.10.1111/1540-6261.00414Search in Google Scholar

Barberis, N., and R. Thaler. 2005. “A Survey of Behavioral Finance.” In Advances in Behavioral Finance, Volume II, edited by R. Thaler, New York: Princeton University Press.10.1515/9781400829125-004Search in Google Scholar

Blundell, R., R. Griffith, and F. A. G. Windmeijer. 2002. “Individual Effects and Dynamics in Count Data Models.” Journal of Econometrics 108: 113–131.10.1016/S0304-4076(01)00108-7Search in Google Scholar

Bradley, M., G. A. Jarrell, and E. H. Kim. 1984. “On the Existence of an Optimal Capital Structure: Theory and Evidence.” Journal of Finance 39: 857–878.10.1111/j.1540-6261.1984.tb03680.xSearch in Google Scholar

Chamberlain, G. 1992. “Comment: Sequential Moment Restrictions in Panel Data.” Journal of Business and Economic Statistics 10 (1): 20–26.Search in Google Scholar

Dhaene, G. and K. Jochmans. 2015. “Profile-Score Adjustments for Incidental-Parameter Problems”, mimeo.Search in Google Scholar

Elsas, R., and D. Florysiak. 2015. “Dynamic Capital Structure Adjustment and the Impact of Fractional Dependent Variables.” Journal of Financial and Quantitative Analysis, 50 (5): 1105–1133.10.1017/S0022109015000496Search in Google Scholar

Graham, J. R., and C. R. Harvey. 2001. “The Theory and Practice of Corporate Finance: Evidence from the Field.” Journal of Financial Economics 60: 187–243.10.1016/S0304-405X(01)00044-7Search in Google Scholar

Harris, M., and A. Raviv. 1991. “The Theory of Capital Structure.” Journal of Finance 46: 297–355.10.1111/j.1540-6261.1991.tb03753.xSearch in Google Scholar

Hansen, L. P. 1982. “Large Sample Properties of Generalised Method of Moments Estimators.” Econometrica 50 (4): 1029–1054.10.2307/1912775Search in Google Scholar

Hausman, J. A., and G. K. Leonard. 1997. “Superstars in the National Basketball Association: economic Value and Policy.” Journal of Labor Economics 15 (4): 586–624.10.1086/209839Search in Google Scholar

Heckman, J. J. 2000. “Causal Parameters and Policy Analysis in Economics: A Twentieth Century Retrospective.” Quarterly Journal of Economics 115 (1): 45–97.10.1162/003355300554674Search in Google Scholar

Heckman, J. J. 2001. “Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture.” Journal of Political Economy 109: 673–748.10.1086/322086Search in Google Scholar

Kayhan, A., and S. Titman. 2004. “Firms’ Histories and their Capital Structures.” Louisiana State University and University of Texas, Working paper.10.3386/w10526Search in Google Scholar

Kraus, A. and R. H. Litzenberger. 1973. “A State-Preference Model of Optimal Financial Leverage.” Journal of Finance 28: 911–922.10.1111/j.1540-6261.1973.tb01415.xSearch in Google Scholar

Korajczyk, R. A., D. J. Lucas, and R. L. McDonald. 1992. “Equity Issues with Time-Varying Asymmetric Information.” Journal of Financial and Quantitative Analysis 27: 397–417.10.2307/2331327Search in Google Scholar

Leary, M., and M. R. Roberts. 2005. “Do Firms Rebalance their Capital Structures?.” Journal of Finance 60: 2575–2619.10.1111/j.1540-6261.2005.00811.xSearch in Google Scholar

Loudermilk, M. S. 2007. “Estimation of Fractional Dependent Variables in Dynamic Panel Data Models with an Application to Firm Dividend Policy.” Journal of Business and Economic Statistics 25 (4): 462–472.10.1198/073500107000000098Search in Google Scholar

Lucas, D. J., and R. L. McDonald. 1990. “Equity Issues and Stock Price Dynamics.” Journal of Finance 45: 1019–1043.10.1111/j.1540-6261.1990.tb02425.xSearch in Google Scholar

Modigliani, F., and M. H. Miller. 1958. “The Cost of Capital, Corporation Finance and the Theory of Investment.” American Economic Review 48: 261–297.Search in Google Scholar

Mullahy, J. 1997. “Instrumental-Variable Estimation of Count Data Models: Applications to Models of Cigarette Smoking Bahavior.” Review of Economics and Statistics 79 (4): 586–593.10.1162/003465397557169Search in Google Scholar

Myers, S. C. 1984. “The Capital Structure Puzzle.” Journal of Finance 39: 574–592.10.1111/j.1540-6261.1984.tb03646.xSearch in Google Scholar

Myers, S. C., and N. S. Majluf. 1984. “Corporate Financing and Investment Decisions when Firms have Information that Investors do not have.” Journal of Financial Economics 13: 187–221.10.1016/0304-405X(84)90023-0Search in Google Scholar

Ospina, R., and S. L. P. Ferrari. 2012. “A General Class of Zero-Or-One Inflated Beta Regression Models.” Computational Statistics and Data Analysis 56 (6): 1609–1623.10.1016/j.csda.2011.10.005Search in Google Scholar

Papke, L. E., and J. M. Wooldridge. 1996. “Econometric Methods for Fractional Response Variables with an Application to 401(k) Plan Participation Rates.” Journal of Applied Econometrics 11 (6): 619–632.10.1002/(SICI)1099-1255(199611)11:6<619::AID-JAE418>3.0.CO;2-1Search in Google Scholar

Papke, L., and J. Wooldridge. 2008. “Panel Data Methods for Fractional Response Variables with an Application to Test Pass Rates.” Journal of Econometrics 145 (1–2): 121–133.10.1016/j.jeconom.2008.05.009Search in Google Scholar

Ramalho, E. A., and J. J. S. Ramalho. 2016. “Moment-Based Estimation of Nonlinear Regression Models with Boundary Outcomes and Endogeneity, with Applications to Nonnegative and Fractional Responses.” Econometric Reviews forthcoming (DOI: 10.1080/07474938.2014.976531).Search in Google Scholar

Ramalho, E. A., J. J. S. Ramalho, and P. D. Henriques. 2010. “Fractional Regression Models for Second Stage DEA Efficiency Analyses.” Journal of Productivity Analysis 34 (3): 239–255.10.1007/s11123-010-0184-0Search in Google Scholar

Ramalho, E. A., J. J. S. Ramalho, and J. M. R. Murteira. 2011. “Alternative Estimating and Testing Empirical Strategies for Fractional Regression Models.” Journal of Economic Surveys 25 (1): 19–68.10.1111/j.1467-6419.2009.00602.xSearch in Google Scholar

Ramalho, J. J. S., and J. V. Silva. 2009. “A Two-Part Fractional Regression Model for the Financial Leverage Decisions of Micro, Small, Medium and Large Firms.” Quantitative Finance 9 (5): 621–636.10.1080/14697680802448777Search in Google Scholar

Ramalho, J. J. S., and J. V. Silva. 2013. “Functional Form Issues in the Regression Analysis of Corporate Capital Structure.” Empirical Economics 44 (2): 799–831.10.1007/s00181-012-0564-6Search in Google Scholar

Santos Silva, J. M. C., and S. Tenreyro. 2006. “The Log of Gravity.” Review of Economics and Statistics 88 (4): 641–658.10.1162/rest.88.4.641Search in Google Scholar

Windmeijer, F. 2000. “Moment Conditions for Fixed Effects Count Data Models with Endogenous Regressors.” Economics Letters 68 (1): 21–24.10.1016/S0165-1765(00)00228-7Search in Google Scholar

Windmeijer, F. 2008. “GMM for Panel Count Data Models.” In The Econometrics of Panel Data, edited by L. Mátyás, and P. Sevestre, 3rd ed. Advanced Studies in Theoretical and Applied Econometrics vol. 46, 603–624. Berlin: Springer.10.1920/wp.cem.2006.2106Search in Google Scholar

Windmeijer, F. A. G., and J. M. C. Santos Silva. 1997. “Endogeneity in Count Data Models: An Application to Demand for Health Care.” Journal of Applied Econometrics 12: 281–294.10.1002/(SICI)1099-1255(199705)12:3<281::AID-JAE436>3.0.CO;2-1Search in Google Scholar

Wooldridge, J. M. 1997. “Multiplicative Panel Data Models without the Strict Exogeneity Assumption.” Econometric Theory 13: 667–678.10.1017/S0266466600006125Search in Google Scholar

Wooldridge, J. M. 2010. “Correlated Random Effects Models with Unbalanced Panels.” mimeo.10.1016/j.jeconom.2018.12.010Search in Google Scholar


Supplemental Material:

The online version of this article (DOI: https://doi.org/10.1515/jem-2015-0019) offers supplementary material, available to authorized users.


Published Online: 2016-9-14

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