## 1. Variables Included in the Estimation of Financial Conditions Index

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### I. Introduction
- In the decade prior to the recent recession, annual GDP growth averaged 4.5 percent in the period from 2004 to 2013.
- Unemployment rate halved; policy rate trended down; lending rates fell by almost 10 percentage points.
- Credit expanded from 25 percent of GDP in 2004 to 55 percent at the end of 2015 (more than doubling as a share of GDP since 2004), with a particularly sharp rise in public sector credit following the global financial crisis.
- Purpose: assess importance of financial market developments for Brazil’s business cycle using statistical cycle extraction and a small semi-structural model that jointly estimates financial and business cycles.

### II. Literature Review
- Two main approaches to analyze financial market developments:
  - Financial/Credit cycles: medium-term concept focusing on credit, credit-to-GDP, and property prices; financial cycles defined via univariate filters or turning-point algorithms; literature finds financial cycles evolve at a relatively slow pace (e.g., average length ~16 years in advanced economies per Drehmann and others, 2012).
  - Financial conditions index (FCI): short-term concept combining multiple financial variables to capture short-term developments (Ng, 2011; Hatzius and others, 2010).
- Financial sector developments are important sources of macroeconomic fluctuations (financial accelerator models such as Bernanke and Gertler, 1989; Bernanke, Gertler and Gilchrist, 1999; Kiyotaki and Moore, 1997).
- Deviations of credit-to-GDP and asset prices from trend are good leading indicators of financial crises (Borio and Drehmann, 2009).
- FCIs are good leading indicators of growth (English and others, 2005; Estrella and Trubin, 2006; Hatzius and others, 2010; Ng, 2011).

### III. Characterizing Brazilian Financial Cycles
- Data focus and limitations:
  - Medium-term credit cycles only (house price indices too short; OECD house prices start 2008; central bank index limited).
- Statistical method:
  - Band-pass filter (Christiano and Fitzgerald, 2003) used to isolate cycles in real credit and credit-to-GDP, targeting medium-term frequencies (assumption: financial cycles have much lower frequency, 8 and 20 years).
  - Estimated spectral density for real credit growth: first peak corresponds to medium-term cycle ~20 years; additional peaks at higher frequency (<4 years) correspond to short-term cycles.
  - Aggregate credit cycle constructed by averaging filtered real credit and credit-to-GDP series.
- Financial Conditions Index (FCI) construction:
  - Constructed via principal component analysis; first principal component explains 42 percent of covariance between included variables.
  - Included variables and loadings:
    - EMBI, y/y — 0.44
    - Money market spread — 0.14
    - Lending rate, y/y — 0.52
    - Selic, y/y — 0.51
    - Total loans, y/y — -0.05
    - Real exchange rate — -0.14
    - Stock prices, y/y — -0.48
  - FCI components: (i) risk measures (money market spread); (ii) collateral values (stock prices, house prices); (iii) quantities (total credit); (iv) external conditions (EMBI, real exchange rate); and interest rates.
  - Stationarity treatment: spreads in levels; collateral values, EMBI, interest rates, quantities in y/y growth rates.
- Quarterly projection model (semi-structural):
  - Two versions: aggregate total real credit; disaggregate real public and real private credit.
  - Financial cycles defined as credit cycle (deviation of real credit from its trend estimated by model) and cycle in the FCI.
  - Models estimated by Bayesian methods; sample 1999 to 2015Q3.
- Key model assumptions:
  - Credit cycle positively correlated with business cycle and lags it by one quarter.
  - FCI leads real GDP growth by two quarters; financial conditions ease with expectations of stronger growth.
  - Autonomous shocks to credit boost demand; autonomous tightening of financial conditions reduces demand.

### IV. Results
- Cycle dating:
  - Medium-term financial cycle in total credit: trough in 2004–05 and peak in 2010–11.
  - Public and private financial cycles differ due to countercyclical use of public banks over 2008–13.
- Financial conditions history:
  - FCI shows four episodes of rapid tightening since 1996: mid-1997 to mid-1999; 2002 sudden-stop; tightening around global financial crisis; tightening starting in 2013.
- Stylized relationships:
  - Financial cycle has longer duration and larger magnitude than business cycle.
  - For every 1 percent increase in output, credit increases by around 3 to 5 percent, on average.
  - Business and financial cycles move in tandem; real GDP growth lags financial conditions.
- Impulse response findings (aggregate and disaggregate models):
  - Credit responds more to output than output responds to credit:
    - Aggregate model: 1 percent shock to output → credit increases by around 0.7 percent; 1 percent shock to credit → output increases around 0.3 percent.
    - Disaggregate: public and private credit responses to demand shocks are less than half the size of demand responses to credit.
  - Peaks occur around one year after shock, with persistent effects:
    - A 1 percent shock to output boosts credit for between 2 and 3 years; impacts of credit shocks on output similarly persistent.
  - Private credit is more responsive to output shocks than public credit:
    - Private credit increases by 1 percent following a positive output shock; public credit increases by around 0.7 percent.
  - Output responds strongly to shocks to financial conditions; financial conditions loosen modestly following positive demand shocks.
- Historical decomposition of output gap:
  - Private credit boosted output in 2005–2008 lead-up to global financial crisis.
  - Public credit boosted output following the crisis (2009–10) due to policy support.
  - Financial conditions were important in 2009 recovery and remained positive until 2013; tightened drastically in 2013 onward.
  - Since early 2015, public and private credit and financial conditions have been a drag on output (policy to limit expansion of public bank credit; tightened financial conditions due to uncertainty).
- Macro-financial linkages:
  - Multiple channels linking macro developments to banking sector, households, corporate sector, mutual funds, public banks, fiscal outcomes, and exchange rate effects.

### V. What Are the Risks from a Credit Slowdown?
- Main concern: autonomous slowdown in private credit could be larger than historical credit–output relationships imply, especially during downturns when buffers are depleted and Basel III transition affects balance sheets.
- Historical evidence:
  - Largest adverse private credit shocks occurred during 2002−03 (sequence beginning 2002Q4), estimated to reduce output by around 1 percent after a year.
- Cost of offsetting private credit slowdown with public credit expansion:
  - Offsetting the 2002Q4 private credit slowdown would have required a 4 percent of GDP expansion in public credit to offset output effects.
- Implication: using public credit to fully offset private credit contractions can be costly and generate fiscal and efficiency challenges.

### VI. Conclusions and Policy Implications
- Rapid past credit growth implies vulnerabilities ahead; Brazil is in the downturn phase of the financial cycle.
- A slowdown in credit could hurt growth despite empirical results showing output has a stronger impact on credit than vice versa.
- Offsetting private credit slowdowns with public-sector credit expansion:
  - Can be effective countercyclically but is costly, difficult to unwind, and contributed to deteriorating fiscal position and doubts about policy credibility.
  - Recommendation: focus public banks on missing markets (e.g., providing guarantees for concessions) to improve allocation of limited financing and effectiveness of monetary policy (Coleman, Feler, 2015; Bonomo, Martins, 2016).
  - Reducing budget earmarking would release fiscal space and improve allocation of limited fiscal resources.

### Appendix: Models and Parameters
- Model structure:
  - Aggregate and disaggregate semi-structural quarterly models specified with equations for output (IS curve), inflation (Phillips curve split into non-regulated and regulated components), policy rule, real interest rate (Fisher equation), real credit gap, financial conditions, Okun’s law, capacity utilization, foreign output gap, real exchange rate gap, and behavioral relationships.
  - Aggregate model: real credit gap driven by lagged credit and lagged output; FCI depends on lagged FCI and expected output growth; output gap responds to leads/lags of itself, real interest rate gap, foreign activity gap, real exchange rate gap, autonomous credit and FCI shocks.
  - Disaggregate model: separates public and private credit with distinct gap equations and allows both to impact aggregate demand; public credit modeled to reflect countercyclical policy use.
- Estimation:
  - Bayesian estimation with sample 1999–2015Q3; appendices provide model specifications and parameter estimates.
- Calibrated parameters (excerpt):
  - g (steady state real GDP growth) = 2.00
  - g_c (steady state real credit growth) = 5.00
  - λ = 0.05
  - δ = 0.05
  - Shock standard deviations calibrated based on HP filter trends (λ=1600).
- Selected estimated parameters (posterior means and selected shock standard deviations):
  - σ_y = 1.09 (Aggregate posterior mean)
  - σ_credit_trend = 1.27 (Aggregate posterior mean)
  - σ_inflation = 5.12 (Aggregate posterior mean)
  - σ_exchange_rate = 4.34 (Aggregate posterior mean)
  - σ_foreign_output = 0.59 (Aggregate posterior mean)
  - σ_FCI = 0.53 (Aggregate posterior mean)

*Source: wp1712 — Fund staff estimates; model and estimation details, parameter tables, and figures as presented in the source content.*

### 1. Variables Included in the Estimation of Financial Conditions Index __________________ 6

### 1. Variables Included in the Estimation of Financial Conditions Index

### Major sections listed
- 1. Variables Included in the Estimation of Financial Conditions Index __________________ 6
- 2. Key Macro-Financial Linkages in Brazil ______________________________________ 14

### Figures enumerated
- Figure 1. Financial Cycles, Business Cycle in Brazil  ____________________________________ 10
- Figure 2. Aggregate Model: Impulse Response Functions  ________________________________ 11
- Figure 3. Disaggregate Model: Impulse Response Functions ______________________________ 12
- Figure 4. Historical Shock Decomposition of Output Gap, Aggregate Model _________________ 13

### Appendix content
- Appendix ________________________________________________________________  17
  - A. Models ____________________________________________________________ 17
  - B. Estimated Parameters _________________________________________________ 23

### Appendix Tables
- A1. Calibrated Parameters ___________________________________________________ 24
- A2. Estimated Parameters  ___________________________________________________ 25

*Source: wp1712 - 1. Variables Included in the Estimation of Financial Conditions Index — wp1712 - 1. Variables Included in the Estimation of Financial Conditions Index __________________ 6*

### References  _______________________________________________________________  26

### wp1712 - References  _______________________________________________________________  26

### I. INTRODUCTION
- In the decade prior to the recent recession, annual GDP growth averaged 4.5 percent in the period from 2004 to 2013.
- Unemployment rate halved; policy rate trended down; lending rates fell by almost 10 percentage points.
- Credit expanded from 25 percent of GDP in 2004 to 55 percent at the end of 2015 (more than doubling as a share of GDP since 2004), with a particularly sharp rise in public sector credit following the global financial crisis.
- Cross-country evidence cited: periods of strong credit growth typically followed by sluggish activity (Jorda and others, 2013); duration and amplitude of recessions influenced by financial cycles (Drehmann and others, 2012; Claessens and others, 2011a).
- Purpose: assess importance of financial market developments for Brazil’s business cycle using statistical cycle extraction and a small semi-structural model that jointly estimates financial and business cycles.

### II. LITERATURE REVIEW
- Two main approaches to analyze financial market developments:
  - Financial/Credit cycles: medium-term concept focusing on credit, credit-to-GDP, and property prices; financial cycles defined via univariate filters or turning-point algorithms; literature finds financial cycles evolve at a relatively slow pace (e.g., average length ~16 years in advanced economies per Drehmann and others, 2012).
  - Financial conditions index (FCI): short-term concept combining multiple financial variables to capture short-term developments (Ng, 2011; Hatzius and others, 2010).
- Financial sector developments are important sources of macroeconomic fluctuations (financial accelerator models such as Bernanke and Gertler, 1989; Bernanke, Gertler and Gilchrist, 1999; Kiyotaki and Moore, 1997).
- Deviations of credit-to-GDP and asset prices from trend are good leading indicators of financial crises (Borio and Drehmann, 2009).
- FCIs are good leading indicators of growth (English and others, 2005; Estrella and Trubin, 2006; Hatzius and others, 2010; Ng, 2011).

### III. CHARACTERIZING BRAZILIAN FINANCIAL CYCLES
- Focus due to data limitations: medium-term credit cycles only (house price indices too short; OECD house prices start 2008; central bank index limited).
- Statistical method:
  - Band-pass filter (Christiano and Fitzgerald, 2003) used to isolate cycles in real credit and credit-to-GDP, targeting medium-term frequencies (assumption: financial cycles have much lower frequency, 8 and 20 years).
  - Estimated spectral density for real credit growth: first peak corresponds to medium-term cycle ~20 years; additional peaks at higher frequency (<4 years) correspond to short-term cycles.
  - Aggregate credit cycle constructed by averaging filtered real credit and credit-to-GDP series.
- Financial Conditions Index (FCI):
  - Constructed via principal component analysis; first principal component explains 42 percent of covariance between included variables.
  - Included variables and loadings:
    - EMBI, y/y — 0.44
    - Money market spread — 0.14
    - Lending rate, y/y — 0.52
    - Selic, y/y — 0.51
    - Total loans, y/y — -0.05
    - Real exchange rate — -0.14
    - Stock prices, y/y — -0.48
  - FCI includes: (i) risk measures (money market spread); (ii) collateral values (stock prices, house prices); (iii) quantities (total credit); (iv) external conditions (EMBI, real exchange rate); and interest rates.
  - Stationarity: spreads in levels; collateral values, EMBI, interest rates, quantities in y/y growth rates.
- Quarterly projection model (semi-structural):
  - Two versions: aggregate total real credit; disaggregate real public and real private credit.
  - Financial cycles defined as credit cycle (deviation of real credit from its trend estimated by model) and cycle in the FCI.
  - Models estimated by Bayesian methods; sample 1999 to 2015Q3.
- Key model assumptions:
  - Credit cycle positively correlated with business cycle and lags it by one quarter.
  - FCI leads real GDP growth by two quarters; financial conditions ease with expectations of stronger growth.
  - Autonomous shocks to credit boost demand; autonomous tightening of financial conditions reduces demand.

### IV. RESULTS
- Cycle dating:
  - Medium-term financial cycle in total credit: trough in 2004–05 and peak in 2010–11.
  - Dynamics differ for public and private cycles due to countercyclical use of public banks over 2008–13.
- Financial conditions history:
  - FCI shows four episodes of rapid tightening since 1996: mid-1997 to mid-1999 (Asian spillovers); 2002 sudden-stop; tightening around global financial crisis (tighter external conditions); tightening starting in 2013 (taper tantrum and adverse domestic developments).
- Stylized relationships (Panel 1 summary):
  - Financial cycle has longer duration and larger magnitude than business cycle.
  - For every 1 percent increase in output, credit increases by around 3 to 5 percent, on average.
  - Business and financial cycles move in tandem; real GDP growth lags financial conditions.
- Impulse response findings (aggregate and disaggregate models; comparisons with bivariate VARs):
  - Credit responds more to output than output responds to credit:
    - Aggregate model: 1 percent shock to output → credit increases by around 0.7 percent; 1 percent shock to credit → output increases around 0.3 percent.
    - Disaggregate: public and private credit responses to demand shocks are less than half the size of demand responses to credit.
  - Peaks occur around one year after shock, with persistent effects:
    - A 1 percent shock to output boosts credit for between 2 and 3 years; impacts of credit shocks on output similarly persistent.
  - Private credit is more responsive to output shocks than public credit:
    - Private credit increases by 1 percent following a positive output shock; public credit increases by around 0.7 percent.
  - Output responds strongly to shocks to financial conditions; financial conditions loosen modestly following positive demand shocks.
- Historical decomposition of output gap (Figures 4 and 5):
  - Private credit boosted output in 2005–2008 lead-up to global financial crisis.
  - Public credit boosted output following the crisis (2009–10) due to policy support.
  - Financial conditions were important in 2009 recovery and remained positive until 2013; tightened drastically in 2013 onward.
  - Since early 2015, public and private credit and financial conditions have been a drag on output (policy to limit expansion of public bank credit; tightened financial conditions due to uncertainty).
- Macro-financial linkages summarized (Table 2): multiple channels linking macro developments to banking sector, households, corporate sector, mutual funds, public banks, fiscal outcomes, and exchange rate effects.

### V. WHAT ARE THE RISKS FROM A CREDIT SLOWDOWN?
- Concern: autonomous slowdown in private credit could be larger than historical credit–output relationships imply, especially during downturns when buffers are depleted and Basel III transition affects balance sheets.
- Historical evidence:
  - Largest adverse private credit shocks occurred during 2002−03 (sequence beginning 2002Q4), estimated to reduce output by around 1 percent after a year.
- Cost of offsetting private credit slowdown with public credit expansion:
  - Offsetting the 2002Q4 private credit slowdown would have required a 4 percent of GDP expansion in public credit to offset output effects.
- Implication: using public credit to fully offset private credit contractions can be costly and generate fiscal and efficiency challenges.

### VI. CONCLUSIONS AND POLICY IMPLICATIONS
- Rapid past credit growth implies vulnerabilities ahead; Brazil is in the downturn phase of the financial cycle.
- A slowdown in credit could hurt growth despite empirical results showing output has a stronger impact on credit than vice versa.
- Offsetting private credit slowdowns with public-sector credit expansion:
  - Can be effective countercyclically but is costly, difficult to unwind, and contributed to deteriorating fiscal position and doubts about policy credibility.
  - Recommendation: focus public banks on missing markets (e.g., providing guarantees for concessions) to improve allocation of limited financing and effectiveness of monetary policy (Coleman, Feler, 2015; Bonomo, Martins, 2016).
  - Reducing budget earmarking would release fiscal space and improve allocation of limited fiscal resources.

### APPENDIX. MODELS AND PARAMETERS
- Aggregate and disaggregate semi-structural quarterly models specified with:
  - Equations for output (IS curve), inflation (Phillips curve split into non-regulated and regulated components), policy rule, real interest rate (Fisher equation), real credit gap, financial conditions, Okun’s law, capacity utilization, foreign output gap, real exchange rate gap, and behavioral relationships.
  - Aggregate model: real credit gap driven by lagged credit and lagged output; FCI depends on lagged FCI and expected output growth; output gap responds to leads/lags of itself, real interest rate gap, foreign activity gap, real exchange rate gap, autonomous credit and FCI shocks.
  - Disaggregate model: separates public and private credit with distinct gap equations and allows both to impact aggregate demand; public credit modeled to reflect countercyclical policy use.
- Estimation:
  - Bayesian estimation with sample 1999–2015Q3; appendices provide model specifications and parameter estimates.
- Calibrated parameters (excerpt):
  - g (steady state real GDP growth) = 2.00
  - g_c (steady state real credit growth) = 5.00
  - λ = 0.05
  - δ = 0.05
  - Shock standard deviations calibrated based on HP filter trends (λ=1600).
- Selected estimated parameters (posterior means shown):
  - IS and Phillips parameters, persistence terms, and various structural coefficients reported in Table A2 (posterior means and standard deviations for both aggregate and disaggregate models).
- Shock standard deviations (selected posterior means):
  - σ_y = 1.09 (Aggregate posterior mean)
  - σ_credit_trend = 1.27 (Aggregate posterior mean)
  - σ_inflation = 5.12 (Aggregate posterior mean)
  - σ_exchange_rate = 4.34 (Aggregate posterior mean)
  - σ_foreign_output = 0.59 (Aggregate posterior mean)
  - σ_FCI = 0.53 (Aggregate posterior mean)

*Source: Fund staff estimates; model and estimation details, parameter tables, and figures as presented in the source content.*

### References

### wp1712 - References

### Financial cycles, credit, and macrofinancial stability
- Aikman, David, Andrew Haldane and Benjamin Nelson, 2013, “Curbing the Credit Cycle,” The Economic Journal, Vol. 125, Issue 585, pp. 1072–1109.
- Borio, Claudio, 2012, “The Financial Cycle and Macroeconomics: What have we Learnt?”, BIS Working Papers No. 395.
- Borio, Claudio and Mathias Drehmann, 2009, “Assessing the Risk of Banking Crises—Revisited,” BIS Quarterly Review (March), pp. 29–46.
- Claessens, Stijn, M. Ayhan Kose and Marco Terrones, 2011a, “Financial Cycles: What? How? When?”, IMF Working Paper No. 11/76 (Washington: International Monetary Fund).
- Claessens, Stijn, M. Ayhan Kose and Marco Terrones, 2011b, “How do Business and Financial Cycles Interact?”, IMF Working Paper No. 11/88 (Washington: International Monetary Fund).
- Dell’ Arriccia, Giovanni, Deniz Igan, Luc Laeven and Hui Tong, 2012, “Policies for Macrofinancial Stability: How to deal with Credit Booms,” IMF Discussion Note, April (Washington: International Monetary Fund).
- Drehmann, Mathias, Claudio Borio and K Tsatsaronis, 2012, “Characterizing the Financial Cycle: Don’t Lose Sight of the Medium Term!”, BIS Working Papers, No. 380 (June).
- Jordá, Oscar, Moritz Schularick and Alan M. Taylor, 2013, “When Credit Bites Back: Leverage, Business Cycles and Crises,” Journal of Money, Credit and Banking, Supplement to Vol. 45, No. 2.
- Kiyotaki, Nobuhiro and John Moore, 1997, “Credit Cycles,” Journal of Political Economy, Vol. 105, February, pp. 211–47.
- Ng, Tim, 2011, “The Predictive Content of Financial Cycle Measures for Output Fluctuations,” BIS Quarterly Review (June), pp. 53–65.
- Bonomo, Marco and Bruno Martins, 2016, “The Impact of Government-Driven Loans in the Monetary Transmission Mechanism: what can we Learn from Firm-Level Data,” Banco Central do Brasil Working Paper No. 419.
- Coleman, Nicholas and Leo Feler, 2015, “Bank Ownership, Lending and Local Economic Performance During the 2008‒09 Financial Crisis,” Journal of Monetary Economics, No. 71, pp. 50−66.

### Models, estimation methods, and filters
- Bernanke, Ben, Mark Gertler and Simon Gilchrist, 1999, “The Financial Accelerator in a Quantitative Business Cycle Framework,” in Taylor and Woodford (eds.), Handbook of Macroeconomics, Amsterdam, pp. 1341–393.
- Carabenciov, Ioan, Igor Ermolaev, Charles Freedman, Michel Juillard, Ondra Kaminek, Dmitry Korshunov, and Douglas Laxton, 2008, “A Small Quarterly Projection Model of the U.S. Economy,” IMF Working Paper No. 08/278 (Washington: International Monetary Fund).
- Christiano, Lawrence J. and Terry J. Fitzgerald, 2003, “The Band Pass Filter,” International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Vol. 44(2), pages 435–65 (May).
- Herbst, Edward, and Frank Schorfheide, 2015, “Bayesian Estimation of DSGE Models,” Unpublished Manuscript. http://sites.sas.upenn.edu/schorf/files/herbst_and_schorfheide_v5.pdf

### Predictive indicators, financial conditions, and yield curve
- English, William, Kostas Tsatsaronis and Edda Zoli, 2005, “Assessing the Predictive Power of Measures of Financial Conditions for Macroeconomic Variables,” BIS Papers, No. 22, pp. 228‒52.
- Estrella, Arturo and Mary R. Trubin, 2006, “The Yield Curve as a Leading Indicator: Some Practical Issues” Federal Reserve Bank of New York, Current Issues in Economics and Finance (12) 5, July/August.
- Hatzius, Jan, Peter Hooper, Frederic Mishkin, Kermit Schoenholtz, Mark Watson, 2010, “Financial Conditions Indexes: a Fresh Look After the Financial Crisis,” NBER Working Papers No. 16150 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Ng, Tim, 2011, “The Predictive Content of Financial Cycle Measures for Output Fluctuations,” BIS Quarterly Review (June), pp. 53–65.

*Source: wp1712 - References — https://www.imf.org/-/media/files/publications/wp/wp1712.pdf*

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_Source: https://www.imf.org/-/media/files/publications/wp/wp1712.pdf_