When Banks Punch Back: Macrofinancial Feedback Loops in Stress Tests*
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

Author’s E-Mail Address: mcatalan@imf.org, alexhoffmaister@gmail.com

In the presence of adverse macroeconomic shocks, simultaneous capital losses in multiple banks can prompt them to contract their balance sheets. These bank responses generate externalities that propagate in the form of macro-financial feedback loops. This paper develops a credit response and externalities analysis model (CREAM) that integrates a disaggregated banking sector into an otherwise standard macroeconomic structural vector autoregressive model. It shows that accounting for macro-financial feedback loops can significantly affect macroeconomic outcomes and bank-specific stress tests results. The heterogeneity in bank lending responses matters: it determines how each bank fares under adverse conditions and the external effects that banks impose on each other and on economic activity. The model can thus be used to assess the contributions of individual banks to systemic risk along the time dimension.

Abstract

In the presence of adverse macroeconomic shocks, simultaneous capital losses in multiple banks can prompt them to contract their balance sheets. These bank responses generate externalities that propagate in the form of macro-financial feedback loops. This paper develops a credit response and externalities analysis model (CREAM) that integrates a disaggregated banking sector into an otherwise standard macroeconomic structural vector autoregressive model. It shows that accounting for macro-financial feedback loops can significantly affect macroeconomic outcomes and bank-specific stress tests results. The heterogeneity in bank lending responses matters: it determines how each bank fares under adverse conditions and the external effects that banks impose on each other and on economic activity. The model can thus be used to assess the contributions of individual banks to systemic risk along the time dimension.

I. Introduction

Recent literature has shown that in the presence of adverse macroeconomic shocks, simultaneous capital losses in multiple banks can prompt them to cut lending and contract their balance sheets. These bank responses can generate externalities that propagate in the form of macro-financial feedback loops. To date, the empirical evidence for these macro-financial effects remains scant, in part reflecting the absence of a general quantitative framework to evaluate them.1

This paper develops a credit response and externalities analysis model (CREAM) that integrates a disaggregated banking sector into an otherwise standard macroeconomic structural vector autoregressive (SVAR) model. In this model, exogenous macroeconomic shocks trigger bank losses that erode risk-adjusted capitalization ratios. To mitigate this erosion, banks cut lending in a differentiated manner that depends on their fundamentals. Bank-specific lending cuts in turn weaken GDP growth and undermine the profitability of other banks. A vicious cycle of reduced lending and a weakening economy is generated. The paper shows that accounting for macro-financial feedback loops can significantly affect the measured impact of shocks on macroeconomic outcomes and bank-specific stress tests results. In addition, the paper shows how CREAM can be used to assess the contributions of individual banks to systemic risk along the time dimension. More specifically, the empirical framework can address the following questions. First, how does individual and collective bank lending behavior contribute to the propagation of shocks and influence macroeconomic outcomes? Second, how is the propagation of shocks affected by initial bank conditions and heterogeneity? To what extent do stronger bank buffers (e.g. higher capital ratios) mitigate the propagation effects? And third, how does accounting for bank lending behavior and the associated macro-financial feedback loops affect bank-specific stress tests results?

To address the first question, this paper quantifies the contribution of bank i’s deleveraging behavior to a macroeconomic downturn following adverse shocks. Bank i’s lending behavior is assessed against a no-deleveraging “quasi-static” benchmark in which its balance sheet grows in line with nominal GDP.2 Its contribution to systemic risk is measured by comparing macroeconomic outcomes under “dynamic” and “quasi-static” balance sheet growth assumptions for the bank. In the same vein, the externality imposed by bank i’s deleveraging on bank j can be quantified by tracing the effects on bank j’s fundamentals (e.g., capitalization, non-performing loan ratios, profitability). To address the second question, the paper shows how capital surcharges can mitigate the externalities generated by individual banks through their lending behavior. In this way, the paper highlights the use of the framework for evaluation of macroprudential policy interventions.

And to address the third question, the paper highlights the use and relevance of the framework for stress testing. It brings to the fore the drawbacks of applying quasi-static and other ad-hoc bank balance sheet growth assumptions in stress tests. The main difficulty with such commonly used assumptions lies in the distortion that they engender on stress tests results across banks. Banks that appear resilient (vulnerable) under a static balance sheet analysis could turn out to be highly vulnerable (resilient) when assessed through a dynamic balance sheet approach.3

The model provides a platform to examine macro-financial feedback loops and perform stress testing exercises in a wide range of economies under a common methodology. This is because the model has been designed to rely on publicly available bank data (Fitch/Bankscope),4 and its flexibility allows it to be adjusted to fit the needs of country-specific applications.

This paper complements recent (theoretical) studies on the role of pecuniary externalities to motivate macroprudential policy, with notable examples including Lorenzoni (2008) and Dávila and Korinek (2018). In these studies, reduced credit provision by a financial intermediary reduces asset prices and tightens price-dependent collateral constraints in other intermediaries, forcing them to also cut credit provision. In contrast, in this paper externalities can take various forms, reflecting a variety of macro-financial transmission channels embedded in the framework. Our analysis suggests that reduced lending by a single systemically important bank i in an adverse scenario exacerbates the credit losses of other banks through the output channel. But the aggregate credit and output contractions lead to lower market interest rates and bond yields, which mitigate other banks’ market losses (i.e., profitability). Thus, the impact on other banks’ capital ratios is ambiguous and depends on bank-specific exposures and estimated sensitivities of losses to changes in macroeconomic factors. Similarly, bank i ‘s deleveraging can result in crowding-in or crowding-out effects on the credit of other banks, depending on bank-specific conditions. Policymakers have recognized the need for enhancing the “realism” of stress tests and hence their “relevance” for policy decision-making, pointing out that allowing for differentiated bank responses and accounting for macrofinancial feedback effects are key areas for improvement.5 The studies by Budnik and others (2019) and Krznar and Matheson (2017) represent concrete first steps to bring these proposals to fruition. A number of studies, such as Meh and Moran (2010) and Gerali and others (2010), have also tried to capture macro-financial feedback effects using dynamic stochastic general equilibrium (DSGE) models with a banking sector. The “truly” structural DSGE modeling approach is appealing and has some well-known advantages, but a realistic description and behavior of banks is not one of them. Since these studies model the behavior of a representative and overly simplistic bank, they cannot capture heterogeneity in individual bank deleveraging behavior, which is highlighted in this paper as a key source of cross-bank externalities and shock propagation, and a key determinant of bank-level stress tests results. To demonstrate how CREAM can be used to address the questions posed above, this paper provides an illustrative application to the case of Indonesia. It is organized as follows: section II describes the macro-financial framework; section III discusses how to take the model to the data; section IV presents the application to the case of Indonesia and section V concludes.

II. The Credit Response and Externalities Analysis Model

CREAM is a semi-structural macro-financial econometric model that captures the two-way linkages between banks and the economy (depicted in Figure 1). The model consists of two broad sets of equations. The first set of equations specifies a macroeconomic (SVAR) block where aggregate bank lending and the lending rate are exogenous. The second set of equations determines individual bank behavior and conditions, reflecting the influence of idiosyncratic and macroeconomic factors on bank profits, capital, and lending. Individual bank decisions are then aggregated to determine bottom-up measures of lending and the lending rate for the banking sector. The macro-financial feedback loop is closed by plugging the aggregated banking sector decisions into the macroeconomic block. CREAM thus incorporates a disaggregated banking sector into an otherwise standard SVAR model. The equations characterizing the model are presented in Appendix I and variable definitions and notation are summarized in Table 1.

Figure 1.
Figure 1.

Macrofinancial Feedback Loops

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Table 1.

Variables: Definitions and Notation1

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Notes. 1/ With the exception of bank-specific ratios, all variables are expressed in nominal terms, unless otherwise indicated with the label “real”; yields, interest rates and funding (credit) spreads are expressed in annual (nominal) terms; the inflation rate is expressed as a quarterly rate.

All aggregate variables except for interest rates and inflation are expressed in logs.

The remainder of this section proceeds as follows. Sub-section A describes the macroeconomic (SVAR) block and sub-section B describes the equations that characterize the disaggregated banking sector. The subscript i differentiates bank-specific variables from macroeconomic variables and, to simplify notation, time subscripts have been suppressed. Note that references to equations follow the numbering of Appendix I rather than the order in which they appear in the text.

A. Macroeconomic Block

The macroeconomic block consists of structural vector autoregressive (SVAR) equations expressed in reduced form and defined over the external and domestic macroeconomic variables included in z˜ (Eq. 1). The dynamics of z˜ is influenced by the evolution of financial conditions (f˜). These are defined by aggregate real bank lending (LR) and the nominal lending rate (iL) and treated as exogenous in the SVAR block. The external variables included in z˜ have potential effects on the domestic economy through trade or financial channels and comprise the following: real GDP of trading partners (RGDP* ), commodity prices (pCOMM), and the nominal U.S. policy interest rate (ius). The domestic variables included in z˜ are the following: real GDP (RGDP), inflation (INF), the real effective exchange rate (REER), and the nominal policy interest rate (f). Thus, in Eq. 1, z˜andf˜ are defined as:

z˜=[RGDP*,PCOMM,iUS,RGDP,INF,REER,i0]andf˜=[LR,iL].

All the variables except for nominal interest rates (ius, i0 and iL) and inflation (INF) are expressed in logs and a time trend is included explicitly in the SVAR, with trend coefficients allowed to differ across equations.

The choice of variables and structure is guided by theory and empirical literature on SVAR models applied to small open economies.6 To identify the structural parameters of the SVAR and capture the “small open economy” assumption, a set of restrictions is imposed on the contemporaneous and lagged relations. On the contemporaneous relations, the reduced form errors are orthogonalized by Cholesky decomposition as in Sims (1980), with the external variables “preceding” the domestic variables. The relation between reduced form (μz) and structural (εz) errors is given by μtz=Bϵtz,whereϵtz(0,Σϵz) and Σεz is diagonal. On lagged relations, block exogeneity restrictions are imposed to preclude lagged effects of domestic shocks on external variables.7 These restrictions, when combined, imply that external variables can affect the domestic economy both contemporaneously and with lags. In contrast, changes in domestic variables do not have contemporaneous or lagged effects on external variables.

Note that the SVAR defined in Eq. 1 includes a single domestic interest rate, the nominal policy rate i0. However, a broader set of interest rates is needed to adequately capture the transmission of macroeconomic shocks to the banking sector. In particular, corporate and government bond yield curves are needed to price securities portfolios held by banks. Also, through their role as benchmark rates, government bond yields influence the determination of banks’ funding costs and lending interest rates.

In this regard, we collect aggregate interest rates in the vector ir (Eq. 7) and introduce a second VAR (Eq. 2) to map trajectories of the domestic policy rate (i0) to 10-year (40 quarters) government bond yields (YG,40) and both short and 10-year corporate bond yields ( YC,0 and YC,40). The corresponding yield curves are obtained through linear interpolation between short and 10-year rates (Eq. 28).8

B. Banks

Balance sheet

Bank i ‘s assets (Ai) are comprised of gross loans (Lt) net of loan loss provisions (PRi), portfolios of government and corporate bonds (BiGandBiC), cash assets (Mi), and other assets (OAi).9 Liabilities are divided into those that qualify as regulatory capital (Ki) and other liabilities (Di) (Eq. 20). Bonds are booked as “marked-to-market” (MTM) or held-to-maturity (HTM), depending on whether valuation effects triggered by changes in market conditions are recognized as profits (Eq. 21).

Profits

Bank i generates net profits (Πi) from various sources (Eq. 10). Interest income from loans (IIiL) and interest expense (IEi) are generated by portfolios of loans and interest-bearing liabilities, respectively. “Loan losses” (LLi) are defined as credit losses in loan portfolios. Returns on securities portfolios ((RiGandRiC)) reflect interest income associated with bond coupon payments and gains or losses triggered by repricing of marked-to-market securities due to shifts in yield curves. “Other net profits” (Oi) collects all remaining items, such as net fee and commission income and operational and tax expenses.

Financial ratios

Bank-specific capital, liquidity, and loan loss ratios play key roles in the model and are collected in the vector xi. (Eq. 8). In the definition of bank i’s “capital adequacy ratio” (Eq. 9), risk-weighted assets RWAi, are defined as the sum of the products of average risk weights (ΘiL,ΘiG,ΘiC) for different asset portfolios and the corresponding exposure amounts (Eq. 31).10 The “liquidity ratio” (LATAi) is defined as the ratio of liquid assets (LAi) to total assets (4), where liquid assets consist of cash and bonds (Eq. 9). The “loan loss ratio” (LLRi) is defined as the ratio of loan losses to gross loans (Eq. 17).

Determination of profits

Profits of individual banks are affected by macroeconomic conditions. The transmission of changes in macroeconomic conditions to bank profits varies across banks, depending on their financial health and sensitivity to shocks. The key channels of transmission of macroeconomic shocks to the banking sector are shown in Figure 1 (left-hand side, “macro-to-banking transmission”).

First, changes in macroeconomic conditions cause shifts in government bond yields which are transmitted to bank deposit and lending rates, thereby impacting interest income and expenses. For any bank i, interest rates on rolled-over deposits and other debt (iiND) adjust not only to reflect the full impact of changes in government bond yields but also predetermined and idiosyncratic changes in cost of funding (Eq. 16), where the idiosyncratic component is a spread (spri) that depends on bank-specific fundamentals and exogenous shocks (Eq. 5).

The pass-through effect of bank funding costs onto lending rates corresponding to newly extended loans (iiNL) is partial and determined by the parameters ψiGandψispr (Eq. 13). The transmission to overall (average) deposit and other debt rates (iiD) and lending rates (iiL) is, in turn, protracted and reflects gradual re-setting of interest rates given laddered maturity structures of deposits and other debt and loan portfolios (Eq. 12 and Eq. 15). More specifically, fractions πiDandπiL of bank i’s deposits and other debt, and loans, mature and can re-set their interest rates in every quarter. Also, interest income is adversely impacted by any deterioration in credit quality of loan portfolios, as interest associated with non-performing loans (NPL) is neither collected nor accrued (Eq. 11). Second, changes in macroeconomic conditions affect loan defaults in different ways. A slowdown in real GDP growth triggers loan defaults, increasing non-performing loan (NPLRi) and loan loss ratios (LLRi). Also, bank-specific increases in lending rates (associated with the pass-through interest rate effects described above) can increase borrowers’ debt service burden, triggering additional defaults.

In the model, loan losses LLi are obtained from Eqs. 3 and 17. The former is an estimated dynamic panel used to forecast the evolution of loan loss ratios LLRi based on macroeconomic and bank-specific conditions.11 Note that a logistic transformation of LLRi introduces non-linearity in the relation between the loan loss ratio and its determinants. It also implies that dynamic responses of loan loss ratios to shocks are bank-specific (affected by the fixed effect term and the financial ratios of each bank). The model thus allows for differentiated sensitivity of bank loan losses to macroeconomic shocks.12

The returns on securities RiGandRiC reflect changes in the values of HTM and MTM bond portfolios (Eqs. 25 and 26 respectively). These returns are driven by (full) re-investment of coupon payments received and gains or losses associated with the repricing of MTM portfolios due to changes in yields. Repricing of MTM bonds is based on modified duration formulas (Eq. 26) where changes in yields are evaluated at the points of the corresponding yield curves given by the durations. Coupon payments received, in turn, adjust over time as interest rates in the economy change (Eq. 27). Other net profit Oi remains constant (Eq. 19).

Determination and dynamic evolution of balance sheet items

Bank i ‘s stock of gross loans and its evolution over time is determined using a dynamic panel set of equations (Eq. 4); we refer to these equations as the “lending block.” The stocks of provisions are driven by recognition of loan losses (Eq. 23). All banks are assumed to implement reinvestment strategies that preserve the initial structure of their bond portfolios. More specifically, the composition of the bond portfolios (mix between corporate and government) and their average duration are assumed to remain unchanged over time.13 Regarding cash balances, bank i targets a constant ratio of cash to deposits and other debt liabilities (mi), according to Eq. 24.

The evolution of bank capital is given by Eq. 30, where the expression in square brackets is the retention ratio, divi denotes the dividend payout ratio when bank profits are positive, and 1+i,t) is an indicator function that takes the value 1 when profits are positive (and 0 otherwise).14 External capital injections, as a ratio of risk-weighted assets, are captured by kiri,t.

In addition to the main balance sheet items, Eq. 22 tracks the evolution of nonperforming loans (NPLi); as noted above, this is necessary because only performing loans are assumed to earn interest income. Loan losses LLi can be mapped into stocks of non-performing loans NPLi only under specific assumptions about loan write-off activity—otherwise the relation is indeterminate. To visualize the full impact of stress on credit losses and non-performing loan ratios, Eq. 22 is derived under a zero loan write-off rate assumption in the projection period.15

The variable “deposits and other debt liabilities” (Di) acts as a residual and adjusts to ensure that the balance sheet identity (Eq. 20) is satisfied. Figure 2 illustrates how the components of the balance sheet would adjust to generate deleveraging. First, macroeconomic shocks reduce bank profitability through various channels: lower economic growth increases non-performing loans and triggers loan losses; net interest income declines because loan defaults reduce interest income and higher costs of funding increase interest expenses; and higher yields reduce the valuation of securities portfolios. Second, banks respond by cutting gross loans and repaying debt liabilities; cash balances also decline to maintain cash-to-debt ratios constant.

Figure 2.
Figure 2.

Bank Stress-Response Diagram

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Aggregation

Gross aggregate bank lending in nominal terms (L) results from aggregation of bank-specific lending decisions (Eq. 32). The aggregate nominal lending rate (iL) is calculated as a weighted average of bank specific lending rates (iiL), where the weights are given by the ratio of individual banks’ performing loans to the total amount of performing loans in the banking system (Eq. 33).

Case of “Quasi-static” Bank Balance Sheet Growth

In the framework above, banks adjust their balance sheets in a differentiated and “dynamic” manner, according to Eq. 4. To perform simulations under a “quasi-static” bank balance sheet growth assumption, Eq. 4 should be replaced by ΔlnLi,t = ΔRGDPt +INFt for all i. In this case, the stock of gross loans for each bank grows at the rate of nominal GDP so that aggregate lending remains unchanged as a percentage of GDP.16

Individual Bank Contributions to Systemic Risk

The contribution of bank i to systemic risk along the time dimension is quantified by comparing results when a dynamic balance sheet assumption is imposed on all banks (including bank i) against results obtained when only bank i adjusts its balance sheet quasi-statically. More precisely, the benchmark where all banks adjust their balance sheets dynamically is compared to the case where bank i lending behavior is given by ΔlnLi,t, = ΔRGDPt + INFt while the lending behavior of all other banks (j ≠ i) is described by Eq. 4.

III. Taking the Model to the Data: Numerical Parameterization and Stress Simulation

Two steps are required to operationalize the framework. The first step consists of assigning numerical values to parameters and initial conditions; the second step consists of simulating macro-financial stress triggered by the realization of adverse shocks.

Numerical Parameterization

Coefficients in Eq. 1 are estimated using standard VAR regression techniques, while those in Eqs. 2–5 are estimated using dynamic panel data techniques.17 Other parameters in the model are calibrated to match the latest observed individual bank data available from Fitch (Bankscope), as described in Table 2.18

Table 2.

Notation and Numerical Calibration of Bank-specific Parameters

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Notes. 1/ For each bank, parameters are calibrated based on data available from Fitch (Bankscope).

First, Fitch reports loan amounts maturing in time bands: “less than 3 months”, “3 to 6 months”, “1 to 5 years”, and “longer than 5 years.” A mid-point duration value is assigned to each time band (0.5 quarter for “less than 3 months”; 2.5 quarters for “3 to 6 months”; 12 quarters for “1 to 5 years”, and 30 quarters for “longer than 5 years”) and these values are used to calculate the loan portfolio duration parameter as a weighted average. Second, the fraction of loans repricing every quarter is calculated as the inverse of the loan portfolio duration parameter: πiL=(1/duriL). Specifically, if loans mature at a constant quarterly rate πiL, the quarterly maturity structure of the loan portfolio is given by: πiL;πiL(1πiL);πiL(1πiL)2;πiL(1πiL)3;.... The duration of the portfolio is then given by: duriL=Σt=1tπiL(1πiL)t1=(1/πiL).

Historical bank dividend payout rates vary across banks. However, forward-looking stress analysis is carried out under common payout rates to eliminate the impact of differentiated profit retention rates on capital ratios and stress tests results. With differentiated payout rates, capital ratios are not fully accounted for by losses associated with shocks and their transmission, which hampers the cross-bank comparability of stress tests results.

In Table 2, 8 of the 18 parameters measure durations of balance sheet items (dur) and related fractions of outstanding balances maturing in every quarter (π). These parameters are calibrated in two steps for portfolios of loans, government and corporate securities, and deposits and other debt liabilities.19 First, Fitch reports on amounts maturing in the following time bands: “less than 3 months,” “3 to 6 months,” “1 to 5 years,” and “longer than 5 years.” Mid-point duration values are assigned to the different time bands (0.5 quarter for “less than 3 months”; 2.5 quarters for “3 to 6 months”; 12 quarters for “1 to 5 years”; and 30 quarters for “longer than 5 years”) and used to calculate the portfolio duration parameter as a weighted average.

Second, the fraction of balances repricing every quarter is calculated as the inverse of the portfolio duration parameter: πi = (1/duri). Specifically, balances are assumed to mature at a constant quarterly rate πi, and hence, the quarterly maturity structure of the loan portfolio is given by: πi; πi η (1-πi); πi η (1-πi)2; πi Δ · (1-πi)3;.... Thus, it follows that the duration of the portfolio can be expressed as: duri=Σt=1t(1πi)t1=(1/πi).

Bank-specific risk weights comprise 4 of the 19 parameters in Table 2. Fitch reports risk weighted asset amounts by asset portfolio type. Precise calibration of portfolio-level average risk weights can therefore be determined—dividing for each portfolio the risk-weighted assets by the outstanding amount in the balance sheet. The calibration of three remaining parameters is straightforward: the fraction of checking deposits in total deposit and debt liabilities (chi) and the cash-to-debt ratio (mi) are directly observed from the latest balance sheet data while the other net income to total assets ratio (Ξi) is calibrated based on average flows of “other net income” for the last 4 quarters.

But the calibration of four parameters merits further discussion. The interest rate pass-through parameters Of and (ψiGandψispr) cannot be calibrated using Fitch data and must be determined by other means—such as country- and/or bank-specific empirical studies of interest rate pass-through. The simulations for Indonesia (section IV) assume pass-through parameters of 0.6. Also, bank-specific LGDt data is not reported by Fitch and must be assumed—but, if available, it could be obtained directly from supervisory sources in specific country applications. Finally, dividend payout rates are available from Fitch and could be used to calibrate the parameter divt on a bank-by-bank basis. However, it is standard practice to conduct the stress tests under common dividend distribution assumptions. Such assumptions ensure that bank capital ratios under stress scenarios reflect losses rather than cross-bank differences in dividend payouts. In the simulations below, we assume a common dividend rate equal to 0.3.

Stress Simulations

The numerical stress simulations integrate the estimated blocks of equations with the rest of the model. For given parameter values, initial conditions, and sequences of adverse macroeconomic structural shocks (applied in the SVAR block) and bank-specific cost of funding shocks, a stress simulation solves for consistent paths of macroeconomic and bank-specific variables that satisfy all the equations of the model (Appendix I). Note that a stress simulation solves simultaneously for bank-specific and macroeconomic outcomes, ensuring micro-to-macro consistency. Thus, in CREAM, there is no sequential separation between the scenario design and bank stress calculation steps. Such separation is only feasible if financial-to-macro feedbacks are ignored, as is common in standard stress testing exercises.20

Appendix II describes the stress simulation algorithm. The algorithm is flexible and can accommodate different types of bank lending behavior. It can be used to compute “quasi-static” solutions where all banks behave quasi-statically; “dynamic” solutions where all banks behave dynamically; or “mixed” runs where some banks behave dynamically while others follow quasi-static behavior. As noted in section II, particular cases of mixed runs can be used to measure individual bank contributions to systemic risk. In country-specific applications, such as the one presented in Section IV, we conduct the four types of simulations shown in the Table below.

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The simulation labeled “Initial” essentially replicates the sequential and quasi-static stress testing approach commonly used in policy institutions. A multi-year scenario is constructed, and then bank stress tests are performed based on these scenarios. There is an ex-post inconsistency between banks’ desired lending responses and the availability of credit assumed under the initial adverse scenario, and there is no account of macro-financial loops in the simulation. To highlight these inconsistencies, we include paths for aggregate lending and lending rates in the “initial” scenarios shown in Section IV. (By doing so, this scenario can also be used to kick-start iterated simulations that exhibit ex-post consistency under the model.)

In the “Dynamic” and “Quasi static” simulations, macroeconomic and bank-specific results are outcomes of the analysis, ex-post consistency between aggregate and bottom-up lending behavior is ensured by application of the model, and all banks exhibit dynamic or quasi-static behavior. In mixed simulations labeled Bi-QS, an individual bank i is the only bank that behaves quasi-statically, while all other banks exhibit dynamic lending behavior.

IV. Country Application: Indonesia

This section applies the framework described in sections II and III to the case of Indonesia. Quarterly macroeconomic data series are obtained from various sources and span from 1990:Q1 to 2018:Q2, covering both the Asian and the global financial crises. Banking data is obtained from Fitch (Bankscope). The dynamic panel regressions cover the entire banking system (118 banks) and are performed using quarterly data from Q1:2001 to Q1:2015. The stress simulation analysis is performed on 12 small and large banks that jointly account for 70 percent of the banking system’s assets. Details on data sources are presented in Appendix III.

Subsection A presents a baseline macroeconomic scenario and an “initial adverse scenario.” Subsection B presents the estimates of dynamic panel models for the bank credit risk and lending blocks. Subsection C contains the main empirical results for the CREAM application to Indonesia, including the stress simulation analysis and the assessment of individual banks’ contributions to systemic risk.

A. Baseline and “Initial Adverse Scenarios”

Impulse Responses

Figures 3 and 4 show impulse responses of macroeconomic variables to single structural shocks obtained from a VAR model that includes equations for aggregate credit (LR) and the lending rate (iL). The impulses consist of one standard deviation (positive) structural shocks that are applied for one quarter and trigger endogenous dynamic responses of macroeconomic variables spanning over 20 quarters. Figures 3 and 4 also depict confidence bands corresponding to (.16,.84) intervals. The following observations are noteworthy:

  • A shock to real GDP of Indonesia’s main trading partners (U.S., China, and the EU) triggers an increase in commodity prices due to high intensity of commodity demand from these economies. Increased demand for Indonesian exports boosts domestic real GDP and appreciates the rupiah in real terms. Inflation declines, possibly reflecting pass-through from a nominal appreciation of the rupiah, while the policy interest rate adjusts downward.

  • Similarly, a positive shock to commodity prices boosts domestic real GDP, since Indonesia is a commodity exporter (e.g. palm oil, natural gas, coal).

  • A positive shock to the U.S. federal funds rate reduces Indonesian real GDP, as the rise in interest rate differentials triggers capital outflows and a depreciation of the rupiah in nominal and real effective terms.

  • In response to a positive shock to domestic real GDP, inflation rises with the policy interest rate following suit.

  • Importantly, the banking sector plays a crucial role in the transmission of shocks. For instance, the real GDP expansion associated with stronger demand for Indonesian exports is fueled by expansion of bank lending—at a much faster rate than real GDP— and reduced lending rates.

  • Note that a positive shock to the lending rate triggers a decline in real bank credit and GDP; it can thus be interpreted as an adverse credit supply shock. On the other hand, a positive shock to real bank credit triggers an increase in the lending rate—consistent with a positive shock to credit demand.21

Figure 3.
Figure 3.

Indonesia—Impulse Responses of External Variables: Unconditional (2 lags)

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Figure 4.
Figure 4.

Indonesia—Impulse Responses of Domestic Variables: Unconditional (2 lags)

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Baseline and Initial Adverse Scenarios

Table 3 shows the structural shocks that jointly generate the (combined) responses presented in Figure 5. These responses are used to produce the “initial adverse scenario” that is presented in Table 4, along with the baseline scenario.

Table 3.

Indonesia—Structural Macroeconomic Shocks

(in standard deviations)

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Table 4.

Indonesia—Paths of Macroeconomic Variables Under the “Initial Adverse” Scenario

(in percent, unless otherwise indicated)

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Note. The model is not used to produce baseline quarterly paths. These reflect projections in the 2017 World Economic Outlook. Impulse responses are used to produce quarterly paths for the “initial adverse scenario.” The quarterly paths are then used to generate the annual numbers presented in the Table.

Government bond yield series available for Indonesia are significantly shorter than other macroeconomic series; thus, we estimated a separate two-equation SVAR to evaluate the relationship between the domestic policy rate (i0) and the 10-year government bond yield (YG,40).22 The model was then used to compute the impulse response of YG,40 to a given shock in i0. Due to the lack of sufficiently long data series for Indonesian corporate bond yields, we assumed that corporate yields follow the movements of government yields amplified by 30 percent, i.e., a 100 basis point (parallel) shift in the government yield curve results in a 130 basis point shift in the corporate yield curve. The amplification parameter can be varied to assess the robustness of results to this assumption.23

B. Dynamic Panel Estimates

Table 6 (a) presents results for the dynamic panel model of credit risk. The logistic transformation of bank non-performing loan ratios ( NPLRi) is regressed on lags of the dependent variable, macroeconomic variables, and bank-specific capital ratios. In Table 6 (a), lagged coefficients of explanatory variables are added up to simplify the interpretation of results.

Table 5.

Indonesia—Bank-specific Cost of Funding Shocks

(annual rates)

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Table 6.

Indonesia—Bank Credit Risk Block: Dynamic Panel Estimates

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Notes. 1/ Estimates in (a) correspond to regressions that include bank-specific fixed effects (not reported). Model estimates are summarized by the sum of each regressor’s coefficients. The F-statistic corresponds to the null hypothesis that all the coefficients for a specific regressor equal zero. The marginal significance indicates the statistical significance level for which the null hypothesis is rejected; for instance, rejecting the null at a 5 percent level requires the marginal significance to be less than 0.05. 2/ Let βl1andβl2 denote the regression coefficients for different lags l corresponding to the regressors ΔRGDP and ΔRGDP2 respectively and let λ2 and λ2 denote the coefficients corresponding to the lagged dependent variable terms included as regressors. The long-term elasticity of the NPLRt with respect to a one percentage point increase in the quarterly rate of real GDP growth is calculated as follows:
NPLRi,ΔRGDP=[(l=25βl1)+2(l=25βl2)ΔRGDP](NPLRi)(1NPLRi)(11λ1λ2).

By dividing the previous expression by 4, we obtain the long-term elasticity of NPLRt with respect to a one percentage point increase in the annual rate of real GDP growth—shown in parentheses in (b). Similarly, the long-term elasticity of NPLRt with respect to a one percentage point increase in the policy interest rate in each quarter is given by NPLRi,Δi0=(l=25βl3)(NPLRi)(1NPLRi)(11λ1λ2),whereβl3 are the regression coefficients corresponding to Δi0.

The determinants have the expected effects on non-performing loan ratios. The signs of estimated coefficients indicate that slower real GDP growth or increases in the policy interest rate lead to higher NPLRi; also, higher bank-specific capital ratios (CARi) are associated with lower NPLRi.

Note that the model exhibits non-linearities due to the logit transformation applied to NPLRi and the presence of a quadratic real GDP growth term. The non-linear features of the model imply that estimated elasticities of NPLRi with respect to changes in macroeconomic determinants vary depending on initial conditions—increasing as NPLRi rises and ΔRGDP declines. Table 6 (b) reports selected elasticities calculated for different initial conditions. Table 7 presents results for the dynamic panel model of bank lending. The estimates correspond to an augmented autoregressive distributed lag (ARDL) framework, which was first proposed in a panel data context by Pesaran and Smith (1995) and Pesaran (2006). The model separates the determinants of bank lending that affect the long-run growth path from those that only influence the transitional dynamics around this path and was applied to Indonesia banking data by Catalán, Hoffmaister, and Harun (2019).24

Table 7.

Indonesia—Bank Lending Block: Dynamic Panel Estimates

article image
Note. Estimates correspond to fixed effects and are based on an unbalanced panel of quarterly data from 2001:Q1 to 2015:Q1 for 118 banks operating in Indonesia at end-2015. The estimated augmented ARDL models contain the contemporaneous and lagged observations for the regressors as indicated; with the exception of the long-run effect of regressors, coefficient estimates have been summarized by their sum. In this regard, two null hypothesis tests are reported for each regressor: (1) the sum of coefficients equals zero, and (2) every coefficient equals zero. In all cases, the null hypothesis is rejected at the 5 (10) percent significance level whenever the p-value (marginal significance level) is less than 5 (10) percent.

C. Accounting for Macrofinancial Feedback Loops: Results

Macroeconomic Outcomes and Bank Stress Tests Results

Figure 6 depicts the numerical paths of macroeconomic variables under “Initial”, “Dynamic,” and “Quasi-static” simulations. Figure 7 presents the evolution of aggregate bank balance sheet items, profits, and selected financial ratios under the different simulations. Figure 8 compares the evolution of aggregate bank balance sheets under the quasi-static and dynamic simulations, highlighting the extent of deleveraging that takes place in the latter simulation.

Figure 5.
Figure 5.

Indonesia—Responses of External and Domestic Macroeconomic Variables to Combined Structural Shocks

(responses to shocks presented in Table 3)

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Figure 6.
Figure 6.

Indonesia—Stress Simulation: Macroeconomic Results

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Figure 7.
Figure 7.
Figure 7.
Figure 7.

Indonesia—Aggregate Bank Results: Balance Sheet Items

(all variables are expressed in real terms)

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Figure 8.
Figure 8.

Evolution of Aggregate Balance Sheets in the Quasi-static and Dynamic Simulations

(balance sheet components, in real terms)

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Note. The figure shows the evolution of the sum of balance sheet components across all banks. Net loans is the difference between gross loans and the stock of provisions.

The “Initial” simulation reflects the one-way impact of the initial adverse macroeconomic scenario on banks. It assesses the ability of banks to withstand stress without deleveraging given that bank balance sheets grow in line with nominal GDP. In this simulation, there is an ex-post inconsistency between the bottom-up and aggregate paths of credit because nominal GDP growth significantly outpaces the nominal credit growth projected under the scenario. (Note that for the “Initial” simulation, Figure 6 shows the real stock of loans projected under the scenario—not the one resulting from a bottom-up aggregation of bank loans.)

In contrast, in the “Quasi-static” and “Dynamic” simulations, the aggregate credit paths are consistent with individual bank lending behaviour. This consistency is achieved by explicitly accounting for macro-financial feedback loops.25 Figure 6 shows how bank deleveraging amplifies the impact of weaker trading partners’ activity, adverse terms of trade shocks, and higher world interest rates on the domestic economy: the paths of real GDP and stock of loans are lower in the “Dynamic” than in the “Quasi-static” simulation. The contractionary effect of deleveraging on activity, however, is cushioned by its effects on interest rates: lending and policy rates, and corporate and government bond yields are lower in the “Dynamic” than in the “Quasi-static” simulation.

Note that there is a delayed and persistent response of real lending and the lending rate under the “Dynamic” simulation relative to the “Initial” adverse scenario, and that these features of the responses are transmitted to the policy interest rate and to bond yields. Under the model, lending rates adjust gradually, reflecting the current composition and maturity structure of loan portfolios. Thus, the delayed response of lending and interest rates in the “Dynamic” simulation could reflect differences between the current and historical maturity structure of loan portfolios or changes in the share of loans with adjustable interest rates.26

Figure 7 compares the evolution of individual balance sheet and profit items under the different simulations, highlighting the role of deleveraging in the “Dynamic” simulation. Reflecting the stress-response adjustment mechanism described in Figure 2, the paths of loans, cash balances, and deposits and other debt are significantly lower in the “Dynamic” simulation than in the “Initial” and “Quasi-static” simulations. The valuations of securities portfolios mirror the differentiated paths of yields across simulations. In particular, market losses are larger in the “Quasi-static” than in the “Dynamic” case, and the wide fluctuations in yields under the “Initial” scenario result in significant market losses in the first 2 years and sharp market gains in the last three years.

In terms of profitability, deleveraging reduces both interest income on loans and interest expense on deposits and other debt—note that the paths of these items are significantly higher in the “Initial” and “Quasi-static” simulations than in the “Dynamic” simulation. Similarly, deleveraging mitigates the rise in total loan losses under the “Dynamic” simulation. And the valuations of securities portfolios reflect the dynamics of yields, declining in the first 2–3 years of the stress scenario and increasing in the last 2–3 years, as yields decline.

The panel on selected financial ratios in Figure 7 shows that deleveraging initially helps banks cushion the impact of the adverse shocks on their capital adequacy ratios. However, as time evolves, second-round effects of widespread deleveraging on the economy materialize and are transmitted back to banks in the form of losses, with impact on capital ratios. Capital ratios are lower in the “Quasi-static” case than in the “Dynamic” case, as the additional credit provision assumed in the “Quasi-static” case requires higher levels of risk-weighted assets. Figure 9 compares changes in capital adequacy ratios for individual banks under the three simulations discussed above to illustrate the heterogeneity of bank-specific results. The top panel compares results corresponding to the “Dynamic” simulation against those obtained under the “Initial” and “Quasi-static” simulations. Capital adequacy ratio (CAR) changes are computed as differences between CAR values at the beginning and at the end of the 5-year projection period. A point above the 45-degree line indicates that the decline in a bank’s CAR is smaller in the “Dynamic” than in the alternative simulation (initial or quasi-static). The middle panel, in turn, shows the results when CAR changes are computed as differences between CAR values at the outset of stress and the minimum values reached during the projection period.

Figure 9.
Figure 9.

Indonesia—Stress Simulation: Bank-specific Results

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Note. 1/ Banks are ranked based on CAR changes (minimum CAR minus CAR in 2018:02). A higher rank indicates a smaller decline in capital ratio due to stress.

The scatter plots show that some banks perform better in the “Dynamic” than in the “Initial” simulations, while others perform worse.

Also, “Quasi-static” stress tests results—obtained in a framework that ensures full consistency between macroeconomic and aggregated bottom-up conditions—are always dominated by “Dynamic” stress tests results—all points lie above the 45-degree line in the top-right and middle-right panels of Figure 9. This result confirms that all banks lend more in the quasi-static simulation and have higher levels of risk-weighted assets. What is most important, however, is that explicitly accounting for macro-financial feedback loops can change the relative ordering of assessed vulnerabilities across banks. A bank that is deemed “resilient” under the standard approach to stress testing (“Initial” simulation) could be considered less resilient relative to other banks when evaluated under alternative behavioral assumptions. This fact is made explicit in the bottom panel of Figure 9, which compares bank rankings (from 1 to 12) across simulations based on CAR changes. (For example, a bank that ranks 2nd in the “Initial” simulation ranks 1st in the “Dynamic” simulation; a bank that ranks 9th in the “Quasi-static” simulation ranks 6th when evaluated in a “Dynamic” simulation.)

The key finding of our analysis is that accounting for macro-financial loops can affect the cross-sectional pattern of stress tests results. Increasing the severity of the ‘initial” adverse scenario by applying larger structural shocks would make all banks worse-off without changing the bank vulnerability ranking. Thus, this option cannot be considered an adequate substitute for macro-financial stress analysis that accounts for heterogeneous bank deleveraging.

Externalities Analysis

Figure 10 shows the effects of deleveraging by selected banks on macroeconomic outcomes. These outcomes are measured by deviations of real GDP, the real stock of credit, and the nominal policy interest rate from baseline projections. In particular, Figure 10 compares the “Dynamic” simulation results against those corresponding to a “Mixed (Bi-QS)” simulation in which bank i behaves quasi-statically while all other banks exhibit dynamic lending behavior. The analysis is performed for three large banks (numbered 1, 2, and 4) that offer loans at different lending rates.

Figure 10.
Figure 10.

Indonesia—Stress Simulation: Effect of Individual Bank De-leveraging on Macroeconomic Outcomes

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Note. Area A is the cumulative output loss when all banks (except bank 2) deleverage. Area B shows the output loss associated with bank 2’s deleveraging behavior.

Consider the macroeconomic effects of a credit expansion by Bank 1 (top panel of Figure 10). Bank 1 is characterized by offering loans at a lending rate that is well above the average for the system. As the bank is large, its initial action boosts aggregate lending, but it also increases the aggregate lending rate significantly. Once cross-bank externalities and macro-financial feedback effects are accounted for, the economy ends up with higher interest rates and yields that offset the expansionary effect on output of Bank 1’s additional lending. The higher level of interest rates also exacerbates market losses and reduces the profitability of other banks, which contribute to nullify the expansionary effect on output of Bank 1’s action. In contrast, Bank 2’s lending rate is close to the average for the system. The upward pressure on interest rates associated with Bank 2’s credit expansion (middle panel of Figure 10) is less intense, and hence the output effect is larger than when Bank 1 expands credit. Bank 4 is smaller (in terms of assets and loans) than Banks 1 and 2, but it provides credit at lending rates that are well below the average rate for the system. Therefore, despite its smaller size, the impact of its lending decisions on GDP is larger than that of Bank 1. In the middle panel of Figure 10, the area A+B measures the 5-year cumulative loss of output in the “Dynamic” simulation, when all banks engage in deleveraging. The area A measures the cumulative loss of output when Bank 2 behaves quasi-statically and all other banks follow dynamic behavior. Thus, the area B (between the two red lines) is the 5-year cumulative loss of output associated with Bank 2 deleveraging. It follows that the contribution of each bank’s deleveraging to the total decline in real GDP is measured by B/(A + B).

Despite the fact that Banks 1 and 2 have a somewhat similar size (in terms of assets and credit), they differ in terms of systemic importance—the GDP impact of their lending decisions, as reflected in the B/(A + B) measure.

The results illustrate a general principle. The systemic importance of a bank along the time dimension depends crucially on factors that include not only its size but also its exposures, the sensitivities of its exposures to shocks, its buffers, and the intensity of its behavioral responses to shocks in terms of both credit (quantity) and lending interest rate (price). Figure 11 shows cross-bank externalities triggered by individual bank’s deleveraging. Each panel presents the results for an individual bank under the “Dynamic” and 12 “Mixed ( Bi-QS)” simulations—measured in terms of changes in CAR and real loan growth rates. Consider the case of Bank 3. Under the dynamic simulation, Bank 3’s loans decline by more than 30 percent in real terms and its CAR declines 7 percentage points (first pair of dots shown in the left-hand side). When Bank 3 is the only bank behaving quasi-statically (B3-QS simulation), its lending expands 25 percent in real terms, with adverse impact on the bank’s CAR, which now declines by 10 percentage points. Quasi-static behavior by Bank I generates a negative externality on Bank 3 (B1-QS simulation), as Bank 3’s capital ratio falls 9 percentage points (2 percentage points more than in the “dynamic” simulation). As the higher level of interest rates associated with Bank 1’s quasi-static behavior adds stress on Bank 3, the latter bank cuts real lending by almost 40 percent, more aggressively than in the “Dynamic” run. Similarly, comparisons between the “Dynamic” run against the other mixed simulations capture the impact on Bank 3 from no deleveraging behavior in each of the other II banks. Banks are ordered from the largest to the smallest (within the group); in general, however, externalities reflect not only bank size (share of loans) but also the sensitivity of lending responses and other sources of cross-bank heterogeneity.

Figure 11.
Figure 11.
Figure 11.
Figure 11.

Indonesia—Stress Simulation: Cross-bank Externalities Associated with Individual Bank De-leveraging

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

Finally, Figure 12 shows how individual banks’ CARs are affected by their own lending decisions and by the collective lending decisions of other banks.

Figure 12.
Figure 12.

Indonesia—Externalities Analysis: Changes in Banks’ Capital Adequacy Ratios (CAR) Depending on their Own and Other Banks’ Behaviors

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

The declines in CARs of individual banks due to stress are smaller when all banks exhibit dynamic lending behavior (compared to the case of collective quasi-static lending behavior).

Observe that a single bank would able to mitigate the impact of stress on its capital ratio by deleveraging individually when all other banks are behaving quasi-statically.

Note also that deleveraging by other banks mitigates the impact of stress on individual banks. As noted earlier, externalities associated with deleveraging are transmitted through various channels. And the quantitative analysis indicates that the negative externalities generated by other banks’ deleveraging behavior, which reduced aggregate credit and output, are more than offset by the positive externalities stemming from the downward pressure on interest rates and bond yields. Overall, Figure 12 suggests that complementarity among banks’ decisions can generate perverse dynamics where deleveraging by individual banks encourages other banks to cut lending as well.

Figure 13 compares the macroeconomic effects of the “Dynamic” simulation described above to those from a new simulation in which all banks receive capital injections equivalent to 3 percentage points of CAR over a two-year period (equally spread across 8 quarters). The effect of the capital injections on aggregate credit is significant but it takes time to materialize. The impact on other macroeconomic variables (e.g., output), however, is found to be modest and meaningful only with a significant time lag.

Figure 13.
Figure 13.

Macroeconomic Effects of System-wide Capital Injections

(equivalent to 3 percentage points of CAR over two years for all banks)

Citation: IMF Working Papers 2020, 072; 10.5089/9781513534916.001.A001

V. Concluding Remarks

This paper presents a general framework for empirical evaluation of macro-financial feedback loops and individual bank contributions to systemic risk along the time dimension. The credit response and externalities analysis model (CREAM) integrates a disaggregated banking sector into an otherwise standard macroeconomic structural vector autoregressive model. The systemic importance of a bank depends on its size, its exposures, the sensitivities of its exposures to shocks, its buffers, and its lending behavior. As the framework is sufficiently rich and embeds various sources of heterogeneity, it provides a platform for stress testing and calculation of systemic risk contributions.

In line with traditional approaches to stress testing, the framework disentangles the channels through which macroeconomic shocks impact bank losses. Separate estimates were made for three types of losses: credit (loan portfolios), market (securities portfolios), and net interest income, and were found to vary across banks. Also, and importantly, bank lending responses are heterogeneous and dependent on bank capitalization ratios. The paper shows that accounting for heterogeneous bank deleveraging and macro-financial loops can affect the cross-sectional pattern of stress tests results. Country-specific applications of the framework can uncover the relevance of different types of bank heterogeneity and risk transmission channels for macroeconomic outcomes, cross-bank externalities, and stress tests results.

Appendix I. Equations of the Model

The equations are organized as follows. Estimated equations are presented first (1 through 5). Next are the definitions and transformations needed to integrate the output from these equations to the rest of the model (6 through 9). These are followed by blocks of equations that determine banks’ net profit items (10 through 19) and the dynamic evolution of their balance sheets (20 through 31). The last set of equations aggregates bank lending decisions, computes the lending interest rate (32 to 33), and describe initial conditions as well as variables with pre-determined paths (34 to 43).

A) Estimated Blocks

Macro block (SVAR)

z˜t=Cz+Cztrt+s=1PMAsz˜ts+s=0PMφsf˜ts+μtz(1)

Macro block (ir)

irt=Cir+s=1PMBsirts+s=1PMhsits0+μtir(2)

Bank credit risk block

ln(LLRi,t1LLRi,t)=αi+s=1PMλsln(LLRi,ts1LLRi,ts)+s=0PLLβsΔzts+s=1PLLγsΔxi,ts+μi,tLL(3)

Bank lending block

ΔlnLi,tR=ξi+θ1zt+θ2xi,t1+Σs=1PηsΔlnLi,tsR+Σs=0PδsΔzts+Σs=1PρsΔxi,ts+μi,tlwhereLi,tR=Li,t/Pt(4)

Bank funding cost block

spri,t=νi+ϑ(zt,xi,t)+μi,tspr(5)

Definitions and transformations of variables related to estimated blocks:

z˜tzt;L˜tLt(6)
z˜t=[RGDPt*,PtCOMM,itUS,RGDPt,REERt,INFt,it0]'whereINFt=lnPtlnPt1(7)f˜t=[LtRitL]'whereLtR=Σi=11Li,tR,irt=[YtG,40YtC,0YtC,40]'
xi,t=(CARi,tLATAi,t,LLRi,t)(8)
CARi,t=Ki,tRWAi,t,LATAi,t=LAi,tAi,t=Mi,t+Bi,tG+Bi,tcAi,t(9)

B) Bank Profit and Loss Block

Definition of total profit

Πi,t=IIi,tLIEi,tDLLi,t+Ri,tG+Ri,tC+Oi,t(10)

Interest income on loans

IIi,tL=0.25(Li,t1NPLi,t1)ii,t1L(11)
ii,tL=(1πiL)ii,t1L+πiLii,tNL(12)
ii,tNL=ii,t1NL+ψiG(YtG,duriLYt1G,duriL)+ψispr(spri,tspri,t1)(13)

Interest expense on deposits and debt

IEi,tD=0.25Di,t1ii,t1D(14)
ii,tD=(1πiD)ii,t1D+πiDii,tND(15)
ii,tND=(1chi)(YtG,duriD+spri,t)(16)

Loan losses

LLi,t=LLRi,tLi,t1(17)

Securities return

Ri,th=Bi,thBi,t1h,h{G,C}(18)

Other net income

Oi,t=ΞiAi,0(19)

C) Bank Balance Sheet Dynamics

Balance sheet

Ai,t=(Li,tPRi,t)+Mi,t+Bi,tG+Bi,tC+OAi,t=Ki,t+Di,t(20)
Bi,th=Bi,th,HTM+Bi,th,MTMforh{G,C}(21)

Dynamics of non-performing loans

NPLi,t=NPLi,t1+1LGDiLLi,t(22)

Dynamics of provisions

PRi,t=PRi,t1+LLi,t(23)

Cash balances

Mi,t=miDi,t(24)

Dynamics of securities portfolios

Bi,th,HTM=(1+0.25ii,t1h)Bi,t1h,HTMforh{G,C}(25)
Bi,th,MTM=[10.25durih(1+Yt1h,durih0.25)(Yth,durihYt1h,durih)+0.25ii,t1h]Bi,t1h,MTMforh{G,C}(26)
ii,th=(1πih)ii,t1h+πihYth,durihforh{G,C}(27)
YtG,s=LINT(s,it0,YtG,40);YtC,s=LINT(s,YtC,0,YtG,40)(28)

Other assets

OAi,t=OAi,0(29)

Dynamics of capital

Ki,t=Ki,t1+Πi,t[1divi1+(Πi,t)]+kiri,tRWAi,t1(30)

Risk-weighted assets

RWAi,t=[ΘiL(Li,tNPLi,t)+(NPLi,tPRi,t)+ΘiGBi,tG+ΘiCBi,tC](11ρiORWA)(31)

D) Aggregation

Aggregate lending

Lt=i=1ILi,t(32)

Aggregate lending interest rate

itL=ilii,tLωi,twhereωi,t=(Li,tNPLi,t)/i(Li,tNPLi,t)(33)

E) Initial conditions and variables with a predetermined path

Macroeconomic data

z0,z1,z2,...;L0,L1,L2,...;ir0,ir1,ir2,...;P0,P1,P2,...(34)

Bank-specific data

LLRi,0,LLRi,1,LLRi,2,...(35)
Xi,0,Xi,1,Xi,2,(36)
{Li,0,PRi,0,Mi,0,Bi,0G,Bi,0C,OAi,0,Ki,0,Di,0},{Li,1,PRi,1,Mi,1,Bi,1G,Bi,1C,OAi,1,Ki,1,Di,1},{Li,2,PRi,2,Mi,2,Bi,2G,Bi,2C,OAi,2,Ki,2,Di,2},(37)
Ai,0=(Li,0PRi,0)+Mi,0+Bi,0G+Bi,0C(38)
Bi,0h=Bi,0h,HTM+Bi,0h,MTMforh{G,C}(39)
NPLi,0(40)
ii,0NL,ii,1NL,ii,1L,ii,1D(41)
μi,0spr,μi,1spr(42)

Variables with a predetermined path (shocks to Eqns. 1, 2 and 5)

εtz,μtir,kiri,tandμi,tsprgivenforalliandt=1,2,...,whereεtz=B1μtz(43)

Appendix II. Description of the Stress Simulation Algorithm

The stress simulation algorithm consists of the following steps:

Step 1. Define a baseline macroeconomic scenario.

Step 2. Specify a sequence of adverse macroeconomic structural shocks ϵtz for t = 1,2,...

Step 3. Produce an “initial adverse scenario” using an auxiliary VAR model that includes equations for aggregate credit and the lending interest rate. The auxiliary VAR model treats aggregate credit and the lending interest rate as endogenous and is defined over the vector [RGDP*,PCOMM iUS,iL,LR,RGDP,INF,REER,i027 Importantly, the “initial scenario” reflects the effects of the shocks ϵtz and includes initial “guesses” for the paths of aggregate credit and the lending interest rate.

Step 4. The algorithm enters a main iteration loop (indexed by if) that will remain active until convergence is achieved between the aggregate paths of credit and lending interest rates from the previous iteration, and those obtained from a bottom-up aggregation of individual bank results in the current iteration. More specifically,

  • A nested bank-by-bank loop (indexed by bb) produces forecasts of individual bank results—losses, stress, and lending responses—conditional on the paths of macroeconomic variables.

  • Once the bb loop ends, bank-specific variables are aggregated, and convergence (or lack thereof) for aggregate credit and lending interest rate paths between the previous and the current iterations can be verified.

  • When convergence has not been achieved, differences between the previous and current iterations of the credit and lending interest rate paths are treated as “shocks,” and impulse responses obtained from the estimated VARX model (Eq. 1) are used to revise the paths of all macroeconomic variables.

  • The ii loop continues iterating until a fixed point (defined over credit and lending interest rates paths) is found.

Appendix III. Data Sources

Macroeconomic data. Data sources include Bank Indonesia, Statistical Bureau Indonesia, IMF International Financial Statistics, CEIC, JP Morgan, Federal Reserve Bank of St. Louis, and Haver Analytics. The tables show definitions of the series and their corresponding sources.

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