2.1. Financial constraints and bankruptcy risk

Financial constraints, or limitations on a firm’s ability to obtain external financing, play a central role in determining corporate survival. When a firm cannot raise sufficient capital to fund its operations or investments at a reasonable cost, it faces significant friction that threatens its long-term viability. Market Timing Theory suggests that firms attempt to issue securities when market conditions are favorable. However, financially constrained firms lack the flexibility to time their financing decisions optimally. When constraints bind, particularly during market downturns or volatility, these firms face a double bind: they cannot access external capital when they need it most, and if they do secure financing, it often comes at prohibitively high costs. This financing inflexibility directly increases bankruptcy risks because the firm cannot smooth out operational shocks or meet debt maturity pressures [2,5].

Recent empirical studies largely support a positive relationship, confirming that financial constraints significantly increase the probability of corporate failure. Karas and Režňáková [17] found that for Small and Medium-sized firms, financial constraints are critical predictors of default because these firms lack the capital buffers necessary to withstand bankruptcy risk. Le et al. [3] expand on this size-centric view in Vietnam, finding that financially constrained firms exhibit significantly higher bankruptcy risk due to their inability to access external capital buffers. They further clarify that this vulnerability effect is universal but disproportionately severe for smaller firms that lack the collateral to bypass credit rationing. This vulnerability is not limited to specific industries. Boateng et al. [18] argue that regardless of the nature or cause of the constraint, whether tax-related or structural, a firm is prone to “complete collapse” when faced with severe financing restrictions because it cannot cover compliance costs or operational liabilities. Furthermore, financial constraints serve as a critical transmission mechanism that amplifies the adverse effects of environmental and external shocks. When firms lack financing flexibility, they are unable to invest in adaptation strategies to mitigate climate change exposure and policy uncertainty [19–21]. Adamolekun [19] documents that financial constraints exacerbate bankruptcy risk for firms with high carbon emissions, as these firms cannot afford the necessary green investments to remain viable in a changing regulatory landscape.

In contrast, Agency theory offers a contrasting perspective. Jensen [22] argues that financial constraints can reduce bankruptcy risk by disciplining managerial behavior. When external financing is scarce, managers face stricter budget constraints and are compelled to be more risk-averse, as the consequences of a bad investment could be fatal for the firm. Yao et al. [4] argue that higher financial constraints act as a tight budget, motivating managers to use funds more cautiously and adopt scientific management strategies. Because these managers cannot afford to waste money on reckless projects, the firm operates more efficiently. As a result, this enforced discipline improves performance and decreases the likelihood of default compared to unconstrained firms that might take unnecessary risks.

China’s financial system is characterized by significant state ownership influence and financial mismatch, where credit allocation is frequently driven by political mandates rather than pure market efficiency [5]. This creates a structural disadvantage for Non-State-Owned Enterprises (NSOEs), which face severe borrowing hurdles compared to State-Owned Enterprises (SOEs). Zhitao and Xiang [5] confirm that this institutional mismatch is a primary driver of default for private firms. In this context, financial constraints are not merely a friction but a systemic vulnerability. Given this unique institutional setting, a critical methodological gap exists in prior research regarding the accurate measurement of financial constraints. While accounting-based indices such as KZ (Kaplan-Zingales), WW (Whited-Wu), or the Z_FC index are widely established in general corporate finance research, Yao and Yang [7] explicitly argue that these traditional indices suffer from severe endogeneity because they rely on financial ratios like leverage and cash flow, which are prone to distortion by earnings management and state intervention. In China’s dual-structure economy, a private firm’s low leverage often reflects involuntary exclusion from the banking system rather than a conservative financial policy; thus, the KZ, WW, and Z_FC indices risk misclassifying the most structurally vulnerable firms as unconstrained. To resolve this endogeneity bias, our study follows Hadlock and Pierce [6] and Yao and Yang [7] by adopting the SA Index. The superiority of the SA Index lies in its construction solely from largely exogenous variables (firm size and age), allowing it to bypass the accounting noise inherent in the KZ and WW measures and directly proxy the structural discrimination described by Zhitao and Xiang [5], where state-owned banks systematically favor large, established entities. By utilizing the SA Index, this study ensures that the measurement of financial constraints captures the persistent, institutional barriers to survival rather than transient fluctuations in financial ratios. Our hypothesis is as follows:

H1: Financial constraints negatively correlate with the Z-score, implying that financially constrained firms have a higher bankruptcy risk in China.

2.2. Cash holdings and bankruptcy risk

The relationship between corporate cash holdings and bankruptcy risk is characterized by a fundamental tension between the immediate survival benefits of liquidity and the long-term systemic risks associated with capital mismanagement [9,23]. According to Trade-off Theory, firms determine an optimal cash level by balancing the marginal benefit of reduced financial distress against the opportunity costs of holding liquid assets, such as taxation on interest and potential agency costs [9,23,24]. A central mechanism in this policy is the precautionary savings hypothesis, which posits that firms maintain cash as a vital buffer against adverse cash flow shocks, particularly when external financing is costly or inaccessible due to market frictions [8,10]. Furthermore, Pecking Order Theory suggests that information asymmetries lead firms to prioritize internal liquidity over debt or equity issuance to preserve financial flexibility and avoid financing traps where credit is withdrawn during periods of peak default risk [8,10,23].

However, Agency Theory warns that abundant liquid resources can exacerbate conflicts between managers and shareholders, providing incentives for managers to extract rents or invest in value-destroying projects [8,9]. Nguyen et al. [8] argue that during severe crises, the survival motive eclipses these concerns, prioritizing business resilience over efficiency. In such contexts, pre-crisis cash reserves become a primary determinant of business resilience, enabling firms to weather rapid revenue declines and maintain investment stability [8, 10, 25].

Analytically, this buffer mechanism operates through two distinct channels: short-term liquidity risk and long-term solvency risk. Cash holdings mitigate the former by providing a mechanical guarantee that the firm can meet its immediate debt obligations and payroll, even if revenue streams are temporarily interrupted [26]. Simultaneously, they address the latter by providing the strategic time necessary to restructure operations without the immediate threat of liquidation. By synthesizing these perspectives, it becomes clear that cash is not merely an idle asset but a critical tool for reducing a firm’s distance to default and improving its overall financial health.

A significant tension between the buffer effect and the signaling effect characterizes the empirical relationship between cash and bankruptcy risk. Supporting the buffer perspective, Zheng [10] describes cash reserves as a panacea during the COVID-19 pandemic, finding that firms with high pre-crisis liquidity significantly outperformed their peers by avoiding the need to cut vital investments. This finding aligns with Nguyen et al. [8], who argue that internal liquidity is a primary driver of business resilience across 97 countries. From this perspective, cash is a direct tool for survival, reducing the probability of failure by ensuring that sudden revenue stops do not lead to immediate insolvency. In the European context, Yousaf and Briš [27] further show that higher liquidity ratios are consistently associated with better financial health and a lower likelihood of distress.

However, Poliakov and Zayukov [26] find that excessive liquidity can sometimes correlate with higher unprofitability, suggesting that holding too much idle cash might lead to operational inefficiencies that hurt a firm in the long run. Zhang et al. [11] found that for many A-share firms in the Chinese market, a rapid increase in cash holdings actually predicted an impending default. This suggests a precautionary hoarding behavior: firms that know they are in trouble might desperately pile up cash because they anticipate being cut off from bank loans. These findings refine the foundational view of Faulkender and Wang [9], who note that the marginal value of cash changes depending on the amount of debt a firm already carries.

Despite the established link between liquidity and survival, current literature is limited by a geographic bias toward developed economies and a methodological reliance on binary default proxies that are ill-suited for the Chinese institutional setting. Even recent studies examining bankruptcy in transition economies, such as Yousaf and Briš [27] in the Visegrad region, predominantly utilize binary logistic regression models where the dependent variable is a dichotomous default indicator. However, applying this binary framework to China is problematic due to the unreliability of standard distress proxies. Zhang et al. [11] demonstrate that the Special Treatment designation, often used as a binary proxy for default in A-share studies, primarily reflects accounting profitability rules rather than a terminal inability to meet debt obligations. Relying on such measures fails to capture the continuous erosion of financial health in a system where implicit government guarantees can sustain technically insolvent zombie firms. To bridge this gap, our study moves beyond binary classification by adopting the multivariate Z-score methodologies advocated by Altman [13] for non-manufacturing firms and emerging markets, alongside the bias-corrected ZM-score established by [14]. This approach provides a granular, continuous assessment of distance to default that captures the subtle protective role of cash buffers, which standard binary models obscure. Our hypothesis is as follows:

H2: Cash holdings positively affect the Z-score, implying lower corporate bankruptcy risk in China.

2.3. Financial constraints and cash holdings

The relationship between financial constraints and bankruptcy risk is not mechanical; it is contingent upon the availability of internal liquid resources to bridge periods of market exclusion. While financial constraints represent a blockade to external capital, cash holdings represent the immediate availability of internal capital. Integrating the Precautionary Savings motive with the Market Timing framework, we posit that cash holdings function as a critical substitution mechanism that attenuates the adverse impact of financial constraints on corporate survival. Theoretical literature suggests that the marginal value of cash is strictly decreasing with the accessibility of external finance [9]. For unconstrained firms, cash is merely one of several liquidity options; however, for financially constrained firms, it is often the sole means of survival against default. Denis and Sibilkov [28] argue that because constrained firms face prohibitively high external financing costs, they must rely on accumulated cash reserves to fund essential investments and service debt. In this context, cash holdings cease to be idle assets and become a strategic buffer that allows the firm to bypass the frictions of capital markets.

This buffering effect is particularly salient in the Chinese institutional setting, characterized by the financial mismatch [5]. In developed Western markets, firms may often rely on committed lines of credit as a backup liquidity source. However, in China’s dual-structure economy, private firms usually face discriminatory lending policies that exclude them from such banking privileges. Consequently, when a Chinese private firm is financially constrained, it cannot rely on bank guarantees; instead, it must depend on self-insurance through cash holdings. Nguyen et al. [8] support this view, finding that during periods of systemic stress, internal liquidity is the primary determinant of resilience for firms that lack political connections or collateral.

Analytically, cash holdings moderate the relationship between constraints and bankruptcy by severing the transmission mechanism of distress. For a constrained firm with low cash reserves, the financial constraint binds tightly; any operational shock or debt maturity creates an immediate liquidity crisis that the firm cannot solve through borrowing (due to constraints) or internal payment (due to liquidity shortages), leading to a rapid erosion of the Z-score and high default risk [11]. Conversely, substantial cash holdings effectively decouple the firm’s immediate survival from its ability to borrow externally. Even if the firm is structurally constrained and locked out of the credit market, high cash reserves allow it to smooth out cash flow volatility and meet obligations without triggering insolvency protocols [2]. Therefore, while financial constraints generally increase bankruptcy risk, this effect is non-linear. We posit that high cash holdings dampen the destructive power of financial constraints, serving as a protective shield that preserves financial health even when external capital channels are blocked. Based on this synthesis, we propose the following hypothesis:

H3: Financially constrained firms with higher cash holdings would decrease bankruptcy risk in China.

3.1. Data

We use data from 2010 to 2023 in China to predict bankruptcy risk. We select the sampling period from 2010 to minimize the adverse impacts of the 2008 financial crisis on the findings. We collect data from the Taiwan Economic Journal (TEJ) database, a reliable data source in Taiwan. The sampling procedure followed previous studies. First, our sample includes the A-shares of listed firms in the SHSE and SZSE stock exchanges. Second, we follow Duong et al. [29] to exclude companies with missing accounting and financial data. We also follow Yu et al. [30] in trimming all variables at the 1% and 99% levels to minimize bias from extreme values. The final sample is an unbalanced panel consisting of 32,081 firm-year observations.

3.2. Variable definitions

Altman [1] recommends measuring a corporation’s financial health using the Z-score. It is also an effective predictor for anticipating the default risk within two subsequent years. Accordingly, we adopt the Z-score as our primary measure of bankruptcy risk. Additionally, we follow Zmijewski [14] and Altman [13] to calculate alternative bankruptcy risk, including ZM-score, Z’-score, and Z“-score, to examine the robustness of results.

The independent variables are the cash holdings ratio and financial constraint. Cash holdings refer to the cash and short-term investments a firm holds for its operational purposes. We follow Duchin [31] in calculating cash holdings as the total of cash and short-term investments divided by total book assets. In addition, we follow Hadlock and Pierce [6] and Yao and Yang [7] in constructing the SA index for financial constraints. The SA index (Size–Age index) is constructed to capture firms’ financial constraints based on firm size and firm age, two relatively stable characteristics that are less volatile than traditional financial indicators. The equations are as follows:

Size is the natural logarithm of total assets, and Age is the difference between the observation year and the year of firm registration. A higher SA index value, particularly when approaching zero or becoming positive, reflects more severe financial constraints. Prior studies, including Hadlock and Pierce [6] and Yao and Yang [7], highlight the advantages of the SA index, noting that it is constructed from exogenous firm characteristics and is therefore less susceptible to endogeneity problems that frequently affect leverage- or cash flow-based measures such as the KZ, WW, and Z_FC index. The variable definitions are described in Appendix A.

3.3. Model construction

In this section, we follow the work of Le et al. [3] and Duong et al. [32,33] in investigating the impact of cash holdings and financial constraints on corporate default risk. In Model 1, we examine the effects of financial constraints, as measured by the SA index, and control variables on the risk of corporate bankruptcy.

(1)

In Model 2, we follow Duchin [31] to examine the impact of cash holdings, as measured by CASH, and control variables on corporate bankruptcy risk.

(2)

In Model 3, we add the cash holding variable to examine the impact of financial constraints and cash holdings on corporate default risk.

(3)

In Model 4, we add the interaction term (SA*CASH) to test whether cash holdings help mitigate default risk in financially constrained firms.

(4)

Besides, we replace the Z-SCORE with ZM-SCORE, Z’-SCORE, and Z“-SCORE to test whether our findings are robust after employing an alternative bankruptcy risk.

Where Z-SCORE is the bankruptcy risk coefficient of companies, the SA index is an indicator of financial constraints, and CASH is the cash holdings ratio of firms. In addition, the CONTROL variables include FAT, FTA, NIG, NPM, TAG, and ROA. The notation “t” represents time; the sign “i” denotes cross-sections; “α” denotes intercept, “j” denotes industry, and ε is the error term. Appendix A contains descriptions of every variable in the model.

3.4. Estimation method

To determine the appropriate estimation method (OLS, FEM, or REM) for each model, we conduct the Hausman test and the Redundant test. However, standard estimations like OLS, FEM, and REM may violate heteroskedasticity, autocorrelation, and endogeneity assumptions, which can substantially influence the findings [3,34]. To detect these issues, we use the modified Wald test for heteroskedasticity, the Wooldridge test for autocorrelation, and the Durbin–Wu–Hausman test for endogeneity. If violations are detected, the Two-step system Generalized Method of Moments is applied to address them. Additionally, we employ this method because corporate bankruptcy risk typically exhibits persistence; a firm’s current bankruptcy risk is partly determined by its past financial health, due to the accumulation of debt and reputation effects. To ensure the validity of statistical inference, we use robust standard errors clustered at the firm level, applying the Windmeijer [35] finite-sample correction, which is essential for correcting the downward bias of standard errors in finite samples. Additionally, to prevent instrument proliferation that could weaken the Hansen test, we collapse the instrument set and limit the lag depth of the endogenous variables.

4.1. Descriptive statistics

Table 1 reports descriptive statistics of the variables. This table includes the mean, max, min, standard deviation, and total observations. Table 1 gives an overview of statistics in the Chinese market. Table 1 indicates that the average value of the Z-score is about 5.11, with a standard deviation of 5.06. Altman [1] suggests that the Z-score is divided into three levels. The company has a serious distress risk if the Z-score is less than 1.81. If the Z-score is between 1.81 and 2.99, the firm is considered to have a low bankruptcy risk over the subsequent two years. If the Z-score exceeds 2.99, the business is in good financial health. As a result, the listed Chinese enterprises are generally in good financial condition. Compared to Le et al. [3] and Duong et al. [33], our sample shows stronger financial stability with average Z-scores of 2.53 and 2.46, respectively. The alternative bankruptcy proxies corroborate this finding of financial resilience. The ZM-score reports a mean of −2.21, which is notably lower than the benchmark mean of −1.58 observed in Zmijewski [14], indicating a lower-than-average risk profile and strong stability. Likewise, the Z’-score (8.98) and Z“-score (12.23) far exceed their respective safety cutoffs of 2.90 and 2.60 Altman [13], confirming robust financial strength across the sample. Regarding financial constraints, our sample shows a slightly less negative mean value of −2.09, compared to the −2.69 reported by Yao and Yang [7]. Our sample reports an average cash holding of 0.22 and a standard deviation of 0.14, respectively. In addition, Table 1 also describes the mean of FAT, FTA, NIG, NPM, TAG, and ROA as 6.75, 0.20, −0.25, 0.07, 0.19, and 0.04, respectively.

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Table 1. Descriptive statistics.

https://doi.org/10.1371/journal.pone.0341114.t001

4.2 Pearson Correlation Matrix

Table 2 reports the Pearson correlation matrix between the variables. Most independent variables exhibit weak correlations, except for NPM and ROA, which show a relatively high correlation coefficient of 0.82. Therefore, we conduct the Variance Inflation Factor (VIF) test to check the multicollinearity problem. The mean VIF is less than 5, implying no multicollinearity issue in our study [3,36].

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Table 2. Pearson correlation matrix.

https://doi.org/10.1371/journal.pone.0341114.t002

4.3. Regression results

Table 3 reports the estimated results of the bankruptcy determination of enterprises in China. Table 3 reports that the P-values of the Hausman test and the Redundant Fixed Effects Test are less than 0.001, so the Fixed Effects Model (FEM) is more suitable than Pool OLS and REM.

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Table 3. Regression results using the FEM estimations.

https://doi.org/10.1371/journal.pone.0341114.t003

Unfortunately, the modified Wald and Wooldridge tests confirm the presence of heteroskedasticity and autocorrelation. While these violations do not bias the coefficients, they invalidate statistical inference under standard FEM. Additionally, this study builds upon the work of Duong et al. [29] in implementing the Durbin–Wu–Hausman test, as the model contains endogenous variables, which would otherwise result in biased estimates.

After performing the Durbin–Wu–Hausman tests, Table 4 indicates that SA, CASH, FTA, NIG, NPM, TAG, and ROA are seven endogenous variables, as their residual coefficients are statistically significant. Therefore, we follow Duong et al. [29] and Vuong et al. [36] in re-estimating our findings using GMM estimations and reporting the results in Table 5. The insignificant Hansen and AR(2) results confirm the validity of our instruments and the absence of second-order serial correlation.

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Table 4. Durbin – Wu- Hausman Test.

https://doi.org/10.1371/journal.pone.0341114.t004

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Table 5. Regression results using the dynamic system GMM estimations with Z_SCORE.

https://doi.org/10.1371/journal.pone.0341114.t005

The analysis of marginal effects in Table 6 and Fig 1 reveals the critical economic role of cash as a structural buffer. At low cash levels (below 0.20), the economic penalty of financial constraints is severe, directly eroding solvency. However, as cash holdings enter the high cash zone (0.50–0.70), a striking economic reversal is observed, where financial constraints begin to contribute positively to stability. Managerially, this indicates that cash is not merely an idle asset but a strategic decoupling mechanism. For constrained firms, accumulating high cash reserves effectively neutralizes the toxicity of external financing frictions. It enables managers to adopt a prudent risk-management stance, transforming the discipline of financial constraints into a competitive advantage in solvency, thereby insulating the firm from market imperfections.

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Table 6. The average marginal effects of financial constraints (SA) on the Z-score at different levels of cash holdings (CASH).

https://doi.org/10.1371/journal.pone.0341114.t006

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Fig 1. The average marginal effects of financial constraints (SA) on the Z-score at different levels of cash holdings (CASH) with 95% CIs.

https://doi.org/10.1371/journal.pone.0341114.g001

4.4 Robustness test

To ensure that our findings are not driven by the specific construction of the Altman Z-score standard, we conduct a robustness test using three alternative proxies for corporate bankruptcy risk. The standard Z-score may not fully capture the nuances of the Chinese institutional setting or the “distance-to-default” for non-manufacturing firms. Therefore, following the methodologies of Altman [13] and Zmijewski [14], we re-estimate our baseline dynamic System GMM model using the ZM-score, Z’-score, and Z”-Score as dependent variables in Table 7.

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Table 7. Regression results using the dynamic system GMM estimations with ZM-SCORE, Z’-SCORE, Z“-SCORE.

https://doi.org/10.1371/journal.pone.0341114.t007

Furthermore, following Fama and French [15], we examine whether the effects of financial constraints and cash holdings differ across firm sizes. Given that small and medium-sized firms often face greater barriers to external financing due to information asymmetry, limited collateral, and weaker ties with financial institutions, we test whether financial constraints and liquidity management strategies affect small and large firms differently. Table 8 presents the robustness test results for small, medium-sized, and large firms.

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Table 8. Robustness test by employing different firm sizes.

https://doi.org/10.1371/journal.pone.0341114.t008

To further validate our findings within the unique institutional context of China, we conduct a sub-sample analysis by splitting the data between the SHSE and SZSE. The Chinese financial system is characterized by a financial mismatch where credit allocation is often driven by political mandates rather than market efficiency [5]. According to Feder-Sempach et al. [16], large and state-owned firms dominate the SHSE, while the SZSE features more private and innovation-driven firms. Zhitao and Xiang [5] state that these private entities face discriminatory lending policies and are structurally more vulnerable to default when access to external capital is restricted. Table 9 presents the robustness results across these two exchanges, testing whether the protective role of cash is more pronounced in environments with weaker institutional support.

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Table 9. Robustness test by splitting the Shanghai and Shenzhen Stock Exchanges.

https://doi.org/10.1371/journal.pone.0341114.t009