Integrated Micro–Meso–Macro Modelling of Small and Medium Enterprise Repayment Behaviour Using Dynamic Panels, Markov Chains, and Stochastic Differential Equations

Understanding SME loan repayment performance requires integrating insights across financial economics, crisis management, public policy, and more recently, public health. The COVID-19 pandemic has renewed scholarly interest in how external shocks propagate through SME financing channels and how policy interventions can stabilise vulnerable firms. This section synthesises five major strands of literature: SME financial resilience, government support measures, banking sector interventions, vaccination and public health economics, and post-pandemic modelling approaches. It also highlights the methodological and conceptual gaps that motivate the present study.

2.1 Small and medium enterprise loan repayment, financial health, and cash-flow resilience

SME loan repayment behaviour has traditionally been examined through the lens of firm-level financial health and credit risk modelling. Late payment of invoices creates cash flow uncertainty that erodes creditworthiness and prompts banks to tighten lending, often through credit rationing and higher interest rates [10].

When banks begin a crisis with limited capital headroom, they cut SME loan commitments by roughly 10 percentage points and see a higher incidence of borrower exits, amplifying repayment pressure on already thin liquidity buffers [4]. Classical studies emphasise the role of cash-flow stability, profitability, leverage, and liquidity in determining a firm’s ability to meet debt obligations. SMEs, compared to large firms, tend to have weaker balance sheets, limited diversification, and greater exposure to market fluctuations. As a result, they exhibit higher sensitivity to shocks such as demand variation, supplier delays, and credit tightening.

Prior literature identifies repayment persistence as a robust empirical regularity: firms with strong repayment histories are statistically more likely to remain compliant, reflecting both behavioural consistency and lenders’ selection effects [11]. During the COVID-19 pandemic, SMEs with weak cash flow buffers experienced a 21 percent rise in insolvency risk, whereas firms that maintained innovation-driven cash reserves were more resilient and preserved access to bank credit [12].

However, SMEs’ dependence on short-term cash flow means even temporary disruptions can trigger delinquency or default. In environments where bank credit is constrained, SMEs turn to trade credit as an alternative source of financing, using supplier-provided credit to smooth payments and sustain operations [13]. Empirical evidence from the SAFE data shows that past credit restrictions increase the likelihood of future restrictions, but firms that have built stronger cash flow cushions can mitigate this state dependence and reduce the probability of later rationing [14].

Studies before COVID-19 show that liquidity shortages, working capital constraints, and unexpected operational interruptions are major predictors of repayment difficulties [15]. Overall, robust cash flow management, through diversified financing, prudent liquidity buffers, and innovation, enhances resilience and helps SMEs meet loan obligations and sustain financial health in turbulent periods. Taken together, these findings indicate that SME financial fragility is highly path-dependent and vulnerable to external shocks.

2.2 Government support as a stabilising mechanism in crisis periods

The role of government intervention has long been studied in financial crises, with research suggesting that fiscal support can serve as a buffer that prevents mass firm failures. During COVID-19, governments worldwide enacted unprecedented support packages that included direct grants, wage subsidies, tax deferrals, guarantee schemes, and low-interest credit programs.

Empirical evidence suggests that such support helped maintain employment, prevent liquidity collapses, and reduce bankruptcy filings [16]. However, the impacts varied significantly across firm size, industry classification, and pre-pandemic financial condition. Some studies argue that support was unevenly distributed, or that schemes may have induced moral hazard or extended the life of non-viable “zombie” firms [17, 18].

Crucially, most existing research treats government support as a static or exogenous variable. Very few studies model how its effectiveness interacts with behavioural dynamics (e.g., firms adapting strategies over time) or structural conditions that shifted throughout the pandemic. Existing reviews point out that studies of SME loan behaviour often ignore core financial mechanisms, such as credit rationing, moral hazard, and institutional economics, when assessing how state interventions affect stability [19, 20].

Even fewer integrate government support into a formalised mathematical modelling framework that incorporates pre- and post-pandemic structural shifts. This gap motivates the inclusion of government support as an explicitly modelled, time-varying determinant of loan repayment in the present study.

2.3 Banking sector interventions and credit market responses

Financial institutions played a central role during the pandemic, implementing moratoria, loan restructuring, grace periods, and flexible classification guidelines. Research shows that moratoria and restructuring helped prevent widespread SME defaults in the early phases of the pandemic by alleviating immediate repayment pressures [21]. These interventions also served broader macroprudential goals by ensuring stability in the banking system.

However, the literature warns of potential unintended consequences. Regulatory forbearance may obscure true credit risk, shift delinquency rates temporarily rather than structurally, and increase future non-performing loans if firms recover slowly [22]. Additionally, studies highlight variation in bank responses depending on risk appetite, customer portfolio composition, and expectations of post-pandemic recovery [23].

Importantly, existing work tends to evaluate banking interventions retrospectively or descriptively. Few studies incorporate these interventions into dynamic models capturing how repayment performance evolves over time under changing banking policies. Moreover, interactions between banking support and other crisis-related determinants, such as vaccination or government fiscal support, remain under-modelled. The present study addresses these gaps by situating banking interventions as a formal input in both micro-level and macro-level repayment models.

2.4 Vaccination, workforce continuity, and economic reopening

Vaccination is rarely explored in classical SME financing literature, yet the pandemic forced researchers to reconsider the relationship between public health and economic performance. Empirical evidence from Latin America showed that higher vaccination rates in 2021 were associated with a faster return to work, especially for disadvantaged groups whose lagging vaccine uptake had been an impediment to labour market recovery [24]. High vaccination rates reduce illness-related absenteeism, ease labour shortages, and support the reopening of retail, services, and manufacturing sectors. These effects restore business continuity and indirectly improve firms’ ability to generate cash flow and maintain loan repayments.

A panel data model covering 43 countries found that each additional 1% of the population vaccinated generated roughly 10 900 extra employed persons per quarter, offsetting the negative employment shock of COVID-19 infections [25]. Studies in public health economics highlight vaccination as a key mechanism enabling economic normalisation, but only a handful of papers explicitly link vaccination progress to firm-level financial outcomes. At the organisational level, a strong COVID-19 safety climate, shaped by clear policies and communication, boosted employees’ adherence to protective measures and increased willingness to be vaccinated, thereby reducing absenteeism and supporting smoother reopening [26]. Systematic reviews of the pandemic’s labour impact confirm that disruptions were most severe for workers in high-contact occupations, but that vaccination helped mitigate these disparities by lowering infection-related absences [27].

Some macroeconomic models incorporate vaccination into growth projections, but microeconomic studies remain scarce. There is virtually no modelling framework in the existing SME finance literature that integrates vaccination as a determinant of repayment dynamics or embeds it in a structural modelling architecture. The current study therefore advances the literature by treating vaccination as a quantifiable, time-varying influence on SME financial performance, integrated directly into the dynamic panel, Markov transition, and SDE models.

2.5 Post-pandemic modelling approaches and gaps in the literature

In the wake of COVID-19, researchers have employed a range of modelling approaches to study economic recovery, including general equilibrium models, agent-based simulations, and time-series forecasting [28-31], as well as a flood-related modelling study [32]. These models provide insights into macroeconomic trajectories, but they often overlook SME-specific repayment behaviour, or fail to integrate firm-level financial dynamics with public health variables.

Meanwhile, the credit risk literature predominantly relies on Markov models, dynamic panel models, and survival analysis to analyse default behaviour, yet each approach exhibits limitations when confronted with pandemic-induced disruptions. Dynamic panel models, while effective at capturing borrower heterogeneity and temporal persistence, rarely incorporate public health indicators or structural break mechanisms that reflect abrupt shifts in economic conditions [33]. Markov models, although widely used to represent transitions between repayment states, typically assume static probabilities or rely solely on financial ratios, thereby overlooking the influence of external interventions such as fiscal support or banking forbearance [34]. Continuous-time formulations, including SDE models, offer strong potential for depicting smooth macro-level repayment trajectories [35], but they remain largely absent in SME-focused applications and are seldom integrated with micro-level credit dynamics or crisis-responsive variables.

As a result, to the best of the author’s knowledge, no existing study unifies all three modelling layers into a single coherent framework that captures interactions between public health progress, fiscal support, and banking interventions.

2.6 Synthesis and research gap

The existing literature on SME loan repayment performance can be broadly classified into four methodological strands: (i) static econometric models of default or delinquency, (ii) dynamic firm-level repayment models, (iii) policy evaluation studies focusing on government or banking interventions, and (iv) macro-level or aggregate recovery models developed in response to the COVID-19 shock. While each strand contributes important insights, the strands remain fragmented in both scope and methodological structure.

First, traditional credit risk and repayment studies predominantly rely on static cross-sectional or short-panel econometric models, such as logit, probit, or hazard specifications, to estimate default probabilities based on firm characteristics and macroeconomic indicators. Although these models are well-suited for prediction, they typically abstract from repayment persistence, state dependence, and structural breaks, limiting their ability to capture crisis-driven dynamics and recovery paths.

Second, more recent studies employ dynamic panel models to account for repayment persistence and unobserved firm heterogeneity. These approaches improve upon static specifications by modelling intertemporal dependence in repayment outcomes. However, most dynamic models treat policy interventions as exogenous controls and rarely distinguish between pre- and post-pandemic structural regimes. Nor do they explicitly incorporate public health variables such as vaccination progress.

Third, policy-oriented analyses examine the effects of government fiscal support (e.g., grants, wage subsidies, guarantees) or banking sector interventions (e.g., moratoria, restructuring) in isolation. These studies often use reduced-form evaluation strategies or difference-in-differences designs, focusing on short-term survival or default outcomes. While informative, they do not model how multiple interventions interact dynamically over time, nor how firms transition between repayment states under evolving policy environments.

Fourth, emerging macroeconomic and recovery-focused models developed during and after the COVID-19 pandemic adopt aggregate or representative-agent frameworks, sometimes using stochastic processes to describe economic recovery. These models provide useful high-level insights but lack a clear linkage to micro-level firm repayment behaviour and do not account for heterogeneity in policy exposure across firms.

In contrast to these existing approaches, the proposed framework in this study offers a deliberately integrated, multi-layer modelling architecture that unifies micro-level dynamics, state transitions, and aggregate behaviour within a single analytical structure. Specifically, the framework differs from prior work in four key methodological dimensions.

First, it explicitly incorporates vaccination rates as a time-varying determinant of repayment performance, reflecting the role of public health in restoring operational continuity, an element largely absent from existing credit risk and SME finance models. Second, it jointly models government support and banking interventions, allowing their effects to vary dynamically across pre- and post-pandemic regimes rather than treating them as static covariates. Third, it combines three complementary modelling layers: a dynamic panel model, a Markov transition model, and a continuous-time SDE model, thereby capturing repayment persistence, discrete state changes, and aggregate trajectories within a coherent framework. Finally, the framework is explicitly designed for simulation-based policy analysis, with clearly defined boundary conditions, transition structures, and scenario pathways, rather than solely for retrospective estimation.

By synthesising insights from the credit risk, SME finance, policy evaluation, and macroeconomic recovery literatures, this study positions its contribution not as a substitute for existing models, but as a methodological bridge that connects these strands into a unified simulation-ready architecture. This positioning clarifies how the proposed framework extends the literature beyond sequential empirical findings toward a structurally coherent representation of SME loan repayment dynamics in crisis and recovery contexts.

The literature makes clear that SMEs remain acutely vulnerable to external shocks due to their structural financial fragility, and that government and banking interventions serve as crucial yet inherently dynamic stabilising forces during periods of disruption. At the same time, improvements in public health conditions, most notably through vaccination, play a decisive role in restoring operational continuity and, by extension, repayment capacity. Yet existing empirical and theoretical models consistently treat these determinants in isolation, failing to account for their interconnected and time-varying nature. No integrated modelling architecture has been developed to unify these factors across both pre- and post-pandemic contexts. This paper responds directly to this gap by advancing a comprehensive, multi-layer modelling framework that incorporates dynamic panel, Markov transition, and SDE models into a single analytical system. By formalising the interactions between vaccination progress, government policy, and banking interventions, the study situates itself at the intersection of financial economics, crisis management, and public health-driven modelling, offering a more holistic account of SME repayment dynamics.

Table 1 summarises the key methodological and conceptual differences between existing studies and the proposed framework.

Table 1. Comparative summary of existing literature on small and medium enterprise (SME) repayment and crisis modelling

This section formalises the mathematical structure underlying the modelling framework. Each model layer (dynamic panel, Markov transitions, and SDEs) is clarified through a set of assumptions, lemmas, and propositions ensuring internal coherence, identifiability, and dynamic stability.

4.1 Assumptions for the dynamic panel model

The analysis begins with the repayment function:

$R_{i, t}=\alpha_i+\rho R_{i, t-1}+\beta_V V_{i, t}+\beta_G G_{i, t}+\beta_B B_{i, t}+\gamma^{\prime} X_{i, t}+\varepsilon_{i, t}$   (7)

The extended specification, which incorporates structural breaks, is given in Eq. (2).

Assumption 1 (Bounded Repayment Performance)

For all firms $i$ and time periods $t$:

$0 \leq R_{i, t} \leq 1$

Because repayment performance is measured as a proportion or index, it must reside within this closed interval. If repayment is modelled as a latent continuous variable, this assumption motivates transformations such as logit or probit link functions.

Assumption 2 (Control Variable Exogeneity)

Control variables do not respond to contemporaneous shocks:

$E\left[\varepsilon_{i, t} \mid X_{i, t}\right]=0$

This rules out reverse causality from sudden repayment shocks to contemporaneous firm characteristics such as size or sector.

Assumption 3 (Weak Exogeneity of Policy Indicators)

Vaccination rates, government support, and banking measures may depend on past repayment but not future shocks:

$E\left[\varepsilon_{i, t} \mid V_{i, s}, G_{i, s}, B_{i, s}\right]=0, \forall s \leq t$

This assumption preserves internal validity while recognising that distressed firms might receive targeted interventions.

Assumption 4 (Pre-Pandemic Stationarity)

Before COVID-19:

$R_{i, t}=\alpha_i+\rho R_{i, t-1}+u_{i, t},|\rho|<1$

This ensures stable repayment behaviour. After the pandemic, the structural break terms $\delta_V, ~\delta_G, ~\delta_B$ capture shifts in the data-generating process.

4.2 Lemma and proof for dynamic stability

Lemma 1 (Dynamic Stability)

The repayment process converges to a long-run equilibrium if and only if:

$|\rho|<1$

Proof:

Starting with:

$R_{i, t}=\alpha_i+\rho R_{i, t-1}+Z$

where, $Z$ is constant (policy conditions fixed). Assume convergence:

$\lim _{t \rightarrow \infty} R_{i, t}=R^*$

Thus:

$R^*=\alpha_i+\rho R^*+Z$

Solving:

$R^*(1-\rho)=\alpha_i+Z$

$R^*=\frac{\alpha_i+Z}{1-\rho}$

A finite equilibrium exists if and only if the denominator is non-zero and bounded, implying $|\rho|<1$. Q.E.D.

4.3 Additional lemmas for identifiability and regularity

Lemma 2 (Identifiability of Structural Break Parameters)

Structural break parameters $\delta_V, ~\delta_G, ~\delta_B$ are identifiable if the pandemic period introduces non-zero variation in policy variables relative to pre-pandemic means.

(Proof omitted; based on full-rank conditions.)

Lemma 3 (Uniqueness of FE-GMM Estimator)

Under assumptions (1)–(4), the System GMM estimator is consistent and asymptotically normal. (The result follows from the standard Arellano–Bover and Blundell–Bond assumptions).

4.4 Markov transition model: Theory and proofs

SMEs transition between two repayment states:

• S: On-time payer

• D: Delinquent/default

The model is:

$p_{S D}(t)=\Lambda\left(\theta_0+\theta_V\left(1-V_t\right)+\theta_G\left(1-G_t\right)+\theta_B\left(1-B_t\right)+\theta_X X_t\right)$

$p_{D S}(t)=\Lambda\left(\phi_0+\phi_V V_t+\phi_G G_t+\phi_B B_t+\phi_X X_t\right)$

4.4.1 Assumptions

Assumption 5 (Markov Property)

The next state depends only on the current state and policy conditions:

$P\left(S_{t+1} \mid S_t, S_{t-1}, \ldots\right)=P\left(S_{t+1} \mid S_t\right)$

Assumption 6 (Strictly Positive Transition Probabilities)

For all $t$:

$0<p_{S D}(t), p_{D S}(t)<1$

This ensures non-absorbing behaviour unless otherwise specified.

4.5 Lemma on stationary distribution

Lemma 4 (Stationary Proportion of SMEs in the On-Time State)

If the transition matrix is time-invariant, the stationary proportion is:

$\pi^*=\frac{p_{D S}}{p_{D S}+p_{S D}}$

Proof:

A stationary Markov chain satisfies:

$\pi^*=\pi^*\left(1-p_{S D}\right)+\left(1-\pi^*\right) p_{D S}$

Solving yields:

$\pi^*=\frac{p_{D S}}{p_{D S}+p_{S D}}$

This ratio has policy implications:

•Higher vaccination → increases $p_{D S}$, thus raises $\pi^*$.

•Higher government and banking support → decreases $p_{S D}$, thereby increasing $\pi^*$.

4.6 Continuous-time stochastic differential equation model: Mathematical foundations

At the aggregate level, SME repayment evolves according to:

$d R(t)=a(R, t) d t+b(R, t) d W_t$

$a(R, t)=\kappa(\bar{R}(V(t), G(t), B(t))-R(t))$

4.6.1 Assumptions

Assumption 7 (Lipschitz Continuity)

Drift and diffusion satisfy:

$\left|a(R, t)-a\left(R^{\prime}, t\right)\right|+\left|b(R, t)-b\left(R^{\prime}, t\right)\right| \leq L\left|R-R^{\prime}\right|$

This ensures that no explosive paths occur.

Assumption 8 (Reflective Boundaries)

At boundaries:

$a(0, t)>0, a(1, t)<0$

This prevents the process from leaving [0, 1].

4.7 Proofs and propositions

Proposition 1: Asymptotic Stationarity of the Dynamic Panel with Exogenous Inputs

Statement.

Under Assumptions 1-4 and if $|\rho|<1$, and if $V_{i, t}, G_{i, t}, B_{i, t}, X_{i, t}$ converge to deterministic limits (or ergodic stochastic processes with finite mean), then $R_{i, t}$ is covariance-stationary in the sense that its mean and autocovariances converge to finite limits.

Proof (Sketch).

The AR(1) representation in companion form:

$R_{i, t}-\mu_{i, t}=\rho\left(R_{i, t-1}-\mu_{i, t-1}\right)+\varepsilon_{i, t}$

where, $\mu_{i, t}=\alpha_i+\beta_V V_{i, t}+\beta_G G_{i, t}+\beta_B B_{i, t}+\gamma^{\prime} X_{i, t}$.

If $V, G, B, X$ converge to finite limits (or have stationary distributions with finite means), then $\mu_{i, t}$ converges to $\mu_i$. For $|\rho|<1$, the homogeneous AR operator is stable, so deviations decay geometrically and the mean of $R_{i, t}$ tends to $\mu_i /(1-\rho)$ (consistent with Lemma 1). Autocovariances are geometric sequences multiplied by finite variances of $\varepsilon$. Hence covariancestationary.

Proposition 2: Ergodicity of Time-Homogeneous Two-State Markov Chain

Statement.

Consider the two-state Markov chain with transition matrix (time-homogeneous):

$P=\left[\begin{array}{cc}1-p_{S D} & p_{S D} \\ p_{D S} & 1-p_{D S}\end{array}\right], 0<p_{S D}, p_{D S}<1$

Then $P$ is irreducible and aperiodic; there exists a unique stationary distribution $\pi=\left(\pi_S, \pi_D\right)$ and the chain converges to $\pi$ irrespective of the starting state.

Proof.

•Irreducible: nonzero probabilities both ways imply every state is reachable from every other state.

•Aperiodic: with self-loop probabilities $1-p_{S D}>0$ and $1-p_{D S}>0$, the gcd of return cycle lengths is 1.

•Existence/uniqueness of stationary distribution follows from standard Markov chain theory. Solve $\pi=\pi P$ with $\pi_S+\pi_D=1$ to get $\pi_S=p_{D S} /\left(p_{D S}+p_{S D}\right), \pi_D=p_{S D} /\left(p_{D S}+p_{S D}\right)$. Convergence holds by ergodic theorem.

Proposition 3: Convergence of Euler–Maruyama to SDE Strong Solution (for Lipschitz coefficients)

Statement.

Let $d R(t)=a(R, t) d t+b(R, t) d W_t$ with $a, b$ Lipschitz in $R$ and satisfying linear growth. Then the Euler-Maruyama discretisation with step $\Delta t$ converges strongly to the true solution as $\Delta t \rightarrow 0$.

Proof (Sketch).

This is a standard result in numerical SDE theory (Kloeden \& Platen, 1992). Under globally Lipschitz and linear-growth conditions, Euler-Maruyama has strong order 0.5: the mean-square error is $O(\Delta t)$. The proof uses Grönwall's inequality applied to the mean-square difference between numerical and exact solutions. (In implementation, the drift and diffusion terms should be modified near the reflecting boundaries to keep the process within $[0,1]$.)

Proposition 4: Consistency of System GMM under Standard Conditions

Statement.

Under the moment conditions implied by the dynamic panel and assuming no second-order serial correlation in the idiosyncratic errors and valid instruments (lags of the dependent variable and predetermined/strictly exogenous instruments), the System GMM estimator is consistent and asymptotically normal.

Proof (Sketch).

The result follows from Arellano–Bond (1991) and Blundell–Bond (1998): the level equations are instrumented by differences, and the difference equations are instrumented by levels. Validity requires the absence of AR(2) serial correlation in the differenced residuals and a Hansen test that does not reject the instrument set. The number of instruments should remain small relative to the number of cross-sectional units $N$.

Proposition 5: Existence and Uniqueness

Under Assumptions 7–8, the SDE has a unique strong solution and satisfies:

$0 \leq R(t) \leq 1, \forall t$.

Proof (Sketch).

•The Lipschitz condition ensures local existence (Itô theory).

•The linear growth condition yields global existence.

The reflective drift makes the boundaries inaccessible. Thus, the process is well-defined for all time.

This section interprets the modelling results conceptually and lays the foundation for empirical application.

6.1 Policy channels and parameter interpretation

The effects of vaccination progress, government support, and banking interventions discussed above correspond directly to the sign and magnitude of the policy coefficients in the dynamic panel model (Eqs. (1) and (2)). In particular, positive coefficients on vaccination $\left(\beta_V\right)$, government support ($\beta_G$), and banking support ($\beta_B$) increase contemporaneous repayment performance $R_{i t}$, while the post-pandemic interaction terms ($\delta_V, \delta_G, \delta_B$) capture structural changes in policy effectiveness following COVID-19. A larger $\beta_V$ shifts the conditional mean of $R_{i t}$ upward by improving operational continuity, whereas higher $\beta_G$ and $\beta_B$ relax liquidity and repayment constraints through fiscal and financial channels. Repayment persistence, governed by $\rho$, determines the speed with which these policy-induced improvements propagate over time. A higher $\rho$ implies stronger path dependence and slower adjustment toward the new equilibrium identified in Lemma 1.

6.2 State transitions, recovery, and nonlinear effects

At the meso level, the conceptual discussion of deterioration and recovery maps directly to the transition probability functions in Eqs. (3) and (4). Increases in vaccination, government support, and banking interventions reduce the probability of moving from on-time to delinquent status by lowering the logit index in $p_{S D}$, while simultaneously increasing the recovery probability $p_{D S}$. The nonlinear nature of the logistic link implies threshold behaviour: once the combined policy index $\left(V_t, ~G_t, ~B_t\right)$ crosses a critical level, small additional policy improvements generate disproportionately large reductions in delinquency risk. These threshold effects explain the sharp improvements observed in the high-intervention scenario. These effects are reflected analytically in the stationary distribution of the Markov chain (Lemma 4), where higher $p_{D S}$ and lower $p_{S D}$ increase the long-run proportion of on-time SMEs.

6.3 Aggregate dynamics and stability mechanisms

The macro-level repayment trajectories discussed in the simulation results are governed by the parameters of the SDE in Eqs. (5) and (6). The mean-reversion speed $\kappa$ controls how quickly aggregate repayment $R_t$ converges toward the policy-dependent equilibrium $\mu\left(V_t, ~G_t, ~B_t\right)$, while the diffusion parameter $\sigma$ captures residual uncertainty arising from unobserved shocks. Coordinated policy interventions raise $\mu(\cdot)$, shifting the long-run repayment benchmark upward, whereas weak or withdrawn support lowers $\mu(\cdot)$ and may induce prolonged fragility. The reflective boundary conditions ensure feasibility ($R_t \in[0,1]$) and formalise the stabilising role of policy interventions in preventing systemic collapse or unrealistic overshooting. Together, these parameters explain the observed convergence, volatility reduction, and divergence across policy scenarios.

6.4 Cross-layer consistency

Crucially, the discussion highlights that the same policy variables operate consistently across all model layers. Coefficients $\left(\beta_V, ~\beta_G, ~\beta_B\right)$ determine firm-level responsiveness, transition probability sensitivities shape repayment state dynamics, and the equilibrium function $\mu(\cdot)$ aggregates these effects into macro-level trajectories. This parameter coherence ensures that conceptual interpretations are not ad hoc but arise directly from the mathematical structure of the framework.

Table 3 summarises how the key conceptual insights discussed in this section map directly to specific model parameters and equations across the micro-, meso-, and macro-level components of the framework.

Table 3. Mapping of key discussion insights to model parameters and equations

This study develops and applies an integrated simulation framework to examine how vaccination progress, government support, and banking sector interventions jointly shape SME loan repayment dynamics during crisis and recovery periods. By combining micro-level repayment persistence, discrete repayment state transitions, and aggregate stochastic adjustment within a unified architecture, the framework captures nonlinear and path-dependent repayment behaviour that cannot be adequately represented by static or single-layer models.

Three main findings follow. First, SME repayment dynamics are strongly path-dependent, implying that early shocks and early interventions have persistent effects. Second, within the simulated scenarios, policy impacts appear nonlinear and complementary: vaccination progress, government support, and banking interventions interact to reduce delinquency risk and accelerate recovery, with coordinated responses producing substantially more stable outcomes than the low-intervention scenario. Third, the simulation results confirm the internal consistency of the framework by showing how micro-level behavioural responses and state transitions propagate into distinct aggregate repayment trajectories under alternative policy scenarios.

The analysis is intentionally modelling- and simulation-focused. Parameters are theoretically calibrated rather than empirically estimated, and repayment outcomes are represented using a simplified two-state structure to preserve analytical clarity. As such, the results should be interpreted as illustrative rather than predictive. Future research may extend the framework through empirical calibration using survey and administrative loan data, as well as by incorporating sectoral differentiation and endogenous policy responses.

Overall, the paper contributes a computational foundation for analysing SME loan repayment under systemic shocks, offering a flexible tool for scenario-based policy evaluation and a platform for subsequent empirical investigation.