Elsevier

Journal of Banking & Finance

Volume 53, April 2015, Pages 84-98
Journal of Banking & Finance

In search of robust methods for dynamic panel data models in empirical corporate finance

https://doi.org/10.1016/j.jbankfin.2014.12.009Get rights and content

Abstract

We examine which methods are appropriate for estimating dynamic panel data models in empirical corporate finance. Our simulations show that the instrumental variable and GMM estimators are unreliable, and sensitive to the presence of unobserved heterogeneity, residual serial correlation, and changes in control parameters. The bias-corrected fixed-effects estimators, based on an analytical, bootstrap, or indirect inference approach, are found to be the most appropriate and robust methods. These estimators perform reasonably well even in models with fractional dependent variables censored at [0, 1]. We verify these results in two empirical applications, on dynamic capital structure and cash holdings.

Introduction

Many empirical studies in corporate finance use dynamic panel data models to investigate the dynamic behavior of a financial policy of interest. In the corporate payout literature, several studies have examined the degree of dividend smoothing by estimating Lintner’s (1956) partial adjustment model (e.g., Brav et al., 2005, Skinner, 2008, Andres et al., 2009). In the capital structure literature, researchers have used this dynamic model extensively to study how quickly firms adjust toward their long-run target leverage ratios.3 The use of dynamic panels is also common in other areas of corporate finance.4

Despite the growing popularity of dynamic panel data models, they are difficult to estimate due to the likely presence of firm fixed effects and several complexities in empirical corporate finance, such as unobserved heterogeneity and endogeneity, residual serial correlation, and the fractional nature of the dependent variable. To begin with, due to the correlation between the fixed effects and the lagged dependent variable, the pooled OLS (hereafter POLS) estimator is biased and inconsistent. The fixed-effects (hereafter FE) method also estimates these models with a finite-sample bias (Nickell, 1981). Previous simulation results (e.g., Judson and Owen, 1999) suggest that this bias is likely to be substantial for corporate finance studies, which typically analyze annual company data over a relatively short period. The econometrics literature has advanced two main approaches to deal with this bias. The first involves using instruments for the lagged dependent variable, and comprises five methods: the just-identified instrumental variable estimator (hereafter AH-IV) (Anderson and Hsiao, 1981), the first-difference generalized methods of moments estimator (hereafter FD-GMM) (Arellano and Bond, 1991), the system GMM estimator (hereafter SYS-GMM) (Blundell and Bond, 1998), and the long-difference GMM estimator (hereafter LD-GMM or LDP-GMM, depending on long-difference parameters used) (Hahn et al., 2007, Huang and Ritter, 2009). The second approach, consisting of three estimators, corrects for the estimation bias either analytically, or by simulation. Specifically, these estimators either develop bias correction formulas in the (fixed-effects) least-squares dummy variable model (hereafter LSDVC) (Kiviet, 1995, Bruno, 2005), or approximate the bias function and search for unbiased estimates using an iterative bootstrap-based correction procedure (hereafter BC) (Everaert and Pozzi, 2007), or a simulation-based indirect inference method (hereafter II) (e.g., Gouriéroux et al., 2010). Although these advanced methods should, in theory, reduce the POLS and FE bias, little is known about their performance in the presence of the complex issues listed above. In what follows, we briefly discuss the possible sources of those issues and their effects on the IV/GMM and bias-corrected estimators.

First, unobserved heterogeneity and endogeneity, caused by non-zero correlation between the firm fixed effects and a regressor, is a common problem in corporate research (Roberts and Whited, 2011, Wintoki et al., 2012). This problem may affect the performance of the estimators that assume the strict exogeneity of the explanatory variables. The second issue is the likely presence of residual autocorrelation, which violates one of the most important assumptions of the IV/GMM estimators, and renders their instruments invalid (Arellano and Bond, 1991). In empirical corporate research, serial correlation may be caused by the persistence of the financial variable (Lemmon et al., 2008), the presence of measurement errors (Welch, 2011, Roberts and Whited, 2011), or the use of an incorrect functional form (e.g., non-linear versus linear models).5 The third problem concerns the measurement of the dependent financial variable. The financial policy variable under consideration (e.g., leverage or debt maturity) can be a ratio bounded by the unit interval [0, 1]. Since the IV/GMM and bias-corrected approaches listed above were originally developed for continuous, unbounded dependent variables, their properties may be affected if the dependent variable is fractional (Loudermilk, 2007).

In this paper, we examine which of the existing estimators are most appropriate and robust for dynamic panels in empirical corporate finance, especially in the likely presence of unobserved heterogeneity, autocorrelation, and fractional dependent variables. As mentioned above, we consider five IV/GMM estimators, AH-IV, FD-, SYS-, LD-, and LDP-GMM, as well as three bias-corrected estimators, LSDVC, BC, and II. We also examine an augmented doubly-censored Tobit estimator (termed DPF by Elsas and Florysiak (2015)) that accounts for the fractional nature of the dependent variable (Loudermilk, 2007). We conduct Monte Carlo simulation studies and empirical applications in order to examine the performance of these estimators.

Our simulation studies show that the bias-corrected estimators, LSDVC, BC, and II, are generally the most appropriate and robust methods for dynamic panel data models in empirical corporate finance. These estimators estimate the coefficient on the lagged dependent variable (i.e., the autoregressive coefficient) and those on the explanatory variables with the most accuracy and efficiency. Among the three, BC performs well in regressions with residual autocorrelation and in specifications with high lag orders. In a special case where the dependent variable is a ratio, censored at 0 and 1, LSDVC, BC, and II may still provide reasonable estimates with a moderate amount of bias, although, at a high percentage of censoring (e.g., more than 20%), DPF emerges as the most robust method.

Our results further suggest that the IV/GMM estimators are outperformed by the bias-corrected methods. The IV/GMM estimates, especially those for the autoregressive coefficient, tend to be unreliable in most of our simulation experiments. Crucially, these methods are very sensitive to the presence of unobserved heterogeneity and serially correlated errors where their instruments become invalid. There are only a few conditions under which these methods would be useful. For example, SYS-GMM could be used for regressions without unobserved heterogeneity, endogeneity, and autocorrelation. In empirical research, however, these conditions are rather restrictive and unlikely to be met. In short, our paper highlights the potential drawbacks of using the IV/GMM estimators in empirical corporate finance.

We verify our simulation results using two empirical applications to dynamic capital structure and cash holdings. In the first application, the dependent variable, leverage, is a ratio bounded by the unit interval, while, in the second, the dependent variable, cash holdings, is measured by the natural logarithm of the cash-to-net-assets ratio, i.e., a continuous, unbounded variable. In these applications, one of our main objectives is to estimate the speeds with which firms adjust toward their target leverage and cash holdings, respectively. We find that LSDVC, BC, and II produce the most plausible estimates of the speeds of dynamic leverage and cash adjustments, as well as the most reasonable coefficients on the explanatory variables, consistent with prior theoretical predictions. In the leverage application, these bias-corrected methods obtain similar speeds of leverage adjustment, ranging between 24% and 28%. DPF, the only method that explicitly accounts for the fractional nature of leverage, yields a similar estimate of 27%. The estimates obtained using FD-, SYS-, and LD-GMM vary between 15% and 18%, putting them very close to the (biased) POLS estimate; these estimates are unreliable because their fundamental assumptions of instrument validity and no autocorrelation are both violated according to our diagnostic tests. In the cash application, we find similar results regarding the performance of the estimators: LSDVC, BC, and II again produce similar estimates of the speed of cash adjustment, at 48–49%.

Our study is related to previous simulation studies in the econometrics literature (Kiviet, 1995, Judson and Owen, 1999, Bun and Kiviet, 2003, Bruno, 2005, Bun and Carree, 2006, Everaert and Pozzi, 2007). Our simulations maintain the rigor of these studies in terms of properly controlling for two key parameters in dynamic panel data models, namely the magnitude of the fixed effects relative to that of the idiosyncratic error (i.e., the loading factor) and the explanatory power of the regressors relative to that of the disturbances (i.e., the signal-to-noise ratio).6 However, we extend these general simulation studies by considering issues relevant to empirical corporate finance. We use data-generating processes that mimic actual company panel data and, moreover, explicitly allow for unobserved heterogeneity, endogeneity, and residual serial correlation. We also conduct additional simulation experiments to examine the properties of the alternative econometric methods when the dependent financial variable of interest is fractional and bounded by the unit interval. Hence, our findings and conclusions are directly applicable to empirical research in corporate finance.

Finally, our study is related to a recent simulation study by Flannery and Hankins (2013, hereafter FH).7 However, our study differs from, and improves on, their analysis in many important respects. First, our benchmark experiment explicitly controls for the loading factor and the signal-to-noise ratio, two fundamental control parameters in dynamic panel data models (Kiviet, 1995). Under a more rigorous simulation design, we show that the IV/GMM estimators are sensitive to the control parameters and perform less well than in FH’s simulations. Second, while FH only examine a bias-corrected estimator based on an analytical approach (LSDVC), we further consider two recently developed bias correction methods based on iterative sampling algorithms, namely BC and II. Compared to LSDVC, these methods rely on less restrictive assumptions, and are computationally less demanding, especially in the case of BC. We find that both perform well with BC being least affected by autocorrelation. Third, we compare the IV/GMM and bias-corrected estimators with DPF in an important simulation exercise allowing for the fractional nature of the dependent variable (Loudermilk, 2007, Elsas and Florysiak, 2015). Inconsistent with FH’s conjecture, we show the non-negligible effect of severe censoring and the relevance of DPF in this case. Fourth, while FH conclude that LSDVC and SYS-GMM are the most appropriate methods, we observe poor performance from SYS-GMM and the related IV/GMM estimators (especially in the presence of autocorrelation). We, thus, caution against the use of these methods and recommend the more robust bias-corrected estimators. Finally, we are able to corroborate our simulation results using empirical applications to two highly relevant areas of corporate finance, capital structure and cash holdings. In sum, our study provides new simulation and empirical results with general and relevant implications for future empirical corporate research.

The remainder of our paper is organized as follows. In Section 2, we discuss the motivation for using dynamic panel data models in empirical corporate finance and review the existing methods for estimating such models. In Section 3, we conduct Monte Carlo simulation studies in order to examine the properties of these estimators. In Section 4, we conduct two empirical applications, on dynamic capital structure and cash holdings. Section 5 concludes.

Section snippets

Model specifications

Empirical studies in corporate finance often examine the dynamics of financial policy variables through the estimation of dynamic panel data models. In such models, the lagged dependent (financial) variables are included as regressors to capture firms’ adjustments toward their optimal financial policies or the degree of persistence in the policies. In particular, in studies on capital structure, cash holdings, and dividends, many researchers employ a dynamic partial adjustment model to study

Monte Carlo simulation studies

We now perform Monte Carlo simulation studies to investigate the finite-sample performance of the estimators. Our simulation design draws on previous simulations in the panel data literature (Kiviet, 1995, Judson and Owen, 1999, Bun and Kiviet, 2003, Bruno, 2005, Bun and Carree, 2006, Everaert and Pozzi, 2007), with several important extensions catered to corporate finance research. First, unlike those studies, we specify the key simulation parameters based on actual company data. Thus, while

Empirical applications

In this section, we evaluate the performance of the estimators in an empirical application in corporate finance. We examine one of the most interesting, yet contentious, questions in empirical capital structure research, i.e., how quickly firms adjust toward their target leverage ratios. To this end, we estimate the following dynamic model:yit=γyi,t-1+βxi,t-1+ηi+τt+vit,which is similar to the baseline dynamic specification (2). The model further includes year dummies, τt, except in the LD-GMM

Conclusions

Many studies in empirical corporate finance have employed dynamic panel data models to examine the dynamic behavior of corporate financial policy variables. However, a major difficulty in using these models is determining how to obtain consistent and efficient estimates, especially in short panels of company data, in the likely presence of (1) unobserved heterogeneity and endogeneity, (2) residual serial correlation, or (3) fractional dependent variables. Which estimators should researchers use

Acknowledgments

We would like to thank Carol Alexander and Ike Mathur (Editors), an Associate Editor, three anonymous reviewers, seminar participants at University of Glasgow, University of Leeds, Yonsei University, and the Bank of Korea, conference participants at the CFE Conference at University of London, December 2010, the Trans-Atlantic Doctoral Conference at London Business School, April 2011, and the FMA Annual Meeting, Colorado, October 2011, and especially Richard Baillie, Michael Binder, Charlie Cai,

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