Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Transcript

Monetary Policy and Financial Distress: Incorporating Financial Risk into Monetary Policy Models Dale Gray (IMF) Leonardo Luna (BCCh) Jorge Restrepo (BCCh) 1 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Index Motivation Contingent Claims Analysis (CCA) Empirical Evidence The Model Impulse Responses Efficiency Frontiers Results, Conclusions & Next Steps 2 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Motivation The integration of the financial sector vulnerability into macroeconomic models is an area of important and growing interest for policymakers. This paper analyze the explicit inclusion of credit risk/financial fragility indicator in the Monetary Policy Rate (MPR) Reaction Function. The main question is: Should a financial fragility indicator be included in monetary policy models? In particular, should it be explicitly included in the reaction function? Or, should the central bank react only indirectly through reacting to its effects on inflation and output gap? 3 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Motivation The economy (interest rates) and the financial sector (assets and liabilities) affect each other, as evidences the US economy over the past year. This paper uses contingent claims analysis (CCA) tools, developed in finance, to estimate the risk of default in the banking sector as proxy for financial sector vulnerability. 4 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Literature Gray, D., Merton, R. C., Bodie, Z. (2006). “A New Framework for Analyzing and Managing Macrofinancial Risks of an Economy,” NBER paper #12637 and Harvard Business School Working Paper #07-026, October. Gray, D., C. Echeverria, L. Luna, (2006) “A measure of default risk in the Chilean banking system”, Financial Stability Report Second Half 2006, Central Bank of Chile. Gray, D. and J. Walsh (2007) “Factor Model for Stress-testing with a Contingent Claims Model of the Chilean Banking System.” IMF Working Paper 05/155. (Washington: International Monetary Fund). Gray, D. and S. Malone (2008) Macrofinancial Risk Analysis. Wiley Finance, UK. 5 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Contingent Claims Analysis Modern finance theory is used to combine forward-looking market prices (e.g. equity prices) and balance sheet data to “calibrate” the implicit value of the assets and asset volatility (Merton,1974). Liabilities derive their value from assets, which are stochastic. The “calibrated” CCA model is used to calculate credit risk indicators, such as distance-to-distress, default probabilities, expected losses on debt (implicit put option), credit spreads, value of risk debt. 6 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Contingent Claims Analysis Banks lend to households, companies, and 7 the government. Households own equity, government guarantees bank deposits. Interlinked CCA balance sheets for corporates, households, banks and government can be constructed. Risky debt of firms is an asset of the banks. Gov. contingent liabilities to banks are modeled as an implicit put option (Merton 1977). This model does not include corporate & households. BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Interlinked CCA Interlinked CCA risk-adjusted balance sheets are a useful tool for understanding: Financial accelerator mechanisms – increased bank deposits, increased lending to corporate and households, higher investment and consumption leading to higher GDP. Credit risk transmission – slower GDP, lower corporate and household assets, lower value of risky debt (from larger implicit put options/spreads), lower bank assets, higher credit risk in banks (e.g. lower distance-to-distress), higher contingent liabilities of government. 8 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 CCA Credit Risk Measures Asset Value Exp. asset value path Distribution of Asset Value Distance to Distress: standard deviations asset value is from debt distress barrier V0 Distress Barrier or promised payments Probability of Default T 9 BANCO CENTRAL DE CHILE Time 28 DE MAYO DE 2008 CCA Core Concept Equity or Jr Claims Assets Risky Debt • Value of liabilities derived from value of assets. • Liabilities have different seniority. • Randomness in asset value. Assets = Equity + Risky Debt 10 Loss = Equity + Default-Free Debt – Expected = Implicit Call Option + Default-Free Debt - Implicit Put Option BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Calibrate (Unobservable) Market Value of Asset and Implied Asset Volatility INPUTS Value and Volatility of Market Capitalization, E Debt Distress Barrier B (from Book Value) Time Horizon USING TWO EQUATIONS WITH TWO UNKNOWNS rt 1 2 E A N (d ) Be N (d ) E E A A N (d1 ) Gives: Implied Asset Value A and Asset Volatility A Distance-to-Distress Default Probabilities Spreads & Risk Indicators 11 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 CCA Model Indicators Distance to Default (DTD) ln( A / D) (r / 2) d2 A t 2 A Probability of Default (PD) PD N (d2 ), where N : normal distributi on fn Credit Spread from Put Option rt s 1 T ln( 1 PUT / De ) 12 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Chilean Banking System 12 DTD of Banking System Output Gap 10 8 6 4 2 1997M01 0 1999M01 -2 2001M01 2003M01 2005M01 2007M01 -4 -6 13 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 DTD in GDP Growth for Chile yt c 1rt 1 2 dtdt 1 3et 1 4 yt 1 t Sample: 1998 2007 (monthly) Included observations: 106 after adjustments Variable Coefficient C R(-1) DLOG(E(-1)) DLOG(DTD(-1)) DLOG(Y(-1)) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 14 0.011 -0.001 0.046 0.012 0.463 0.574 0.557 0.008 0.007 358.890 1.912 Std. Error t-Statistic 0.002 0.000 0.019 0.003 0.074 4.830 -3.723 2.438 3.551 6.283 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) BANCO CENTRAL DE CHILE Prob. 0.000 0.000 0.017 0.001 0.000 0.009 0.013 -6.677 -6.552 34.036 0.000 28 DE MAYO DE 2008 DTD in Output Gap for Chile gapt c 1dtdt 1 2 et 1 4 gapt 1 t Sample (adjusted): 1998M02 2007M02 Included observations: 109 after adjustments Variable Coefficient C DLOG(TCR(-3),0,3) LOG(DTDS(-1)) YGAP(-1) YGAP(-3) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat 15 -1.736 4.134 0.934 0.513 0.225 0.661 0.648 0.712 52.766 -115.126 1.842 Std. Error 0.470 1.639 0.256 0.082 0.072 t-Statistic -3.691 2.522 3.653 6.275 3.113 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic) BANCO CENTRAL DE CHILE Prob. 0.000 0.013 0.000 0.000 0.002 -0.035 1.201 2.204 2.328 50.695 0.000 28 DE MAYO DE 2008 CCA Applied to Chilean Banking System GDP is affected by financial stability in the banking system. Financial distress in banks and bank’s borrowers reduces lending as borrower’s credit risk increases, which reduces investment and consumption affecting GDP. There are a number of different financial stability credit risk indicators. 16 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 CCA Applied to Chilean Banking System 17 This study uses the distance-to-distress for the banking system (dtd for each mayor public traded bank, weighted by the bank’s implied assets). Chile’s estimation of the output gap shows that a credit risk indicator (distance to default) is significant and has a positive effect on the output gap. BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Monetary Policy Model 18 The primary tool for macroeconomic management is the interest rates set by the Central Bank. Simple monetary policy models are widely used by Central Banks to understand macroeconomic and interest rate relationships as well as to forecast. Traditionally, central banks (models) target inflation and GDP-gap. BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Monetary Policy Model This paper uses a simple five equation monetary policy model, with two modules: Macro Monetary Policy Module. 2. CCA Financial System Module. 1. 19 This model begins by including the financial stability credit risk indicator (banking system distance to distress) in the output gap equation. The model is calibrated with parameters (instead of estimated). BANCO CENTRAL DE CHILE reasonable 28 DE MAYO DE 2008 Monetary Policy Model GDP Gap: yt 1 yt 1 2 (rsd ,t L t L ) 3 X S ,t L 4 dtdt 1,t or yt yt * 4 dtdt 1,t Traditional Taylor Rule: rsd ,t rd ,t 1 (1 ) ( ( e t ,t T ) (1 ) yt ) 4,t T Taylor Rule with Financial Stability Indicator: rsd ,t rd ,t 1 (1 ) ( ( te,t T T ) (1 ) yt *) 10dtdt 4,t 20 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Monetary Policy Model 21 Thus the model includes a GDP-gap equation and a Taylor Rule equation which includes financial stability indicator. The remaining three equations are for inflation, exchange rate, and the yield curve. The model was also run with a exchange rate equation (interest parity condition) that includes the financial fragility indicator (dtdarbitrage, country risk premium). BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Monetary Policy Model Inflation: t 5 t 1 6 yt 7 te,t T 8X S ,t 9 sLCD 2,t Exchange Rate: X S ,t 11 X S ,t 1 12rsd ,t 13rsf ,t 14 st ,t T 15dtd 5,t Yield Curve: Rt 16 Rt 17 ( Rt 1 Rt ) 18 ( Rt 1 Rt ) t 1 19 (rt 1 rt )t 2,t 22 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 CCA Endogeneity DTD and GDP-gap affect each other. In order to include this into the model, we define one last equation where the value of the equity depends on the GDP-gap. Et Et 1 yt This beta is a macro factor. The model is also run without this effect. 23 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Impulse Response Function (IRF) IR is the standard tool to analyze the behavior of a model (we are not presenting standard deviations). The model needs to be solved using the Gauss-Seidel (GS) algorithm and Fair-Taylor (FT) for calculating the expectations. Starting from a fix value (zero), it iterates until a the solution is achieved. This solve the Macro Model and also the asset’s level & volatility. So, for each period of time, the model solves a system of equations for the current and expected value of the main variables (FT). 24 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Impulse Responses The 25 impulse responses are obtained using Winsolve. In each case a response of GDP, inflation, exchange rate, r (MPR) and R are shown for a shock of 100 bp in each variable. In addition, the response of the CCA (DTD) variables is shown. The basic model is the classic Taylor Rule (theta=0.5, rho=0.6 & gamma =0.6). We added a reaction of the monetary policy to the DTD, with a coefficient equal to 0.5. BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Shock to inflation 1.2% 1.0% 0.8% dp y e r rl ldtd 0.6% 0.4% 0.2% 0.0% 200004 -0.2% 200204 200404 200604 200804 -0.4% -0.6% 26 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 201004 Shock to output gap 1.2% 1.0% dp y e 0.8% r rl ldtd 0.6% 0.4% 0.2% 0.0% 200004 -0.2% 200204 200404 200604 200804 -0.4% -0.6% -0.8% 27 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 201004 Shock to real exchange rate 1.2% dp y e r rl ldtd 1.0% 0.8% 0.6% 0.4% 0.2% 0.0% 200004 200204 200404 200604 200804 -0.2% 28 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 201004 Shock to real short interest rate 1.5% 1.0% dp y e r rl ldtd 0.5% 0.0% 200004 200204 200404 200604 200804 -0.5% -1.0% -1.5% 29 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 201004 Shock to real long interest rate 1.5% 1.0% dp y e r rl ldtd 0.5% 0.0% 200004 200204 200404 200604 200804 -0.5% -1.0% 30 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 201004 Shock to distance to default 2.0% dp y e r rl ldtd 1.5% 1.0% 0.5% 0.0% 200004 200204 200404 200604 200804 -0.5% -1.0% -1.5% 31 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 201004 Impulse Response Conclusions The model works as expected: magnitudes seem reasonable. signs and There is high interaction of macro variables, but they do not affect very much DTD. DTD have a high impact on MPR, R and Output- Gap. Real exchange rate could be unstable for some specifications of the model. 32 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Efficiency Frontiers Different stochastic simulated scenarios are solved, for different monetary policy rules. MPR that reacts to Financial Fragility (DTD) is compared with the Non-Policy case. A variance-covariance matrix is set, given the standard error from the regression and some judgment (for simplicity we set all the standard deviations to 1bp). Each set of monetary rules is solved for different values of gamma: the relative reaction to inflation and GDP (output gap). 33 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Efficiency Frontiers This process generates a frontier for the steady 34 state volatility of GDP and inflation. A base scenario is set where there is no reaction of the monetary policy to DTD, but GDP and exchange rate still react to it. Shocks to DTD could be understood as shocks to risk appetite. Starting from a Base Model a higher reaction to DTD and lower endogeneity are tested. Then several features are turned off simultaneously. BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Efficiency Frontiers: Base Model 3.5% Output volatility 3.0% 2.5% 2.0% 1.5% No Policy MPR to DTD 1.0% 1.0% 1.5% 2.0% 2.5% 3.0% Inflation volatility 35 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Higher reaction to DTD in MPR 3.5% Output volatility 3.0% 2.5% 2.0% 1.5% No Policy MPR to DTD 1.0% 1.0% 1.5% 2.0% 2.5% 3.0% Inflation volatility 36 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Smaller GDP effect on bank’s equity (endogeneity) 3.5% Output volatility 3.0% 2.5% 2.0% 1.5% No Policy MPR to DTD 1.0% 1.0% 1.5% 2.0% 2.5% 3.0% Inflation volatility 37 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Efficiency Frontiers In what follows, some characteristics of the based model are changed: Lower endogeneity (LE). LE + no effect of DTD in exchange rate (EE). LE+EE+lower pass-through of the nominal exchange rate to inflation. 38 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Previous +: no effect of DTD in real exchange rate 3.5% Output volatility 3.0% 2.5% 2.0% No Policy 1.5% MPR to DTD 1.0% 1.0% 1.5% 2.0% 2.5% 3.0% Inflation volatility 39 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Previous +: Lower pass-through 3.5% Output volatility 3.0% 2.5% 2.0% No Policy 1.5% MPR to DTD 1.0% 1.0% 1.5% 2.0% 2.5% 3.0% Inflation volatility 40 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 The model is robust to: Leads in the real exchange rate (forward looking). Sign of the real exchange rate in the output gap. Magnitude of the reaction of MPR to output gap and inflation. 41 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 The model changes with The degree of arbitrage to DTD in the real exchange rate (↑Effect → ↓Frontier). Magnitude of the reaction of the MPR to DTD (↑Effect → ↓Frontier). Magnitude of the Pass- through reaction of MPR to output gap and inflation (↑Effect → ↓Frontier). Endogenity of the value of the equity to movements of the output gap (↑Effect → ↓Frontier). 42 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Results and Conclusions A simple, but powerful model for monetary 43 policy. The model has the main variables analyzed by policymakers, but is small enough to understand it easily. Empirical evidence supports the model. IRF in accordance with theory. Robust efficient frontier, but there is a trade off in the results. A stronger reaction to DTD reduces inflation volatility but increases output volatility. BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Next Steps / To Follow Combinations of financial scenarios normal, fragility) should be incorporated. (strong, Changes in the dynamic of the macro model should be tested (maybe move to DGE). More realistic Variance-Covariance matrix. Look for empirical evidence in other countries and comparison of the model with other economies. 44 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Monetary Policy and Financial Distress: Incorporating Financial Risk into Monetary Policy Models (ANNEX) Dale Gray (IMF) Leonardo Luna (BCCh) Jorge Restrepo (BCCh) 45 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 CCA Model Prob( At Bt ) Prob A0 exp A A2 / 2 t A t Bt = Prob d 2, Distributions of Asset Value at T Asset Value Expected Asset Drift of μ A0 Drift of r Promised Payments: Bt “Actual “ Probability of Default “Risk-Adjusted “ Probability of Default Time T 46 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 After Calibration Several Types of Risk Indicators are Derived Distance to Distress (number of standard deviations of asset value from distress) Default Probability Risk Neutral Default Probability = N(- d2) Estimated Actual Default Probability = N(- d2 -λ) The market price of risk is λ, λ=(u-r)/σ Model Spread, s, in basis points Implicit Put Option (Expected Loss) and Value of Risky Debt (Default-free value of debt – expected loss) 47 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008 Monetary Policy and Financial Distress: Incorporating Financial Risk into Monetary Policy Models Dale Gray (IMF) Leonardo Luna (BCCh) Jorge Restrepo (BCCh) 48 BANCO CENTRAL DE CHILE 28 DE MAYO DE 2008