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Chapter 4 The Global Macro-Financial Model: A Stress Test Scenario Simulation Tool

Author(s):
Li Lian Ong, and Andreas A. Jobst
Published Date:
September 2020
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Author(s)
Francis Vitek

This chapter presents the global macro-financial model (GFM) and discusses its application to simulating banking sector solvency stress test scenarios. The GFM is a structural macroeconometric model of the world economy, disaggregated into 40 national economies, which features a range of nominal and real rigidities, extensive macro-financial linkages, and diverse spillover transmission channels. The simulation of a stress test scenario using the GFM is demonstrated with an example.

1. Introduction

Banking sector solvency stress tests are generally based on severe but plausible macro-financial scenarios. These scenarios specify the future evolution of a variety of macroeconomic and financial market variables, given sets of shocks that perturb them from their baseline paths, as well as feasible policy responses. These sets of shocks represent scenario narratives capturing key macro-financial risks to which the banking sector is exposed, and typically have structural interpretations. These risks may originate domestically or abroad, with the banking sector exposed to them either directly via determinants of profitability and capitalization such as funding costs and loan impairments, or indirectly through macro-financial linkages to these determinants.

Estimated dynamic stochastic general equilibrium (DSGE) models are widely used by monetary and fiscal authorities for policy analysis and forecasting purposes because they can generate theoretically coherent and empirically adequate dynamic interrelationships across macro-financial variables, driven by shocks having structural interpretations. This class of structural macroeconometric models has many variants, with the estimated New Keynesian DSGE models used by policymaking institutions incorporating a range of nominal and real rigidities, as well as an expanding array of macro-financial linkages. These properties make New Keynesian DSGE models well suited for simulating stress test scenarios, in particular those that feature a banking sector, as this internalizes key macro-financial feedback loops.

This chapter presents the global macro-financial model (GFM), documented more fully in Vitek 2015, and discusses its application to simulating banking sector solvency stress test scenarios. The GFM is a structural macroeconometric model of the world economy, disaggregated into 40 national economies within a panel framework. This estimated New Keynesian DSGE model features a range of nominal and real rigidities, extensive macro-financial linkages, and diverse spillover transmission channels. These macro-financial linkages encompass bank-and capital-market-based financial intermediation, with cross-border balance sheet exposures and contagion effects. These features enable the GFM to simulate diverse stress test scenarios, generating theoretically coherent and empirically adequate dynamic interrelationships across macro-financial variables driven by sets of shocks having structural interpretations, potentially subject to policy constraints. These scenarios internalize key macro-financial feedback loops, in particular between the banking sector and the rest of the economy, while capturing its direct and indirect exposures to risks originating domestically or abroad.

The organization of this chapter is as follows. Section 2 presents the equations governing the evolution of the endogenous and exogenous variables of the GFM. Estimation of the model is the subject of Section 3. The simulation of stress test scenarios using the GFM is discussed in Section 4, with reference to an example for the United Kingdom. Finally, Section 5 offers conclusions and outlines future model development plans.

2. The Model

The theoretical foundation of the GFM is the canonical New Keynesian DSGE model of an open economy, extended to incorporate additional macro-financial linkages and spillover transmission channels, while preserving analytical and computational tractability. Following Smets and Wouters 2003, the GFM features short-term nominal price and wage rigidities generated by monopolistic competition, staggered reoptimization, and partial indexation in the output and labor markets. Following Christiano, Eichenbaum, and Evans 2005, the resultant inertia in inflation and persistence in output is enhanced with other features such as habit persistence in consumption, adjustment costs in investment, and variable capital utilization. Following Galí 2011, the model incorporates involuntary unemployment through a reinterpretation of the labor market. Households are differentiated according to whether they are bank intermediated, capital market intermediated, or credit constrained. Bank-intermediated households have access to domestic banks where they accumulate deposits, whereas capital-market-intermediated households have access to domestic and foreign capital markets where they trade financial assets. Motivated by Tobin 1969, these capital-market-intermediated households solve a portfolio balance problem, allocating their financial wealth across domestic and foreign money, bond and stock market securities that are imperfect substitutes. To cope with the curse of dimensionality, targeted parameter restrictions are imposed on the optimality conditions determining the solution to this portfolio balance problem, avoiding the need to track the evolution of granular asset allocations. Firms are grouped into differentiated industries. The energy and nonenergy commodity industries produce internationally homogeneous goods under decreasing returns to scale, while all other industries produce internationally heterogeneous goods under constant returns to scale. Banks perform global financial intermediation subject to financial frictions and a regulatory constraint. Building on Hülsewig, Mayer, and Wollmershäuser 2009, they issue risky domestic currency-denominated loans to domestic and foreign firms at infrequently adjusted predetermined lending rates. Also building on Gerali, Neri, Sessa, and Signoretti 2010, they obtain funding from domestic bank-intermediated households via deposits and from the domestic money market via loans, accumulating bank capital out of retained earnings given credit losses to satisfy a regulatory capital requirement. Motivated by Kiyotaki and Moore 1997, the GFM incorporates a financial accelerator mechanism linked to collateralized borrowing. Finally, following Monacelli 2005, the model accounts for short-term incomplete exchange rate pass-through with short-term nominal price rigidities generated by monopolistic competition, staggered reoptimization, and partial indexation in the import markets.

Simulation is based on an estimated linear state space representation of an approximate multivariate linear rational expectations representation of this New Keynesian DSGE model of the world economy. This multivariate linear rational expectations representation is derived by analytically linearizing the equilibrium conditions of the model around its stationary deterministic steady state equilibrium, and consolidating them by substituting out intermediate variables. In what follows, x^i,t denotes the deviation of variable xi,t from its steady state equilibrium value xi, while Et xi,t+s denotes the rational expectation of variable xi,t+s conditional on information available in period t. Bilateral weights wi,jZ for evaluating the trade weighted average of variable xi,t across the trading partners of economy i are based on exports for Z = X, imports for Z = M, and their average for Z = T. In addition, bilateral weights wi,jZ for evaluating the weighted average of variable xi,t across the lending destinations and borrowing sources of economy i are based on bank lending for Z = C and nonfinancial corporate borrowing for Z = F. Furthermore, bilateral weights wi,jZ for evaluating the portfolio weighted average of variable xi,t across the investment destinations of economy i are based on debt for Z = B and equity for Z = S. Finally, world weights wi,jZ for evaluating the weighted average of variable xi,t across all economies are based on output for Z = Y, money market capitalization for Z = M, bond market capitalization for Z = B, and stock market capitalization for Z = S.

Endogenous Variables

Output price inflation π^i,tY depends on a linear combination of its past and expected future values driven by the contemporaneous labor income share, output, and internal terms of trade according to the output price Phillips curve:

Output price inflation also depends on contemporaneous, past and expected future changes in the internal terms of trade, where the polynomial in the lag operator P1(L)=1γY1+γYβLβ1+γYβEtL1. The response coefficients of this relationship vary across economies with their trade openness and commodity export intensities.

Consumption price inflation π^i,tC, depends on a linear combination of its past and expected future values driven by the contemporaneous labor income share, output, and the internal terms of trade according to the consumption price Phillips curve:

Consumption price inflation also depends on contemporaneous, past, and expected future changes in the external terms of trade. The response coefficients of this relationship vary across economies with their trade openness and commodity export intensities.

Output ln Y^i,t depends on a weighted average of its past and expected future values driven by a weighted average of the contemporaneous real ex ante portfolio return and short-term real market interest rate according to output demand relationship:

Reflecting the existence of credit constraints, output also depends on contemporaneous, past, and expected future real profit and disposable labor income. In addition, output depends on contemporaneous, past, and expected future investment and public domestic demand. Finally, reflecting the existence of international trade linkages, output depends on contemporaneous, past, and expected future export weighted foreign demand, as well as the export weighted average foreign external terms of trade and the domestic external terms of trade. The response coefficients of this relationship vary across economies with the composition of their domestic demand, the size of their government, their labor income share, their trade openness, and their trade pattern.

Domestic demand In D^i,t depends on a weighted average of its past and expected future values driven by a weighted average of the contemporaneous real ex ante portfolio return and short-term real market interest rate according to domestic demand relationship:

Reflecting the existence of credit constraints, domestic de-mand also depends on contemporaneous, past, and expected future real profit and disposable labor income. Finally, domestic demand depends on contemporaneous, past, and expected future investment and public domestic demand. The response coefficients of this relationship vary across economies with the composition of their domestic demand, the size of their government, and their labor income share.

Consumption ln C^i,t depends on a weighted average of its past and expected future values driven by a weighted average of the contemporaneous real ex ante portfolio return and short-term real market interest rate according to consumption demand relationship:

Reflecting the existence of credit constraints, consumption also depends on contemporaneous, past, and expected future real profit and disposable labor income, where polynomial in the lag operator P2(L)=1α1+αL11+αEtL1 response coefficients of this relationship vary across economies with their consumption intensity, the size of their government, and their labor income share.

Investment In I^i,t, depends on a weighted average of its past and expected future values driven by the contemporaneous relative shadow price of capital according to investment demand relationship:

Reflecting the existence of a financial accelerator mechanism, the relative shadow price of capital In Q^i,tP^i,tC depends on its expected future value as well as the contemporaneous real ex ante portfolio return, and the contemporaneous real ex ante corporate loan rate net of the expected future loan default rate, according to investment Euler equation:

The relative shadow price of capital also depends on the expected future capital utilization and tax rates. Auxiliary parameter λQ is theoretically predicted to equal one, and satisfies λQ ≥ 0. The capital utilization rate ln u^i,tK depends on the contemporaneous real wage according to capital utilization relationship:

The capital utilization rate also depends on the contemporaneous deviation of utilized capital from employment. The capital stock ln K^i,t+1 satisfies ln lnK^i,t+1=(1δ)lnK^i,t+δln(V^i,tII^ai,t).

Exports ln X^i,t depend on contemporaneous export weighted foreign demand as well as the export weighted average foreign external terms of trade, according to export demand relationship:

The response coefficients of this relationship vary across economies with their trade pattern and the trade openness of their trading partners. Imports In M^i,t depend on contemporaneous domestic demand, as well as the domestic external terms of trade, according to import demand relationship:

The response coefficients of this relationship vary across economies with their trade openness.

The nominal ex ante portfolio return Eti^i,t+1AA,H depends on the contemporaneous short-term nominal market interest rate according to return function:

Reflecting the existence of internal and external macro-financial linkages, the nominal ex ante portfolio return also depends on contemporaneous domestic and foreign duration risk premium, equity risk premium, and currency risk premium shocks. The response coefficients of this relationship vary across economies with their domestic and foreign money, bond, and stock market exposures. The real ex ante portfolio return Eti^i,t+1AA,H satisfies Etr^i,t+1AA,H=Eti^i,t+1AA,HEtπ^i,t+1C.

The nominal policy interest rate i^i,tP depends on a weighted average of its past and desired values according to monetary policy rule:

Under a flexible inflation targeting regime j = 0, and the desired nominal policy interest rate responds to contemporaneous consumption price inflation and output. Under a managed exchange rate regime j = 1, and it also responds to the contemporaneous real effective exchange rate. Under a fixed exchange rate regime j = 2, and the nominal policy interest rate instead tracks the contemporaneous nominal policy interest rate for the economy that issues the anchor currency one for one, while responding to the contemporaneous corresponding nominal bilateral exchange rate. For economies belonging to a currency union, the target variables entering into their common monetary policy rule are expressed as output weighted averages across union members. The real policy interest rate r^i,tP satisfies r^i,tP=i^i,tPEtπ^i,t+1C.

The short-term nominal market interest rate r^i,tP=i^i,tPEtπ^i,t+1C depends on the contemporaneous nominal policy interest rate and the net foreign asset ratio according to the money market relationship,

where credit risk premium shock υ^i,tiS satisfies dynamic factor process υ^i,tiS=λkMΣj=1NwjMv^j,tS+(1λkMwiM)v^i,tiS. The intensity of international money market contagion varies across economies, with k = 0 for low-debt contagion economies, k = 1 for medium-debt contagion economies, and k = 2 for high-debt contagion economies, where λ0M<λ1M<λ2M. For economies belonging to a currency block, the ratio of national financial wealth to nominal output is expressed as an output weighted average across block members. The short-term real market interest rate r^i,tS satisfies r^i,tS=i^i,tSEtπ^i,t+1C.

The long-term nominal market interest rate r^i,tS=i^i,tSEtπ^i,t+1C depends on a weighted average of its expected future value and the contemporaneous short-term nominal market interest rate according to bond market relationship,

where duration risk premium shock ln υ^i,tB satisfies dynamic factor process ln lnυ^i,tB=λkBΣj=1NwjBlnv^j,tB+(1λkBwiB)lnv^i,tB. The intensity of international bond market contagion varies across economies, with k = 0 for low-debt contagion economies, k = 1 for medium-debt contagion economies, and k = 2 for high-debt contagion economies, where λ0B<λ1B<λ2B. The long-term real market interest rate r^i,tL satisfies the same bond market relationship, driven by the contemporaneous short-term real market interest rate.

The price of equity In V^i,tS depends on its expected future value driven by expected future net profits and the contemporaneous short-term nominal market interest rate according to the stock market relationship,

where equity risk premium shock ln υ^i,tS satisfies dynamic factor process In υ^i,tS=λkSΣj=1NwjSlnv^j,tS+(1λkSwiS)lnv^i,tS. The intensity of international stock market contagion varies across economies, with k = 0 for low-equity contagion economies, k = 1 for medium-equity contagion economies, and k = 2 for high-equity contagion economies, where λ0S<λ1S<λ2S.

Real net profits In Π^i,tSP^i,tY depends on contemporaneous output, the labor income share, and the tax rate, as well as the deviation of investment from output and the terms of trade, according to profit function:

Reflecting the existence of a financial accelerator mechanism, real net profits also depend on the contemporaneous and past nonfinancial corporate debt ratio, as well as the contemporaneous nominal corporate loan rate net of the contemporaneous loan default rate and nominal output growth rate. Auxiliary parameter λπ is theoretically predicted to equal one, and satisfies λπ ≥ 0. The response coefficients of this relationship vary across economies with the size of their government, their labor income share, their investment intensity, and their trade openness.

Reflecting the existence of international bank lending linkages, bank credit In B^i,t+1C,B depends on the contemporaneous bank lending weighted average of domestic currency denominated domestic and foreign nonfinancial corporate debt according to bank credit-demand function:

Nonfinancial corporate debt satisfies lnB^i,t+1C,F=lnP^i,tC+lnK^i,t+1. Furthermore, the nominal corporate loan rate i^i,tC,E depends on the nonfinancial corporate-borrowing weighted average of past domestic and foreign nominal bank lending interest rates, adjusted for contemporaneous changes in nominal bilateral exchange rates, according to:

Finally, the credit-loss rate δ^i,tC,E depends on the bank lending weighted average of contemporaneous domestic and foreign loan default rates according to credit-loss rate function:

The real ex ante corporate loan rate Etr^i,t+1C,E satisfies Etr^i,t+1C,E=Eti^i,t+1C,EEtπ^i,t+1C.

The nominal bank lending interest rate i^i,tC depends on a weighted average of its past and expected future values driven by the deviation of the past short-term nominal market interest r ate from the contemporaneous nominal bank lending interest rate net of the contemporaneous credit-loss rate according to lending rate Phillips curve:

Reflecting the existence of a regulatory capital requirement, the nominal bank lending interest rate also depends on the past deviation of the bank capital ratio from its required value, as well as the past deviation of the regulatory bank capital ratio from its funding cost. The real bank lending interest rate r^i,tC satisfies r^i,tC=r^i,tCEtπ^i,t+1C.

The money stock In M^i,t+1S depends on contemporaneous bank credit and the bank capital stock according to bank balance sheet identity:

The bank capital ratio κ^i,t+1 satisfies κ^i,t+1=κR(lnK^i,t+1BlnB^i,t+1C,B). Retained earnings In I^i,tB, depends on a weighted average of its past and expected future values driven by the contemporaneous shadow price of bank capital according to retained earnings relationship:

The shadow price of bank capital In Q^i,tB depends on its expected future value net of the expected future credit-loss rate, as well as the contemporaneous short-term nominal market interest rate, according to retained earnings Euler equation:

Reflecting the existence of a regulatory capital requirement, the shadow price of bank capital also depends on the contemporaneous deviation of the bank capital ratio from its required value. The bank capital stock ln K^i,t+1B satisfies lnK^i,t+1B=(1χBδC)lnK^i,tB+χBδClnI^i,tB+χBδ^i,tC,E.

The real wage In W^i,tP^i,tC depends on a weighted average of its past and expected future values driven by the contemporaneous unemployment rate according to wage Phillips curve:

The real wage also depends on contemporaneous, past, and expected future consumption price inflation, where the polynomial in the lag operator P3(L)=1γL1+γLβLβ1+γLβEtL1. The unemployment rate u^i,tL satisfies u^i,tL=lnN^i,tlnL^i,t.

The labor force In N^i,t, depends on contemporaneous employment and the after-tax real wage according to the labor supply relationship:

Employment In L^i,t depends on contemporaneous output and the utilized capital stock according to production function:

The response coefficients of this relationship vary across economies with their labor income share, their trade openness, and their commodity export intensities.

The nominal bilateral exchange rate In ϵ^i,t*,t, depends on its expected future value driven by the contemporaneous short-term nominal market interest rate differential according to foreign exchange market relationship:

For economies belonging to a currency union, the variables entering into their common foreign exchange market relationship are expressed as output weighted averages across union members. The real bilateral exchange rate In Q^i,i*,t, satisfies lnQ^i,i*,t=lnϵ^i,i*,t+lnP^i*,tYlnP^i,tY.1

The internal terms of trade In T^i,tX depends on the contemporaneous relative domestic currency-denominated prices of energy and nonenergy commodities according to internal terms of trade function:

The response coefficients of this relationship vary across economies with their trade openness and commodity export intensities.

The change in the external terms of trade ln T^i,tM depends o n a linear combination of its past and expected future values driven by the contemporaneous deviation of the import weighted average real bilateral exchange rate from the external terms of trade according to import price Phillips curve:

The change in the external terms of trade also depends on the contemporaneous domestic and import weighted average foreign internal terms of trade. In addition, the change in the external terms of trade depends on contemporaneous, past, and expected future output price inflation and the change in the internal terms of trade, where polynomial in the lag operator P4(L)=1γM(1μiM)1+γMβ(1μiM)Lβ1+γMβ(1μiM)EtL1. Finally, the change in the external terms of trade depends on the contemporaneous, past, and expected future domestic currency-denominated prices of energy and nonenergy commodities. The response coefficients of this relationship vary across economies with their trade openness, their trade pattern, and their commodity import intensities.

Public domestic demand ln G^i,t, depends on a weighted average of its past and desired values according to fiscal expenditure rule:

Desired public domestic demand responds to the contemporaneous net government asset ratio. The tax rate τ^i,t, depends on a weighted average of its past and desired values according to fiscal revenue rule:

The desired tax rate responds to the contemporaneous net government asset ratio. The response coefficients of the former relationship vary across economies with the size of their government.

The regulatory bank capital ratio κ^i,t+1R depends on a weighted average of its past and desired values according to macroprudential policy rule:

The desired regulatory bank capital ratio responds to the contemporaneous bank credit ratio, as well as the contemporaneous expected excess portfolio return. The loan default rate δ^i,tC depends on a weighted average of its past and attractor values according to default rate relationship:

The attractor loan default rate responds to the contemporaneous nonfinancial corporate debt ratio, as well as the contemporaneous expected excess portfolio return. The response coefficients of these relationships vary across economies with the size of their bank credit exposures and non-financial corporate debt loads.

The fiscal balance ratio FB^i,tPi,tYYi,t depends on a weighted average of the past short-term nominal market interest rate and the effective long-term nominal market interest rate, as well as the past net government asset ratio, and the contemporaneous growth rate of nominal output and the primary fiscal balance ratio, according to government dynamic budget constraint:

In addition, the primary fiscal balance ratio FB^i,tPi,tYYi,t depends on the contemporaneous tax rate and the deviation of public domestic demand from output, as well as the terms of trade according to:

Furthermore, the net government asset ratio A^i,t+1GPi,tYYi,t depends on its past value, as well as the contemporaneous growth rate of nominal output and the fiscal balance ratio according to:

Finally, the effective long-term nominal market interest rate i^i,tL,E depends on a weighted average of its past value and the contemporaneous long-term nominal market interest rate according to i^i,tL,E=χGi^i,t1L,E+(1XG)i^i,tL. The linearization of these relationships accounts for long-term balanced growth at nominal rate g. Their response coefficients vary across economies with their public financial wealth, the size of their government, and their trade openness.

The current account balance ratio CA^i,tϵi*,i,tPi,tYYi,t depends on the contemporaneous quotation currency-denominated world money market portfolio return, as well as the past net foreign asset ratio, and the contemporaneous growth rate of world nominal output and the trade balance ratio, according to national dynamic budget constraint:

Furthermore, the trade balance ratio TB^i,tEi*,i,tPi,tYYi,t depends on the contemporaneous deviation of exports from imports and the terms of trade according to:

Finally, the net foreign asset ratio A^i,t+1Pi,tYYi,t depends on its past value, as well as the contemporaneous growth rate of world nominal output and the current account balance ratio according to:

The linearization of these relationships accounts for long-term balanced growth at nominal rate g. Their response coefficients vary across economies with their national financial wealth and their trade openness.

The price of commodities P^k,tY depends on a weighted average of its past and expected future values driven by the contemporaneous world output weighted average labor income share, output, and the relative domestic currency-denominated price of commodities according to commodity price Phillips curve:

The price of commodities also depends on the contemporaneous, past, and expected future world output weighted average nominal bilateral exchange rate, where the polynomial in the lag operator P5(L)=111+βLβ1+βEtL1. The response coefficients of this relationship vary across commodity markets 1 ≤ k ≤ M*, with k = 1 for energy commodities and k = 2 for nonenergy commodities.

Exogenous Variables

The productivity ln A^i,t labor supply ln V^i,tL consumption demand ln V^i,tC investment demand ln V^i,tI, export demand ln V^i,tX, and import demand ln V^i,tM shocks follow stationary first-order autoregressive processes:

In addition, the credit risk premium v^i,tS, duration risk premium ln v^i,tB, equity risk premium ln v^i,tS, currency risk premium ln v^i,tϵ, and lending rate markup ln θ^i,tC, shocks follow stationary first-order autoregressive processes:

Furthermore, the output price markup ln θ^i,tY, import price markup ln θ^i,tM, wage markup ln θ^i,tL, and commodity price markup ln θ^k,tY, shocks follow white noise processes:

Finally, the monetary policy V^i,tP, fiscal expenditure V^i,tG, fiscal revenue V^i,tT, capital requirement V^i,tκ, and default rate V^i,tδ shocks follow white noise processes:

As an identifying restriction, all innovations are assumed to be independent, which combined with our distributional assumptions, implies multivariate normality.

3. Estimation

The traditional econometric interpretation of an approximate linear state space representation of this New Keynesian DSGE model of the world economy regards it as a representation of the joint probability distribution of the data. We employ a Bayesian maximum likelihood estimation procedure that respects this traditional econometric interpretation while conditioning on prior information concerning the generally common values of structural parameters across economies. In addition to mitigating potential model mis-specification and identification problems, exploiting this additional information may be expected to yield efficiency gains in estimation.

Data Transformations

Estimation of the structural parameters of our New Keynes-ian DSGE model is based on the estimated cyclical components of a total of 661 endogenous variables observed for 40 economies over the sample period (the first quarter of 1999 through the third quarter of 2014). The advanced and emerging economies under consideration are Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, New Zealand, Norway, the Philippines, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States. The observed macroeconomic and financial market variables under consideration are the price of output, the price of consumption, the quantity of output, the quantity of private consumption, the quantity of exports, the quantity of imports, the nominal policy interest rate, the short-term nominal market interest rate, the nominal bank lending interest rate, the long-term nominal market interest rate, the price of equity, the nominal wage, the unemployment rate, employment, the nominal bilateral exchange rate, the quantity of public domestic demand, the fiscal balance ratio, and the prices of nonrenewable energy and nonenergy commodities. For a detailed description of this multivariate panel data set, refer to Appendix 4.1.

We estimate the cyclical components of all of the observed endogenous variables under consideration with the generalization of the flter described in Hodrick and Prescott 1997 due to Vitek 2014, which parameterizes the difference order associated with the penalty term determining the smoothness of the trend component. For the price of output, the price of consumption, the quantity of output, the quantity of private consumption, the quantity of exports, the quantity of imports, the price of equity, the nominal wage, employment, the nominal bilateral exchange rate, the quantity of public domestic demand, and the prices of energy and nonenergy commodities, we set the difference order to two and the smoothing parameter to 16,000. For the nominal policy interest rate, the short-term nominal market interest rate, the nominal bank lending interest rate, the long-term nominal market interest rate, the unemployment rate, and the fiscal balance ratio, we set the difference order to one and the smoothing parameter to 400.

Parameter Estimates

We estimate the structural parameters of an approximate linear state space representation of our New Keynesian DSGE model by Bayesian maximum likelihood, conditional on prior information concerning their generally common values across economies. Inference on these parameters is based on an asymptotic normal approximation to the posterior distribution around its mode, which is calculated by numerically maximizing the logarithm of the posterior density kernel with a customized implementation of the differential evolution algorithm due to Storn and Price 1997. We assume a multivariate normal prior distribution, which implies that the mode of the posterior distribution equals its mean. For a detailed discussion of this estimation procedure, refer to Vitek 2014.

The marginal prior distributions of parameters are centered within the range of estimates reported in the existing empirical literature, where available. The conduct of monetary policy is represented by a flexible inflation targeting regime in Australia, Canada, Chile, the Czech Republic, the euro area, Israel, Japan, Mexico, New Zealand, Norway, Poland, Sweden, the United Kingdom, and the United States; by a managed exchange rate regime in Argentina, Brazil, China, Colombia, India, Indonesia, Korea, Malaysia, the Philippines, Russia, South Africa, Switzerland, Thailand, and Turkey; and by a fixed exchange rate regime in Denmark and Saudi Arabia, consistent with the de facto classif-cation in IMF 2013. The high-debt contagion economies are Argentina, Brazil, Colombia, Indonesia, Mexico, the Philippines, Poland, Russia, South Africa, Thailand, and Turkey, while the low-debt contagion economies are Chile, China, India, and Malaysia. The high-equity contagion economies are Argentina, Brazil, Colombia, India, Indonesia, Mexico, the Philippines, Poland, Russia, South Africa, Thailand, and Turkey, while the low-equity contagion economies are Chile, China, and Malaysia. The quotation currency for transactions in the foreign exchange market is issued by the United States. All macroeconomic and financial great ratios are calibrated to match their observed values in 2012. The same is true of all bilateral trade, bank lending, nonfinancial corporate borrowing, portfolio debt investment, and portfolio equity investment weights, normalized to sum to one across economies.

Parameter estimation results based on the effective sample period (the third quarter of 1999 through the third quarter of 2014) are reported in Appendix Table 4.2.1 and Appendix Table 4.2.2. The posterior means of most parameters are close to their prior means, reflecting the imposition of tight priors to preserve empirically plausible impulse responses. Nevertheless, the data are quite informative regarding some of these parameters, as evidenced by substantial updates from prior to posterior, which collectively result in substantial updates to impulse responses.

4. Scenario Analysis

We illustrate the simulation of banking sector solvency stress test scenarios using the GFM with reference to an example for the United Kingdom, which was an input into IMF 2016. This stress test scenario for the United Kingdom features a balance sheet recession there triggered by monetary normalization in the United States, and was the first such application of the GFM, necessitated by the large cross-border balance sheet exposures and contagion effects involved. The GFM has since been used to simulate stress test scenarios for many other economies, but this example is representative of the general approach.

Scenario Assumptions

Our stress test scenario for the United Kingdom consists of three layers, two external and one domestic (Table 4.1). The external layers are driven by foreign shocks that impact banking sector profitability and capitalization directly by increasing funding costs and foreign loan impairments, as well as indirectly through macro-financial spillovers that raise domestic loan impairments. The domestic layer amplifies and propagates these adverse impacts. All of these shocks occur relative to the baseline.

Table 4.1Scenario Assumptions
Layer 1: Disorderly Accelerated Monetary Normalization in United States, 2016–2017
Nominal policy interest rate; investment and consumption demand shocks+200 basis points
Money market interest rate spread; credit risk-premium shocks+50 basis points
Long-term nominal market interest rate; duration risk-premium shocks+200 basis points
Real equity price; equity risk-premium shocks-20 percent
Real effective exchange rate; currency risk-premium shocks-10 percent
Layer 2: Financial Stress in Fragile Four, 2016–2017
Private investment; investment demand shocks-4 percent
Private consumption; consumption demand shocks-1 percent
Long-term nominal market interest rate; duration risk-premium shocks+200 basis points
Real equity price; equity risk-premium shocks-40 percent
Primary fiscal balance ratio; fiscal expenditure shocks+2 percentage points
Real bilateral exchange rate; currency risk-premium shocks+10 percent
Layer 3: Property and Equity Market Corrections in United Kingdom, 2016 –2017
Private investment; investment demand shocks-12 percent
Private consumption; consumption demand shocks-4 percent
Money market interest rate spread; credit risk-premium shocks+100 basis points
Long-term nominal market interest rate; duration risk-premium shocks+100 basis points
Real equity price; equity risk-premium shocks-40 percent
Source: Author.Note: All scenario assumptions are expressed as deviations from the October 2015 World Economic Outlook baseline (IMF 2015).
Source: Author.Note: All scenario assumptions are expressed as deviations from the October 2015 World Economic Outlook baseline (IMF 2015).

The first external layer of our stress test scenario for the United Kingdom features a disorderly accelerated monetary normalization in the United States. In particular, it assumes a 200- basis-point nominal policy interest rate increase in the United States during 2016 and 2017, induced by a strong private domestic demand-driven macroeconomic expansion. Private investment rises four times as much as private consumption, driven by investment and consumption demand shocks. This accelerated monetary normalization is accompanied by a drying up of liquidity in the money market in the United States, reflecting heightened policy uncertainty, represented by a widening of the spread of the short-term nominal market interest rate over the nominal policy interest rate by 50 basis points during 2016, driven by internationally correlated credit risk premium shocks. It is also accompanied by an initial steepening of the yield curve in the United States, with the long-term nominal market interest rate rising by 200 basis points during 2016, reflecting a rebound of the term premium driven by internationally correlated duration risk premium shocks that shift investor preferences away from long-term bonds. Furthermore, there is a stock market correction in the United States, with the real equity price falling by 20 percent during 2016, driven by internationally correlated equity risk premium shocks that shift investor preferences away from equities. Finally, the dollar appreciates by 10 percent in real effective terms during 2016, driven by currency risk premium shocks that shift investor preferences toward dollar-denominated financial assets.

The second external layer of our stress test scenario features financial stress in the “Fragile Four” economies (Brazil, Indonesia, South Africa, Turkey). Given their high vulnerability to monetary normalization in the United States, we assume these four countries experience sudden stops, characterized by large domestic demand-driven macroeconomic contractions associated with a tightening of financial conditions. In particular, we assume autonomous 4 percent reductions in private investment driven by investment demand shocks, and autonomous 1 percent declines in private consumption driven by consumption demand shocks, during 2016 and 2017. Furthermore, we assume 200- basis-point increases in the long-term nominal market interest rate, driven by internationally correlated duration risk premium shocks, and 40 percent reductions in the real equity price driven by internationally correlated equity risk premium shocks, during 2016. In addition, we assume procyclical expenditure-based fiscal consolidation reactions to public debt sustainability concerns, which raise the primary fiscal balance ratio by 2 percentage points during 2016 and 2017. Finally, we assume 10 percent real depreciations of the real, rupiah, rand, and lira against the dollar during 2016, driven by currency risk premium shocks.

The domestic layer of our stress test scenario amplifies the macro-financial impact on the United Kingdom of this monetary normalization in the United States. It assumes an autonomous private domestic demand-driven macroeconomic contraction in the United Kingdom, featuring a 12 percent reduction in private investment driven by investment demand shocks, and a 4 percent decline in private consumption driven by consumption demand shocks, during 2016 and 2017. This autonomous private domestic demand contraction reflects large residential and commercial property market corrections in the United Kingdom, as well as confidence losses by households and firms. The domestic layer of our stress test scenario also assumes a drying up of liquidity in the money market in the United Kingdom, reflecting counterparty credit risk concerns driven by internationally correlated credit risk premium shocks, with the spread of the short-term nominal market interest rate over the nominal policy interest rate widening by 100 basis points during 2016. Furthermore, it assumes a decompression of the term premium in the United Kingdom driven by internationally correlated duration risk premium shocks, with the long-term nominal market interest rate rising by 100 basis points during 2016. Finally, it assumes a large stock market correction in the United Kingdom driven by internationally correlated equity risk premium shocks, with the real equity price falling by 40 percent during 2016.

We constrain monetary and fiscal policy responses, as well as bank credit-supply behavior, under this stress test scenario. Conventional monetary policy responds endogenously with nominal policy interest rate cuts subject to zero lower bound constraints worldwide. However, we abstract from unconventional monetary policy responses worldwide, and assume that quantitative easing programs remain at their baseline scales in the euro area and Japan. Furthermore, automatic fiscal stabilizers are not allowed to operate in the United Kingdom, given nascent public debt sustainability concerns there. We also abstract from fiscal stimulus measures worldwide. Finally, we constrain bank credit-supply behavior in the United Kingdom through macroprudential policy loosening, roughly equating bank credit growth to nominal output growth. In particular, we abstract from nominal bank lending interest rate increases there in response to bank capital ratio declines, ensuring that nominal bank lending interest rate adjustments only reflect bank funding costs and credit risk, by reducing regulatory capital requirements.

Simulation Results

Under this stress test scenario, the United Kingdom experiences a deep recession exacerbated by an induced contraction in bank credit supply. Indeed, output falls 7.5 percent below baseline by 2017, while consumption price inflation falls 2.9 percentage points below, and the unemployment rate rises 2.1 percentage points above. Of this output loss, about one third is accounted for by spillovers from the disorderly accelerated monetary normalization in the United States and the financial stress it triggers in the Fragile Four economies. This deep recession induces a nominal policy interest rate cut of 1.4 percentage points below baseline by 2017. But the assumed increase in bank funding costs, in the form of a higher money market interest rate spread, together with the rise in the credit-loss rate, induce a 1.8 percentage point increase in the nominal bank lending interest rate above baseline by 2017, and bank credit falls 7.8 percent below. Finally, the fiscal balance ratio falls 1.3 percentage points below baseline by 2017, and the government debt ratio rises 11.1 percentage points above, while the current account balance ratio rises 3.5 percentage points above (Figure 4.1 and Figure 4.2).

Simulated Peak Output Effects

Source: Author.

Note: The gray shade represents countries for which simulation results are not available. There is no country that falls into the 2.0 to 4.0 percent category.

Simulation Results

In the rest of the world, the macroeconomic expansion in the United States is offset by contractions in other advanced economies and vulnerable emerging economies. In particular, while output rises 4.3 percent above baseline in the United States by 2017, it falls 2.9 percent below in other advanced economies, 10.7 percent below in the Fragile Four economies, and 1.3 percent below in other emerging economies. These output losses reflect private domestic demand contractions due to tighter global financial conditions, which generally dominate gains from higher net exports. In aggregate, world output falls 1.4 percent below baseline by 2017, while energy and nonenergy commodity prices fall 20.5 and 14.2 percent below respectively, largely reflecting appreciation of the dollar in nominal effective terms.

5. Conclusion

This chapter presents the GFM, the theoretical structure and empirical properties of which are fully documented in Vitek 2015. It also discusses the application of the GFM to simulating banking sector solvency stress test scenarios, with reference to an example for the United Kingdom.

The GFM consolidates existing theoretical and empirical knowledge concerning business cycle dynamics in the world economy, provides a framework for a progressive research strategy, and suggests explanations for its own defciencies. Future model development work will focus on extending or refning its macro-financial linkages and spillover transmission channels.

Appendix 4.1. Data Description

Estimates are based on quarterly data on a variety of macroeconomic and financial market variables observed for 40 economies over the sample period (the first quarter of 1999 through the third quarter of 2014). The economies under consideration are Argentina, Australia, Austria, Belgium, Brazil, Canada, Chile, China, Colombia, the Czech Republic, Denmark, Finland, France, Germany, Greece, India, Indonesia, Ireland, Israel, Italy, Japan, Korea, Malaysia, Mexico, the Netherlands, New Zealand, Norway, the Philippines, Poland, Portugal, Russia, Saudi Arabia, South Africa, Spain, Sweden, Switzerland, Thailand, Turkey, the United Kingdom, and the United States. Where available, this data was obtained from the Global Data Source and World Economic Outlook databases compiled by the IMF. Otherwise, it was extracted from the International Financial Statistics database produced by the IMF.

The macroeconomic variables under consideration are the price of output, the price of consumption, the quantity of output, the quantity of private consumption, the quantity of exports, the quantity of imports, the nominal wage, the unemployment rate, employment, the quantity of public domestic demand, the fiscal balance ratio, and the prices of nonrenewable energy and nonenergy commodities. The price of output is measured by the seasonally adjusted gross domestic product price deflator, while the price of consumption is proxied by the seasonally adjusted consumer price index. The quantity of output is measured by seasonally adjusted real gross domestic product, while the quantity of private consumption is measured by seasonally adjusted real private consumption expenditures. The quantity of exports is measured by seasonally adjusted real export revenues, while the quantity of imports is measured by seasonally adjusted real import expenditures. The nominal wage is derived from the quadratically interpolated annual labor income share, while the unemployment rate is measured by the seasonally adjusted share of total unemployment in the total labor force, and employment is measured by quadratically interpolated annual total employment. The quantity of public domestic demand is measured by the sum of quadratically interpolated annual real consumption and investment expenditures of the general government, while the fiscal balance is measured by the quadratically interpolated annual overall fiscal balance of the general government. The prices of energy and nonenergy commodities are proxied by broad commodity price indexes denominated in United States dollars.

The financial market variables under consideration are the nominal policy interest rate, the short-term nominal market interest rate, the nominal bank lending interest rate, the long-term nominal market interest rate, the price of equity, and the nominal bilateral exchange rate. The nominal policy interest rate is measured by the central bank policy rate, the short-term nominal market interest rate is measured by a reference bank deposit rate, the nominal bank lending interest rate is measured by a reference bank lending rate, and the long-term nominal market interest rate is measured by a long-term government bond yield. In cases where these interest rates are not reported, the closest available substitute is used. The price of equity is proxied by a broad stock price index denominated in domestic currency units, while the nominal bilateral exchange rate is measured by the domestic currency price of one US dollar. All of these financial market variables are expressed as period average values.

Calibration is based on annual data obtained from databases compiled by the IMF where available, and from the Bank for International Settlements (BIS) or the World Bank Group otherwise. Macroeconomic great ratios are derived from the World Economic Outlook and World Development Indicators databases, while financial great ratios are also derived from the International Financial Statistics and BIS databases. Bilateral trade weights are derived for goods on a cost, insurance, and freight basis from the Direction of Trade Statistics database. Bilateral bank lending and nonfinancial corporate borrowing weights are derived on a consolidated ultimate risk basis from the BIS database. Bilateral portfolio debt and equity investment weights are derived from the Coordinated Portfolio Investment Survey, BIS, and World Development Indicators databases.

Appendix 4.2. Parameter Estimates
Appendix Table 4.2.1Parameter Estimation Results(Endogenous variables)
Source: Author.Note: All priors are normally distributed, while all posteriors are asymptotically normally distributed. All auxiliary parameters have degenerate priors with mean zero.
Source: Author.Note: All priors are normally distributed, while all posteriors are asymptotically normally distributed. All auxiliary parameters have degenerate priors with mean zero.
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1

The nominal effective exchange rate, ln ϵ^i,t satisfies lnϵ^i,i*,tΣj=1Nwi,jTlnϵ^j,i*,t, while the real effective exchange rate, ln Q^i,tQ^i,tsatisfieslnQ^i,t=lnQ^i,i*,tΣj=1Nwi,jTlnQ^j,i*,t.

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