## 1. Granger Causality Tests of Alternative FCIs and GDP

## Source details

**Canonical URL:** [1. Granger Causality Tests of Alternative FCIs and GDP](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12196.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12196.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12196.pdf.json)

---

### Overview and purpose
- Objective: construct a Financial Conditions Index (FCI) for South Africa to be used as a leading indicator for short-term economic activity and as a tool to assess financial conditions across time.
- Methodological approach: primarily follows the methodology proposed by Hatzius and others (2010) and applied in Osorio, Pongsaparn, and Unsal (2011), which “strips the unobservable principal component factor from the feedback of economic activity.”
- Alternative methodology: a Kalman filter approach is also applied to provide an estimated FCI with greater auto-correlation over time (greater dynamics).

### Methodologies discussed
- Principal Component Approach (PCA)
  - FCI reflects a common factor extracted from a group of financial indicators that captures the greatest common variation among them.
  - PCA limitations (feedback from economic activity) are addressed by the Hatzius-style adjustment (purging feedback from current GDP growth).
- Weighted-sum approach
  - Weights assigned according to estimated impact on real GDP growth in VAR or structural macroeconomic models (examples referenced: OECD, Goldman Sachs, Bloomberg, Citigroup).
  - South Africa example: Quantec FCI regresses real short-term interest rates, the yield spread, excess money supply growth, company earnings yield, and the real effective exchange rate on manufacturing production and uses coefficients as weights.
- Kalman filter alternative
  - Allows for auto-correlation in the unobserved factor, yielding an FCI with greater persistence over time.

### Data, variables, and PCA implementation
- Sample period for common factor: 1999q1–2011q4.
- Global factors included:
  - S&P500 volatility index (VIX)
  - S&P500 stock price index (SP500)
  - JP Morgan EMBI total return index (EMBI)
  - Spread between three-month LIBOR and three-month US Treasury bill (TED)
- Domestic (South Africa-related) indicators:
  - total loans and advances to the private sector (LOANS_ADV)
  - South African sovereign spread (SOVEREIGN)
  - nonperforming loans (NPL)
  - negotiable certificates of deposit rate (NCD)
  - nominal effective exchange rate (NEER)
  - all-share Johannesburg Stock Exchange index (JSE)
  - ABSA house price index (ABSA)
- Variable treatment:
  - Selection based on factor “loadings” with a threshold set at 30 percent.
  - All variables demeaned and transformed to I(0).
  - NEER, JSE, ABSA, LOANS_ADV, EMBI, and SP500 are measured on a y-o-y basis; the rest measured at levels.
- Loadings and interpretation:
  - Common factor is negatively correlated with VIX and TED, positively correlated with SP500 and EMBI.
  - Factor explains more than 80 percent of the VIX variation.
  - Among SA-specific indicators: common factor positively affected by JSE, ABSA, credit to the private sector, and NEER (an appreciation of the rand reflects looser financial conditions); negatively affected by NCD, NPL, and SOVEREIGN.

### Kalman filter state-space specification
- Motivation: PCA constructs a factor as stationary with zero mean and lacks autocorrelation; Kalman filter captures gradual shifts via autocorrelation.
- State-space components:
  - Signal equation: includes observable variables, their mean, the estimated common factor, and current GDP growth to strip observable variables from feedback of economic activity.
  - State equation: describes the statistical process of the estimated common factor.
  - Error terms (and ) are independent disturbances with zero mean.
- Implementation note: same set of financial indicators used in both PCA and Kalman methodologies; Kalman filter-based FCI is smoother owing to built-in autocorrelation.

### Trajectories and comparative behavior of PCA- and Kalman-based FCIs
- Interpretation convention: upward movement => more accommodative financial conditions; decline => tighter conditions.
- Correlations:
  - Simple correlation between PCA- and Kalman-based FCIs: around 0.4 for the whole period.
  - Correlation in first half (1999–2006) = 0.68; second half = 0.2.
- Key period-specific observations:
  - Financial conditions started deteriorating in 2007Q3 and worsened in 2008.
  - PCA-based FCI reached low point of -3.2 in 2008q4 and recovered strongly by 2009q4.
  - Kalman filter-based FCI reached record-low in 2009q2 (reacted two quarters later) and recovered more gradually, remaining below pre-crisis level.
  - PCA-based FCI showed gradual deterioration in 2010 and 2011, entering negative territory in recent months (relative phrasing used in source).
  - Kalman filter-based index remained flat from 2010q2 to 2011q3 and deteriorated to just below zero in 2011q4.
- Standard-deviation scaling interpretation:
  - Index scaled by sample standard deviation: value of -1 = tighter than average by one standard deviation; 1 = looser than average by one standard deviation.
  - Looser conditions > one standard deviation observed in:
    - PCA: 2003q3 to 2004q2 and 2009q3 to 2010q1.
    - Kalman FCI: 2004q1 to 2007q4.
  - Both FCIs indicate conditions significantly tighter and exceeding one standard deviation in 2008Q3 to 2009Q1 and 2009q1 to 2009q4, respectively.
- Economic implications during tight periods:
  - House prices plummeted by a larger proportion than historic averages.
  - Stock prices lost significant value.
  - Nonperforming loans and other impaired loans increased.
  - Credit extension to the private sector shrank significantly.
  - Resulting illiquidity and price devaluation weakened wealth and collateral channels and may have impaired monetary policy transmission.
  - Latest deteriorations coincide with lingering European sovereign debt problems affecting sovereign risk and risk appetite.

### Granger causality and forecasting evaluation
- Granger causality test results (Table 1):
  - FCI by Kalman filter does not Granger Cause GDP: F-Statistic 4.15663, P-value 0.0219*.
  - GDP does not Granger Cause FCI by Kalman filter: F-Statistic 1.99865, P-value 0.14710.
  - FCI by PCA does not Granger Cause GDP: F-Statistic 9.67749, P-value 0.0003*.
  - GDP does not Granger Cause FCI by PCA: F-Statistic 1.79838, P-value 0.17700.
  - (*) represents significance at 5 percent.
- Predictive regressions setup (Eq. (5)):
  - INX denotes indices examined: PCA, Kalman filter, and the SARB’s leading indicator.
  - Forecast horizons h = 1, 2 and 4 quarters ahead.
  - Estimation period: 1999q1–2011q4.
  - Optimal lag of GDP growth determined by AIC; lag chosen = 2 for comparability.
  - Explanatory power assessed via Sum Squared Residuals (SSR).

### SSR results — Full sample and sub-sample comparisons (exact reported values)
- Full sample SSR (1999q1-2012q1) — AR model variants:
  - AR model with FCI (PCA):
    - h=1 11.309*
    - h=2 33.959*
    - h=4 89.817*
  - AR model with FCI (Kalman filter):
    - h=1 14.943*
    - h=2 52.164*
    - h=4 141.412*
  - AR model with Leading indicator:
    - h=1 16.439
    - h=2 60.527
    - h=4 117.152
  - AR model w/o indices:
    - h=1 17.036
    - h=2 63.009
    - h=4 118.328
  - (*) indicates index’s coefficient significantly different from zero at 95 percent.
- Sub-sample SSR (1999q1-2007q4):
  - AR with FCI (PCA):
    - h=1 5.426*
    - h=2 10.483*
    - h=4 10.148*
  - AR with FCI (Kalman):
    - h=1 5.112*
    - h=2 8.764*
    - h=4 11.306*
  - AR with Leading indicator:
    - h=1 7.069
    - h=2 21.438
    - h=4 29.819*
  - AR w/o indices:
    - h=1 7.261
    - h=2 21.951
    - h=4 36.525
- Interpretation:
  - Both FCIs help explain near-term GDP growth; coefficients significantly different from zero with expected positive sign.
  - Both FCIs outperform SARB’s leading indicator (lower SSRs for all horizons).
  - Across the entire sample, PCA-based FCI has greater explanatory power.
  - For sub-sample 1999q1–2007q4, Kalman FCI has slightly smaller SSR for h=1 and h=2.
  - SARB leading indicator significant only at four-quarter horizon in the sub-sample.

### Comparison of FCI versus individual variables (SSR: 1999q1-2011q4)
- SSRs for h=1, h=2, h=4 (exact reported values; * indicates coefficient significantly different from zero at 95 percent)
  - PCA-Based FCI: h=1 11.309*; h=2 33.959*; h=4 89.817*.
  - Kalman filter-based FCI: h=1 14.943*; h=2 52.164*; h=4 141.412*.
  - VIX: h=1 11.594*; h=2 36.728*; h=4 105.849*.
  - EMBI: h=1 16.377; h=2 60.194; h=4 154.043.
  - SP500: h=1 15.392; h=2 54.012*; h=4 139.536*.
  - SOVEREIGN: h=1 13.944*; h=2 46.405*; h=4 115.836*.
  - TED: h=1 14.637*; h=2 49.062*; h=4 101.064*.
  - NPL: h=1 15.391*; h=2 56.495*; h=4 154.604.
  - JSE: h=1 13.339*; h=2 45.056*; h=4 126.362*.
  - ABSA: h=1 14.449*; h=2 46.354*; h=4 90.063*.
  - NEER: h=1 16.551; h=2 60.474; h=4 142.815.
  - NCD: h=1 16.641; h=2 59.438; h=4 145.169.
  - LOANS_ADV: h=1 15.574*; h=2 57.408*; h=4 160.291.
- Findings:
  - PCA-based FCI has the lowest SSR overall.
  - VIX performs well, especially for h=1 and h=2.
  - Kalman filter outperforms some individual variables but falls short compared to VIX, ABSA, SOVEREIGN, and JSE for some horizons.

### Crisis-period predictive performance (2008q1–2011q4) — RMSE results (Table 4)
- RMSE (in-sample static forecast) — exact reported values:
  - AR model with FCI (PCA):
    - h=1 0.575
    - h=2 1.096
    - h=4 1.877
  - AR model with FCI (Kalman filter):
    - h=1 0.703
    - h=2 1.405
    - h=4 2.400
  - AR model with Leading indicator:
    - h=1 0.721
    - h=2 1.467
    - h=4 2.400
  - AR model w/o indices:
    - h=1 0.740
    - h=2 1.508
    - h=4 2.505
- Interpretation:
  - PCA index performs significantly better than other indices for all horizons during 2008q1–2011q4.
  - Kalman FCI marginally better than SARB’s leading indicator.
  - Both FCIs outperform simple AR without indices.
  - For 1- and 2-quarter ahead forecasts, differences between PCA-FCI and SARB leading indicator relatively small.
  - Substantial difference at four-quarter horizon: PCA-FCI almost fully captures GDP contraction while leading indicator envisages only modest slowdown.
  - In 2010 both indices tend to overshoot recovery due to AR specification inertia.

### Dynamic forecast exercise and scenario analysis for 2012
- Dynamic forecast horizon: next three quarters up to 2012q4 using Eq. (5); PCA-based FCI used for forecasts.
- Scenarios analyzed (three FCI scenarios for 2012):
  1. "No change" scenario: FCI remains constant at its 2012q1 level (0.5).
  2. "Gradual deterioration" scenario: financial conditions gradually deteriorate and return to the average level of the second half of 2011 (-0.5).
  3. "Sharp deterioration" scenario: financial conditions sharply deteriorate and reach the average level observed in 2008 (-1.4).
- Forecast results — quarterly GDP growth (year-on-year) and 2012 average growth (Table 5; exact reported values):
  - 2012Q1 (Actual):
    - FCI remains constant: 2.1
    - FCI gradually deteriorates: 2.1
    - FCI sharply deteriorates: 2.1
  - 2012Q2:
    - FCI remains constant: 2.3
    - FCI gradually deteriorates: 2.3
    - FCI sharply deteriorates: 2.3
  - 2012Q3:
    - FCI remains constant: 2.9
    - FCI gradually deteriorates: 2.4
    - FCI sharply deteriorates: 2.0
  - 2012Q4:
    - FCI remains constant: 3.4
    - FCI gradually deteriorates: 2.4
    - FCI sharply deteriorates: 1.4
  - 2012 growth (average):
    - FCI remains constant: 2.7
    - FCI gradually deteriorates: 2.3
    - FCI sharply deteriorates: 2.0
- Key quantitative implications:
  - "No change" scenario:
    - Quarterly GDP growth projected to accelerate to 3.4 percent in 2012q4.
    - Average 2012 GDP growth projected at 2.7 percent (noted as consistent with the growth projection of the 2012 budget).
  - "Gradual deterioration" scenario (return to second half 2011 level):
    - Quarterly GDP growth projected to remain broadly stable compared to 2012q1 growth (2.1 percent) for the rest of the year.
    - Average 2012 GDP growth would decelerate to 2.3 percent compared to 3.1 percent in 2011.
  - "Sharp deterioration" scenario (reach 2008 level):
    - GDP growth projected to decelerate to 1.4 percent in 2012q4.
    - Average 2012 GDP growth would be 2.0 percent.

### Synthesis and implications
- Both PCA and Kalman filtered FCIs identify an unobservable common factor from external and domestic financial indicators.
- Both FCIs provide powerful predictive information for near-term GDP growth (up to four quarters), with PCA-based FCI generally outperforming alternatives across the full sample.
- Recent deterioration in the financial condition indices implies that economic activity in South Africa is likely to moderate in the period ahead; the magnitude of the slowdown depends on the extent and speed of further deterioration (scenarios summarized above).

*Source: _wp12196 - 1. Granger Causality Tests of Alternative FCIs and GDP (excerpt) — IMF working paper chapter/section*

### 1. Granger Causality Tests of Alternative FCIs and GDP .........................................................9

### 1. Granger Causality Tests of Alternative FCIs and GDP

### Overview and purpose
- Objective: construct a Financial Conditions Index (FCI) for South Africa to be used as a leading indicator for short-term economic activity and as a tool to assess financial conditions across time.
- Methodological approach: primarily follows the methodology proposed by Hatzius and others (2010) and applied in Osorio, Pongsaparn, and Unsal (2011), which “strips the unobservable principal component factor from the feedback of economic activity.”
- Alternative methodology: a Kalman filter approach is also applied to provide an estimated FCI with greater auto-correlation over time (greater dynamics).

### Methodologies discussed
- Principal Component Approach (PCA)
  - FCI reflects a common factor extracted from a group of financial indicators that captures the greatest common variation among them.
  - Acknowledged limitations of PCA (feedback from economic activity), addressed by the Hatzius-style adjustment referenced above.
- Weighted-sum approach (examples and practice)
  - Weights assigned according to estimated impact on real GDP growth in VAR or structural macroeconomic models.
  - Examples include OECD, Goldman Sachs, Bloomberg, Citigroup; in South Africa, the Quantec FCI regresses real short-term interest rates, the yield spread, excess money supply growth, company earnings yield, and the real effective exchange rate on manufacturing production and uses coefficients as weights.
- Kalman filter alternative
  - Allows for auto-correlation in the unobserved factor, yielding an FCI with greater persistence over time.

### Key empirical findings (from the supplied content)
- Timing of financial conditions deterioration and recovery:
  - Financial conditions started deteriorating in 2007Q3.
  - Financial conditions worsened in 2008.
  - Financial conditions recovered strongly in late-2009 and 2010.
  - Financial conditions tightened in recent months (relative phrasing used in the source).
- Predictive performance:
  - The estimated FCIs were found to have powerful predictive information for near-term GDP growth by up to four quarters.
  - The estimated FCIs outperform the current South African Reserve Bank (SARB) leading indicator as well as other individual financial indicators.
- Implication:
  - Based on the recent deterioration in the financial condition indices, economic activity in South Africa is likely to moderate in the period ahead.

### Paper structure (as provided)
- Section II: describes the PCA and presents the financial indicators used to construct the FCI under PCA.
- Section III: offers the Kalman filter alternative that allows for auto-correlation.
- Section IV: compares alternative indices and their evolution over time.
- Section V: evaluates FCIs by performing Granger causality tests and assessing explanatory power for near-term GDP growth; compares to SARB’s leading indicator.
- Section VI: assesses the impact of recent deterioration of financial conditions on GDP growth via dynamic simulations under three different scenarios for 2012.

*Source: _wp12196 - 1. Granger Causality Tests of Alternative FCIs and GDP (excerpt) — IMF working paper chapter/section*

### Section VII concludes.

### _wp12196 - Section VII concludes.

### II. PRINCIPAL COMPONENT APPROACH (PCA)
- PCA aims at extracting a common factor that captures the greatest common variation in a group of P variables.
- Model components:
  - is a vector of the variables’ means.
  - is a matrix of coefficients.
  - is a vector of unobserved variables, termed as common factors.
  - is a vector of errors.
- Assumptions:
  - Errors are orthogonal to the common factors, [ .
  - Common factors have zero mean.
- Data and period:
  - Common factor calculated for the period of 1999q1 and 2011q4.
  - Variables cover measures of market risk and liquidity, with implications for monetary policy, financial stability and economic activity.
- Global factors included:
  - S&P500 volatility index (VIX).
  - S&P500 stock price index (SP500).
  - JP Morgan EMBI total return index (EMBI).
  - Spread between three-month LIBOR and three-month US Treasury bill (TED).
- Domestic (South Africa-related) indicators:
  - total loans and advances to the private sector (LOANS_ADV).
  - South African sovereign spread (SOVEREIGN).
  - nonperforming loans (NPL).
  - negotiable certificates of deposit rate (NCD).
  - nominal effective exchange rate (NEER).
  - all-share Johannesburg Stock Exchange index (JSE).
  - ABSA house price index (ABSA).
- Variable treatment:
  - Selection based on factor “loadings” with a threshold set at 30 percent.
  - All variables demeaned and transformed to I(0).
  - NEER, JSE, ABSA, LONS_ADV, EMBI, and SP500 are measured on a y-o-y basis; the rest measured at levels.
- Loadings and interpretation:
  - Among global indicators, the common factor is negatively correlated with VIX and TED, positively correlated with SP500 and EMBI.
  - The factor explains more than 80 percent of the VIX variation.
  - Among SA-specific indicators, the common factor is positively affected by JSE, ABSA, credit to the private sector, and NEER (an appreciation of the rand reflects looser financial conditions).
  - The common factor is negatively affected by NCD, NPL, and SOVEREIGN.
- Endogeneity and purging:
  - To capture exogenous financial shocks, the estimated common factor is purged of feedback from current GDP growth ( ).
  - Regression purges feedback so that the resulting estimated FCI reflects only exogenous shifts and should have predictive power for future economic activity.

### III. EXTRACTING THE COMMON FACTOR BY A KALMAN FILTER
- Motivation:
  - PCA constructs the factor as stationary with zero mean and lacks dynamic (autocorrelation) pattern.
  - Predicting near-term GDP growth requires capturing more gradual shifts via autocorrelation.
- State-space specification:
  - Signal equation: includes observable variables, their mean, the estimated common factor, and current GDP growth to strip observable variables from feedback of economic activity.
  - State equation: describes the statistical process of the estimated common factor.
  - Error terms ( and ) are independent disturbances with zero mean.
- Implementation note:
  - Same set of financial indicators used in both PCA and Kalman methodologies to construct FCIs.
  - Kalman filter-based FCI is smoother owing to built-in autocorrelation.

### IV. THE ESTIMATED FINANCIAL CONDITIONS INDICES: A COMPARISON
- Interpretation:
  - Upward movement of index => more accommodative financial conditions; decline => tighter conditions.
- Correlation:
  - Simple correlation between PCA- and Kalman-based FCIs is around 0.4 for the whole period.
  - Correlation in first half (1999–2006) = 0.68; second half = 0.2.
- Trajectory and period-specific behavior:
  - Pre-crisis (early-2000s): slightly negative levels; improvement during 2004–07 associated with upturn in global activity and high GDP growth in South Africa.
  - Financial crisis period:
    - PCA-based FCI reached low point of -3.2 in 2008q4 and recovered strongly by 2009q4.
    - Kalman filter-based FCI reached record-low in 2009q2 (reacted two quarters later).
  - Post-crisis:
    - Kalman filter-based FCI recovered more gradually and remained below pre-crisis level.
    - PCA-based FCI showed gradual deterioration in 2010 and 2011, entering negative territory in recent months.
    - Kalman filter-based index remained flat from 2010q2 to 2011q3 and deteriorated to just below zero in 2011q4.
- Standard-deviation scaling:
  - Index scaled by sample standard deviation: value of -1 = tighter than average by one standard deviation; 1 = looser than average by one standard deviation.
  - Looser conditions > one standard deviation observed in:
    - PCA: 2003q3 to 2004q2 and 2009q3 to 2010q1.
    - Kalman FCI: 2004q1 to 2007q4.
  - Both FCIs indicate conditions significantly tighter and exceeding one standard deviation in 2008Q3 to 2009Q1 and 2009q1 to 2009q4, respectively.
- Economic implications during tight periods:
  - House prices plummeted by a larger proportion than historic averages.
  - Stock prices lost significant value.
  - Nonperforming loans and other impaired loans increased.
  - Credit extension to the private sector shrank significantly.
  - Resulting high illiquidity and price devaluation weakened wealth and collateral channels and may have impaired monetary policy transmission.
  - Latest deteriorations coincide with lingering European sovereign debt problems affecting sovereign risk and risk appetite.

### V. EVALUATION OF THE FINANCIAL CONDITIONS INDICES
- Tests conducted:
  - Granger causality tests between the two FCIs and GDP.
  - Forecasting exercises to evaluate ability to explain and predict GDP growth near-term; comparison with SARB’s composite leading business cycle indicator.
  - Assessment of predictive performance of FCI relative to individual included variables.
- Granger causality results (Table 1):
  - FCI by Kalman filter does not Granger Cause GDP: F-Statistic 4.15663, P-value 0.0219*.
  - GDP does not Granger Cause FCI by Kalman filter: F-Statistic 1.99865, P-value 0.14710.
  - FCI by PCA does not Granger Cause GDP: F-Statistic 9.67749, P-value 0.0003*.
  - GDP does not Granger Cause FCI by PCA: F-Statistic 1.79838, P-value 0.17700.
  - (*) represents significance at 5 percent.
- Predictive regressions (Eq. (5)):
  - INX refers to examined indices: PCA, Kalman filter, and the SARB’s leading indicator.
  - Forecast horizons h = 1, 2 and 4 quarters ahead.
  - Estimation period: 1999q1–2011q4.
  - Optimal lag of GDP growth determined by AIC; lag chosen = 2 for comparability.
  - Explanatory power assessed via Sum Squared Residuals (SSR).
- SSR results (Table 2) — Full sample (1999q1-2012q1) and sub-sample (1999q1-2007q4):
  - Full sample SSR:
    - AR model with FCI (PCA): h=1 11.309*; h=2 33.959*; h=4 89.817*.
    - AR model with FCI (Kalman filter): h=1 14.943*; h=2 52.164*; h=4 141.412*.
    - AR model with Leading indicator: h=1 16.439; h=2 60.527; h=4 117.152.
    - AR model w/o indices: h=1 17.036; h=2 63.009; h=4 118.328.
  - Sub-sample SSR (1999q1-2007q4):
    - AR with FCI (PCA): h=1 5.426*; h=2 10.483*; h=4 10.148*.
    - AR with FCI (Kalman): h=1 5.112*; h=2 8.764*; h=4 11.306*.
    - AR with Leading indicator: h=1 7.069; h=2 21.438; h=4 29.819*.
    - AR w/o indices: h=1 7.261; h=2 21.951; h=4 36.525.
  - (*) indicates index’s coefficient significantly different from zero at 95 percent.
- Interpretation of SSR results:
  - Both FCIs help explain near-term GDP growth; coefficients significantly different from zero with expected positive sign.
  - Both FCIs outperform SARB’s leading indicator (lower SSRs for all horizons).
  - Across the entire sample, PCA-based FCI has greater explanatory power.
  - For sub-sample 1999q1–2007q4, Kalman FCI has slightly smaller SSR for h=1 and h=2.
  - SARB leading indicator significant only at four-quarter horizon in the sub-sample.
- Comparison of FCI vs individual variables (Table 3; 1999q1-2011q4; SSR for h=1,2,4):
  - PCA-Based FCI: h=1 11.309*; h=2 33.959*; h=4 89.817*.
  - Kalman filter-based FCI: h=1 14.943*; h=2 52.164*; h=4 141.412*.
  - VIX: h=1 11.594*; h=2 36.728*; h=4 105.849*.
  - EMBI: h=1 16.377; h=2 60.194; h=4 154.043.
  - SP500: h=1 15.392; h=2 54.012*; h=4 139.536*.
  - SOVEREIGN: h=1 13.944*; h=2 46.405*; h=4 115.836*.
  - TED: h=1 14.637*; h=2 49.062*; h=4 101.064*.
  - NPL: h=1 15.391*; h=2 56.495*; h=4 154.604.
  - JSE: h=1 13.339*; h=2 45.056*; h=4 126.362*.
  - ABSA: h=1 14.449*; h=2 46.354*; h=4 90.063*.
  - NEER: h=1 16.551; h=2 60.474; h=4 142.815.
  - NCD: h=1 16.641; h=2 59.438; h=4 145.169.
  - LOANS_ADV: h=1 15.574*; h=2 57.408*; h=4 160.291.
  - Findings:
    - PCA-based FCI has the lowest SSR overall.
    - VIX performs well, especially for h=1 and h=2.
    - Kalman filter outperforms some individual variables but falls short compared to VIX, ABSA, SOVEREIGN, and JSE for some horizons.
- Crisis-period predictive performance (2008q1–2011q4):
  - In-sample static forecast evaluated using RMSE.
  - RMSE results (Table 4):
    - AR model with FCI (PCA): h=1 0.575; h=2 1.096; h=4 1.877.
    - AR model with FCI (Kalman filter): h=1 0.703; h=2 1.405; h=4 2.400.
    - AR model with Leading indicator: h=1 0.721; h=2 1.467; h=4 2.400.
    - AR model w/o indices: h=1 0.740; h=2 1.508; h=4 2.505.
  - Interpretation:
    - PCA index performs significantly better than other indices for all horizons during 2008q1–2011q4.
    - Kalman FCI marginally better than SARB’s leading indicator.
    - Both FCIs outperform simple AR without indices.
  - Forecast dynamics:
    - For 1- and 2-quarter ahead forecasts, differences between PCA-FCI and SARB leading indicator relatively small.
    - Substantial difference at four-quarter horizon: FCI almost fully captures GDP contraction while leading indicator envisages only modest slowdown.
    - In 2010 both indices tend to overshoot recovery due to AR specification inertia.

### VI. WHAT CAN THE FINANCIAL CONDITIONS INDEX TELL ABOUT THE NEAR-TERM GDP GROWTH?
- Dynamic forecast exercise:
  - Dynamic forecast for the next three quarters (up to 2012q4) using Eq. (5).
  - For every quarter the starting point is the model’s prediction.
  - Uses the PCA-based FCI (found to outperform Kalman FCI and SARB leading indicator).
- Scenarios considered (focus on euro-area sovereign crisis repercussions):
  - Three main scenarios for the remainder of the year are defined; the first scenario is provided in the source:
    1. Financial conditions remain at their current level (as of 2012q1) throughout the forecast horizon (0.5).

*Italic source attribution: Section VII concludes. Source PDF: _wp12196 - Section VII concludes.*

### 2. Financial conditions gradually deteriorate, and return to the average level of the

### _wp12196 - 2. Financial conditions gradually deteriorate, and return to the average level of the

### Scenarios and dynamic forecast overview
- Three financial conditions index (FCI) scenarios are analyzed for 2012:
  - "No change" scenario: FCI remains constant.
  - "Gradual deterioration" scenario: Financial conditions gradually deteriorate and return to the average level of the second half of 2011 (-0.5).
  - "Sharp deterioration" scenario: Financial conditions sharply deteriorate and reach the average level observed in 2008 (-1.4).
- The FCI trajectories under the three scenarios and dynamic forecasts are summarized in Figure 6 (2012q1-2012q4).
- The impact on GDP growth depends on both the magnitude and the pace at which financial conditions deteriorate; forecast results indicate substantial effects on economic activity.

### Forecast results (quarterly and annual GDP growth under three scenarios)
- Table 5. Forecast Results under Three Scenarios (GDP growth, year-on-year)
  - 2012Q1 (Actual):
    - FCI remains constant: 2.1
    - FCI gradually deteriorates: 2.1
    - FCI sharply deteriorates: 2.1
  - 2012Q2:
    - FCI remains constant: 2.3
    - FCI gradually deteriorates: 2.3
    - FCI sharply deteriorates: 2.3
  - 2012Q3:
    - FCI remains constant: 2.9
    - FCI gradually deteriorates: 2.4
    - FCI sharply deteriorates: 2.0
  - 2012Q4:
    - FCI remains constant: 3.4
    - FCI gradually deteriorates: 2.4
    - FCI sharply deteriorates: 1.4
  - 2012 growth (average):
    - FCI remains constant: 2.7
    - FCI gradually deteriorates: 2.3
    - FCI sharply deteriorates: 2.0

### Key quantitative implications reported
- Under the "no change" scenario:
  - Quarterly GDP growth is projected to gradually accelerate to 3.4 percent in 2012q4.
  - Average 2012 GDP growth is projected at 2.7 percent (noted as consistent with the growth projection of the 2012 budget).
- Under the "gradual deterioration" scenario (return to second half 2011 level):
  - Quarterly GDP growth is projected to remain broadly stable compared to 2012q1 growth (2.1 percent) for the rest of the year.
  - Average 2012 GDP growth would decelerate to 2.3 percent compared to 3.1 percent in 2011.
- Under the "sharp deterioration" scenario (reach 2008 level):
  - GDP growth is projected to decelerate to 1.4 percent in 2012q4.
  - Average 2012 GDP growth would be 2 percent.

### Construction and predictive performance of the FCI
- Two alternative approaches used to extract the FCI: principal component analysis (PCA) and Kalman filter.
- The FCI identifies an unobservable common factor from a group of external and domestic financial indicators.
- Predictive exercises:
  - Out-of-sample forecasting and an in-sample exercise tested the FCI's predictive power.
  - Forecasts compared PCA- and Kalman-based FCIs against:
    - An autoregressive model of GDP growth.
    - The SARB’s leading indicator.
    - The predictive capacity of various key financial market variables at one, two, and four quarters ahead.
- Main results:
  - Both PCA and Kalman filtered FCIs performed better as leading indicators of real activity relative to the SARB’s leading indicator and to an autoregressive model of GDP growth.
  - The PCA-based FCI outperforms the individual financial indicator that it includes.
  - PCA-based FCI has greater explanatory power over the entire sample.
  - During the pre-crisis period, the Kalman filter-based FCI performed better in predicting GDP growth, particularly for one and two quarters ahead.

### Dynamics and implications
- The FCIs indicate a strong recovery in late-2009 and 2010, followed by deterioration in recent months (relative to the paper's sample), though not as sharply as in 2008.
- Because estimated FCIs have powerful predictive information for near-term GDP growth (up to four quarters), further deterioration in financial conditions would likely imply a slowdown in economic activity in the period ahead.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12196.pdf*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12196.pdf_