Excessive External Borrowing in China: Evidence from a Nonparametric Threshold Regression Model with Fixed Effects

Abstract

We investigated the excessive external financing problem in Chinese industrial firms by examining the potential threshold effect of the leverage ratio on the total factor productivity of firms. We hypothesized the existence of a turning point in leverage ratio at which the productivity of these firms is maximized, and this point may vary by firm ownership type. To test our hypotheses, we proposed a nonparametric panel threshold regression model. From a modeling perspective, our approach contributes to the literature by allowing the threshold variable to be endogenous, accounting for unobserved firm heterogeneities, and imposing no restrictions on the functional form of regression. We employed a two-step estimation procedure, first estimating the threshold using an extreme kernel estimator and then conducting local linear regression based on the estimated threshold. We obtained standard errors via bootstrapping and demonstrated the favorable numerical performance of our estimator through simulation studies. Consistent with our hypotheses, we found that excessive leverage relative to the identified turning point significantly restrains productivity growth. Additionally, the estimated turning point varies by ownership type, particularly in state-owned enterprises (SOEs), where leverage exceeding the threshold negatively impacts productivity. Consequently, regions with a higher concentration of SOEs experience stagnant productivity growth. Our results were statistically supported by nonparametric tests and remained consistent when using leverage growth rate as an alternative measure of external financing.

1. Introduction

There has been a well-established view that financial development spurs economic growth [1]. A well-developed financial market is associated with low external financing constraints, which enhances the productivity of firms by providing external funds at lower costs and greater availability [2,3]. However, in the case of China, the financial market’s development over the past few decades is malfunctioning, resulting in firms with different ownership types facing different degrees of external financing constraints [4,5]. Historically, state-owned enterprises (SOEs) have benefited from strong ties to local governments, as top executives are often government appointees with political connections, such as current or former officials. Consequently, SOEs can access external financing more easily and at lower costs [6,7]. Non-SOEs such as private and foreign firms, however, access external financing with limited availability, higher interest rates, and strictly monitoring by financial intermediaries [6]. Despite the malfunctioning financial markets, non-SOEs have achieved remarkable productivity growth, making the finance–growth nexus in China puzzling. Many studies explain the puzzle by showing that the non-SOEs improve productivity growth mainly through internal financing, such as cash flow [4,5,8].

The limitation of China’s financial markets has induced a set of major reforms in the financial sector, targeting on the improvement of firms’ access to external financing through corporate debt [9]. In recent years, however, the corporate debt of firms has increased significantly, which has made China a debt outlier relative to other economies [10]. By 2016, for instance, corporate debt accounted for 145% of the GDP compared to government debt (40% of GDP) and household debt (40% of GDP), which is a considerably high level by any international measure [11]. In addition, the corporate debt relative to its total assets, or the leverage ratio, has been growing excessively in Chinese industrial firms. As a major indicator of external financing, a higher leverage ratio is strongly indicative of potential growth risks, such as production overcapacity, unsustainable productivity growth, and financial instability [10,11]. Ref. [12] documents that Chinese industries are over-leveraged compared to other developing countries and thus calls for the authority to “deleverage” the economy to mitigate the associated risks.

The surging trend of leverage ratio raises concerns over its impact on firms’ productivity growth. In a perfect financial market, a firm’s investment behavior is independent of its capital structure and financing decisions by the M-M theorem [13]. However, the financial market in China is far from perfect because of its inability to catch up with fast-paced industry reforms and the existence of asymmetric information [14]. As a result, the external financing provision in China’s financial markets becomes relevant to a firm’s productivity growth through influencing its decisions on investment, labor, and innovative activities [14,15]. While the positive effect of internal financing on firms’ productivity growth is well documented in the literature, the role of external financing, or specifically leverage ratio, in Chinese firms’ productivity growth has received relatively less attention. Since the growth of a firm’s productivity has been a primary engine of Chinese economy growth [5], understanding the extent to which the leverage ratio impacts firms’ productivity growth can be profound for achieving China’s sustainable economy growth.

In this paper, we provide (to our best knowledge) the first study in the literature that analyzes the impact of leverage ratio on Chinese firms’ productivity growth. The recent literature suggests that leverage ratio may impact firms’ productivity growth in a non-monotonic fashion. On the one hand, a reasonable level of leverage ratio can lower a firm’s monetary waste and external financial constraints, promoting its productivity growth through facilitating the use of uptake technology in the production function [15]. Firms with moderate leverage ratio can smooth the innovation process more easily to promote productivity growth [16]. On the other hand, an excessive leverage ratio may create the soft budget constraint problem, which induces risk-taking rather than profit-maximizing behaviors of firm managers. As a consequence, funds may be reallocated away from making promising investments, and the decrease in which distorts firms’ productivity [17,18]. Therefore, an optimal level, or a threshold, of leverage ratio may exist at which a firm’s productivity growth is maximized. In regression analysis, it implies that once the leverage ratio surpasses this threshold, its positive effect on productivity would diminish significantly. We expect such a threshold effect of leverage ratio to exist in Chinese industrial firms by proposing our first economic hypothesis (H1) as follows.

H1. 

All else constant, a firm’s productivity growth is maximized at a threshold of leverage ratio, above which the productivity growth declines.

In addition, the presence of malfunctioning financial markets in China implies that the optimal level of leverage ratio may vary with different ownerships of firms. Historically, the SOEs do not have full incentives to improve productivity but to fulfil political objectives [5]. As a result, SOEs can easily borrow loans from state-owned banks to finance productivity-irrelevant investments regardless of their firms’ performance. The resulting soft budget constraint brings about a moral hazard problem, which negatively influences the productivity growth due to inefficient resource allocation and management discretion [19]. In contrast, the hard budget constraint in non-SOEs may effectively discipline their managers through financial pressure to focus more on productivity-enhancement investments, yielding positive returns on their firms’ productivity [20]. Hence, the negative (positive) effect of the moral hazard (discipline) role in leverage ratio may be more dominant in influencing productivity growth in SOEs (non-SOEs). Due to the different nature of budget constraints in different ownerships, we conjecture that the threshold above which the leverage ratio declines a firm’s productivity growth is potentially lower in SOEs than that in non-SOEs. In regression analysis, it implies that the estimated threshold may differ significantly across firms with different ownerships. As a consequence, we propose our second economic hypothesis (H2) as follows.

H2. 

All else constant, the threshold of leverage ratio is heterogeneous across SOEs and non-SOEs due to their different characteristics of budget constraint in the imperfect financial market.

Our two economic hypotheses above are ultimately empirical questions that need to be tested. The closely related study stems from the more recent study [15]. The authors show that a firm’s productivity growth among China’s many industrial firms is affected non-monotonically by financial constraint, proxied by an index based on a firm’s leverage ratio and additional financial indicators. However, a more direct evidence of the hypothesized threshold effect of leverage remains unexplored. We provide empirical evidences of H1 and H2 from a micro-level foundation by employing comprehensive Chinese industrial firm-level data from the years 1998–2007. We further test the hypotheses for firms in regions with different geography and economic development. We follow [21] to use firms’ leverage ratio as a reasonable proxy for external financing, since the corporate debt in China mainly consists of bank loans [22]. We follow [23] to proxy productivity growth by total factor productivity (TFP) growth based on [24], which accounts for possible endogeneity in production inputs.

The potential threshold of leverage ratio in H1 implies its nonlinear effect, which can be evaluated through a standard regression analysis. In this study, we examine the threshold effect through a threshold regression analysis, which greatly facilitates performing inferences on the existence and significance of the threshold level. The parametric threshold regression models by [25,26] have been a popular choice in applied works (see, for instance, [23,27]). The threshold and regression functions are estimated through a least square estimator (LSE), the consistency of which depends upon an exogenous threshold variable and correct regression specifications. However, leverage ratio is often subject to the decision-making process of firms and can therefore be potentially endogenous. Also, the underlying functional form of productivity regression is rarely given or guided by economic theories from the literature. A misspecified empirical model with the endogeneity problem yields biased estimation and misleading conclusions, therefore limiting our ability to render solid policy implication.

We propose a nonparametric panel threshold regression model, which offers two main advantages over the conventional parametric panel threshold models. First, our model estimates the unknown threshold with an endogenous threshold variable and fixed effects. Ref. [28] shows that the threshold estimator by an LSE is inconsistent if the threshold variable is endogenous and dependent with other covariates. A common practice to handle the endogeneity in the literature is to implement instrumental variables [23,29]. However, the LSE of the threshold can still be inconsistent with a direct application of instrumental variable approach [30]. In contrast, our model estimates the threshold consistently through an estimator recently developed by the authors of [31], which allows for the endogeneity in the threshold variable and does not require the use of instrumental variables. Second, our model does not make pre-assumptions on the underlying model structures, such as linearity; rather, the threshold effect is estimated with unknown nonlinearity and interaction in productivity regression, thus significantly alleviating the risk of model misspecification. To deal with the potentially endogenous leverage ratio, we nonparametrically estimate the regression models through a combined use of a profile local linear estimator from [32] and a control function approach from [33].

We find that the leverage ratio significantly increases a firm’s growth in a threshold fashion, where the positive return of a leverage ratio diminishes significantly when the threshold level is surpassed. SOEs exhibit the lowest threshold, above which the TFP growth becomes negative. Private and collective firms as non-SOEs are affected less severely by the leverage ratio above the threshold. Notably, foreign firms on average exhibit a positive return of leverage ratio on TFP growth regardless of whether their leverage ratio is excessive. Compared to regions where non-SOEs dominate, regions where SOEs dominate exhibit a negative trend in TFP growth given the excessive leverage ratio. We demonstrate that our empirical results continue to align with our hypotheses when using leverage growth as an alternative measure of external financing.

Given the important linkage between firm productivity and China’s economic growth, our findings are non-trivial for policy implication on promoting a firm’s productivity growth. Our results shed light on effectively regulating the leverage ratio based on the reference of identified threshold. Our findings also complement the literature on the importance of leverage ratio regulation to reduce any future banking credit risks [34], to prevent financial crisis [35] and to restrain macroeconomic instability [36]. Thus, improving firms’ productivity by effectively controlling the leverage ratio would contribute to lowering the risks associated with China’s economic development and thus achieve sustainable economic growth. As emphasized by He Liu, the Vice-Premier of China, one major task for the Chinese government in the near future is to effectively control the overall leverage ratio [37].

Beyond the scope of our empirical study, our proposed model contributes to the literature by providing a useful framework for threshold effect analysis. For instance, it can examine the threshold effect of market volatility on stock returns, where different volatility regimes might lead to different return patterns [38]. Additionally, the model can explore the threshold effect of foreign direct investment inflows on economic growth, revealing how the impact of FDI varies with a country’s level of development [39]. Moreover, it can investigate the threshold effect of CEO power on firms’ debt financing decisions [40]. Therefore, our model has the potential to enhance the understanding of the threshold effect of different regimes in finance and many other fields.

The remainder of this paper is organized as follows. Section 2 illustrates our empirical methodology with relevant hypothesis tests. Section 3 presents the data description, and Section 4 in turn presents our estimation results and related discussions. Section 5 performs a robustness check on our empirical results, and Section 6 concludes this paper.

2. Empirical Model

2.1. Nonparametric Panel Threshold Regression

We explore the potential threshold effect of firms’ leverage ratio on TFP growth through a threshold regression model. The parametric threshold panel regression with fixed effect from [25] (PTM-FE thereafter) has been commonly employed in the applied literature:

$$\begin{array}{cc}\hfill TFP{G}_{it}& ={\mu }_i+L_{it}{\alpha }_1+X_{it}^{\prime }{\beta }_1+e_{it},\mathrm{if}{L}_{it}\le {\gamma }_0,\hfill \end{array}$$

(1)

$$\begin{array}{cc}\hfill TFP{G}_{it}& ={\mu }_i+L_{it}{\alpha }_2+X_{it}^{\prime }{\beta }_2+e_{it},\mathrm{if}{L}_{it}>{\gamma }_0,\hfill \end{array}$$

(2)

where $i=1,\dots ,n$ refers to a total of n firms, and $t=2,\dots ,T$ indexes $(T-1)$ time periods, due to our dependent variable $TFPG$, as a firm’s TFP growth rate over two consecutive years (i.e., $TFP{G}_{it}=(TF{P}_{it}-TF{P}_{it-1})/TF{P}_{it-1}$). L is our key explanatory variable of a firm’s leverage ratio, and X is a random vector of control variables with dimension $d-1$. The fixed effect ${\mu }_i$ captures unobserved heterogeneities across firms that are potentially correlated with $Z_{it}={[L_{it},X_{it}^{\prime }]}^{\prime }$, i.e., $E\left({\mu }_i\right|Z_{it})\ne 0$. Finally, $e_{it}$ is the additive zero-mean error term that satisfies the exogeneity condition $E\left(e_{it}\right|{\mu }_i,Z_{it})=0$. The model allows for the existence of an unknown threshold value ${\gamma }_0$ in L, which splits the sample into two “regimes” with potentially different marginal impacts of Z, i.e., ${\delta }_1\ne {\delta }_2$, with ${\delta }_j={[{\alpha }_j,{\beta }_j^{\prime }]}^{\prime }$. With T fixed, ref. [25] shows that the unknown parameters ${\gamma }_0$ and ${\delta }_j$ can be consistently estimated as $n\to \infty$ through the LSE, where the fixed effect is eliminated through within-transformation. Clearly, a non-zero threshold ${\gamma }_0$ in (1) and (2) indicates that the partial effects of L on $TFPG$ differ between the two regimes. Our H1 posits that ${\beta }_1$ is significantly larger than ${\beta }_2$, while H2 states that ${\gamma }_0$ is significantly different for SOEs and non-SOEs, both of which require empirical investigation.

Inspired by [31,32], in this paper, we propose a nonparametric threshold panel regression model (NPTM-FE hereafter) as opposed to the PTM-FE for two main reasons. First, the leverage ratio is likely to be endogenous in our study, since firms with different TFP growths may opt for different strategies of setting their leverage ratios (i.e., the reverse causality). The LSE of ${\gamma }_0$ in PTM-FE would be inconsistent if L is endogenous and correlated with X [28]. Second, the conditional mean functions in PTM-FE imposes linear structures a priori in both regimes. While parametric methods possess the advantage of parsimony, the potential disadvantage of model misspecification leads to the inconsistent estimation of threshold models, thus making its nonparametric counterparts alluring. Specifically, our NPTM-FE is modeled as

$$\begin{array}{c}\hfill TFP{G}_{it}={\mu }_i+m_1\left(Z_{it}\right)+e_{it},\mathrm{if}{L}_{it}\le {\gamma }_0,\end{array}$$

(3)

$$\begin{array}{c}\hfill TFP{G}_{it}={\mu }_i+m_2\left(Z_{it}\right)+e_{it},\mathrm{if}{L}_{it}>{\gamma }_0,\end{array}$$

(4)

where $Z_{it}$ now affects $TFPG$ in each regime through an unknown and smooth function $m_j(·):{\mathcal{R}}^d\to \mathcal{R}$ for $j=1,2$. In other words, $m_j(·)$ allows for arbitrary nonlinear and interactive effects in Z to alleviate the model misspecification problem, and therefore nests the linear functional forms in (1) and (2) as a special case, i.e., $m_j\left(Z_{it}\right)=Z_{it}^{\prime }{\delta }_j$. We further allow L to be endogenous, so $E\left(e_{it}\right|{\mu }_i,Z_{it})\ne 0$. Below, we employ a two-step estimation for the unknown threshold ${\gamma }_0$, the function $m_j\left(Z\right)$, and the derivatives $\partial m_j\left(Z\right)/\partial Z^{\prime }\equiv m_j^{\left(1\right)}{\left(Z\right)}^{\prime }$ in regime j. To be consistent with the theoretical arguments in [31,32], we assume that $m_j(·)$ is twice continuously differentiable and consider T to be finite. For ${\gamma }_0$, $m_j(·)$, and $m_j^{\left(1\right)}(·)$ to be identified, we follow [32] to assume ${\sum }_{i=1}^n{\mu }_i=0.$ Similarly to the interpretation in PTM-FE, a non-zero threshold ${\gamma }_0$ in (3) and (4) implies a different partial effect of L on $TFPG$ (i.e., $\partial m_j\left(Z\right)/\partial L$) between the two regimes. H1 posits that the partial effect of L is significantly larger than that when $L>{\gamma }_0$, while H2 once again states that ${\gamma }_0$ varies across different types of firms.

In the first step, we estimate ${\gamma }_0$ with the endogenous threshold variable L and fixed effects ${\mu }_i$. In parametric threshold models, the endogeneity problem is commonly resolved through applying the two-stage least square estimator. We do not follow such conventions to avoid inconsistent model estimation as shown in [30]. Instead, we apply an integrated difference kernel estimator (IDKE) based on [31] to estimate ${\gamma }_0$ consistently without using instrumental variables. Let NPTM-FE in (3) and (4) be expressed compactly as

$$TFP{G}_{it}={\mu }_i+m_1\left(Z_{it}\right)+\Delta m\left(Z_{it}\right)·\mathbb{I}(L_{it}>{\gamma }_0)+e_{it},$$

(5)

where $\Delta m\left(Z_{it}\right)=m_2\left(Z_{it}\right)-m_1\left(Z_{it}\right)$ measures the “jump size” of the regression at ${\gamma }_0$ nonparametrically. Assuming $E\left(e_{it}\right|Z_{it},{\mu }_i)=E\left(e_{it}\right|L_{it})\equiv \varphi \left(L_{it}\right)$ is a smooth function of $L_{it}$, we rewrite (5) alternatively as $TFP{G}_{it}={\mu }_i+m_1^{*}\left(Z_{it}\right)+\Delta m\left(Z_{it}\right)·\mathbb{I}(L_{it}>{\gamma }_0)+e_{it}^{*},$ where $m_1^{*}\left(Z_{it}\right)=m_1\left(Z_{it}\right)+\varphi \left(L_{it}\right)$ and $e_{it}^{*}=e_{it}-\varphi \left(L_{it}\right)$. Define $m(Z_{it};\gamma )\equiv m_1^{*}\left(Z_{it}\right)+\Delta m\left(Z_{it}\right)·\mathbb{I}(L_{it}>\gamma )$; we then have $E\left(TFP{G}_{it}\right|Z_{it},{\mu }_i,\gamma ={\gamma }_0)={\mu }_i+m(Z_{it};{\gamma }_0)$, where $E\left(e_{it}^{*}\right|Z_{it},{\mu }_i)=0$ by construction.

To motivate the identification of ${\gamma }_0$, suppose that the functional form of $m(Z_{it},\gamma )$ is known. We may eliminate the fixed effect ${\mu }_i$ through within-transformation such that $E\left({\widetilde{TFPG}}_{it}\right|Z_{it},\gamma )=\tilde{m}(Z_{it},\gamma )$, where ${\widetilde{TFPG}}_{it}$ is the demeaned $TFPG$. Let us define ${\gamma }_0$ as an extreme estimator from

$${\gamma }_0=\underset{\{\gamma \in \Gamma \}}{argmax}S\left(\gamma \right)=E{\left[E\left(\widetilde{TFPG}\right|Z,L=\gamma -)-E\left(\widetilde{TFPG}\right|Z,L=\gamma +)\right]}^2,$$

where $E\left(\widetilde{TFPG}\right|Z,L=\gamma \pm )={lim}_{\zeta \to \pm 0}E\left(\widetilde{TFPG}\right|Z,L=\gamma +\zeta )$, and $\gamma$ belongs to a bounded set $\Gamma =[\underline{\gamma },\overline{\gamma }]\subset [\underline{\mathit{L}},\overline{L}]$, with $\underline{\mathit{L}}$ and $\overline{L}$ being the lower and upper boundaries in support of L, respectively. Since $E(\widetilde{TFPG}|Z,\gamma )$ is continuous in Z, the discontinuity in the limit takes place only at $\gamma ={\gamma }_0$, which provides the identification information. Furthermore, the “jump” at ${\gamma }_0$ acts as a “local shifter”, enabling the identification of ${\gamma }_0$ in the presence of endogenous Z without the use of instrumental variables. See [31] for its both theoretical and intuitive explanations.

In practice, both of the functional forms of $m(·)$ and ${\gamma }_0$ are unknown. Let $N=n(T-1)$; we estimate ${\gamma }_0$ by a feasible estimator $\widehat{\gamma }$ that maximizes the sample-analogue of $S\left(\gamma \right)$ as

$$\widehat{\gamma }=\underset{\{\gamma \in \Gamma \}}{argmax}{\displaystyle \frac{1}{N}}{S}_N\left(\gamma \right)={\displaystyle \frac{1}{n(T-1)}}\sum _{i=1}^n\sum _{t=2}^T{\left[{\widehat{m}}_{-i}(Z_{it};\gamma -)-{\widehat{m}}_{-i}(Z_{it};\gamma +)\right]}^2,$$

(6)

where

$${\widehat{m}}_{-i}(Z_{it};\gamma \pm )={\displaystyle \frac{{\sum }_{s=1\ne i}^n{\sum }_{t=2}^{T}W\left(K_h^{\pm }(Z_{st},Z_{it})TFP{G}_{st}\right)}{{\sum }_{s=1\ne i}^n{\sum }_{t=2}^{T}W\left(K_h^{\pm }(Z_{st},Z_{it})\right)}}$$

is the (leave-one-out) profile local constant function estimator from [32], which estimates the limiting function $m(·)$ conditioning on $Z_{it}$ and $\gamma \pm$ in the presence of fixed effect ${\mu }_i$ in (5). With a short-hand notation $K_h^{\pm }(Z_{st},Z)\equiv K_{st}^{\pm }$, function $W(·)$ wipes out ${\mu }_i$ such that, for any real values ${\left\{v_{st}\right\}}_{s=1,t=2}^{n,T}$, $W\left(K_{st}^{\pm }{v}_{st}\right)=K_{st}^{\pm }(v_{st}-{\sum }_{\tau =2}^T(d_s{K}_{s\tau }^{\pm }{v}_{s\tau }+{\sum }_{s^{\prime }=1\ne s}^n{d}_{s{s}^{\prime }}{K}_{s^{\prime }\tau }^{\pm }{v}_{s^{\prime }\tau })),$ where $d_s={\left(K_{s.}^{\pm }\right)}^{-1}-{\left(K_{s.}^{\pm }\right)}^{-2}/{\sum }_{s=1}^n{\left(K_{s.}^{\pm }\right)}^{-1}$, $d_{s{s}^{\prime }}={\left(K_{s.}^{\pm }\right)}^{-1}{\left(K_{s^{\prime }.}^{\pm }\right)}^{-1}/{\sum }_{s=1}^n{\left(K_{s.}^{\pm }\right)}^{-1}$, with $K_{s.}^{\pm }={\sum }_{t=2}^n{K}_{st}^{\pm }.$ In the absence of fixed effects, $W(·)$ reduces to an identify function, and ${\widehat{m}}_{-i}(Z_{it};\gamma \pm )$ becomes the pooled local constant estimator in [31], weighted by the density at $Z_{it}$. The kernel function $K_h^{\pm }(Z_{st},Z_{it})={\prod }_{l=1}^d{k}_h(Z_{l,st}-Z_{l,it},Z_{l,it})·k_h^{\pm }(L_{st}-\gamma )$ is a product of d two-sided kernel functions $k_h(·,·)$, multiplied by a one-sided kernel function $k_h^{\pm }\left(u\right)={\displaystyle \frac{1}{h}}{k}_{\pm }\left({\displaystyle \frac{u}{h}}\right)\equiv {\displaystyle \frac{1}{h}}{k}_{\pm }({\displaystyle \frac{u}{h}},0)$, where the two-sided kernel is boundary-corrected as

$$k_h(u,v)=\left\{\begin{array}{cc}{\displaystyle \frac{1}{h}}{k}_{+}({\displaystyle \frac{u}{h}},{\displaystyle \frac{v}{h}}),\hfill & \mathrm{if}\underline{v}\le v<h\left(\mathrm{left}\mathrm{boundary}\right)\hfill \\ {\displaystyle \frac{1}{h}}k\left({\displaystyle \frac{u}{h}}\right),\hfill & \mathrm{if}h\le v<\overline{v}-h\left(\mathrm{interior}\right)\hfill \\ {\displaystyle \frac{1}{h}}{k}_{-}({\displaystyle \frac{u}{h}},{\displaystyle \frac{v}{h}}),\hfill & \mathrm{if}\overline{v}-h\le v\le \overline{v}\left(\mathrm{right}\mathrm{boundary}\right)\hfill \end{array}\right.$$

where $k\left({\displaystyle \frac{u}{h}}\right)$ is the conventional kernel function with $\underline{v}$ and $\overline{v}$ as the lower and upper boundary values v, respectively, and the one-sided kernel function is the rescaled Epanechnikov kernel $k_{-}(\varphi ,r)={\displaystyle \frac{3}{4}}(1-{\varphi }^2)1(-1\le \varphi \le r)/({\displaystyle \frac{1}{2}}+{\displaystyle \frac{3}{4}}r-{\displaystyle \frac{1}{4}}{r}^3)$ for $0\le r\le 1$, and $k_{+}(\varphi ,r)=k_{-}(-\varphi ,r)$ [31]. Clearly, $k_{-}(\varphi ,1)$ reduces to the standard second-order Epanechnikov kernel, so we let $k\left({\displaystyle \frac{u}{h}}\right)=k_{-}({\displaystyle \frac{u}{h}},1)$ in $k_h(u,v)$, as defined above for an interior value of v. With T fixed, we expect that ${\displaystyle \frac{1}{N}}{S}_N\left(\gamma \right)$ in (6) converges in probability to $S\left(\gamma \right)$ as $n\to \infty$ uniformly over $\gamma \in \Gamma$, so $\widehat{\gamma }$ is a n-consistent estimator of ${\gamma }_0$, as shown in Theorem 1 of [31]. Our simulation results provided in Appendix A supports its consistency property in the direction of n.

In the second step, we estimate $m_j(·)$ and $m_j^{\prime }(·)$ in regime j, classified accordingly based on $\widehat{\gamma }$ from (6). In regime j, one could directly estimate $m_j(·)$ and $m_j^{\prime }(·)$ by a conventional nonparametric estimator for the panel model. However, such an estimator is subject to inconsistency due to the potential endogeneity in L. Instead, we apply a two-stage local polynomial panel estimator similar to [33], which can be regarded as a nonparametric analogue of a two-stage least square estimation in parametric panel regression. For notation brevity, we drop the subscript j in $m_j\left(Z_{it}\right)$ below. In each regime, we have $TFP{G}_{it}={\mu }_i+m\left(Z_{it}\right)+e_{it},$ where $E\left(e_{it}\right|{\mu }_i,Z_{it})\ne 0$. Let

$$L_{it}=g(X_{it},Q_{it})+u_{it},$$

(7)

where $Q_{it}$ contains relevant and valid instrumental variables and $E\left(u_{it}\right|X_{it},Q_{it})=0$. We choose the one-year lag of leverage ratio (i.e., $L_{i,t-1}$) as a common choice of the instrument variable in the literature (see, for example, [23]). Following [33], we assume $E\left(e_{it}\right|{\alpha }_i,Z_{it},Q_{it},u_{it})=E\left(e_{it}\right|u_{it})\equiv \theta \left(u_{it}\right)$ as a smooth and unknown function of $u_{it}$. By the law of iterative expectation, $E\left(TFP{G}_{it}\right|{\mu }_i,L_{it},X_{it},u_{it})={\mu }_i+M(Z_{it},u_{it})$, where $M(Z_{it},u_{it})=m\left(Z_{it}\right)+\theta \left(u_{it}\right)$ is an additive model. We construct the nonparametric panel regression $TFP{G}_{it}={\mu }_i+M(Z_{it},u_{it})+{\tilde{e}}_{it},$ where ${\tilde{e}}_{it}=e_{it}-\theta \left(u_{it}\right)$ satisfies $E\left({\tilde{e}}_{it}\right|{\mu }_i,Z_{it},u_{it})=0$. The additivity structure in $M(·)$ requires $E\left(e\right)=0$ to identify our interested function $m\left(Z\right)$ and derivatives $m^{\left(1\right)}\left(Z\right)$, both of which can be estimated consistently via the following two stages.

In the first stage, we estimate $g(X,Q)$ in (7) by the pooled local quadratic function estimator $\widehat{g}(X,Q)$, and obtain the residual ${\widehat{u}}_{it}=L_{it}-\widehat{g}(X_{it},Q_{it})$. In the second stage, we estimate $m\left(Z\right)$ by $\widehat{m}\left(Z\right)$ through marginal integration as

$$\widehat{m}\left(Z\right)={\displaystyle \frac{1}{n(T-1)}}\sum _{i=1}^n\sum _{t=2}^T\widehat{M}(Z,{\widehat{u}}_{it}),$$

(8)

where $\widehat{M}(Z,{\widehat{u}}_{it})$ is the profile local linear function estimator from [32]. In a similar fashion, we follow [41] to obtain each derivative ${\widehat{m}}_l^{\left(1\right)}\left(Z\right)\equiv \partial m\left(Z\right)/\partial Z_l$, $l=1,\dots ,d$, by replacing the function estimate $\widehat{M}(Z,{\widehat{u}}_{it})$ in (8) with ${\widehat{M}}_l^{\left(1\right)}(Z,{\widehat{u}}_{it})$ as

$${\widehat{m}}_l^{\left(1\right)}\left(Z\right)={\displaystyle \frac{1}{n(T-1)}}\sum _{i=1}^n\sum _{t=2}^T{\widehat{M}}_l^{\left(1\right)}(Z,{\widehat{u}}_{it}),$$

(9)

where $M_l^{\left(1\right)}(Z,{\widehat{u}}_{it})$ is the profile local linear derivative estimator with respect to $Z_l$ from [32]. We purposely choose a local quadratic estimator in stage 1 and a local linear estimator in stage 2 to impose assumption A5 in [33], which governs the order of bandwidths in the two stages for estimation consistency. We note that both the estimated function and partial effects of $Z_l$ in each regime are observation-specific as opposed to constant partial effects in the parametric counterpart in (1) and (2), thus allowing the heterogeneous marginal impact of variables to be modeled. (Our proposed estimators in (6) and (8) are programmed by the authors in R).

2.2. Parametric Panel Threshold Regression

To be consistent with the literature, we also implement a parametric threshold panel regression model similar to [25], except with modifications for the endogenous L as in Section 2.1. Model PTM-FE in (1) and (2) can be expressed as the parametric counterpart of NPTM-FE:

$$TFP{G}_{it}={\mu }_i+Z_{it}{\left({\gamma }_0\right)}^{\prime }\delta +e_{it},$$

(10)

where $Z_{it}\left({\gamma }_0\right)=[Z_{it}^{\prime },Z_{it}^{\prime }·\mathbb{I}(L_{it}>{\gamma }_0)]$, $\delta ={[{\delta }_1^{\prime },\Delta {\delta }^{\prime }]}^{\prime }$, and $\Delta \delta ={\delta }_2-{\delta }_1$. In other words, the conditional mean function $E(\widetilde{TFPG}|Z,L=\gamma )$ is discontinuous at $\gamma ={\gamma }_0$, except with a “jump” size now evaluated parametrically through $Z_{it}^{\prime }\Delta \delta$. We estimate ${\gamma }_0$ in (10) again by $\widehat{\gamma }$ in (6) to handle fixed effects and endogenous L, since the function $m(Z_{it};\gamma )=m_1^{*}\left(Z_{it}\right)+Z_{it}^{\prime }\Delta \delta ·\mathbb{I}(L_{it}>\gamma )$ still needs to be estimated nonparametrically as $m_1^{*}\left(Z_{it}\right)=Z_{it}^{\prime }{\delta }_1+\varphi \left(L_{it}\right)$. With the updated observations ${\left\{Z_{it}\left(\widehat{\gamma }\right)\right\}}_{i=1,t=2}^{n,T}$, we estimate $\delta$ in (10) by the standard two-stage least square estimator $\widehat{\delta }$, except $g(·)$ in (7) is now parameterized and fixed effect ${\mu }_i$ is eliminated through within-transformation. We follow [25] to perform the inference of $\widehat{\gamma }$ and ${\widehat{\delta }}_j$ through the bootstrap method.

2.3. Hypothesis Testing

In this section, we outline two testing procedures relevant to our empirical results. Regarding the NPTM-FE, we are interested in accessing whether the unknown functional form of $m_j(·)$ in NPTM-FE can be sufficiently captured by certain parametric specifications. We denote the nonparametric conditional mean function in (5) alternatively as $m_{np}(Z;{\gamma }_0)=m_1\left(Z\right)+\Delta m\left(Z\right)·\mathbb{I}(L>{\gamma }_0)$, and the parametric counterpart in (10) as $m_{para}(Z;{\gamma }_0,\delta )=Z{\left({\gamma }_0\right)}^{\prime }\delta$. We test for the correct parametric specification by considering the null hypothesis $H_0:Pr(m_{np}(Z;{\gamma }_0)=m_{para}(Z;{\gamma }_0,\delta ))=1$ for almost all $Z\in {\mathcal{R}}^d$ and some $({\gamma }_0,\delta )$ from a compact subset of ${\mathcal{R}}^{d+1}$.

Inspired by [42], we test $H_0$ through the test statistic $I_n={\int }_{{\mathcal{R}}^d}[m_{np}(Z;{\gamma }_0)-$$m_{para}(Z;{\gamma }_0,\delta ){]}^{2}dZ,$ which converges to zero if and only if $H_0$ is true. Our setup differs from theirs in terms of the threshold structure. With finite T and faster convergence rates of the parametric estimators $\widehat{\gamma }$ and $\widehat{\delta }$, we replace $({\gamma }_0,\delta )$ with $(\widehat{\gamma },\widehat{\delta })$ in $I_n$ above to form $I_n={\int }_{{\mathcal{R}}^d}{[{\widehat{m}}_{np}(Z;\widehat{\gamma })-{\widehat{m}}_{para}(Z;\widehat{\gamma },\widehat{\delta })]}^{2}dZ$, where ${\widehat{m}}_{np}(Z;\widehat{\gamma })$ is obtained by (8) and ${\widehat{m}}_{para}(Z;\widehat{\gamma },\widehat{\delta })$ is the kernel-smoothed version of the parametric function estimate, both of which are discussed thoroughly in [42]. Define the residual ${\widehat{ϵ}}_{it}=TFP{G}_{it}-{\widehat{m}}_{para}(Z_{it};\widehat{\gamma },\widehat{\delta })$, and its within-transformed version as ${\widetilde{ϵ}}_{it}={\widehat{ϵ}}_{it}-{\displaystyle \frac{1}{T-1}}{\sum }_{t=2}^T{\widehat{ϵ}}_{it}$. We employ a centered feasible test statistic as

$${\widehat{T}}_n={\displaystyle \frac{n\sqrt{h^d}{\widehat{I}}_n}{{\widehat{\sigma }}_n}},$$

(11)

where ${\widehat{I}}_n={\displaystyle \frac{1}{n^2{h}^d}}{\sum }_{i=1}^n{\sum }_{s=1\ne i}^n{\sum }_{t=2}^T{\sum }_{\tau =2\ne t}^T{K}_h(Z_{it},Z_{s\tau }){\widetilde{ϵ}}_{it}{\widetilde{ϵ}}_{s\tau },$${\widehat{\sigma }}_n={\displaystyle \frac{2}{n^2{h}^d}}{\sum }_{i=1}^n{\sum }_{s=1\ne i}^n{\sum }_{t=2}^T$${\sum }_{\tau =2\ne t}^T{K}_h^2(Z_{it},Z_{s\tau }){\widetilde{ϵ}}_{it}^2{\widetilde{ϵ}}_{s\tau }^2,$ and $K_h(Z_{it},Z_{s\tau })={\prod }_{l=1}^{d}k((Z_{l,it}-Z_{l,s\tau })/h)$ is a product kernel function, with $k\left(v\right)$ as the univariate Gaussian kernel. Under similar conditions in [42], we expect that ${\widehat{T}}_n\stackrel{d}{\to }\mathcal{N}(0,1).$ We detail the bootstrap procedure of the test ${\widehat{T}}_n$ in Appendix B.

Regarding the PTM-FE, we follow [25] to evaluate the existence of ${\gamma }_0$ by testing the null hypothesis $Pr({\delta }_1={\delta }_2)=1$ for all ${\gamma }_0\in \Gamma$ with the feasible test statistic:

$${\widehat{J}}_n={\displaystyle \frac{SSW{R}_0-SSW{R}_1}{SSW{R}_1}}$$

(12)

where $SSW{R}_0$ ($SSW{R}_1$) denotes the sum of squared within-transformed residuals ${\tilde{e}}_{it}$ in (10) without (with) the threshold structure. Clearly, ${\widehat{T}}_n$ converges to zero if and only if the null is true. We follow [25] to implement a bootstrap version of the test to improve its empirical power.

3. Data

We obtain our data from the Chinese Annual Surveys of Industrial Production (ASIP), covering the period from 1998 to 2007. The ASIP provides firm-level data for all state-owned and non-state-owned enterprises with annual sales of at least RMB five million. (The rapid growth in the industrial sector during 1998–2007 made it relatively rare for firms to have sales below the RMB five million criterion. As noted by [43], this sales threshold likely had minimal impact on sample selection.) The National Bureau of Statistics of China (NBSC) oversees the ASIP dataset, ensuring consistency in data collection across regions and industries, as well as auditing selected companies to monitor data accuracy [44]. Under the strict supervision of the NBSC, firms have little incentive to misreport information in the ASIP, as this information is not shared with other local government agencies. Consequently, the ASIP provides reliable statistical measures due to its standardized computation methods and minimal issues related to data-recording errors or misreporting [45]. This dataset has been widely employed in many seminal works on China’s economy [8,46,47,48]. The ASIP covers enterprises across 31 provinces and municipalities (including Beijing, Shanghai, Tianjin, and Chongqing), accounting for over 90% of China’s gross industrial output. For a list of the 2-digit Chinese Industrial Classification Codes (CICCs) and corresponding industry names, see Appendix C.

As mentioned in hypothesis H2, we are interested in whether the potential threshold effect of the leverage ratio varies with a firm’s ownership. The ASIP contains different types of paid-in capital, including state, collective, legal person, private, Hongkong, Macau and Taiwan, and foreign firms. Following [4,5], we classify state-owned enterprises (SOEs) and collective enterprises, respectively, as firms with more than 50% of the firm’s paid-in capital owned by the state and by urban or rural communities; private enterprises are firms with more than 50% paid-in capital owned by private persons and legal persons; and foreign firms are ones with more than 50% of paid-in capital from Hongkong, Macau and Taiwan, or foreign countries. We further account for regional heterogeneity, since the substantial differences in geography, natural resources, and local development polices across regions in China may ultimately impact a firm’s investment decision as well as a firm’s productivity growth [49,50]. We classify geographic regions into eastern, northeastern, central, and western areas. The eastern area has eight provinces located near or along coastlines, which have been the most developed regions of the economy since the outset of the economic reforms. The northeastern regions contain three provinces in which most of the nation’s old SOEs have started up. The central region with eight provinces is known to lead primarily in the development of heavy industries due to its rich endowment of metal and non-metal resources. Finally, the western area with 12 provinces exhibits the slowest economic growth due to limited transportation and complex terrain. See Appendix D for the specific province names in each region.

Our dependent variable TFPG is the growth rate (i.e., annual percentage change) of firms’ TFP. Variables used in TFP calculation include output (Y) as a firm’s real gross industrial product; capital (K) as real total fixed capital, including book value of tangible fixed assets such as land and building, fixtures and fittings, and plant and vehicles; labor (L) as the sum of real wages and benefits; and material (M) as the real intermediate material in production process. Following [24], the TFP is measured by the productivity parameter $\omega$ from a (logged) Cobb–Douglas production function $Y_{it}={\beta }_0+L_{it}{\beta }_L+K_{it}{\beta }_K+M_{it}{\beta }_M+{\omega }_{it}+{ϵ}_{it}$, where $\omega$ is a state variable impacting the firm’s decision rules and $ϵ$ is an idiosyncratic error representing unexpected shocks. We estimate the TFP via a consistent semiparametric estimator ${\widehat{\omega }}_{it}$ in [24].

Our key independent variable L is the leverage ratio, defined as a firm’s total debt divided by its real total assets. Total debt includes current liabilities, such as bank loans (which constitute the majority), accounts payable, and other current liabilities. Real total assets comprise the sum of a firm’s real fixed and current assets. Fixed assets include tangible fixed assets, intangible fixed assets, and other fixed assets, while current assets encompass inventories, accounts receivable, and other current assets. Both total debt and total assets for each firm are obtained directly from the ASIP dataset.

According to the literature on a firm’s productivity growth [4,23], we specify the vector X to include the control variables of the CF ratio, defined as a firm’s real cash flow divided by real total assets; Age, the difference between a firm’s observation year and establishment year; Size, a firm’s real total asset; and Export, defined as the total export divided by total outputs (i.e., the export intensity). We considered the natural log for Age and Size in our empirical analysis, and computed all real variables using ex-factory producer price indexes from various issues of Chinese statistical yearbooks [5]. To mitigate the impact of a firm’s entry and exit in our analysis, we created a balanced panel of data from 8319 incumbent industrial firms that operated during 1998–2007, resulting in 83,190 observations in total.

Table 1. Descriptive data summary.

Variable		Whole-Sample	SOEs	Private	Foreign	Collective	Eastern	Western	North-Eastern	Central
TFP growth rate (TFPG)	25%	−0.200	−0.184	−0.183	−0.211	−0.196	−0.203	−0.205	−0.237	−0.167
	50%	0.066	0.054	0.078	0.062	0.073	0.062	0.062	0.059	0.096
	75%	0.432	0.386	0.432	0.452	0.438	0.423	0.452	0.490	0.468
	mean	0.262	0.253	0.259	0.279	0.257	0.251	0.280	0.315	0.299
Leverage ratio (L)	25%	0.348	0.379	0.428	0.278	0.407	0.366	0.348	0.305	0.348
	50%	0.530	0.558	0.601	0.462	0.584	0.546	0.540	0.506	0.547
	75%	0.693	0.725	0.749	0.631	0.740	0.710	0.703	0.701	0.716
	mean	0.516	0.548	0.579	0.458	0.563	0.532	0.523	0.502	0.528
Cash flow ratio (CF ratio)	25%	0.031	0.015	0.032	0.042	0.032	0.032	0.022	0.021	0.029
	50%	0.063	0.038	0.063	0.084	0.068	0.065	0.046	0.053	0.067
	75%	0.119	0.070	0.118	0.144	0.137	0.119	0.087	0.104	0.160
	mean	0.098	0.050	0.106	0.104	0.122	0.095	0.067	0.077	0.140
Firms’ age (Age)	25%	8.0	15.0	7.0	7.0	9.0	7.0	8.0	8.0	8.0
	50%	11.0	30.0	11.0	9.0	13.0	11.0	13.0	12.0	14.0
	75%	18.0	43.0	17.0	12.0	21.0	16.0	29.0	19.0	30.0
	mean	15.6	29.8	14.7	9.9	16.7	14.4	19.4	17.0	19.4
Real total asset (Size)	25%	46.2	76.1	35.3	70.8	32.6	45.2	64.0	52.9	32.0
	50%	107.8	200.9	77.4	175.2	63.9	101.2	152.6	127.1	85.2
	75%	302.8	587.7	205.0	500.0	134.8	275.0	410.0	394.6	263.2
	mean	694.2	1734.5	504.2	780.6	232.0	535.7	780.7	1171.3	1023.9
Export intensity (Export)	25%	0.000	0.000	0.000	0.005	0.000	0.000	0.000	0.000	0.000
	50%	0.000	0.000	0.000	0.574	0.000	0.013	0.000	0.000	0.000
	75%	0.709	0.000	0.319	0.950	0.000	0.794	0.396	0.820	0.000
	mean	0.299	0.046	0.219	0.515	0.129	0.335	0.246	0.334	0.081
Observations		74,871	12,251	30,626	16,924	10,672	53,232	8640	4771	8151

Note: The table reports 25th, 50th, 75th percentile and the sample mean of each variable. TFP growth rate was calculated by [24]; L is a firm’s total liabilities divided by real total assets; CF ratio is a firm’s cash flow divided by real total asset; Age is the difference between a firm’s observation year and establishing year; Size is a firm’s real total assets, or total assets deflated by price deflators from NBSC; and Export is total export divided by total output. Source: ASIP dataset 1998–2007.

provides descriptive statistics for the whole sample, as well as samples classified by ownerships and regions. In the whole sample, the TFP growth rate has an average of 0.262 consistent with the findings in [51]. The mean of leverage ratio is 0.516 in Chinese industrial firms, a fairly high level compared to 0.42 in Central and Eastern European countries [23]. Data across ownerships reveal an average of 0.262 in $TFPG$, with foreign firms having the highest mean of 0.280. SOEs, however, exhibit the lowest mean of TFPG of 0.253, which can be attributed to the divergence of SOEs’ managers’ interests away from improving firms’ productivity due to the nature of state ownership as well as the soft budget constraint [4,15,19]. This finding also complements with that of [52], showing that firms with soft budget constraints in transition economies can be motivated to undertake inefficient activities rather than productivity-enhancing investments. In addition, SOEs on average have considerably lower CF ratio and Export but larger Size and Age compared to other ownerships, consistent with empirical findings in [4,51].

Table 2. Cumulative distribution of leverage ratio (L) among different samples.

Percentile	10%	25%	50%	75%	90%
Whole sample	0.187	0.348	0.530	0.693	0.817
Ownership
SOEs	0.227	0.379	0.558	0.725	0.849
Private	0.262	0.428	0.601	0.749	0.859
Foreign	0.140	0.278	0.462	0.631	0.765
Collective	0.233	0.407	0.584	0.740	0.856
Regions
Eastern	0.203	0.366	0.546	0.710	0.834
Western	0.183	0.348	0.540	0.703	0.833
Northeastern	0.146	0.305	0.506	0.701	0.849
Central	0.172	0.348	0.547	0.716	0.841

provides the cumulative distribution of L in each sample. The relatively higher leverage ratio in SOEs is likely due to their easier access to external funds in the financial market at fairly low interest rates compared with a competitive market [44,53]. On the other hand, foreign firms have a consistently lower leverage ratio than other ownerships at all percentiles. Given their higher average cash flow ratio of 0.104, the result corroborates [5], showing that foreign firms facing higher cost for external financing have an incentive to resort to finance through their own retailed earnings.

Data across regions reveal that the lowest and highest averages of productivity growth rate are found in eastern and northeastern regions, respectively. This observation may seem to be counter-intuitive since the northeastern area was initially targeted as the nation’s “industrial base”, containing many “heavy” industries and SOEs with a stagnant productivity growth. However, SOEs in the northeastern region have undergone a series of reforms since the early 1990s, and many relevant policies have been established to attract high-tech industries, such as electronic manufacturing [54]. In addition, ref. [55] shows that the northeastern region is relatively more marketized, which enhances local entrepreneurship that facilitates productivity improvement. Finally, the eastern region has the highest mean of leverage ratio (0.532), followed by the central region (0.528), western region (0.523), and northeastern region (0.502).

4. Empirical Results

4.1. Whole Sample

We first investigate our first hypothesis H1 regarding the significance of leverage threshold ${\gamma }_0$. Prior to the estimation, Panel A of

Table 3. Nonparametric test results for correct parametric specification.

		${\widehat{\mathit{T}}}_{\mathit{n}}$	p-Value
Panel A	Whole sample	6.1253	0.0000
Panel B	Ownerships
	SOEs	0.7782	0.7800
	Private	4.4231	0.0050
	Foreign	0.5647	0.9950
	Collective	1.8998	0.0950
Panel C	Regions
	Eastern	4.1230	0.0000
	Western	2.3102	0.0200
	Northeastern	1.4125	0.1500
	Central	2.3546	0.0475

Note: The test statistic ${\widehat{T}}_n$ is defined in (11), with the null hypothesis that the parametric functional form of $m_{para}(Z;{\gamma }_0,\delta )$ in (10) is correctly specified against the nonparametric alternative $m_{np}(Z;{\gamma }_0)$ defined in Section 2.3. The reported p-values are obtained with 399 bootstrap repetitions.

reports the bootstrapped p-values of ${\widehat{T}}_n$ in (11) with 399 repetitions. We reject the null hypothesis that PTM-FE in (10) is correctly specified at a 1% level, suggesting that our proposed NPTM-FE model is better suited for examining the leverage–productivity nexus.

Table 4. Regression results of NPTM-FE for the whole sample and selected ownerships.

	Whole		Private		Collective
	$\widehat{\gamma }={0.5024}^{***}$		$\widehat{\gamma }={0.5085}^{***}$		$\widehat{\gamma }={0.5154}^{***}$
	$[0.4765,0.5283]$		$[0.4817,0.5361]$		$[0.4686,0.5630]$
Variable	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2
Leverage ratio	0.3610 ***	0.0810	0.2699 **	0.1284 **	0.2198**	0.1057
	(0.0670)	(0.0577)	(0.0693)	(0.0592)	(0.0933)	(0.0810)
ln(Age)	−0.0715 **	0.045 *	−0.0050	−0.0003	0.0665	−0.0323
	(0.0309)	(0.0231)	(0.0498)	(0.0191)	(0.0672)	(0.0252)
Export	0.3046 ***	0.1708 ***	0.7233 ***	−0.0873 **	−0.4513 ***	0.2591 ***
	(0.0521)	(0.0390)	(0.0900)	(0.0354)	(0.1121)	(0.0683)
CF ratio	0.3231 **	1.0461 ***	0.0207	0.3400 ***	0.4231 ***	2.5366 ***
	(0.1301)	(0.1011)	(0.2030)	(0.0684)	(0.1677)	(0.1020)
ln(Size)	0.0171	0.0236 **	0.0399	0.0316 ***	0.0135	−0.0060
	(0.0156)	(0.0114)	(0.0255)	(0.0107)	(0.0308)	(0.0183)
Observations	35,406	39,465	10,936	19,690	4128	6544

Note: The estimated threshold effect of the leverage ratio ($\widehat{\gamma }$) and its corresponding 95% confidence interval based on the bootstrapped standard error of $\widehat{\gamma }$, in brackets, are reported beneath each sample’s name. Regimes 1 and 2 report the median of estimated derivatives of each variable from $m_1(·)$ and $m_2(·)$, respectively, holding all other variables at median. The asymptotic standard errors are in parentheses beneath the estimated derivatives. *** p < 0.01, ** p < 0.05, and * p < 0.1.

reports the estimation results for the whole sample. The estimated threshold value $\widehat{\gamma }$ is 0.5024, fairly close to its median of 0.530. Thus, more than half of the observations in leverage ratio exceed its estimated threshold.

We proceed to split the sample based on $\widehat{\gamma }$ and estimate the derivatives $m^{\prime }\left(Z\right)$ by the estimator in (9). The complexity of the multivariate function $m_j(·)$ makes their estimation results difficult to present. We follow conventional practices in the literature to present our results by highlighting the difference in leverage effect between the two regimes. To disclose the partial effect of each variables in Z by holding all else constant, Table 4 reports the 50th quantile of the estimated derivatives of each variable with their asymptotic standard errors in parentheses, holding all other variables at median level. All else constant, we observe that a one percentage point increase in a firm’s leverage ratio significantly rises its $TFPG$ by a percentage point of 0.361 before the threshold level, but decreases by almost half to 0.081 afterwards.

The results seem to suggest a threshold effect of leverage ratio as hypothesized in H1; however, the interpretation can be spurious if the leverage effect varies with the level of its covariates. To avoid rending misleading conclusions, we present graphical results in Figure 1 for the estimated derivatives of L without holding X constant. Figure 1a shows a 45-degree graph from [56], which plots the derivative estimates of L against itself in regime 1 (small filled circle in black) and regime 2 (large unfilled square in blue). The estimated derivative given $\widehat{\gamma }=0.5024$ is 0.24 (the red diamond crossed by dash lines). The 95% confidence interval (CI) with lower bound (triangle point-down) and upper bound (triangle point-up) is given around each estimate in regime 1 (filled in gray) and regime 2 (unfilled in blue). Derivative estimates in Figure 1a are significant in the sense that their CIs do not cover zero, accounting for 92% of our whole sample. We observe that 89% of the estimated partial effects are positive in the first regime, and 53% are negative in the second regime, thus indicating a considerable rise in the share in negative impact of leverage ratio above the threshold.

Figure 1b discloses more vividly the sign difference of estimated derivatives of L by reporting their respective kernel density before (solid line, skewed to the right) and after the threshold (dash line, skewed to the left). The estimates in the first regime cluster around its mean of 0.5 (solid vertical line), but exhibits a mean of −0.47 (dash vertical line) in the second regime. The results again indicate a large drop in the impact of leverage ratio on average. Overall, our findings support H1: the positive marginal effect of leverage on TFP growth sharply diminishes once the threshold is exceeded, likely due to moral hazard issues.

Other variables also exhibit significant effects on Chinese firms’ TFP growth as indicated in Table 4. The CF ratio is positively associated with firms’ TFP growth in both regimes. This is consistent with [4], where it was reported that Chinese firms facing harder financial constraints are induced to support their growth through internal financing. Interestingly, the marginal effect of the CF ratio drops when the leverage ratio exceeds the estimated threshold. This indicates that firms with excessive leverage ratios may suffer from “bankrupt cost” and have to use their internal earnings to pay off liabilities, thus weakening its impact on rising firms’ TFP growth. Engaging in exports impacts TFP growth positively, which is in line with the findings in [27] that states that exporters are more productive in China. We also observe that a higher age of firms rises (declines) TFP growth with a leverage ratio higher (lower) than the threshold level, and a larger firm size only improves the TFP growth in the second regime.

4.2. By Ownerships

We now empirically test our second hypothesis H2 regarding whether the leverage threshold varies significantly among firms with different ownership structures. Panel B of Table 3 presents the test results for samples from four different ownership categories. We reject the null hypothesis of a correct parametric regression structure for private and collective firms at a significance level of 10% or less. Therefore, we apply the NPTM-FE model to private and collective firms, as shown in Table 4, while using the PTM-FE model for SOEs and foreign firms, with results provided in

Table 5. Regression results of PTM-FE for selected ownerships and regions.

	SOEs		Foreign		Northeastern
	$\widehat{\gamma }={0.2782}^{***}$		$\widehat{\gamma }=0.3295$		$\widehat{\gamma }=0.4849$
	$[0.1829,0.3735]$		$[0.0000,0.8101]$		$[0.0000,0.9328]$
Variable	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2
Leverage ratio	0.096 ***	−0.122 **	0.392 ***	0.389 ***	0.172 ***	−0.1020
	(0.0341)	(0.0580)	(0.0930)	(0.0840)	(0.0810)	(0.3298)
ln(Age)	−0.093 ***	0.0531 **	−0.074 *	−0.0512	−0.076 ***	0.154 **
	(0.0110)	(0.0245)	(0.0390)	(0.0412)	(0.0320)	(0.0659)
Export	−2.339 ***	−1.569 ***	0.184 ***	0.1013	0.491 ***	0.215
	(0.0940)	(0.1102)	(0.0610)	(0.0825)	(0.0970)	(0.1584)
CF ratio	2.214 ***	2.345 ***	0.477 ***	0.358 **	−0.139 *	1.251 ***
	(0.0980)	(0.1025)	(0.1610)	(0.1451)	(0.0770)	(0.0848)
ln(Size)	−0.028	0.0125	0.213 *	−0.125	−0.024	0.133 ***
	(0.0560)	(0.0214)	(0.1090)	(0.1020)	(0.0220)	(0.0350)
Observations	1961	10,290	4521	12,403	2605	2523

Note: All samples are analyzed with PTM-FE in (10). The estimated threshold value of leverage ratio ($\widehat{\gamma }$) is reported beneath each sample’s name along with its 95% confidence interval. The estimated coefficients ${\widehat{\delta }}_j$ in (10) are reported in regime j with its standard error in parentheses. The results for constant is omitted for brevity. *** p < 0.01, ** p < 0.05, and * p < 0.1.

to enhance estimation efficiency (for brevity, we do not report the constant term estimates in the PTM-FE model in Table 5).

For the sample of SOEs, Table 5 reports an estimated leverage threshold of 0.2782, with an estimated impact of −0.05 at the 1% significance level. This threshold is significant, indicated by a p-value of 0.0000 from the bootstrap test ${\widehat{J}}_n$ in Equation (12). This threshold is positioned at around the 14.6th percentile of the sample, suggesting that over 84% of SOE observations have leverage ratios above this estimated threshold. In contrast to our findings from the overall sample, the marginal impact of leverage now decreases significantly from 0.096 to −0.122 once the leverage ratio exceeds the threshold, holding other variables constant. Figure 2a illustrates this trend by displaying the distribution of estimated effects of leverage without controlling for other variables across the two regimes. We observe a sharp decline in the average effect of leverage, dropping from 0.12 to −0.34 as we move between the two groups. These results provide strong evidence of excessive external borrowing in SOEs, which clearly hampers their total factor productivity (TFP) growth.

The nature of the state ownership may play a central role in explaining their excessive borrowing. First, the managers of SOEs are known to typically have a strong affiliation with the government, and senior executive managers may be directly appointed by local governments [15]. The strong connection with the government allows SOEs to borrow loans at a much lower rate compared with non-SOEs in the financial market [44]. The loans to SOEs are also made considerably available without close monitoring by the central and local governments, who have intensively intervened in lending during economic reforms [53]. In addition, the state power may increase over time that diverts the interests of SOEs’ managers to engage more in productivity-irrelevant activities, such as maintaining government’s reputation, providing resources for social stability, or pursuing non-profitability targets such as stabilizing employment rates [15,46]. As a result, the historical soft budget constraint problem has enlarged the moral hazard effect, rather than the discipline role, of leverage ratio, leading to the excessive leverage ratio in SOEs associated with a negative trend of TFP growth. Our result may serve as an empirical evidence to explain the phenomenon that SOEs with pervasively high leverage ratios exhibit low TFP growth as documented by the authors of [4,15].

Regarding the sample of non-SOEs, we first observe that private and collective firms in Table 4 show a significant threshold effect of leverage ratio. Private firms, which make up 40.9% of our sample, have a significant estimated threshold of 0.509 at the 1% level, which is about the 35th percentile of L in the sample. Similarly, collective firms show an estimated threshold of 0.5154, which is also significant at the 1% level, at approximately the 49th percentile. All else constant, we continue to observe a significant decrease in the positive marginal impact of leverage by 110% (from 12.3%) when this threshold is exceeded in private and collective firms. Panels (b) and (c) of Figure 2 illustrate a marked decline in the average partial effects of leverage by about five-fold for private firms and one-fold for collective firms. Since non-SOEs typically do not receive special government support, they face higher borrowing costs and stricter oversight [5]. This financial pressure likely encourages profit-maximizing behavior among the managers of non-SOEs. Consequently, the positive effect of leverage in these firms does not drop sharply into negative territory as it does for SOEs. However, since more than half of the observations of L in private and collective firms exceed the threshold, excessive borrowing is still present in non-SOEs, aligning with our H1.

Foreign firms, as another category of non-SOEs, differ from private and collective firms in that they do not exhibit a clear threshold effect. Specifically, the estimated threshold for foreign firms is 0.33, which is not significantly different from zero, as shown in Table 5. Consequently, the marginal impact of leverage changes slightly from 0.392 to 0.389 across the regimes, holding other factors constant. Compared to other ownership types, panel (d) of Figure 2 reveals that TFP growth in foreign firms is least affected by excessive leverage, with an average partial effect of 0.35 in the second regime, down from 0.54 in the first. Notably, only 1.2% of estimated partial effects of leverage are negative before the threshold, and none are negative afterward. Like private firms, foreign firms in the Chinese financial market do not receive special treatment or preferential loan policies, and local banks tend to be cautious about lending to majority-owned foreign firms [4]. Our findings suggest that the stricter external financial constraints on foreign firms may effectively reduce moral hazard issues, helping to maintain a positive return on leverage.

Overall, our H1 is supported by all but foreign firms; more importantly, the 95% confidence interval of the estimated threshold in SOEs does not overlap with those intervals in private and collective firms. This result supports our H2 that the leverage threshold is significantly different across SOEs and non-SOEs. In particular, the lowest estimated threshold value stems from SOEs, whose TFP growth rate discloses a negative trend associated with excessive leverage ratio. In contrast, non-SOEs exhibit a much higher estimated threshold. The excessive leverage ratio relative to the threshold lowers $TFPG$ considerably in private and collective firms, but exhibits minimum impact in foreign firms. We expect that the heterogeneous threshold across ownerships is potentially driven by the soft and hard budget constraint due to the difference in the nature of ownership, which negatively impacts a firm’s TFP growth by a magnitude depending upon whether the discipline or moral hazard effect dominates.

4.3. By Region

The testing results in Panel C of Table 3 indicate that the NPTM-FE is suitable for all regions except the northeastern one. Therefore, we first apply the PTM-FE method to the northeastern region, with the corresponding results shown in Table 5. The estimated threshold of 0.4849 is not significantly different from zero, as indicated by a p-value of 0.2500 for ${\widehat{J}}_n$ in (12). Panel (a) of Figure 3 illustrates this finding, as the densities of the estimated derivatives of leverage (L) are quite similar across both regimes. Consequently, we do not find evidence of a threshold effect for leverage in the northeastern region; instead, we observe a positive marginal impact of leverage in the first regime, with other variables held at their median values, resulting in average impacts of 0.36 and 0.21 in both regimes without controlling other variables. Ref. [55] documents that the level of marketization in the northeastern region is higher than the national average, which significantly boosts local non-SOE entrepreneurship. This is consistent with the fact that approximately two-thirds of the firms in this region are either foreign or privately owned, as detailed in Appendix E. Thus, the positive effect of leverage in northeastern firms is likely due to the high proportion of non-SOEs in this area.

We proceed to apply the NPTM-FE for the eastern, western, and central regions, with the numerical results presented in

Table 6. Regression results of NPTM-FE for selected regions.

	Eastern		Western		Central
	$\widehat{\gamma }={0.5137}^{***}$		$\widehat{\gamma }={0.3945}^{***}$		$\widehat{\gamma }=0.4837$
	$[0.3794,0.6479]$		$[0.2840,0.5050]$		$[0.2370,0.7328]$
Variable	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2
Leverage ratio	0.3251 ***	0.1192 **	0.463 ***	−0.039 *	−0.3851 ***	0.0800
	(0.0657)	(0.0614)	(0.1271)	(0.0911)	(0.022)	(0.0903)
Ln(Age)	−0.0478	0.0222	0.1176	−0.0306	−0.1069	0.0466
	(0.0359)	(0.0307)	(0.1337)	(0.0305)	(0.0347)	(0.0348)
Export	0.3014 ***	0.3843 ***	−1.4682 ***	−0.8572 ***	0.6319 ***	−0.2006 **
	(0.0564)	(0.0394)	(0.2416)	(0.0580)	(0.1415)	(0.0945)
CF ratio	0.5822 ***	0.5465 ***	−0.9089	0.4608	0.7878 ***	0.3719 ***
	(0.1429)	(0.1009)	(0.9810)	(0.2497)	(0.1653)	(0.1105)
Ln(Size)	0.0540 ***	0.0421 ***	−0.0074	−0.0117	0.0082	−0.0087
	(0.0196)	(0.0131)	(0.0691)	(0.0196)	(0.0242)	(0.0144)
Observations	24,874	25,358	2807	5833	3520	4631

Note: The estimated threshold effect of leverage ratio ($\widehat{\gamma }$) and its corresponding 95% confidence interval based on a bootstrapped standard error of $\widehat{\gamma }$, in brackets, are reported beneath each sample’s name. Regimes 1 and 2 report the median of estimated derivatives of each variable from $m_1(·)$ and $m_2(·)$, respectively, holding all other variables at median. The asymptotic standard errors are in parentheses beneath the estimated derivatives. *** p < 0.01, ** p < 0.05, and * p < 0.1.

. In the eastern region, we find a significant threshold estimate of 0.514 at the 1% level, which is close to the median of 0.530. Similar to the overall sample, a one percentage point increase in leverage before the threshold leads to a TFP growth increase of 0.593, but this drops significantly to 0.133 afterward, with all other variables held at their median values. As shown in panel (a) of Figure 3, the excessive leverage in regime 2 noticeably stretches the left tail of the density, resulting in a mean of 0.05, which is three times lower than the mean of 0.2 observed in the first regime.

The western region shows an estimated threshold value of 0.395 at the 1% significance level, which is close to the 33rd percentile of L in the sample. Consequently, about two-thirds of the observations exceed this leverage threshold. Notably, western firms have the lowest threshold value compared to other regions. As the leverage ratio increases beyond this threshold, the improvement in TFP growth attributable to leverage significantly declines from 0.923 to 0.21, holding all other variables constant. Additionally, the average marginal impact of leverage decreases sharply from 0.5 to −0.05, as illustrated in panel (d) of Figure 3. These findings indicate the presence of “excessive borrowing” in the western region, likely driven by a relatively high share of state-owned enterprises (31.8%) compared to other firm types. Ref. [57] found that lower productivity in this region is linked to underdeveloped infrastructure, education, and technology. Our results suggest that excessive leverage may be another important factor contributing to stagnant TFP growth in the western area.

Unlike other regions, the central region presents an insignificant threshold estimate of 0.4837. Holding all other variables at median, Table 6 shows that the leverage ratio in the area declines a firm’s TFP growth marginally by 0.385 percentage points at a 1% significance level only in the first regime, but exhibits a fairly small and insignificant impact of 0.08 in the second regime. Correspondingly, panel (c) of Figure 3 reveals no significant difference in the densities of derivative estimates of L in two regimes, with an average of −0.23 (−0.5) in regime 1 (2). We conjecture that the negative impact of the leverage ratio in the central region may be resulted from the dominating role of SOEs, accounting for 30.3% of the sample. Thus, western and central areas with a relatively higher share of SOEs exhibit a more detrimental impact of excessive leverage ratio on TFP growth relative to eastern and northwestern areas, where non-SOEs dominate.

We further observe that a higher volume of export significantly improves productivity growth in eastern firms. The result may not be surprising, given that most exporting Hi-tech sectors, typically with higher productivity, are located in the eastern region [4]. The coefficients of cash flow ratio are positive and highly significant in eastern and central areas, which are again consistent with the internal finance–growth hypothesis in [4]. To summarize, we observe a similar pattern of the threshold structure of leverage ratio when the region heterogeneity is taken into account.

In practical terms, all results in Section 4 suggest that firms with excessive debt become much less productive, whereas those that manage their debt levels within a moderate range (i.e., below the threshold) can maintain higher productivity. For business leaders, it is crucial to recognize that focusing on disciplined debt management, rather than solely on expansion, can help to preserve long-term productivity and profitability. Policymakers, on the other hand, should consider implementing policy frameworks that encourage external borrowing for financial constrained firms while providing clear guidelines to prevent firms from reaching detrimental debt levels. Such policies would be particularly effective in addressing the risks of moral hazard, especially in SOEs or regions dominated by SOEs. Implementing the related policies could promote sustainable corporate growth and contribute to sustainable economic growth in China.

5. Robustness Check: An Alternative Indicator of External Financing

The leverage ratio of a firm has been served as a major indicator for external financing in the literature. However, it may not be a perfect indicator for policy implications. For instance, firms may raise external debts and total assets proportionally to maintain the leverage ratio purposely at a targeted level. For this reason, we use leverage growth ($LG$), defined as the annual growth rate of a firm’s total debt D between two consecutive years (i.e., $L{G}_{it}=(D_{it}-D_{it-1})/D_{it-1}$), as an alternative measure of external financing to evaluate the robustness of our empirical findings regarding H1 and H2. We follow a similar practice to our previous analysis by choosing $L{G}_{i,t-1}$ as the instrumental variable for our derivative estimator in (9). See Appendix F for the summary statistics of $LG$ across different samples based on ownerships and regions.

We present the partial effect of variables in

Table 7. Regression results of NPTM-FE with the annual growth rate of leverage ratio ($LG$).

	Whole Sample
	$\widehat{\gamma }={0.1037}^{***}$
	$[0.0599,0.1474]$
	Regime 1	Regime 2
Leverage growth	0.1051 ***	0.0376 *
($LG$)	(0.0201)	(0.0208)
Observations	39,070	27,336
	By ownership
	SOEs		Private		Foreign		Collective
	$\widehat{\gamma }={0.0343}^{***}$		$\widehat{\gamma }={0.1035}^{***}$		$\widehat{\gamma }={0.1137}^{**}$		$\widehat{\gamma }={0.0673}^{***}$
	$[0.0168,0.0517]$		$[0.0666,0.1403]$		$[0.0179,0.2095]$		$[0.0210,0.1136]$
	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2
Leverage growth	0.0628 **	−0.0720 ***	0.0381 ***	0.0250 ***	0.1694 ***	0.1419 ***	0.0250 ***	0.0082 ***
($LG$)	(0.0284)	(0.0190)	(0.0014)	(0.0018)	(0.0271)	(0.0216)	(0.0063)	(0.0024)
Observations	4818	5022	14,701	11,151	6068	3992	4807	3626
	By region
	Eastern		Western		Central		Northeastern
	$\widehat{\gamma }={0.1125}^{***}$		$\widehat{\gamma }={0.1004}^{***}$		$\widehat{\gamma }={0.1093}^{**}$		$\widehat{\gamma }={0.1256}^{*}$
	$[0.0676,0.1574]$		$[0.0388,0.1620]$		$[0.0136,0.2049]$		$[-0.0231,0.2744]$
	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2	Regime 1	Regime 2
Leverage growth	0.0539 ***	0.0209 **	0.0621 *	0.0327 **	0.0157 **	−0.0312 *	0.0443 *	0.0270 *
($LG$)	(0.0036)	(0.0091)	(0.0320)	(0.0146)	(0.0069)	(0.0180)	(0.0262)	(0.0140)
Observations	27,541	19,713	4483	3137	4497	2714	2639	1594

Note: The results are obtained using annual growth rate of leverage ($LG$) as the threshold variable. The estimated $\widehat{\gamma }$ and its corresponding 95% confidence interval based on the bootstrapped standard error in brackets are reported beneath each sample’s name. Regimes 1 and 2 report the estimated median derivatives of each variable from $m_1(·)$ and $m_2(·)$, respectively, holding all other variables at the median. The asymptotic standard errors are in parentheses beneath the estimated derivatives. *** p < 0.01, ** p < 0.05, and * p < 0.1.

. Given the qualitatively similar results for control variables, we report only the marginal impact of $LG$ for brevity. The whole sample reports an estimated threshold of 0.1037 in $LG$ at a 1% significance level, about the 59.3th percentiles of L in the sample. Similar to the threshold effect of leverage ratio, a one percentage increase in $LG$ significantly raises the TFP growth by 0.105 and 0.038 of a percentage point before and after the threshold level, respectively. The suggested threshold effect of $LG$ can be visualized in Figure 4. Panel (a) shows that 87.5% of the estimated effects without holding covariates constant are positive in regime 1, and 62.1% of that are negative with excessive $LG$. Also, panel (b) reveals that the $LG$ improves TFP growth in regime 1 by a median of 0.49, which falls significantly down to −0.22 in regime 2. The findings support H1 qualitatively, indicating that excessive leverage growth hinders productivity improvement.

A similar pattern of the threshold effect is observed among firms with different ownership types. The corresponding estimated thresholds for $LG$ are 0.0343 (49th percentile) for SOEs, 0.1035 (57th percentile) for private firms, 0.1137 (60th percentile) for foreign firms, and 0.0673 (58th percentile) for collective firms. Holding all else constant, a leverage growth exceeding its threshold significantly reduces the TFP growth for SOEs, indicating an inverted-U relationship associated with excessive borrowing. In contrast to our previous results, foreign firms now exhibit a significant threshold effect for $LG$, with an estimated $\widehat{\gamma }$ of 0.114 at the 5% level. However, the partial impact of $LG$ across the two regimes does not change significantly, as consistent with our findings in Table 5. As previously observed, the estimated thresholds for $LG$ differ across ownership types, with the lowest magnitude observed in SOEs, followed by collective, private, and foreign firms. Notably, the estimated threshold for SOEs is significantly lower than that for private firms, as indicated by their non-overlapping 95% confidence intervals (The graphical results for derivative estimates of $LG$ across ownership types and regions remain qualitatively similar to those in Figure 2 and Figure 3. Therefore, we do not report them here to save space, but they are available upon request from the corresponding author). This finding further supports H2 qualitatively, suggesting that the threshold of leverage at which a firm’s productivity is maximized varies by ownership type.

The threshold effect of leverage growth also holds across different regions. The respective threshold estimates are given by 0.1037 (58.3th percentile) for the eastern region, 0.1004 (58.6th percentile) for the western region, 0.1093 (62th percentile) for the central region, and 0.1256 (62th percentile) for the northeastern region, all of which are significant at a 10% or lower level. The partial effect of $LG$ diminishes by roughly one-half in magnitude for most regions in the second regime. Notably, the central region now discloses an inverted-U relationship between $LR$ and $TFPG$, where the estimated marginal effect of $LR$ changes significantly from 0.0157 to −0.0312 when the threshold level at 0.1093 is passed over.

Overall, the empirical evidence continues to support our economic hypotheses H1 and H2 when $LG$ is used as an alternative indicator of external financing. This suggests that excessive borrowing is prevalent in China’s industrial sectors, particularly in ownership types or regions where the soft budget constraint problem is more severe.

6. Conclusions

The excessive corporate debt problem in recent Chinese industrial firms raises concerns over its impact on firm productivity growth. In this paper, we hypothesize that a firm’s total factor productivity (TFP) growth is maximized at a threshold leverage ratio, above which TFP growth declines significantly (H1). Given the malfunctioning financial market in China, we further hypothesize that this threshold effect of leverage (L) is heterogeneous across different firm ownership types (H2). Inspired by a recently developed threshold model by the authors of [31], we empirically tested these two hypotheses by proposing a nonparametric threshold panel regression model. Our study makes two types of contributions to the literature.

Theoretically, we propose a new methodology to estimate the threshold using panel data. It has three appealing features from a modeling perspective. First, our model allows the threshold effect to be endogenous, which is particularly useful in applications with omitted variables or reversed causality. Second, we introduce the fixed effects in the model, controlling for unobserved, time-invariant firm-specific characteristics and thereby further mitigating omitted variable problems. Third, our model is nonparametric, imposing no restrictions on the regression function, which significantly reduces the risk of model misspecification. We estimate the unknown threshold through an extreme kernel estimator, which exhibits appealing finite sample performance in simulation studies. We probe the validity of our model through a nonparametric test, which suggests that a nonparametric threshold model is better suited for our empirical study.

Empirically, we provide solid evidence that excessive leverage ratios constrain TFP growth in China. Our results support both hypotheses. We observe that once leverage (either in ratio or growth rate) surpasses the threshold, average productivity growth decreases sharply. Notably, SOEs have a lower estimated threshold compared to non-SOEs and experience a negative trend in TFP growth when their leverage is excessive. Additionally, regions dominated by SOEs, particularly in the western and central areas, suffer more severely from excessive leverage than those in the eastern and northeastern regions dominated by private and foreign firms (i.e., non-SOEs). This indicates that the excessive borrowing problem is more pronounced in firms and regions facing soft budget constraints.

Our empirical analysis provides important insights into the existence of an optimal leverage ratio for productivity maximization in Chinese industrial firms, which is crucial for maintaining sustainable growth in China’s economy. Based on our findings, we offer policy recommendations with a particular focus on constraining excessive leverage in firms with soft budget constraints, especially state-owned enterprises (SOEs) and regions characterized by these constraints. First, borrowing regulations for SOEs should be strengthened, including tighter debt-to-equity ratio limits and an improved monitoring of debt accumulation. Second, corporate governance in SOEs must be enhanced to promote financial discipline and reduce government interference, aligning their practices more closely with private firms. Third, more efficient capital allocation is needed to rebalance financial flows, encouraging greater private and foreign investment in regions dominated by SOEs to mitigate the effects of soft budget constraints. Although our data cover the period from 1998 to 2007, we expect that these recommendations remain highly relevant to address China’s current corporate debt issues and ensure that leverage contributes positively to firm productivity and economic growth.

Our study suggests several avenues for future research. For instance, further investigation into microeconomic mechanisms through which corporate debt influences TFP could yield valuable insights. The examples may include the role of management practices, technological adoption, and market competition. Additionally, empirical investigation can be performed to examine the impact of different types of financing—such as bank loans versus equity financing—on firm performance, particularly in the context of varying ownership structures. Last but not the least, incorporating additional economic constraints, such as regulatory changes and macroeconomic conditions, may enhance the understanding of their interplay with corporate debt and productivity. We further discuss the limitation of our study in Appendix G.