1. Systemic Real and Financial Risks: Measurement, Forecasting, and Stress Testing Gianni De Nicolò International Monetary Fund and CESifo Marcella Lucchetta Marcella Lucchetta University of Venice The views expressed in this paper are those of the authors and do not necessarily represent those of the IMF.

2. Motivation Available monitoring technologies failed to provide early warnings on the crisis in 2007- 2008. Available monitoring technologies failed to provide early warnings on the crisis in 2007- 2008. Building on De Nicol and Lucchetta (2010), we develop a model that can be useful for Building on De Nicolò and Lucchetta (2010), we develop a model that can be useful for  positive analysis, and  as a systemic risk monitoring system.

3. Limitations of current modeling  DSGE models 1. Incorporation of interactions between financial and real sectors still in its infancy 2. Forecasting performance not yet firmly established.  Stress testing procedures 1. “shocked” variables typically endogenous (shock to the “cause” or the “symptom”?) 2. difficult to assess the quantitative results.

4. Our contribution Our model complements DSGE modeling by exploiting: Our model complements DSGE modeling by exploiting:  the forecasting power of a Dynamic Factor Model (DFM) with many predictors  structural identification based on explicit theoretical constructs (such as DSGE models)  Flexibility (applicable to multiple countries/sector datasets, and different data frequencies).

5. Output of the Model a) density forecasts of indicators of systemic real risk and systemic financial risk; b) reduced-form stress tests, as historical simulations; c) structural stress-tests, as impulse responses of systemic risk indicators to structural shocks identified by standard macroeconomic and banking theory.

6. Systemic Real Risk Systemic Real Risk is measured by GDP- Expected Shortfall (GDPES), given by the expected loss in GDP growth conditional on a given level of GDP-at-Risk (GDPaR) GDPaR is the worst predicted realization of quarterly growth in real GDP at a given (low) probability

7. Systemic Financial Risk A financial health indicator (FS) : return of a portfolio of financial firms less the return of the market Systemic Financial Risk is measured by FS- Expected Shortfall (FSES), given by the expected loss in FS conditional on a given level of FS-at-Risk (FSaR) FSaR is the worst predicted realization of the FS indicator at a given (low) probability level

8. The statistical models GDP growth and FS are modeled through a version of a factor-augmented VAR (FAVAR) model (e.g. Stock and Watson, 2002 and 2005) GDP growth and FS are modeled through a version of a factor-augmented VAR (FAVAR) model (e.g. Stock and Watson, 2002 and 2005) Density forecasts of GDPG and FS obtained estimating a set of quantile auto-regressions Systemic Risk Indicators constructed using density forecasts

9. STRESS TESTING = Measurement of impact and persistence of configurations of unexpected (structural) shocks on systemic risk indicators   Reduced-form stress tests : based on shocks recovered from a statistical model of the quantiles (distribution) of GDP growth and FS   Structural stress tests:   based on shocks derived from theoretical models  Identification of structural shocks accomplished with theory-based sign restrictions (Canova and De Nicolò, JME 2002)

10. Implementation We use macroeconomic and financial series for the G-7 economies for the period 1980:Q1-2010:Q1 For each country, the vector of quarterly series includes about 95 series classified into 1. 1. equity markets data 2. 2. credit conditions 3. 3. indicators of real activity

11. Main Results 1. Significant forecasting power for tail risk realizations of real activity and financial health 2. Both reduced-form and structural stress tests provide early warnings of real and financial vulnerabilities 3. In all countries: aggregate demand shocks drive the real cycle aggregate demand shocks drive the real cycle bank credit demand shocks drive the bank lending cycle bank credit demand shocks drive the bank lending cycle real drives financial real drives financial

12. Plan of the presentation The Model The Model Estimation and Forecasting (details) Estimation and Forecasting (details) Forecast Evaluation Forecast Evaluation Reduced-Form Stress Tests Reduced-Form Stress Tests Structural Stress Tests Structural Stress Tests Modeling Developments Modeling Developments

13. The Dynamic Factor Model (DFM) (static form) (5) (8) (7) (6)

14. Density Forecasts Density forecasts of GDP growth and FS obtained estimating 99 quantile auto-regressions: Density forecasts of GDP growth and FS obtained estimating 99 quantile auto-regressions: These “raw” quantile estimates are “rearranged” at each date to overcome potential “crossing” (novel application of Chernuzikhov et al., Econometrica 2010) These “raw” quantile estimates are “rearranged” at each date to overcome potential “crossing” (novel application of Chernuzikhov et al., Econometrica 2010)

15. (2008q3 and 2010q2) Density Forecasts (2008q3 and 2010q2)

16. For any given Systemic Risk Indicators

17. Systemic Risk Fan Charts

18. Estimation and Forecasting (details) Four steps: 1) 1) Number of factors and lags 2) 2) Quantile estimation 3) 3) Density estimates and Expected Shortfalls 4) 4) Forecasting

19. (1) (1) Number of Factors and Lags Extract all factors with eigenvalues greater than 1 Extract all factors with eigenvalues greater than 1 Order factors according to the explanatory power of the variance of the data and construct Order factors according to the explanatory power of the variance of the data and construct Choose the number of lags L and the number of static factors that maximize BIC Choose the number of lags L and the number of static factors that maximize BIC Criterion among 4 by R specifications of the FAVAR

20. (2) Quantile Estimation use the optimal number of lags, the number of static factors, and the estimated factors to estimate quantile auto-regressions for specified as in (7) and (8) address the crossing problem by adopting the “ rearrangement ” procedure introduced by Chernuzukhov, Fernandez-Val and Galichon (2010)

21. (3) Continuous Density Estimates   obtain continuous densities and compute expected shortfalls as where is the quantile corresponding to probability and with

22. (4) Expected Shortfall Regress the series of 99 quantiles to obtain the continuous function Then, the expected shortfall estimates are

23. Forecasting in 3 steps 1. 1. construct forecasts of conditional densities and of systemic risk indicators 2. 2. use the VAR of static factors to compute dynamic forecasts k quarters ahead 3. 3. use these forecasts are used to obtain recursive forecasts of quantile estimates

24. Forecast Evaluation 1   Density forecasts are satisfactory if the Probability Integral Transforms (PIT) based on estimated quantiles satisfies independence and uniformity   We constructed PITs for both our real activity and FS indicators for each of the seven countries   Properties broadly satisfied

25. est based on Pearson’s Q statistics Forecast Evaluation 2 Test based on Pearson’s Q statistics  Is the fraction of observed realizations of GDPG and FS close to the fractions implied by estimated or forecast quantiles?  In sample partitions [ Q20] : left-tail [ Q20] : left-tail [ Q90]. entire distribution [ Q90]. entire distribution  Out –of- sample partition: [ Q20] left tail  BROADLY SATISFIED

26. Forecast Evaluation

27. Reduced-Form Stress Tests A historical sequence of shocks to the distributions of GDP growth and the FS indicator is obtained by assuming that each quantile follows a AR(1) process

28. Reduced-Form Stress Tests Statistics Stressed quantile series Expected Shortfall ST deviations (ESSTDs) STATISTICS: Average ESSTDs for each

29. Average ESSTDs (2008Q1 and 2008Q2)

30. Structural Stress Testing At a given date, the size of impulse responses to identified shocks measures the sensitivity of systemic risk indicators to these shocks. At a given date, the size of impulse responses to identified shocks measures the sensitivity of systemic risk indicators to these shocks. Between dates, changes in the size of these impulse responses provide a measure of changes in the resilience of an economy to these shocks. Between dates, changes in the size of these impulse responses provide a measure of changes in the resilience of an economy to these shocks. The impulse responses of observable variables can be used to detect which sectors of the economy are most sensitive to a particular shock (risk maps). The impulse responses of observable variables can be used to detect which sectors of the economy are most sensitive to a particular shock (risk maps).

31. Theoretical Sign Restrictions Table A. Responses of key variables to positive shocks Macroeconomic Model Aggregate SupplyAggregate Demand GDP growthPositive InflationNegativePositive Banking ModelBank Credit Demand Bank Credit Supply Bank Credit GrowthPositive Change in Lending Rates PositiveNegative

32. Identification In all countries all identified shocks are aggregate demand shocks associated with bank credit demand shocks In all countries all identified shocks are aggregate demand shocks associated with bank credit demand shocks Consistent with results in Canova and De Nicolò (JIE 2003) Consistent with results in Canova and De Nicolò (JIE 2003) Slowdowns in aggregate bank credit growth are the results of real activity downturns (consistent with Berrospide and Edge, 2010) Slowdowns in aggregate bank credit growth are the results of real activity downturns (consistent with Berrospide and Edge, 2010)

33. A Simple Example of Structural Stress Test Gauge weather the stress test signals lower resilience to structural shocks in the G-7 economies prior to 2007Q3 (pre-crisis) Gauge weather the stress test signals lower resilience to structural shocks in the G-7 economies prior to 2007Q3 (pre-crisis) Compute the difference of the cumulative impact of the impulse response functions of GDPES and FSES to each structural shock estimated for (1980Q1-2007Q2) and (1993Q2-2007Q2) Compute the difference of the cumulative impact of the impulse response functions of GDPES and FSES to each structural shock estimated for (1980Q1-2007Q2) and (1993Q2-2007Q2) A positive difference would indicate a lower resilience of the economies to these shocks A positive difference would indicate a lower resilience of the economies to these shocks

34. Results In all countries the first two shocks become predominant in the last sub-period Increased risk concentrations in these economies on both the real and financial sides The U.S. economy had increased its vulnerability to shocks both on the real and financial sides, in absolute terms as well as relatively to the other G-7 economies

35. Modeling Developments Extension of our framework to the simultaneous modeling of countries and regions of the world Refinement of stress testing statistics and construction of risk maps