Foreign bank presence, threshold effects, and institutional moderation: a causal machine learning approach to financial stability in Vietnamese banks

In the era of financial globalization and deepening integration, the growing presence of foreign banks (FBP) in developing and emerging economies has become a defining trend. Financial liberalization, facilitated by multilateral and bilateral commitments, has accelerated the entry of international banks into domestic markets, including Vietnam (Pham et al., 2021; Thu Huong et al., 2022). The expected benefits of FBPs are well-documented: they can enhance operational efficiency, foster competition, transfer technology, expand access to capital, and disseminate international governance standards (Horen and Claessens, 2012).

Yet, an important stream of research warns of potential drawbacks. In environments characterized by weak institutional frameworks, FBPs may increase financial instability, trigger capital reversals during market fluctuations, and even undermine the supervisory capacity of domestic regulators (Haque and Shahid, 2016; Williams, 2025). More recent contributions emphasize that such effects are nonlinear, with benefits or risks materializing only once foreign participation surpasses a certain threshold (Sui et al., 2023). This introduces a critical dimension to the literature, suggesting that the impact of FBPs cannot be captured adequately through linear models.

Vietnam offers a pertinent case study. Since its accession to the WTO in 2007, the share of assets and credit controlled by foreign banks has steadily risen, reflecting the country's deepening financial integration (Thu Huong et al., 2022). However, the domestic banking system remains under restructuring, struggling with persistent non-performing loans, limited transparency, and uneven risk management capacity. This dual reality highlights the urgency of reassessing how FBPs affect systemic stability in the Vietnamese context.

Within this nexus, institutional quality emerges as a decisive factor. Strong institutions can enhance supervisory effectiveness, ensure transparency, and mitigate potential risks associated with foreign participation (La Porta et al., 1998). Conversely, weak institutions may allow FBPs to exploit regulatory gaps, foster unfair competition, or intensify capital flight risks (Pozo, 2023). Importantly, 21st-century institutions are not confined to traditional pillars, such as rule of law, transparency, and government effectiveness, but increasingly encompass digital dimensions linked to e-government and technology-driven governance (Castro and Lopes, 2022; Malodia et al., 2021).

This study operationalizes institutional quality through a composite Enhanced Worldwide Governance Index (EWGI). The EWGI integrates six traditional governance indicators (rule of law, control of corruption, regulatory quality, government effectiveness, voice and accountability, political stability) with three e-government dimensions from the UN's EDGI (online services index, human capital index, telecommunication infrastructure index). Using principal component analysis (PCA), this index captures the multifaceted role of both traditional and digital institutions in shaping financial stability. Such a framework allows for a more comprehensive assessment of how institutional quality moderates the effects of FBPs.

Despite its importance, the literature reveals notable gaps. First, most studies have not treated institutional quality as a moderating variable in the FBP-stability relationship. Second, no integrated institutional index explicitly combining digital governance dimensions has been developed. Third, methodological approaches remain dominated by linear regressions, overlooking potential nonlinearities and heterogeneity of effects. Yet, recent evidence indicates that both the level of foreign bank presence and the strength of institutions can fundamentally reshape the FBP-stability nexus (Brana et al., 2024; Ghosh, 2024).

Addressing these gaps, the present study pursues four objectives: (1) to evaluate the impact of FBPs on the financial stability of Vietnamese banks, measured by ZSCORE; (2) to identify thresholds in this relationship using Hansen's (1999) threshold regression; (3) to examine the moderating role of institutional quality (EWGI, including EDGI components); and (4) to apply Causal Forests with Double Machine Learning as a heterogeneity-analysis tool to examine how banks respond differently to system-wide FBP exposure across institutional environments.

The contributions of this paper are threefold. First, it extends the theoretical debate by highlighting the moderating role of institutions, particularly digital governance, in shaping FBP outcomes. Second, it introduces a methodological innovation by combining threshold regression with causal machine learning, enabling the identification of nonlinearities alongside rigorous heterogeneity analysis. Third, it provides novel empirical evidence from Vietnam, an emerging economy undergoing both financial liberalization and digital institutional reform, thereby offering practical insights for conditional financial integration strategies.

The remainder of the paper is structured as follows. Section 2 reviews the theoretical framework and related literature. Section 3 develops the research hypotheses. Section 4 outlines the data and methodology. Section 5 presents the empirical results. Section 6 discusses the findings, and Section 7 concludes with policy implications.

The impact of foreign bank presence (FBP) in emerging and developing economies remains the subject of considerable debate. On the one hand, a strand of research suggests that FBPs foster competition, enhance efficiency, and improve capital access in host banking systems. For instance, Liu (2022) demonstrates that FBPs raise interest rate spreads in Asian emerging markets, thereby strengthening efficiency and performance, while Brana et al. (2024) provide evidence that international parent banks stabilize their affiliates by maintaining capital flows during crises. These findings lend support to the view that FBPs may contribute to systemic resilience by importing governance standards and liquidity from global networks.

On the other hand, an equally substantial body of work cautions that FBPs may generate new vulnerabilities, particularly under weak institutional conditions. Williams (2025) shows that in many emerging markets, foreign banks retrench from household and SME lending, effectively pushing borrowers toward informal finance. In Vietnam, Huynh (2024) finds that heightened competition induced by FBPs leads domestic banks to assume greater risk exposure, especially through corporate lending. This aligns with the argument that reliance on foreign funding may amplify instability when supervisory capacity is limited (Pozo, 2023).

Differences in entry mode further complicate the debate. Polovina and Peasnell (2023) distinguish between M&A-based entry and greenfield branches, showing that each adopts distinct credit strategies under stress, acquired banks emphasizing consumer lending, while branches sustain trade credit. This suggests that not only the scale but also the form of FBP shapes its systemic consequences.

What remains unsettled are the transmission channels through which FBPs affect stability. Some emphasize competition and efficiency as primary mechanisms (Ghosh, 2024; Liu, 2022), whereas others underscore capital withdrawal and dependence on international funding (Williams, 2025; Pozo, 2023). The mixed evidence reflects a high degree of context dependence, with outcomes conditioned by institutional quality.

For Vietnam, despite a notable rise in FBPs following WTO accession, empirical studies remain sparse and contradictory. Thu Huong et al. (2022) find stabilizing effects of foreign ownership on commercial banks, but these are not uniform across ownership groups. By contrast, Huynh (2024) and Pham et al. (2021) reveal heightened risks among smaller banks. Taken together, these results highlight the importance of adopting advanced methodologies capable of capturing nonlinearities, threshold dynamics, and heterogeneous effects, which remain largely absent from prior research.

Institutional quality is widely recognized as a cornerstone of financial stability. Strong institutions mitigate moral hazard, strengthen supervisory capacity, and enhance transparency, thereby reinforcing the resilience of banking systems. Tran et al. (2022), for instance, show that in 133 emerging and developing economies, market concentration and capitalization exert stabilizing effects only when institutional quality is sufficiently high. This underscores the view that institutional frameworks are not merely background conditions but active determinants of how financial structures affect stability.

Despite this, much of the literature treats institutions primarily as control variables, rather than testing them as formal moderators in the foreign bank presence-stability nexus (Gafarovna, 2023; Nandom et al., 2022). As a result, the conditional role of institutions remains underexplored. Moreover, existing measures of institutional quality are often limited. Most studies rely on the WGI or single proxies such as rule of law, neglecting emerging institutional dimensions linked to digitalization and e-government capacity.

Some recent contributions begin to bridge this gap by considering digital institutions and FinTech. Nguyen and Dang (2022) show, using data from 37 Vietnamese banks, that FinTech development can undermine financial stability, although market discipline partly offsets this risk. However, their analysis emphasizes market forces while leaving digital governance institutions unexamined. At the policy level, the United Nations (2022) highlights the E-Government Development Index (EDGI), covering online services, human capital, and telecommunication infrastructure, as a key dimension of modern governance, yet its application in finance and banking research remains minimal.

A promising methodological trend is the use of principal component analysis (PCA) to synthesize multiple institutional dimensions into composite indices. Yuan and Yan (2022) employ this approach to study foreign bank spillovers in developed markets. Nevertheless, applying PCA to integrate both traditional governance measures and EDGI into a multidimensional index for financial stability analysis is still rare, especially in emerging economies.

Taken together, prior research leaves three important gaps: institutions are seldom treated as formal moderators; multidimensional measures that incorporate digital governance are underutilized; and empirical applications in Vietnam, a country undergoing rapid digital institutional reforms, are almost absent. Addressing these gaps is essential for understanding how institutional quality, both traditional and digital, conditions the relationship between foreign bank presence and financial stability.

Although recent studies have advanced understanding of foreign bank presence (FBP) and institutional quality, several gaps remain. In Vietnam, where financial liberalization has progressed rapidly, empirical evidence is still limited and inconclusive regarding the net impact of FBPs on systemic stability. Moreover, institutional quality has rarely been examined as a formal moderator in the FBP-stability nexus. Most studies treat it as a control, overlooking its capacity to condition both the direction and magnitude of effects.

Measurement practices are also inadequate. Reliance on traditional indicators such as the Worldwide Governance Indicators (WGI) or Rule of Law neglects the digital and e-government dimensions that increasingly shape supervisory capacity and market discipline. This lack of a multidimensional index limits the ability to capture institutional realities in emerging economies.

Methodologically, prior research relies heavily on linear models, with little attention to threshold dynamics or heterogeneous effects. Advanced approaches, such as threshold regression and causal machine learning, remain underutilized, and no study has combined them to detect structural breakpoints and conditional impacts simultaneously.

These limitations restrict both academic insight and policy relevance, especially in Vietnam, where digital institutional reforms and financial integration are advancing in parallel.

The relationship between foreign bank presence (FBP) and financial stability in emerging economies is complex and context-dependent, driven by the interplay between institutional structures, market mechanisms, and non-linear dynamics. This study develops an integrated theoretical framework that consolidates multiple strands of economic theory, Institutional Theory, Competitive Advantage, Information Asymmetry, Liability of Foreignness, Threshold Theory, and Disruptive Innovation, into a coherent explanation of how and under what conditions FBP influences the stability of the banking system in Vietnam.

Institutional theory provides the foundational logic for this framework. Institutions, as defined by North (1990) and La Porta et al. (1998), establish the “rules of the game” that govern economic behavior, shape incentives, and influence risk-taking in the financial system. In environments characterized by strong governance, transparency, and effective supervision, foreign banks complement domestic institutions by transferring advanced technology, governance standards, and capital discipline. Conversely, in weak institutional settings, foreign banks may partially substitute for missing governance mechanisms, improving efficiency in the short term but potentially exposing the system to external vulnerabilities such as contagion or capital outflows (Pozo, 2023; Williams, 2025). This asymmetry suggests that institutional quality plays a moderating role, determining whether the influence of FBP on stability is stabilizing or destabilizing.

The contemporary understanding of institutional quality extends beyond traditional governance to include digital and technological dimensions. The Enhanced Worldwide Governance Index (EWGI), developed in this study, integrates the six traditional governance indicators from the WGI with the three e-government dimensions from the UN's EDGI. This integrated measure captures not only the legal and regulatory foundations of governance but also the digital capacity that strengthens monitoring and transparency. As digitalization increasingly underpins financial supervision and data governance, institutional quality becomes a multidimensional construct shaping how FBP translates into financial stability (Castro and Lopes, 2022; Tiganasu and Lupu, 2023).

The mechanism through which FBP affects stability operates primarily through competition and information channels. From the competitive advantage perspective (Porter, 1985), the entry of foreign banks enhances efficiency and market discipline by introducing superior managerial and technological capabilities, thereby fostering financial stability. However, information asymmetry theory (Berger and Udell, 2002; Mian, 2006) suggests that foreign banks often face disadvantages in acquiring soft information about local borrowers, particularly small and medium-sized enterprises, leading to credit rationing and risk redistribution. The net outcome depends on the institutional environment that regulates transparency and information flows, strong institutions mitigate these frictions, while weak institutions amplify them.

As FBP expands, the liability of foreignness (Hymer, 1960; Miller and Parkhe, 2002) becomes increasingly relevant. Foreign institutions incur higher costs and risks when operating in unfamiliar regulatory and cultural settings. While moderate levels of foreign participation can reinforce stability through diversification and improved governance, excessive dominance may increase systemic vulnerability by heightening dependence on external funding and global shocks (Sethi and Judge, 2009). This non-linearity aligns with Threshold Theory (Hansen, 1999), which posits that relationships between economic variables may change direction once critical levels are surpassed. Hence, the impact of FBP is expected to be positive up to an optimal threshold and negative beyond it, illustrating a “too much of a good thing” dynamic (Morgan and Strahan, 2003).

The role of digital transformation and disruptive innovation (Christensen, 1997) adds another layer of complexity. Foreign banks frequently act as technological disruptors, introducing FinTech-based solutions, AI-driven credit models, and cross-border digital compliance frameworks. When supported by robust digital institutions, such innovations enhance efficiency, risk monitoring, and systemic resilience. However, under weak digital governance, the same disruptions may magnify disparities between domestic and foreign institutions, exacerbate information asymmetries, and weaken system stability.

These theoretical elements are integrated in Figure 1, which presents the conceptual framework of the study. As illustrated, Foreign Bank Presence influences Financial Stability through competition and information channels. This relationship is subject to Threshold Effects, reflecting its non-linear nature, and is moderated by Institutional Quality (EWGI), which encompasses both traditional and digital governance. High institutional quality is expected to strengthen the stabilizing effect of FBP, while weak institutional environments may reverse it.

Building on this theoretical synthesis, four research hypotheses are proposed:

In summary, this integrated theoretical framework provides a coherent narrative explaining how FBP, institutional quality, and digital governance jointly shape financial stability in emerging economies. It unifies classical and contemporary theories under a single causal logic: foreign bank presence enhances financial stability through competition and governance spillovers, yet its effect is conditional on institutional strength and bounded by nonlinear thresholds. This conceptual foundation directly informs the empirical strategy that follows, particularly the use of threshold regression and causal machine learning to capture the nonlinearity and heterogeneity implied by the theoretical model.

The dataset is constructed from the financial statements of 28 Vietnamese commercial banks over the period 2010–2024. After data cleaning, processing, and standardization, the final dataset constitutes a balanced bank-year panel of 28 banks observed continuously over 15 years, yielding 420 bank-year observations. This framework reflects the specific context of Vietnam's banking system during its process of integration and digital transformation, while allowing for an in-depth analysis of the roles of FBP and institutional quality in financial stability.

Dependent variable (Financial Stability). Dependent variable (Financial Stability). Financial stability is primarily measured by the ZSCORE, a widely used indicator of bank insolvency risk in banking research, particularly in Vietnam (Pham et al., 2021; Tran et al., 2022). It is calculated as:

where ROA_it is return on assets, ETA_it is the equity-to-total-assets ratio, and $σ(ROAi)$ is the standard deviation of bank i's ROA over the sample period. A higher ZSCORE indicates a lower probability of insolvency and stronger financial stability. For robustness, the non-performing loan ratio is employed as an alternative stability-risk measure:

A higher NPL indicates weaker asset quality and greater credit risk. The use of both ZSCORE and NPL provides complementary evidence on bank stability and credit-risk conditions.

Key variable (Foreign Bank Presence–FBP). FBP is measured using two system-level annual indicators: (1) FS1, defined as the number of foreign bank branches operating in Vietnam relative to the total number of banks, and (2) FS2, defined as the share of total banking assets held by foreign banks. Because both variables are measured at the banking-system level, they are common to all banks within the same year and vary over time. FS1 captures the breadth of foreign bank participation, whereas FS2 reflects the depth of foreign bank penetration through asset-scale influence (Huynh, 2024; Pham et al., 2021; Thu Huong et al., 2022).

Moderator (Institutional Quality). This study introduces a multidimensional measure of institutional quality, the EWGI, which integrates six governance dimensions from the WGI (voice and accountability, political stability, government effectiveness, regulatory quality, rule of law, and control of corruption) with three digital governance indicators from the UN EDGI (online services, telecommunication infrastructure, and human capital). These nine components collectively capture both the normative and operational dimensions of institutional capacity. EWGI is a national/system-year variable, common to all banks in a given year, and is interpreted as capturing how institutional conditions moderate the FBP-bank stability nexus.

The construction of the EWGI rests on the premise that institutional quality in the digital era extends beyond traditional governance toward the state's ability to implement and enforce rules through digital means. Recent studies (Castro and Lopes, 2022; Tiganasu and Lupu, 2023; Behera et al., 2024) emphasize that e-government, digital infrastructure, and human capital are not merely technological indicators but essential elements of institutional effectiveness, enhancing transparency, regulatory enforcement, and accountability. Accordingly, integrating WGI and EDGI dimensions allows the EWGI to represent a more comprehensive and conceptually coherent understanding of modern institutional quality.

Methodologically, PCA is employed to extract the common latent factor underlying these dimensions, interpreted as overall institutional capacity. The PCA results (KMO = 0.75; Bartlett's χ² = 569.21, p < 0.001) confirm strong internal consistency and justify the aggregation. The first principal component explains 68% of the total variance, indicating that the combined indicators converge toward a single underlying construct of institutional quality. The resulting EWGI thus provides a robust, unified, and empirically validated measure that captures both the quality of formal institutions and the digital capacities that sustain them. Detailed PCA results are reported in Appendix (Table B and Figure A).

Control variables. To isolate the pure effects of FBP and institutional quality, the model incorporates a set of control variables grounded in theory and prior empirical research (Giannetti and Ongena, 2012; Gopalan and Rajan, 2017; Kowalewski and Pisany, 2022): (1) Bank characteristics: lag_ZSCORE (one-period lag of financial stability), SIZE (bank size, log of total assets), NIM (net interest margin), LERNER index (market power), LDR (loan-to-deposit ratio), CTI (cost-to-income ratio), LLP (loan loss provisions), and OWNERSHIP (ownership type); (2) Macroeconomic factors: GDP growth, inflation (INF); and (3) Systemic shocks: a COVID-19 dummy to control for the exceptional impact of the global pandemic.

The inclusion of these controls mitigates omitted variable bias and ensures that results capture the true relationships among FBP, EWGI, and ZSCORE. The dataset combines bank-level and system-level variables. While ZSCORE and bank controls vary across banks and years, FS1, FS2, and EWGI are system-year variables, common to all banks in a given year and varying only over time. Detailed definitions of the variables and their measurement are provided in Appendix (Table A).

The study is based on a balanced bank-year panel of 28 Vietnamese commercial banks covering 2010–2024, yielding 420 observations. The research design proceeds in two steps. First, threshold regression (Hansen, 1999) is applied to identify thresholds at which the impact of foreign banks changes in nature, from positive to negative, or vice versa. Second, the study employs causal machine learning, specifically Causal Forests combined with Double Machine Learning (Athey and Imbens, 2017), to examine effect heterogeneity and evaluate the moderating role of institutions.

This combination leverages the strengths of traditional econometrics in modeling nonlinearity while harnessing modern machine learning's capacity to uncover heterogeneous treatment effects, resulting in a research design that is both methodologically rigorous and scientifically persuasive.

A potential endogeneity issue may arise from omitted variables and reverse causality, which could bias the estimated relationship between FBP and ZSCORE. Unobserved factors such as macroeconomic conditions, market competition, or regulatory reforms may simultaneously influence both FBP and domestic bank stability. Similarly, financially sound banks may attract greater foreign participation rather than being stabilized by it.

To mitigate these concerns, the empirical design incorporates an extensive set of macroeconomic, institutional, and bank-specific control variables to reduce omitted variable bias. The threshold regression captures structural nonlinearities that conventional linear models may overlook, while the causal forest method, grounded in the potential outcomes framework (Athey and Imbens, 2017), balances confounding covariates and estimates heterogeneous treatment effects. This approach approximates quasi-experimental conditions and helps isolate the conditional causal influence of FBP on financial stability.

While endogeneity cannot be entirely eliminated due to data and instrument limitations, the consistency of results across econometric and causal learning methods lends confidence to the structural validity of the findings. Future research may extend this framework using panel estimators or instrumental variables to further strengthen causal inference.

To examine the existence of FBP thresholds, this study applies the threshold regression approach developed by Hansen (1999). This method enables the detection of whether the relationship between FS1/FS2 and financial stability changes in nature once a certain level is exceeded. Specifically, the model estimates potential threshold values and employs a bootstrap procedure to select the optimal threshold while testing the statistical significance of regime shifts.

The core idea is that the relationship between foreign bank presence and financial stability may change fundamentally once it crosses a critical level, denoted as γ. The general model can be expressed as follows:

Where: ZSCORE_it​ denotes financial stability of bank i at time t; FBP_t​ represents foreign bank presence, proxied by FS1 or FS2; I(⋅) is an indicator function splitting the sample into two regimes depending on whether FBP is below or above the threshold γ; X_it is a vector of control variables; μ_i​ captures bank-specific effects; ε_it​ is the error term.

This specification allows for differential impacts of FBP on financial stability depending on whether the observed level of foreign bank presence is below or above the estimated threshold.

The estimation procedure follows three steps: (1) testing for the existence of a threshold, (2) estimating the optimal threshold value γ using a bootstrap procedure, and (3) comparing the coefficients β₁​ and β₂​ to evaluate how the effect changes before and after the threshold. This approach directly addresses the central question: whether there exists a “critical level” of FBP at which its impact shifts from positive to negative, or vice versa. This forms the empirical basis for testing the nonlinear hypothesis (H2).

To further examine heterogeneity in bank-level responses, the study employs Causal Forests combined with Double Machine Learning (CDML). In this setting, FS1 and FS2 are not interpreted as bank-level treatments, because all banks face the same FBP level within a given year. Rather, they are treated as system-wide exposure variables, and CDML is used to assess how banks with different characteristics respond differently to common changes in FBP over time.

Within this framework, the key objective is to estimate the CATEs:

Here, $τ(x)$ is interpreted as a conditional heterogeneous response function rather than a strict bank-level treatment effect. It captures how bank characteristics X are associated with different stability responses to system-wide FBP exposure over time.

This approach is particularly well-suited to testing the moderating role of institutional quality. By stratifying banks into groups with high versus low EWGI, CDML generates three key outputs: (1) ATE for the full sample, reflecting the average effect of foreign bank presence; (2) CATEs for subgroups defined by strong and weak institutions, which reveal effect heterogeneity; and (3) The difference in ATEs (ΔATE) between groups, accompanied by statistical tests (p-values) and confidence intervals (CIs).

Accordingly, CDML provides complementary evidence for H3 and H4 by examining whether bank-level responses to system-wide FBP exposure differ across institutional conditions. This constitutes a novel contribution compared with most prior studies, which largely relied on homogeneous linear specifications.

The adoption of the CDML is driven by its capacity to estimate heterogeneous response patterns without imposing restrictive functional assumptions. CDML integrates the flexibility of ensemble learning with the orthogonalization principle, mitigating bias from high-dimensional confounders and enabling valid inference on CATEs (Athey and Imbens, 2017). Compared with alternatives, CDML is more suitable for this setting: propensity score and OLS methods capture only average effects; instrumental variable (IV) approaches require strong exclusion restrictions often unavailable in banking data; and BART or TMLE models rely on priors and are prone to overfitting in smaller samples. The CDML framework, through sample splitting and double estimation, reduces these risks and remains computationally efficient. Robustness checks based on honest sample splitting and out-of-bag diagnostics confirm model stability, supporting the reliability of the estimated heterogeneity patterns.

To verify the robustness of the findings, financial stability is alternatively measured by the non-performing loan ratio (NPL) instead of the ZSCORE. If the estimated effects of foreign bank presence remain statistically significant under this alternative specification, the results provide stronger evidence of consistency and reliability.

Because FS1, FS2, and EWGI are system-year variables, CDML is not used to infer causal effects from differential bank-level treatment assignment. Instead, it is used as a heterogeneity-analysis tool to examine how banks with different ownership, size, and balance-sheet characteristics respond to common annual changes in FBP and institutional quality. Thus, temporal variation identifies system-wide exposure, while bank-level covariates explain heterogeneous responses.

The CDML procedure was implemented using honest sample splitting and cross-fitting. FS1 and FS2 were defined as system-year exposure variables, while ZSCORE was used as the outcome. The conditioning covariates included lagged ZSCORE, bank-specific controls, ownership type, COVID-19 period, and EWGI-based institutional groups. Forest hyperparameters, including the number of trees, tree depth, and minimum leaf size, were selected to ensure sufficient observations in terminal nodes and to reduce overfitting. ATEs and CATEs were reported with standard errors, 95% confidence intervals, and two-sided p-values. Since FS1, FS2, and EWGI vary at the system-year level, the estimates are interpreted as heterogeneous bank-level responses to common annual FBP exposure rather than causal effects from differential bank-level treatment assignment.

To provide an overview of the research sample and the preliminary relationships among variables, Table 1 presents the descriptive statistics for all variables. This analysis not only highlights the distributional characteristics of the dataset but also reveals potential linkages, thereby guiding subsequent empirical testing in later sections.

The results in Table 1 indicate that the research variables exhibit moderate dispersion, reflecting both diversity and overall stability of the dataset. The financial stability measure, ZSCORE, has a mean of 2.862 with a standard deviation of 0.512, suggesting that most banks maintain a relatively sound level of stability, though notable differences remain across observations.

The two indicators of FBP, FS1 and FS2, report mean values of 0.213 and 0.101, respectively. This implies that foreign banks account for a moderate share in terms of both number and assets, yet their presence is sufficient to influence industry structure. Control variables such as SIZE, NIM, LDR, and CTI display reasonable variation, capturing differences in scale and operational efficiency among banks.

Notably, the institutional quality index (EWGI) records a mean of −1.095 with a standard deviation of 0.688, highlighting considerable institutional variation during the observation period, consistent with Vietnam's ongoing transformation in governance and digitalization.

Figure 2 presents correlation matrix among the main variables, revealing several noteworthy patterns. ZSCORE and FS1 exhibit a negative correlation (−0.13), suggesting that an increase in the number of foreign bank branches may intensify competitive pressure and, in the short run, undermine the stability of domestic banks. In contrast, ZSCORE and FS2 show a modest positive correlation (0.09), indicating that greater asset shares held by foreign banks are associated with improved systemic stability, albeit weakly. This divergence underscores the importance of measurement choice in assessing the effects of FBP.

Over the study period, ZSCORE and EWGI display a negative correlation (−0.12), contrary to theoretical expectations that stronger institutions are linked with higher stability. This finding may reflect Vietnam's context, where institutional improvements have not yet translated directly into enhanced banking stability, but rather interact with mediating factors such as ownership structure and international integration. Overall, the descriptive and correlation analysis reveals that the core variables do not align uniformly with financial stability. While FS1 suggests heightened risk, FS2 conveys a positive signal, and EWGI's role remains inconclusive. These observations provide an important foundation for further examination through threshold regressions and causal estimation in subsequent sections.

Dynamic trend analysis in Figure 3 indicates that ZSCORE declined in the pre-COVID-19 period but showed signs of recovery afterward. In contrast, both FS1 and FS2 dropped markedly following the pandemic, reflecting a contraction in the role of foreign bank presence (FBP). Meanwhile, EWGI demonstrates a steady upward trajectory, suggesting that institutional reforms continued despite the COVID-19 shock.

The descriptive statistics and correlation analysis thus provide preliminary evidence that FBP and institutional quality may not yet align with financial stability in Vietnam. These findings underscore the necessity of applying threshold regression and causal methods in subsequent sections to test more complex relationships among the variables.

The threshold regression estimates reported in Table 2 confirm a pronounced nonlinear effect of FBP on financial stability.

Specifically, for FS1 (the share of foreign banks by number), the optimal threshold is identified at 0.1923. Below this threshold, the estimated coefficient is negative (−20.78) and statistically significant at the 5% level, implying that initial increases in FBP substantially undermine ZSCORE. By contrast, once the threshold is exceeded, the effect turns positive (1.51) and becomes marginally significant at the 10% level. This suggests that a sufficiently large foreign bank presence may enhance stability through mechanisms such as market discipline, governance spillovers, and diversification of funding sources.

For FS2 (the asset share of foreign banks), the optimal threshold is identified at 0.0969. Below this level, the effect of FS2 is positive (13.00), while beyond the threshold the coefficient turns negative (−5.78). However, neither effect is statistically significant, suggesting that a small foreign asset share is insufficient to exert a meaningful influence on systemic stability. Nonetheless, caution is warranted regarding potential instability once the market share of foreign bank assets rises, consistent with concerns about sudden capital withdrawal and excessive competition.

These results align with Threshold Theory (Hansen, 1999), which posits that the impact of FBP is nonlinear and may change direction once a critical level is exceeded. The findings also reinforce Hypothesis H2, which argues that FBP can generate both benefits and risks depending on the threshold. Compared with Morgan and Strahan (2003), the Vietnamese case illustrates a dual role: a larger number of foreign banks may exert positive disciplinary pressure, whereas excessive concentration of foreign bank assets could heighten systemic vulnerabilities.

Overall, the empirical evidence suggests that the effect of FBP on financial stability in Vietnam is nonlinear and highly sensitive to measurement choice (FS1 vs. FS2). This implies that financial liberalization policies should be carefully calibrated: while encouraging entry in terms of the number of foreign banks may foster competition and governance standards, tighter control over asset concentration is needed to prevent systemic risks.

While threshold regression provides evidence of nonlinear FBP effects, it still assumes homogeneity within each regime. To address this limitation and assess the heterogeneity of impacts, the study employs the CDML approach, which allows estimation of both the ATE and the CATEs across subgroups.

The results in Table 3 show that, on average, both measures of system-level FBP are associated with stronger bank-level financial stability, with heterogeneous responses across bank groups, with heterogeneous responses across bank groups. Specifically, FS1 yields an ATE = 54.50 (CI: 26.46–82.54, p < 0.01), while FS2 produces an ATE = 53.84 (CI: 18.86–88.82, p < 0.01). These findings suggest that, on average, system-level FBP is associated with stronger bank-level stability after conditioning on observed bank characteristics, although this average pattern should be interpreted alongside the nonlinear regime-specific evidence from the threshold model (Claessens and Van Horen, 2014).

However, when disaggregating by ownership type, bank size, and the COVID-19 period, the effects reveal noteworthy heterogeneity:

1. By OWNERSHIP: Foreign banks exert positive effects on both SOEs (23.47) and JSCBs (25.18), though the impact is slightly stronger among JSCBs. This suggests that foreign banks enhance governance capacity more effectively in private-sector environments, where market mechanisms play a dominant role.

2. By SIZE: The effect is substantially weaker for large banks (16.25) compared to smaller banks (33.62), implying that smaller institutions benefit more from FBP, potentially through improved access to technology, capital, and managerial expertise.

3. By COVID-19 period: Before the pandemic, the effect of FS1 was stronger (31.42) than in the post-COVID period (11.97), indicating that the crisis diminished the stabilizing benefits of FBP in terms of bank numbers. For FS2, however, the opposite trend emerges: the post-COVID effect (30.88) exceeds the pre-COVID effect (22.65), suggesting that in times of heightened uncertainty, the asset share of foreign banks becomes increasingly critical for sustaining stability.

These findings both reinforce and extend prior research (Jeon et al., 2011; Boubakri et al., 2020), demonstrating that the benefits of FBP are not homogeneous but strongly contingent on ownership structure, institutional scale, and macroeconomic shocks. From a hypothesis-testing perspective, the results support H3, emphasizing the heterogeneous nature of FBP's impact and confirming that its role cannot be adequately assessed by average effects alone. The CDML evidence indicates that smaller banks and those in the private sector derive greater benefits from FBP, while systemic shocks such as COVID-19 can alter the transmission channels, particularly when foreign bank assets are considered.

The threshold and CDML findings are complementary. The threshold model captures regime-specific nonlinear associations and therefore shows that FS1 changes sign around the estimated threshold, while FS2 has weak regime-specific effects. CDML, by contrast, summarizes average and heterogeneous bank-level responses to system-wide FBP exposure after conditioning on observed bank characteristics. Thus, threshold regression explains when the FBP–stability relationship changes, whereas CDML explains which banks respond more strongly to FBP exposure.

To examine the moderating role of institutional quality, the study applies CDML using EWGI as the grouping variable. The results in Table 4 reveal substantial differences in the bank-level responses to FBP exposure between periods of high and low institutional quality.

For FS1, the overall ATE reaches 48.29 (CI: 39.59–56.99, p < 0.01), confirming the average positive impact of FBP on financial stability. However, subgroup analysis reveals stark contrasts: during years characterized by stronger institutional quality, the effect drops to only 2.11, while during years characterized by weaker institutional quality it rises to 88.70, yielding a difference of −86.59 (p < 0.01). This suggests that in weaker institutional environments, FBP acts as a critical substitute, reinforcing systemic stability, whereas in stronger institutional settings its additional contribution becomes negligible.

For FS2, the average impact is even stronger, with an ATE of 107.83 (CI: 105.37–110.28, p < 0.01). Yet, similar to FS1, significant heterogeneity emerges: in the high-institution group the effect is 85.24, compared to 127.59 in the low-institution group, a difference of −42.35 (p < 0.01). This indicates that in periods of weaker institutional quality, a larger foreign asset share may serve as a “stability shield,” leveraging international capital, managerial expertise, and crisis resilience.

These findings align with Institutional Theory (North, 1990; La Porta et al., 1998), which posits that the impact of FBP is highly contingent on the host-country institutional framework. They also extend prior studies (Peek and Rosengren, 2000; Cull and Martínez Pería, 2013), underscoring that FBP is not unconditionally beneficial; rather, its effectiveness is context-dependent, its stabilizing role is amplified under weak institutional environments.

Evidence from Table 4 thus supports Hypothesis H4, demonstrating that institutional quality moderates both the magnitude and direction of FBP's effect on financial stability.

To verify the reliability of the main results, robustness tests were conducted by substituting the financial stability measure from ZSCORE to NPL, a direct indicator of asset quality and credit risk. The results, presented in Table 5, show that the findings remain broadly consistent, although variations in the sign and magnitude of effects are observed.

For FS1, the average effect on NPL is negative (ATE = −2.08, CI: −2.31 to −1.85, p < 0.01), indicating that higher foreign bank presence helps reduce non-performing loans. This effect also varies by institutional quality: in the high-institution group, the effect is only −1.10, whereas in the low-institution group it reaches −2.93, with a statistically significant difference (Δ = 1.82, p < 0.01). This reinforces the view that in weaker institutional environments, FBP plays a more important role in mitigating credit risk.

By contrast, for FS2, the average effect is positive (ATE = 2.97, CI: 2.22–3.72, p < 0.01), suggesting that a higher foreign asset share may be associated with increased credit risk. Disaggregation by EWGI reveals a striking divergence: in the high-institution group, FS2 has a negative effect (−2.11), whereas in the low-institution group the effect is strongly positive (7.42), with a significant difference of −9.53 (p < 0.01). This implies that in weak institutional contexts, rising foreign asset shares may exacerbate NPL risk, opposite to the mitigating effect observed with FS1.

Overall, the robustness checks confirm that the impact of FBP is not confined to a single measure of financial stability. Although the magnitude and direction of effects differ, the evidence consistently underscores the moderating role of institutions and supports the argument that FBP's impact is context-dependent. These results enhance both the credibility and generalizability of the study's findings.

The empirical results from threshold regressions and Causal Forest analysis indicate that FBP exhibits nonlinear associations with financial stability and heterogeneous bank-level responses. This is consistent with the theoretical framework: according to the discipline effect (Horen and Claessens, 2012), foreign banks bring market discipline, international governance standards, and modern technology, thereby improving efficiency and reducing systemic risk. The stronger stability effects observed in smaller and private banks are also aligned with the spillover effect, as weaker domestic banks benefit from competition and governance spillovers. Because FS1, FS2, and EWGI vary at the system-year level, the findings should be interpreted as heterogeneous bank-level responses to changes in Vietnam's foreign bank presence and institutional environment. Such heterogeneity arises from differences in bank characteristics, including ownership, size, and balance-sheet structure, rather than from within-year cross-bank variation in FBP or EWGI.

However, the findings also show that when the foreign asset share (FS2) exceeds the optimal threshold, financial risk tends to increase. This provides empirical support for the liability of foreignness argument (Hymer, 1960; Miller and Parkhe, 2002; Sethi and Judge, 2009), which posits that excessive reliance on FBP can expose the system to external shocks.

The moderating role of EWGI, a modern institutional construct encompassing e-government, governance quality, and transparency, emerges prominently. The results suggest that in countries with strong institutions, the marginal stabilizing effect of FBP diminishes, whereas in weaker institutional contexts, foreign banks serve as an important substitute for deficient supervisory capacity. This extends prior research, which mainly emphasized traditional legal frameworks (La Porta et al., 1998; Barth et al., 2004), by showing that digital and technology-driven institutions can fundamentally shape the transmission mechanism of FBP.

From the hypothesis-testing perspective, the results support H1 and H2 by confirming the nonlinear and differentiated impacts of FS1 and FS2 on financial stability. H3 is validated through significant heterogeneity by ownership, size, and the COVID-19 shock. Finally, H4 is strongly supported, as institutional quality (EWGI) is shown to be a critical moderator of FBP's effects.

Policy implications highlight that financial liberalization alone, i.e. increasing foreign bank presence without institutional reforms, may generate adverse effects, particularly when foreign asset shares exceed sustainable thresholds. Therefore, financial integration strategies must be coupled with institutional strengthening, focusing on supervisory capacity, transparency, and digital governance to fully harness the benefits of foreign bank participation.

This study examines how foreign bank presence (FBP) influences financial stability in emerging economies, using Vietnam as a case study. Employing threshold regression and Causal Forest-based heterogeneity analysis, the results show that the relationship between FBP and financial stability is nonlinear and heterogeneous. Moderate levels of foreign participation enhance stability through competition, efficiency, and governance spillovers, while excessive penetration may generate systemic vulnerabilities. The effect also differs across ownership types, bank sizes, and periods, with notable variations before and after the COVID-19 shock. Importantly, institutional quality, measured by EWGI, which combines traditional and digital governance, plays a decisive moderating role. Under weak institutional settings, foreign banks act as stabilizing substitutes for governance gaps, whereas in stronger institutional environments their marginal impact declines. These findings extend existing literature by revealing how modern institutional and digital capacities condition the outcomes of financial integration.

Policy implications follow directly from these insights. Financial liberalization should be managed within prudent thresholds, preventing excessive foreign dominance that could threaten systemic resilience. Liberalization must proceed in parallel with institutional strengthening, enhancing transparency, supervisory effectiveness, and digital oversight. Private and smaller banks should be encouraged to leverage FBP's technological and governance advantages, while regulators must remain vigilant to macroeconomic shocks, balancing openness with prudential safeguards. Moreover, the role of digital institutions highlighted by the EWGI underscores the need to develop robust e-government and data-governance frameworks, which can reinforce traditional supervision and promote financial stability in the digital era.

While this study contributes novel empirical and methodological insights, certain limitations remain. The focus on emerging economies limits comparability with advanced systems; the EWGI, though comprehensive, does not capture all institutional dimensions; and the Causal Forest-based heterogeneity analysis, despite its strengths, remains subject to omitted-variable risks and should not be interpreted as relying on differential bank-level treatment assignment. Future research should compare cross-country differences, refine institutional indices, and further integrate causal AI tools to deepen understanding of how FBP interacts with evolving institutional architectures. Another limitation is that FS1, FS2, and EWGI are measured at the system-year level and therefore vary over time but not across banks within the same year. As a result, the estimated relationships are identified primarily from temporal variation in Vietnam's foreign bank presence and institutional conditions. Future research may extend this design by using cross-country panels, bank-level foreign exposure measures, dynamic panel GMM, or panel threshold specifications when richer cross-sectional variation becomes available.

In summary, foreign bank presence is neither inherently stabilizing nor destabilizing, it is conditional on institutional quality, digital capacity, and regulatory thresholds. A balanced approach to financial openness, grounded in institutional reform and digital governance, is essential to ensure that foreign banks become anchors of stability rather than sources of fragility in emerging financial systems.

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