Testing the Dynamic Trade-off Theory of Capital. Structure: An Empirical Analysis

Testing the Dynamic Trade-off Theory of Capital Structure: An Empirical Analysis Viet Anh Dang, Minjoo Kim and Yongcheol Shin This version: 15 May 2012 Abstract We employ a new empirical approach based on dynamic threshold partial adjustment models to study the asymmetry in firms adjustment towards their target leverage ratios. We examine several factors proxying for differential costs of adjustment that may lead to the heterogeneity in the speed with which firms adjust their capital structure. Using an unbalanced panel of UK firms, we find that firms having high dividend payments, large investment, high profitability, high growth opportunities, or a large deviation from their target leverage have slower speeds of adjustment than those with the opposite characteristics. We further observe a consistent pattern that firms move towards target leverage quickly when they are over-levered, possibly to avoid the large financial distress associated with having above-target leverage. Taken together, our results provide strong empirical support for the dynamic trade-off theory. JEL Classification: G32. Keywords: Capital Structure, Target Leverage, Dynamic Trade-off Theory, Partial Adjustment Model, Dynamic Panel Threshold Model. We would like to thank seminar participants at Leeds University Business School (Economics and CASIF), Sung Kyun Kwan and Yonsei Universities, and the EFMA 2008 conference, and Richard Baillie, Michael Brennan, Charlie Cai, Yoosoon Chang, Ian Garrett, David Hillier, Kevin Keasy, Joon Park, Krishna Paudyal, Kevin Reilly, Kasbi Salma and Myung Seo for helpful comments and suggestions. Partial financial support from the ESRC (Grant No. RES-000-22- 3161) is gratefully acknowledged. We are responsible for any remaining errors and omissions. Viet Anh Dang, Manchester Business School, Booth Street West, Manchester, M15 6PB,UK. Email: Vietanh.Dang@mbs.ac.uk. Minjoo Kim, University of Glasgow, G12 8QQ, the UK. Email: Minjoo.Kim@glasgow.ac.uk. Yongcheol Shin, University of York, YO10 5DD, the UK. Email: yongcheol.shin@york.ac.uk. 1

1 Introduction Since the irrelevance theorem by Modigliani and Miller (1958), three main views of corporate capital structure have been advanced in which the method of financing matters: the trade-off theory, the pecking order theory and the market-timing hypothesis. The trade-off theory, in both its static and dynamic forms, predicts an optimal capital structure that balances the costs (e.g., financial distress) against the benefits (e.g., debt interest tax shields) of debt financing; see, for example, Kraus and Litzenberger (1973) for a static trade-off model and Strebulaev (2007) for a dynamic model. Under this framework, corporate leverage is predicted to exhibit mean reversion as firms seek to adjust towards their target leverage. The pecking order theory, based on asymmetric information and adverse selection, suggests that firms observed mix of debt and equity simply reflects their cumulative financing decisions over time, whereby internal finance is preferred over external finance and debt is preferred over equity (Myers and Majluf, 1984; Myers, 1984). The market timing hypothesis posits that capital structure decisions are driven by market timing considerations in which firms attempt to time the equity market by issuing shares when market conditions are favourable (Baker and Wurgler, 2002). 1 Both the pecking-order theory and market timing hypothesis do not predict the existence of target leverage and firms adjustment towards such target. Hence, a large body of empirical research has tested the trade-off theory against these alternative views of capital structure by examining whether and how fast firms move towards target leverage; see Frank and Goyal (2007) for a comprehensive survey. Existing studies have so far used a linear partial adjustment model of leverage to estimate the speed of adjustment (hereafter SoA), i.e., the speed with which firms adjust their capital structure towards target leverage. 2 For example, Flannery and Rangan (2006) find that US firms adjust at a rate of more than 30% per year. Examining international data in the G-5 countries, Antoniou et al. (2008) also document reasonably fast adjustment speeds for firms in the US (32%), the UK (32%) and France (39%). Taken together, these empirical studies provide evidence of active target adjustment behaviour as predicted by the trade-off framework. Most recent research has begun to investigate two important issues in the study of the SoA, issues 1 There is a growing literature examining the effect of capital market conditions on corporate capital structure. Welch (2004) observes that stock returns are a first-order and persistent determinant of (market) leverage. However, recent research calls into question the validity of this strand of research, e.g., Leary and Roberts (2005), Kayhan and Titman (2007), Strebulaev (2007), and Lemmon et al. (2008). 2 Alternative approaches include the use of a VAR framework or VAR co-integration techniques for aggregate or industry data (Frank and Goyal, 2004; Tucker and Stoja, 2011). 2

that have not been thoroughly investigated by the aforementioned studies. The first issue is how to obtain a consistent estimate of the SoA in short, dynamic panels with (unobserved) individual firm fixed effects, in which the precision of the SoA estimated is highly sensitive to the econometric methods and procedures used (e.g., Huang and Ritter, 2009; Ilev and Welch, 2010; Flannery and Hankins, 2011; Dang et al., 2011). 3 The second issue is whether there exists asymmetry in target adjustment behaviour such that firms may take different paths towards their target leverage, at potentially heterogeneous rates. The source of this asymmetry is the differences in the costs of adjustment facing firms with different characteristics or at different positions relative to target leverage. Dynamic trade-off models, for example, suggest that firms may have a range of leverage targets and that they only adjust their capital structure when the costs of adjustment can be offset by the benefits of such adjustment (i.e., the benefits of firms being close to or at leverage targets) (Fischer et al., 1989). One implication follows that the magnitude and speed of the adjustment are dependent on how far the actual leverage ratio is from the target ratio. Firms deviating away from target leverage may have an incentive to undertake quick adjustment, especially when they face a fixed adjustment cost. However, if the cost function is proportional rather than fixed, firms with a large deviation from target leverage may have a slower SoA than those with a small deviation (see also Leary and Roberts, 2005). Overall, these arguments clearly suggest that the SoA should be heterogeneous because firms facing higher costs of adjustment are likely to adjust more slowly than those facing lower costs. In this paper, we adopt a new approach to address these important empirical issues regarding the estimation of SoA and asymmetry in capital structure adjustment. Specifically, we employ a dynamic threshold partial adjustment model of leverage to estimate heterogeneous adjustment speeds under different regimes associated with differential adjustment costs. Thus, our approach is capable of testing the validity of the dynamic trade-off theory because it explicitly allows for asymmetric and costly capital structure adjustment. We consider several firm-specific variables that potentially affect the costs of capital structure adjustment, namely profitability, the dividend payout ratio, firm investment, growth options, firm size and deviations from target leverage. Using an unbalanced panel of UK firms over the period 1996-2003, we document strong evidence of asymmetry in target adjustment behaviour in that the 3 It is well-established in the literature that the pooled OLS estimates of the SoA (e.g., Fama and French, 2002) are biased downwards and the fixed effects estimates (e.g., Flannery and Rangan, 2006) are biased upwards, while the GMM (e.g., Ozkan, 2001) and system GMM estimates (e.g., Antoniou et al., 2008) provide the intermediate (unbiased) cases. 3

SoA is heterogeneous for firms facing differential adjustment costs. Specifically, we find that firms facing potentially less financial flexibility and more financial constraints due to having to make large dividend payments and/or investment undertake slower leverage adjustment towards target leverage. On the other hand, firms with high profitability and/or high growth opportunities adjust towards target leverage more slowly than those with the opposite characteristics. Importantly, we find that firms deviating away from their target leverage have a slower adjustment speed than those with a relatively small deviation ratio. This finding is consistent with the above prediction regarding firms facing a proportional adjustment cost function that increases with the magnitude of the deviation. Finally, throughout the empirical analysis, we also reveal a consistent pattern of firms with a fast SoA: these firms tend to be over-levered. This observation suggests that firms with above-target leverage face potentially large financial distress costs and, thus, are forced to revert to the target quickly. Taken together, our main findings are consistent with the dynamic trade-off view of capital structure. Our paper is related to, and improves on, a few recent studies that have started to examine the implications of costly adjustment on dynamic leverage rebalancing. Drobetz and Wanzenried (2006) and Drobetz et al. (2006) investigate the impact of various firm-specific and macroeconomic variables on the SoA, although unlike our paper, these studies does not explicitly account for the asymmetry in capital structure adjustment. More recently, some research has explicitly allowed for the heterogeneity in the SoA, conditional on a number of factors, namely (i) firms specific characteristics proxying for financial constraints or flexibility (e.g., Flannery and Hankins, 2007), (ii) the magnitude of firms deviation from target leverage and/or their financing gaps (e.g., Byoun, 2008) or (iii) firms cash flow realisations (e.g., Faulkender et al., 2012). Unlike our paper, however, these studies adopt a simple approach based on dummy variables or sample splitting using given thresholds (e.g., the medians or quartiles), which involve a degree of arbitrariness and are likely to suffer from a sample selection bias problem (Hansen, 2000). Moreover, in the special case where the sample is split into multiple groups prior to estimating the dynamic partial adjustment model of leverage, the group-specific estimation results may be fundamentally misleading because the time-varying regime switching mechanisms are not allowed within firms by construction. Simply put, these existing studies are unlikely to provide accurate estimates of the heterogeneous adjustment speeds. Consequently, their conclusions regarding target adjustment behaviour must be taken with great caution. We address this crucial drawback by employing a threshold partial adjustment model in which the threshold is estimated within the 4

model rather than being imposed arbitrarily ex ante. Hence, our approach is able to provide consistent estimates of the (heterogeneous) SoA. In addition, by categorising firms into different financing regimes using the threshold estimates, we are able provide important insights into the characteristics of firms that have differential adjustment costs and consequently take asymmetric adjustment paths. Our paper is closely related to a contemporaneous study by Dang et al. (2012), who employ dynamic panel threshold models to examine asymmetric capital structure adjustment in a general setting, under which both the SoA and the long-run relationships between target leverage and its (firm-specific) determining factors can be heterogeneous under different financing regimes. In our study, however, we follow the conventional approach in the literature (Byoun, 2008; Faulkender et al., 2012) and assume homogeneous long-run target relationships. Hence, in line with most theoretical and empirical research in the literature, 4 the focus of our paper is to identify and compare the (heterogeneous) speeds with which firms adjust towards a common long-run target leverage ratio (or a target range more generally), albeit under different regimes. Also note that while Dang et al. (2012) document mixed evidence of heterogeneous SoA and target relationships, the results in the current paper provide stronger evidence of heterogeneity in the SoA. The remainder of our paper proceeds as follows. In Section 2, we review the linear partial adjustment model of leverage and then develop a two-regime threshold model, accounting for asymmetry in capital structure adjustment. Next, we discuss the potential determinants of the SoA to be employed as transition variables under the proposed regime-switching framework. In Section 3, we briefly describe the GMM estimation and testing procedures. In Section 4, we report and discuss the empirical results. In Section 5, we provide some concluding remarks. In Appendices 1 and 2, we derive the GMM estimators and describe the bootstrap-based inference in details. 4 In previous theoretical research, firms are considered to have homogenous target leverage, although the target may vary within a range (Fischer et al., 1989), possibly caused by changes in the determinants of such target rather than by changes in the nature of the relationships with the target. 5

2 Dynamic Capital Structure Adjustment Models 2.1 Linear and Threshold Partial Adjustment Models of Leverage Linear Partial Adjustment Model To test the dynamic trade-off theory s prediction that firms adjust towards target leverage in the longrun, extant empirical research has used the following partial adjustment model of leverage (e.g., Ozkan, 2001; Flannery and Rangan, 2006): d it = λ (d it d it 1 ) + v it, (1) where d it is the actual leverage (debt) ratio while d it is the target leverage ratio. 5 v it is an error component such that v it = µ i +e it where µ i is the (unobserved) firm fixed effects which capture unique industry- and firm-specific characteristics and e it is the well-behaved error term with zero mean and constant variance. λ is the speed of adjustment (SoA), which should vary between 0 and 1 due to the presence of positive adjustment costs. The magnitude of the SoA is the key subject of empirical capital structure studies because it indicates how fast firms move towards their target leverage and thus it sheds light on the question of whether firms follow the trade-off theory s prediction. In the empirical work below, we first estimate this model before focusing on the threshold partial adjustment model. Note that in (1), target leverage is unobserved. However, this target can be proxied by as a function of firm-specific characteristics, as follows: d it = d it + u it = β x it + u it, (2) where x it is a k 1 vector of the (exogenous) determinants, β is a vector of the corresponding coefficients, and u it is the error term with zero mean and constant variance. Based on previous research (e.g., Rajan and Zingales, 1995), we employ the most widely-used determinants of target leverage, namely asset tangibility, non-debt tax shields, profitability, growth opportunities and firm size. Based on (1) and (2), we employ a two-stage procedure typically used in the literature to estimate the SoA (e.g., Shyam-Sunder and Myers, 1999; Fama and French, 2002). First, we regress actual 5 We follow previous research (Strebulaev, 2007) and measure leverage by the market leverage ratio. The main results for book leverage are qualitatively similar and so are not reported in the paper to preserve space. 6

leverage on the determinants in (2) and obtain the fitted values as proxies for target leverage, ˆ d it = ˆβ x it, where ˆβ is the consistent estimate of β. Second, given the (estimated) target leverage, ˆ d it, we estimate the SoA, λ, in (1). Note that an alternative approach is to substitute (2) into (1), thus obtaining the following model that can be estimated in one stage (e.g., Ozkan, 2001; Flannery and Rangan, 2006): d it = φd it 1 + γ x it + v it, (3) where φ = 1 λ and γ = λβ. In one-stage estimation, the SoA and target leverage relationships are estimated jointly such that ˆλ = 1 ˆφ and ˆβ = ˆγ. In estimating the linear, partial adjustment model 1- ˆφ (1), we consider both the one- and two-stage estimation approaches. Dynamic Threshold Partial Adjustment Model Using the linear, partial adjustment model (1) assumes symmetry in firms capital structure adjustment such that the speed with which firms adjust towards target leverage is homogeneous. However, this assumption is not always valid because firms have different degrees of financial constraints or flexibility and thus do not adjust in the same manner. As mentioned, firms only adjust their capital structure when the costs of their adjustment are more than offset by the benefits of being close to target leverage (Fischer et al., 1989). It logically follows that firms with high levels of financial constraints face higher adjustment costs, resulting in potentially slower adjustment. In contrast, firms which enjoy good access to capital markets should have the capability to adjust their capital structure relatively quickly. In addition, firms may take different adjustment paths according to the position of their actual leverage relative to the target leverage. Assuming a fixed adjustment cost function, firms should adjust their capital structure more frequently, at the lower or upper boundaries of the target leverage range. The larger the deviation from the target, the faster the speed of adjustment. However, when firms have a proportional adjustment cost function (Leary and Roberts, 2005), an opposite prediction can be reached. In this case, firms with actual leverage deviating away from the target leverage may find it costly to revert to the target, so that their adjustment is small in magnitude and takes place more slowly. These arguments simply suggest that firms adjustment speed should be different, according to their degrees of financial constraints, or their position relative to target leverage. To account for such asymmetry in capital structure adjustment, we employ the following threshold partial adjustment 7

model, which will form the main part of our analysis: d it = λ 1 (d it d it 1 )1 (qit c) + λ 2 (d it d it 1 )1 (qit >c) + v it, v it = µ i + e it (4) where 1 ( ) is an indicator function used to divide firms into two financing regimes, conditional on the (regime-switching) transition variable, q it, which captures differences in firms adjustment costs (see Section 2.2 for detailed discussions of several candidates). Firms are categorised into the low regime if q it c and into the high regime if q it > c. 6 c is the threshold parameter that will be estimated within the model rather than being imposed ex ante. Model (4) improves on the (linear) partial adjustment model, (1), in a crucial aspect: it explicitly allows for asymmetry in capital structure adjustment, and more specifically, heterogeneity in the SoA for firms in two different financing regimes. Further, our modeling has an important advantage over the typical approach used in recent research to study asymmetric adjustment based on sample-split or dummy variables (e.g., Flannery and Hankins, 2007; Byoun, 2008). While the sample-splitting or dummy variable approach selects regimes in an ad hoc and arbitrary manner ex ante (e.g., the median or quartiles), our model allows the threshold parameter to be estimated within the model (Hansen, 2000). Thus, our approach completely avoids any arbitrariness in choosing threshold values that may lead to nontrivial estimation biases in the SoA and inference complexities in testing for the threshold effects, problems that may affect the conclusions drawn. 2.2 The Regime-switching Variable and Determinants of the Speed of Adjustment Here we discuss several candidates for the (regime-switching) transition variable, q, in the threshold dynamic panel model of leverage, (4). Profitability The impact of profitability on the SoA is ambiguous. First, firms with high profitability tend to be less financially constrained than those with low profitability. The former firms are likely to have 6 It is in theory straightforward to develop threshold models with multiple regimes, although, practically, the larger the number of regimes, the heavier the computational burden. In unreported experiments, we found (statistically) insignificant results in favour of three over two regimes. 8

internal funds, with which they can use to repurchase shares or retire debts appropriately to adjust towards target leverage. In terms of accessing external finance, these firms are also likely to face lower security issuance costs. Further, profitable firms that are under-levered have strong incentive to lever up to enjoy the tax benefit of debt. These arguments together suggest that firms with high profitability should have a faster SoA than those with the opposite characteristic. However, although firms with low profitability may have a higher degree of (both internal and external) financial constraints and higher costs of capital, they may face greater pressure to make capital structure adjustment. The reason is that firms with low profitability tend to have higher leverage as indicated by theory, such as the pecking order (Myers and Majluf, 1984) and dynamic trade-off models (e.g., Strebulaev, 2007), as well as evidence (e.g., Titman and Wessels, 1988; Rajan and Zingales, 1995), thus suggesting they may suffer potentially larger financial distress and bankruptcy costs. The implication follows that firms with low profitability may undertake faster adjustment to reduce the costs of financial distress associated with high leverage. Dividend payout ratio and Firm investment Dividend payments and investments have important effects on the degrees of financial constraints facing the firm. While dividend policies tend to be sticky, capital expenditures are much more fluctuating, but more importantly, both of them tend to be mainly funded by the firm s internally generated cash flow (e.g., Myers, 1984). Hence, dividend and investment decisions affect the firm s capital structure (Lang et al., 1996), as well as its adjustment towards target leverage (Flannery and Hankins, 2007). Specifically, large dividend payments and capital expenditures reduce the retained earnings available for (internal) capital structure adjustment in the form of share repurchases or debt retirements, implying a negative impact of dividends and investment on the SoA. However, an opposite argument can be made. Firms with a high dividend payout ratio is generally classified as financially unconstrained since substantial dividend payments may signal good quality, implying greater access to capital markets (e.g., Fazzari et al., 1988). 7 Similarly, firms with large capital expenditures may require external funds, which may present them with an opportunity to change their capital structure appropriately as the cost of adjustment can be shared with the cost of raising external funds. These 7 Mechanically, a high dividend payout ratio decreases the equity value, leading to a high leverage ratio and potentially high financial distress costs associated, hence more incentive for firms to make quick adjustment. 9

arguments suggest that dividends and investments can also have a positive effect on the SoA. Growth opportunities The effect of growth opportunities on the SoA is ambiguous. Firms having high growth opportunities tend to be young with limited profitability and retained earnings so they must heavily rely on external funds to finance their investments. Frequent visits to the external capital markets mean that the costs of leverage adjustment are relatively smaller because they can be shared with the cost of issuing securities (Faulkender et al., 2012). More importantly, through active external financing activities, high-growth firms can choose an appropriate mix of debt and equity to move towards their target leverage quickly (Drobetz et al., 2006). This argument suggests that growth opportunities and the SoA have a positive relation. However, a counter-argument can be made too. Although high-growth firms visit capital markets frequently, they may prefer equity over debt to avoid underinvestment concerns (Myers, 1977). Therefore, these firms are restricted in how much debt they can adjust, especially when they are under-levered and wish to lever up to move towards their target. Firms with limited growth opportunities, on the other hand, tend to operate in mature industries with large cash holdings and potentially higher profitability. Compared to their high-growth counterparts, low-growth firms face lower costs of capital and thus can undertake faster capital structure adjustment. Moreover, low-growth firms that have large free cash flows tend to adopt a high leverage policy to reduce overinvestment incentives (Jensen, 1986); yet high leverage with potentially high financial distress costs may provide these firms with greater incentive to adjust their capital structure, especially when they are over-levered. Firm size Large firms generally have better access to external capital markets than small firms because they face lower degrees of asymmetric information and agency problems (Drobetz et al., 2006). They also tend to be more mature with higher asset tangibility and profitability and so face lower costs of capital structure adjustment. This therefore suggests that firm size and the SoA be positively related. However, larger firms may use more public debt that is costly to adjust (Flannery and Rangan, 2006). Further, large firms tend to have lower financial distress costs, less cash flow volatility, and fewer debt covenants, implying less incentive and external pressure to undertake capital structure adjustment. 10

The prediction follows that large firms have a slower SoA than small firms. Deviations from target leverage The dynamic trade-off theory suggests that capital structure adjustment does not take place frequently because firms allow leverage to deviate from the target as long as adjustment costs (transactional and contractual costs) outweigh the benefits of reverting to the target (Fischer et al., 1989; Leland, 1994). If adjustment costs are mainly fixed, the larger the deviation from target leverage, the more likely firms will undertake adjustment towards the target. There will be some lower or upper bounds where the benefits of achieving the target leverage outweigh the fixed costs of adjustment. At these restructuring points, capital structure adjustment takes place more quickly, implying a positive relationship between the absolute deviation from the target and the SoA. However, if adjustment costs are an increasing function of the target leverage deviation, i.e., a proportional cost function (Leary and Roberts, 2005), we may reach a conflicting prediction. Firms deviating away from target leverage may find it costly to revert to such target, meaning any adjustment tends to be small in magnitude. Alternatively, when adjustment costs become prohibitively high, firms tend to avoid external adjustment in the form of security issues or repurchases (or retirements), and rely more on internal adjustment, which is limited in scope and magnitude (Drobetz et al., 2006). Further, firms tend to refrain from using all internal funds for adjustment purposes because they wish to preserve their financial flexibility to take future investment opportunities. All these arguments imply a negative relationship between the magnitude of target leverage deviation and the SoA. 3 Methods In this section, we combine three branches of literature, namely (linear) dynamic panel data models (Alvarez and Arellano, 2003), threshold models in nonlinear time series analysis (Chan, 1993; Hansen, 2000) with threshold models in static panels (Hansen, 1999) to develop estimation and testing procedures for the threshold dynamic panel data model, (4). Specifically, we first develop a method to consistently estimate the adjustment speeds and the threshold parameter in (4). Next, we propose a bootstrap-based testing procedure for the threshold effect and the heterogeneity in the SoA. 11

3.1 Estimating the Threshold Partial Adjustment Model As in the linear case described in Subsection 2.1, we now adopt the two-stage procedure to estimate the threshold partial adjustment model, (4). 8 In the first stage, we estimate (2) to obtain the long-run target leverage ˆ d it = ˆβ x it. In the second, we estimate the heterogeneous adjustment speeds, λ 1 and λ 2 corresponding to two regimes, in (4): d it = λ 1 ( ˆ d it d it 1 ) 1(qit c) + λ 2 ( ˆ d it d it 1 ) 1(qit >c) + v it, i = 1,...,N; t = 2,...,T, (5) which can be compactly written as: l it = λ 1 dev 1it (c) + λ 2 dev 2it (c) + v it, v it = µ i + e it (6) where dev 1it (c) = ( ˆ d it d it 1) 1(qit c) and dev 2it (c) = ( ˆ d it d it 1) 1(qit >c) are the deviations from target leverage for firms in the low and high regimes, respectively, and µ i s are unobserved firm fixed effects. In estimating λ 1 and λ 2 in (5), the pooled OLS estimator (hereafter POLS) is biased downwards because the two regressors, dev 1it (c) and dev 1it (c), are correlated with the fixed effects µ i. Even the fixed-effects (hereafter FE) estimator, which wipes out the individual effect, µ i, from the model, is biased upwards for fixed T (Nickell, 1981). To avoid this problem, we consider the first-difference transformation of (6): 2 d it = λ 1 dev 1it (c) + λ 2 dev 2it (c) + e it, i = 1,...,N; t = 3,...,T, (7) which is free of the unobserved fixed effects, α i. However, applying the POLS to this first-difference model still produces biased estimates of the SoA because dev 1it (c) and dev 2it (c) are correlated 8 Here we follow conventional theoretical and empirical research in the literature (Byoun, 2008; Fischer et al., 1989; Faulkender et al., 2012), and assume that the long-run target leverage relationships are homogeneous. Hence, our focus is to compare the (heterogeneous) speeds with which firms adjust toward common long-run target leverage ratios. An alternative way to develop the threshold partial adjustment model of leverage is to substitute (2) into (5) to yield: d it = ( φ 1 d it 1 + γ 1 x it) 1{qit c} + ( φ 2 d it 1 + γ 2 x it) 1{qit c} + v it. We consider this one-stage estimation approach in a related study (see Dang et al., 2012), and allow both the SOA and the long-run target leverage relationships to be heterogeneous under different regimes. Notice, however, that it is much more complex to estimate this model under the assumption of common target leverage, which imposes the following nonlinear restrictions: β 1 = β 2 where β j = γ j φ j, j = 1,2. 12

with e it via the correlation between d i,t 1 (c) with e i,t 1. To address this crucial issue, we follow the literature and consider using instrumental variable (henceforth IV) and GMM estimators. Specifically, we need to find instruments for dev 1it (c) and dev 2it (c) in (7) that satisfy the orthogonal condition with e it. Two obvious candidates are dev 1i,t 1 (c) and dev 2i,t 1 (c), which we consider in the justidentified IV estimator (AH-IV) (Anderson and Hsiao, 1982). Although the AH-IV estimator is consistent, it is potentially inefficient. Hence, we follow Arellano and Bond (1991) and consider deeper lagged values of dev 1i,t 1 (c) and dev 2i,t 1 (c) as instruments for dev 1it (c) and dev 2it (c) in (7). We are then able to construct the matrix of the full GMM instruments, denoted W(c), and derive the one and the two-step GMM estimators, ˆλ s (c), with s = GMM1,GMM2, for given threshold, c. Appendix 1 provides a detailed derivation of these GMM estimators. Next, we estimate the threshold parameter, c, consistently by using a grid search over the support of the transition variable, q it, that minimises a generalised distance measure, such that: ĉ = argminq(c). (8) c C where C is the grid set and Q(c) is the generalised distance measure, given by: Q(c) = ( ) 1 ( ) 1 1 ( ) N W(c) ê(c) N ˆV 1 GMM1 (c) N W(c) ê(c), (9) where ê(c) = 2 d dev(c) ˆλ s (c). W(c) is the matrix of the GMM instruments, and ˆV GMM1 (c) is the estimated covariance matrix in the one-step GMM regression. See Appendix 1 for further definitions and notational details. Note that because the model is linear in λ for each c, our grid search algorithm should produce a consistent estimate of the threshold value, ĉ. For practical reasons such as to avoid the effects of extreme values, our grid set, C, is restricted between the 15th and 85th percentiles of the transition variable. Chan (1993) theoretically shows under the assumption of exogenous transition variables that the threshold estimate, ĉ, is super-consistent, though its asymptotic distribution is complex and depends on nuisance parameters. However, this finding is not useful for inference in practice. Hence, in this paper, we follow Hansen (1999, 2000), and construct the confidence interval for ĉ by forming the non-rejection region using the LR statistic for the null hypothesis, 13

H 0 : c = c 0. 9 Finally, it is important to assess the (potential) impact of dˆ it, the estimated regressor of d it (2), on the GMM estimators of the SoA, λ in (6). It is well-established in the econometric literature that ˆλ, the two-stage estimator of λ, will be asymptotically efficient and no asymptotic efficiency gains are available by switching to a full MLE of (2) and (5) simultaneously, though the least-square estimator of the variance of ˆλ, is potentially inconsistent (e.g., Pagan, 1984). However, for any given threshold parameter, c and for large N, the two-step GMM estimator is consistent and asymptotically normally distributed with the covariance matrices consistently estimated (see Newey, 1984; Hall, 2005, and also Appendix 1). Hence, in our empirical analysis, we adopt the two-step GMM estimator to take advantage of its superior efficiency and robustness. 10 3.2 Testing for Threshold Effects We briefly outline our procedure to test the null hypothesis of no threshold effect in (4) against the alternative hypothesis of threshold effect. Formally, we set the null hypothesis of no threshold effects as: H 0 : Rλ, (10) where R = (1, 1) and λ = (λ 1,λ 2 ). We then consider the following Wald statistic: W (ĉ) = (R ˆλ ( ) (ĉ)) (R Var ˆλ (ĉ) R ) 1 (R ˆλ (ĉ)). (11) where ˆλ (ĉ) is the GMM estimator. It is straightforward to evaluate the Wald statistic for each c using the (asymptotic) variance estimates as described in (19) in Appendix A. However, inference 9 Hansen (1999) shows that an analytic inverse form of the asymptotic distribution of the LR statistic is given by 2log ( 1 1 α ). In this case, the critical values are 6.53, 7.35 and 10.5 for α = 10%, 5% and 1%, respectively. However, we find that the confidence intervals for ĉ, denoted C α, tends to be too narrow that only a small number of grids are selected in finite samples. See also Seo and Linton (2007). To overcome this issue, we will construct the confidence intervals by the following linear interpolation: [ (ĉ ) ] c [ĉinf,ĉ sup = ĉ crit,ĉ + LR ( c ĉ LR ) ] crit where c and c (c < ĉ < c) are two nearest neighborhoods, and LR and LR are the corresponding LR statistics, both of which are greater than the critical value, crit. 10 The AH-IV and GMM estimators and the bootstrap-based procedure are implemented using Stata codes based on xtabond2 (Roodman, 2009). While our framework allows for the SYSGMM estimator, we do not use this method in empirical applications because the validity of the SYSGMM instruments is strongly rejected at the 1% level for all cases considered. This suggests that the over-fitting bias problem is more serious in dynamic panel threshold models. 14

here is nonstandard due to the well-established problem that the (nuisance) threshold parameter, c, is not identified under the null (Davies, 1987; Andrews and Ploberger, 1994, 1996; Hansen, 1996). To overcome this problem, we follow Hansen (1996, 1999) and obtain a valid asymptotic p-value of the statistic using a bootstrap technique, the details of which are presented in Appendix 2. 11 4 Data and Empirical Results 4.1 Data and Sample Selection We collected financial and accounting data for UK firms from the Datastream database for the period 1990-2004 and applied the following standard data restrictions. First, we removed financial firms and utilities because they are subject to different accounting considerations. Second, we removed firms that have fewer than five years of observations so that we can use the GMM estimators that require the use of lagged instruments (Arellano and Bond, 1991). Finally, we also removed observations that have missing data. The final sample comprises 859 companies and 5,393 firm-year observations, over the period 1996-2003. In Tables 1 and 2, we provide the definitions and summary statistics for the variables. Tables 1 and 2 about here 4.2 One- and Two-Stage Regression Results for the Partial Adjustment Model Table 3 reports the regression results for both the (linear) static and the dynamic models of leverage given, respectively, by Equations (2) and (3). 12 The static model is estimated by the POLS and FE estimators. The dynamic, partial adjustment model is estimated by the AH-IV and GMM estimators, 13 both of which seem to produce appropriate regression results (as confirmed by the AR(2) and Sargan test statistics), with the coefficients being significant and having the expected signs. 11 We have also conducted Monte Carlo simulation exercises to investigate the performance of the GMM estimators and inferences in two-stage estimation (allowing for generated regressors). These (unreported) simulation results show that the two-step GMM estimator is reasonably precise, and more importantly, the associated bootstrap-based Wald test has almost negligible size distortion, and sufficiently high power. 12 Throughout the empirical analysis, we include (strictly exogenous) time effects in the dynamic models to control for macroeconomic and global effects (e.g., Ozkan, 2001). 13 Note that the estimators are for the linear case as opposed to the estimators for the more general, non-linear case discussed in Subsection 3.1 above. 15

Table 3 about here The results show that growth opportunities and target leverage are negatively related, which is in line with the underinvestment hypothesis that firms with high growth options avoid using leverage to alleviate the debt overhang problem (Myers, 1977). Next, profitability has a significantly negative effect on target leverage, which is consistent with both the pecking order theory (Myers and Majluf, 1984; Myers, 1984) and the dynamic trade-off model (Strebulaev, 2007), as well as with previous empirical evidence (Titman and Wessels, 1988; Rajan and Zingales, 1995). The relation between tangibility and target leverage is significantly positive, which supports the argument that tangible assets can be used as collateral to avoid the asset substitution problem and reduce the agency costs of debt (e.g., Frank and Goyal, 2007). Non-debt tax shields have a significantly negative effect on target leverage (except in the FE model where a positive effect is found), 14 in line with the hypothesis that non-debt tax shields can substitute for debt tax shields (DeAngelo and Masulis, 1980). Firm size and target leverage are positively related, which is consistent with the prediction that large firms face generally lower bankruptcy, agency and transaction costs than small firms (Frank and Goyal, 2007). Most importantly, we find that the (implied) SoA is estimated at 53% and 60%, respectively, by the AH-IV and GMM estimators, implying that 53-60% of firms deviations from target leverage are closed within a year. These results show that UK firms on average undertake reasonably fast adjustment, which is consistent with previous UK evidence (e.g., Ozkan, 2001) and is in line with the trade-off theory s prediction. 15 As commented above, the difference in the estimates suggests that the magnitude of the SoA is sensitive to the estimator used. To further examine the robustness of the one-stage estimation results, we estimate the partial adjustment model of leverage using the two-stage procedure based on (1) and (2). To derive the estimated target leverage from (2) in the first stage, we employ the FE estimates reported in the column 2 of Table 3. 16 In Table 4, we report the results obtained by using four alternative estimators, including two traditional, yet biased methods for dynamic panels (i.e., POLS and FE) and two advanced and unbiased methods (i.e., AH-IV and GMM). The estimated SoA, given by the coefficient on the 14 The positive effect of non-debt tax shields may be caused by their association with tangibility, which has a strong positive impact on target leverage, particularly when the depreciation of tangible assets is the primary component of nondebt tax shields (Mackie-Mason, 1990). See also Titman and Wessels (1988), Harris and Raviv (1991) and Antoniou et al. (2008). 15 Using the concept of half-lives, these estimates indicate that it takes between 0.76 and 0.91 years for deviations from target leverage to be halved. 16 Using the POLS estimates (Column 1 of Table 3) provides qualitatively similar results. 16

distance between target and lagged leverage, is significantly positive in all models. The POLS and FE estimates of the SoA are 67% and 63%, respectively. 17 Turning to the more reliable estimates provided by the AH-IV and GMM estimators, the SoA is about 44%, again demonstrating that UK firms, on average, adjust at a relatively quick rate, thus consistent with target adjustment behaviour. Overall, our results provide robust evidence for the trade-off theory of capital structure. 18 Table 4 about here The results discussed so far assume that firms adjustment paths towards target leverage are symmetric and undertaken at a homogeneous rate. We now turn to discuss the main empirical results obtained from the proposed dynamic panel threshold model of leverage, (4) using (7). 4.3 Regression Results for the Threshold Partial Adjustment Model In Tables 5-11, we report the regression results for the threshold partial adjustment model, (4) with the (regime-switching) transition variable being profitability, the dividend payout ratio, investment, growth opportunities, firm size, the deviation from target leverage and the deviation ratio (both in absolute values), respectively. Note that all these transition variables are lagged one period to mitigate endogeneity concerns. Panel A of the tables presents the results obtained by using the AH-IV and two-step GMM estimators, respectively for the low and high regimes, where in the low (high) regime, the value of the transition variable is less than (greater than) the estimated threshold value. Note that although both estimation methods are consistent, the two-step GMM estimator is more efficient when the instruments are valid (Arellano and Bond, 1991) and, as shown in the previous section, produces a valid procedure for testing the threshold effect. We report the AR(2) and Sargan test statistics to assess the validity of the instruments used. 19 Panel B of the tables contains the characteristics of firms that are categorised into the low and high regimes. Here we also report the t-tests to ascertain whether these characteristics are statistically different from each other. In what follows, we discuss the results for each (regime-switching) transition variable. 17 This finding is somewhat surprising, considering that the POLS (FE) estimates of the dynamic AR(1) coefficient should be biased upwards (downwards) in our short panels with unobserved individual firm fixed-effects. 18 This statement is still qualitatively valid despite the invalid instruments used by the GMM as indicated by the Sargan test. In this case, it can be argued that the AH-IV estimate is more reliable than the GMM estimate, although in theory we could search for an optimal set of instruments for the GMM, the validity of which cannot be rejected by the data. 19 We find that there is no evidence of second-order serial correlation while the Sargan test does not reject the validity of the GMM instruments at the 1% significance level. 17

Profitability Focusing on the GMM regression reported in Panel A of Table 5, we find that the threshold value of profitability is estimated at 0.1145 so that 67% (33%) of the sample belongs to the low (high) regime. Firms with low profitability adjust towards target leverage significantly more quickly than those with high profitability. Specifically, the SoA of the former firms is 47% while that of the latter firms is 32%; the difference in the SoA is statistically significant as the Wald test for the null of no threshold effects is rejected at 5%. This finding is in conflict with the prediction that highly profitable firms, with available internal funds, potentially high debt tax shields and financial flexibility, are able to adjust their capital structure more easily and quickly (Flannery and Hankins, 2007). It is, however, consistent with the alternative hypothesis that less profitable firms may rely more on debt financing and thus have more incentive to make quick adjustment towards target leverage to avoid financial distress. 20 Table 5 about here Next, we turn to Panel B of Table 5 to investigate the characteristics of firms in different regimes. The t-tests show that these firm-specific characteristics are significantly different between the low and high regimes (with the exception of firm age and net debt issued). In particular, we document that less profitable firms have, on average, limited growth opportunities and capital expenditures (i.e., firm investment) as well as a lower dividend payout ratio than more profitable firms. Importantly, the former firms have above-target leverage with significantly higher leverage and lower cash flow than the latter firms. These characteristics support our argument that less profitable firms with above-target leverage have more incentive to revert to the target in order to alleviate financial distress/bankruptcy costs. Less profitable, over-levered firms also have a significantly larger financing deficit, which is mainly offset by their active equity issues rather than by debt retirements. Dividend payout ratio The results in Table 6 show how the SoA varies with firms dividend payout ratio. Focusing on the statistically more efficient GMM results (as confirmed by both the AR(2) and Sargan tests), we find 20 We also follow Faulkender et al. (2012) and consider cash flow as an alternative transition variable for profitability, and obtain qualitatively similar results. 18

evidence of a threshold effect in which threshold value is estimated at 0.0374 such that 78% of firms are categorised into the low regime. More importantly, the results show that the dividend payout ratio is significantly and negatively associated with the SoA. Firms with a low (high) dividend payout ratio adjust towards target leverage at a rate of 45% (24%) per year; the difference in the SoA (of more than 20%) is both economically and statistically significant (the latter confirmed by the Wald test). This finding supports the prediction that firms with a low dividend payout ratio have a better scope for internal capital structure adjustment, and consequently have a faster SoA. Table 6 about here Firm investment Table 7 presents the regression results for threshold partial adjustment model (4) with firm investment used as the regime-switching variable. In the GMM model, we find evidence of a threshold effect (as indicated by the Wald test) with the threshold value estimated at 0.10 and 71.2% firms categorised into the low regime. Moreover, the results also show that the SoA is significantly higher for firms in the low regime (i.e., those with less investment) than firms in the high regime (i.e., those with more investment). Specifically, the former firms adjust at a rate of 50% while the latter adjust at a much slower rate of 30%. The difference (of 20%) in the SoA is both economically and statistically significant. This finding is clearly in line with the hypothesis that firms with large spending on investment projects funded by retained earnings may have internal financial constraints and thus have difficulty making (internal) capital structure adjustment. Table 7 about here A further analysis of the firm-specific characteristics in Panel B of Tables 6 and 7 suggests that firms classified as having a low dividend payout ratio or less investment, i.e., those belonging to the low regime and adjusting at relatively faster rates, tend to have significantly lower profitability (except in the GMM regression in Table 7) and fewer growth opportunities than those with the opposite characteristics. More importantly, we obtain the same observation as in Panel B of Table 5 in that these firms have significantly large leverage, which explains their strong incentive to revert quickly to the target. As in Table 5, these firms adjustment towards target leverage is mainly driven by net equity issues, rather than by debt retirements. 19

Growth opportunities Table 8 contains the the results for the SoA estimated from the threshold partial adjustment model (4), conditional on growth opportunities. The Wald test suggests a threshold effect is present; the threshold estimate is 1.00 meaning 24% of firms are in the low regime. More importantly, low-growth firms adjust their capital structure significantly more quickly than their high-growth counterparts. In the GMM estimation, the SoA is estimated at 55% and 39% for low- and high-growth firms, respectively; the difference in these estimates is also statistically significant. Next, we observe from Panel B that low-growth firms are typically more mature with significantly lower dividend payments, less investment, more tangible assets and less cash flow than their highgrowth counterparts. Low-growth firms also maintain much higher leverage, which is consistent with the free cash flow hypothesis (Jensen, 1986). Importantly, this finding is line with our earlier observation that firms undertaking quick adjustment tend to be over-levered. The results on external financing activities suggest that low-growth firms (with above-target leverage) adjust their capital structure via both debt retirements and equity issues, which is not in line with the patterns discussed above where adjustment mainly takes the form of equity issues. On the other hand, high-growth firms appear to time the equity market as they make large equity offerings when their market valuations are favourable. However, this behaviour leaves high-growth firms deviate further away from target leverage, i.e., becoming increasingly more under-levered, which may explain why, on average, these firms have a slower SoA. Table 8 about here Firm size The results in Table 9 show how the SoA varies with firm size, another measure of financial constraints. We observe from Panel B that larger firm size is positively associated with the following characteristics: older firm age, higher tangibility, profitability and cash flow. These good quality characteristics may suggest that large firms should have lower transaction and asymmetric information costs, face less severe adverse selection and moral hazard problems, thus implying greater access to external financing. However, we find that, on average, large firms are far less active in the capital markets than small firms as demonstrated by the limited net debt and equity issues. Importantly, the 20