## _wp09241 - References

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### I. Introduction — context, goals, and literature
- Context and motivation
  - Large bank losses and financial turbulences are direct consequences of the subprime mortgages crisis that erupted in the United States after July 2007.
  - Two years later, financial turmoil and the global recession have renewed focus on macro-linkages and the role of financial factors as amplifiers of international transmission of real shocks.
- Research goal
  - Study determinants of quarterly euro area GDP in the context of financial turbulences originated in the U.S.
  - Assess whether considering financial variables helps track observed linkages between the U.S. and the euro area.
- Key channels and literature cited
  - Trade channel: U.S. imports represent around 15% of euro area exports; euro area exports contribute for only 10% to its GDP growth.
  - Third-country effects may cause bilateral trade statistics to underestimate linkages (Dees and Vansteenkiste, 2007).
  - Commodity prices channel considered but found not consequential by Bayoumi and Swiston (2007).
  - Financial sector/global financial conditions emphasized as central channel (Dees et al., 2005; Bayoumi and Swiston, 2007).
    - Dees, di Mauro, Smith and Pesaran (2005): a 4 percent fall in U.S. real equity prices reduces U.S. output by 0.4 percent within a year, depresses European financial markets by around 4 percent and euro area GDP growth by 0.4 percent in the second year after the shock.
  - Financial accelerator and credit-quantity channels (Bernanke and Gertler, 1989; Carlson et al., 2008; Goodhart et al., 2006).
    - Carlson et al. (2008): one standard deviation shock to an aggregate index of distance to default of financial institutions leads to a cumulative decrease in investments of about 2% over the subsequent two years (in-sample result).
  - Forward-looking asset prices and forecasting literature (Ang, Piazzesi and Wei, 2006; Stock and Watson, 2003; Liew and Vassalou, 2000; Gilchrist et al., 2008).
  - Evidence on predictive value for the euro area is limited (Forni et al., 2003).

### II. VAR models — data, specification, and estimation
- Data coverage and construction
  - Quarterly seasonally adjusted real GDP for three economic areas observed between 1970q1 and 2007q4: U.S., euro area, Rest of the World (ROW).
  - Rest of the World: weighted aggregate of seven countries (Australia, Canada, Denmark, Norway, New Zealand, Sweden and Switzerland) with weights being the 1995 GDP expressed in U.S. dollars.
  - Financial data: stock market indices, dividend yields, 10-year and 3-month yields for all sample countries; dividend yield used with Government bond yield to construct a disequilibrium measure (the ‘Fed’ model).
  - Stock market returns used to generate time-varying volatilities as 4-quarter backward-looking moving averages of absolute values.
  - Slope of yield curve: difference between 10-year government bond and 3-month T-Bill; euro area slope relies on German data.
  - Monthly financial variables collected between March 1970 and March 2008; monthly transformations mirror quarterly transformations (12-month moving averages for monthly data).
  - To limit VAR size, only two financial variables per economic area are included at once; largest VAR has 9 variables.
- VAR specification and estimation choices
  - VARs with four lags chosen; standard lag tests (AIC, SIC) suggest one lag but authors fix four due to quarterly frequency and desire to capture 12–24 month predictive relationships.
  - Variable transformations:
    - GDP-only VARs specified in levels with or without cointegration.
    - Models with financial variables are also estimated in log-difference to limit impact of higher volatility of financial variables.
  - Cointegration:
    - Trace statistic (Johansen, 1988) finds evidence of at most one cointegrating vector among the three economic areas.
    - Cointegration model estimated with a 2-step procedure; cointegrating vector λ links dynamics of the two or three GDPs.
  - General model form (cointegration model):
    - y_t = A_1 y_{t-1} + A_2 y_{t-2} + A_3 y_{t-3} + C·λ·y_{t-4} + ε_t
    - Matrices A_0,...,A_3, C estimated by OLS; λ estimated in a preliminary step and imposed via 2-step procedure.
  - Modeling caveats
    - Avoid forcing cointegration among nearly integrated financial variables; level specifications are superconsistent in presence of cointegration but may be misspecified for stationary variables.

### III. Model families and benchmark specifications
- Benchmark models
  - Model 0: the random walk for the GDP growth rate.
  - BiVARL: 2-country BiVAR estimated in levels (unconstrained).
  - BiVARC: 2-country BiVAR with cointegration.
- 2-country and 3-country specifications
  - BiVARL and BiVARC: U.S. and euro area log GDP in levels; BiVARC includes cointegration.
  - TriVar model: 3-country model (U.S., euro area, ROW) log GDP in levels with cointegration.
  - FiVAR1 family: 3-country log GDP with cointegration, plus stock market volatility and slope.
    - FiVAR1D: log-difference.
    - FiVAR1C: cointegrating VAR.
    - FiVAR1L: level VAR.
  - FiVAR2 family: 3-country log GDP with cointegration, plus stock market index (level) and slope (level).
    - FiVAR2D, FiVAR2C, FiVAR2L analogous variants.
  - FiVAR3L: 3-country log GDP plus dividend yield, bond yield and slope (level VAR).
- Purpose
  - Use multiple forms (levels, log-differences, cointegrating VARs) to assess robustness of dynamics and cross-country linkages and to incorporate financial variables (stock market volatility, stock market index, dividend yield, bond yield, slope).

### IV. In-sample empirical findings — IRFs, sub-samples, variance decompositions, counterfactuals
- IRF and identification details
  - Reduced-form VARs identified by Choleski ordering separating slow-moving (real) from fast-moving (financial) variables; ordering: euro area GDP first, ROW second, U.S. last.
  - VARs estimated between 1970Q1 and 2007Q4 with four lags.
  - Confidence bands reported at 68%; orthogonalized IRFs with error bands from 500 Monte-Carlo draws.
- IRF main results
  - U.S. GDP adjusts faster to shocks and leads other areas.
  - Spillovers:
    - Some U.S.–ROW spillovers.
    - U.S.–euro area spillovers appear one-way, coming from the U.S.
  - Financial variables’ marginal impact:
    - Including stock market volatility (sm) and slope of the yield curve (sl) suggests sm and sl affect GDP growth, but financial variables contribute only to a small extent to future GDP growth; significance is borderline in most cases and sample-dependent (pre/post-1985).
    - Literature benchmark: an 8% increase in the U.S. stock market index boosts U.S. and euro area activity by around 0.2% quarter-on-quarter during the first year after the shock (Dees et al., 2007).
- Sub-sample (1970–1984 vs 1985–2007) evidence
  - Amplitude of IRFs decreased after 1985; linkages across variables changed.
  - After 1985:
    - Response of euro area and ROW to U.S. GDP shocks flattened significantly at short horizons; long-term effects remain similar.
    - Synchronization between ROW and U.S. strengthened; not observed for the euro area.
    - U.S. started to respond positively to a GDP shock in ROW after 1985.
    - Linkages with slope of the yield curve increased and became more stable; post-1985 they are positive and significant at all horizons in the U.S. and euro area.
    - Role of U.S. stock market volatility: a 1% positive volatility shock would have lowered GDP by about 1% annualized in the U.S. and the euro area within 8 quarters; effect for ROW is half a percentage point at same horizon and significant.
- Forecast error variance decomposition (selected insights)
  - From model with 3 GDPs plus U.S. and euro area slope and stock market:
    - At long horizons the U.S. GDP and U.S. slope explain the majority of movements in euro area GDP; at short horizons domestic variables matter more.
    - Euro area cycles have little effect on U.S. cycles.
  - Table 1 — Euro area GDP attribution (percent of total variance):
    - horizon 1: Euro area GDP 100.0, ROW GDP 0.0, U.S. GDP 0.0, euro area slope 0.00, euro area stock market 0.0, U.S. slope 0.0
    - horizon 4: Euro area GDP 75.14, ROW GDP 0.55, U.S. GDP 11.66, euro area slope 0.23, euro area stock market 11.05, U.S. slope 0.35, U.S. stock market 1.00
    - horizon 8: Euro area GDP 47.36, ROW GDP 2.11, U.S. GDP 25.19, euro area slope 5.73, euro area stock market 17.66, U.S. slope 1.19, U.S. stock market 0.76
    - horizon 12: Euro area GDP 31.42, ROW GDP 2.21, U.S. GDP 37.02, euro area slope 9.77, euro area stock market 12.72, U.S. slope 5.78, U.S. stock market 1.10
    - horizon 24: Euro area GDP 13.39, ROW GDP 1.16, U.S. GDP 45.82, euro area slope 10.12, euro area stock market 5.52, U.S. slope 20.29, U.S. stock market 3.68
- Counterfactual experiments and historical decomposition
  - Trivariate VARs with restrictions generate counterfactual series assuming historical shocks to other countries’ GDP equations are zero.
  - Key quantified results:
    - Across whole sample: The United States would have explained about 15% of euro area GDP growth rates and 10% of ROW GDP growth.
    - Decadal variation: On average, U.S.-originating shocks explained about 23% of euro area GDP growth between 1970 and 2000; this percentage rose to 36% since that year.
    - Including financial variables: U.S. and ROW real shocks alone would have explained 12% and 8% of euro area GDP growth rates across the whole sample; these percentages rise to 18% and 16% when financial shocks are also considered.
  - Historical decomposition highlights:
    - 1974 recession worsened by negative U.S. and ROW cycles.
    - Early 1980s growth hurt by restrictive monetary policy, especially in the U.S.
    - 1992 long contraction followed German reunification — not explained by international or financial factors.
    - Financial factors mattered in 2002 recession and the current episode (sample end).
    - U.S. stock market shocks did not play a major role in U.S. recessions until 2001; since 2001 they significantly affected activity.
    - The slope of the yield curve was particularly sizeable between 1979 and 1983, but marginal afterwards.

### V. Out-of-sample evidence — unconditional and conditional forecasting
- Forecast evaluation framework
  - Main statistics: Root Mean Square Error (RMSE) for out-of-sample forecast errors between 1 and 12 quarters ahead; rolling RMSEs over 12-quarter moving windows; Giacomini and White (2006) conditional predictive ability (GW) test.
  - GW test re-estimates models on fixed-length rolling windows (practical minimum noted as 48 quarters; 60 quarters used in analysis).
- A. Unconditional RMSE results (selected findings)
  - Table 3 summary:
    - Except 1-step-ahead forecast, model 1 (VAR with two GDPs) has best performance across most horizons.
    - Performance of model 1 very close to the VAR including three GDPs and to the VAR with GDPs complemented by stock market volatility and slope.
    - Random walk model never a winning choice.
    - Adding other financial variables beyond slope and stock market volatility worsens out-of-sample forecasts at horizons shorter than one year; gap tends to shrink when forecasting 2 to 3 years ahead.
  - Selected RMSE values (Panel A minima and comparisons):
    - RW (Random walk) horizon 1..12: 0.45 0.44 0.45 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47
    - BiVARC 2 gdp coint. horizon 1..12: 0.43 0.41 0.41 0.40 0.40 0.40 0.40 0.40 0.41 0.42 0.42 0.43
    - TriVARC 3 gdp coint. horizon 1..12: 0.42 0.42 0.43 0.42 0.41 0.42 0.43 0.44 0.44 0.45 0.45 0.45
    - Panel C summary lines:
      - minimum all: 0.42 0.41 0.41 0.40 0.40 0.40 0.40 0.41 0.42 0.42 0.43 0.43
      - minimum fin: 0.47 0.43 0.48 0.47 0.45 0.44 0.45 0.45 0.43 0.44 0.44 0.44
      - relative gap: 0.05 0.02 0.07 0.07 0.05 0.04 0.05 0.04 0.01 0.02 0.02 0.01
      - % gap: 12.43 4.34 16.66 16.86 11.88 11.18 12.75 8.87 2.48 3.73 3.67 2.32
- B. Conditional forecasts (conditioning on more recent financial data)
  - Short-term forecaster setup: forecasts for t+1 and beyond using financial data up to t+1 while most recent GDP known refers to t.
  - Table 4 findings:
    - Up to the 8th step ahead, forecasting performance deteriorates for all models with financial variables by between 15 and 35%.
    - Between the 2- and the 3-year ahead horizon, RMSE gets close to overall minimum from unconditional exercise.
    - Panel B (GDP known only to t-1 while financials known to t and t+1): similar picture — optimal forecast need not use the most recent quarterly financial data.
  - Selected conditional RMSE summary (Panel A minima and gaps):
    - minimum: 0.49 0.47 0.45 0.53 0.53 0.51 0.50 0.49 0.47 0.44 0.44 0.44
    - gain/loss over unco: 0.07 0.05 0.05 0.13 0.13 0.11 0.10 0.07 0.05 0.02 0.01 0.00
    - % gap: 17.1 13.2 11.6 32.2 33.1 28.0 25.4 18.0 12.9 4.9 1.6 1.1
- C. Monthly financial information conditioning (Table 5)
  - Conditioning on monthly financial variables dated t+1/3, t+2/3, t+3/3 of a quarter generally worsens forecasting ability for many models relative to unconditional forecasts.
  - Selected Panel minima:
    - Panel A (month t+1/3) minimum: 0.50 0.46 0.47 0.47 0.45 0.42 0.43 0.45 0.42 0.43 0.44 0.44
    - Panel B (month t+2/3) minimum: 0.47 0.46 0.46 0.48 0.45 0.42 0.43 0.44 0.42 0.43 0.44 0.44
    - Panel C (month t+3/3) minimum: 0.47 0.45 0.44 0.48 0.46 0.42 0.44 0.44 0.43 0.43 0.44 0.43
  - Noted exceptions: models including slope, stock market volatility, and distance to default are particularly successful in certain episodes when monthly releases are used.
- D. Additional financial indicators tested
  - Fama and French factors (hml, smb), distance to default and its interquartile range, Consumer and Industrial (C&I) bank loans, consumer credit loans, real estate loans.
  - Stationarity and transformations:
    - Fama and French factors are stationary.
    - Distance to default and interquartile range found stationary (ADF with 4 lags).
    - Three types of bank loans are I(1) and considered in first differences.
  - Forecasting results: these measures produce some improvement relative to models with price-related financial information but worse predictions relative to VARs with only 2 or 3 GDPs.

### VI. Conditional evaluation — rolling RMSEs and Giacomini–White tests
- Rolling RMSEs (12-quarter windows)
  - Rolling RMSEs at 4- and 8-quarters-ahead show time variation in predictive performance.
  - Between March 1996 and March 1999 and between 2002 and 2005 monthly information improved forecasting performance over the unconditional forecast.
  - Dramatic loss in forecasting ability when using quarterly information; substantial gain when using monthly releases, especially the second month of the quarter for 4-step-ahead, and the first month for 8-step-ahead.
  - VARs including slope, stock market volatility, and distance to default (which depends on equity volatilities) were particularly successful in these episodes.
- Giacomini–White (GW) conditional predictive ability test
  - GW test applied for horizons τ = 1, 4 and 8 quarters; computed using fixed-length rolling windows (60 quarters).
  - Test results (Table 6 highlights):
    - GW test shows differences in forecasting performance between financial models and random walk or GDP-only models can often be predicted (p-values lower than 0.05) for several models (FiVar1D, FiVar2D, model including Fama-French factors, C&I loans model).
    - Decision-choice functions indicate when a model with financial variables would have been preferred; models with financial variables performed best in 1999 and between 2001 and 2003 — periods when historical decomposition attributes large revisions to financial shocks.
  - Conditional-choice takeaway:
    - Random walk preferred only in a significant fraction of quarters compared to model 1 (two GDPs) and less frequently to model 2 (three GDPs); random walk is by far surpassed by nearly all models with financial variables.
    - VAR with 2 GDPs, despite strong RMSE performance, would frequently be outperformed by the VAR that includes stock market volatility and yield curve slope beyond the 3 GDPs.

### VII. Conclusions and research directions
- Summary conclusions
  - In-sample evidence: financial shocks matter for euro area real activity.
  - Out-of-sample RMSE assessment: financial variables do not help forecasting real activity on average, even accounting for timeliness (consistent with Stock and Watson (2003)).
  - Conditional predictive ability: financial variables play a role in predicting euro area GDP in particular episodes (notably 1999 and 2001–2003), consistent with historical decomposition findings.
- Caveats and future research
  - Analysis conducted within linear models; financial variables may have nonlinear impacts on macroeconomic variables.
  - Nonlinear frameworks (e.g., Markov-Switching) can reveal forecasting gains from financial variables for turning points (Fornari and Lemke (2009)).
  - Potential larger forecasting power of financial variables during broadband negative movements in financial indicators is an important avenue for future research.

### Key tables — selected exact figures and model comparisons
- Table 1 — Euro area GDP variance decomposition (percent of total variance):
  - horizon 1: Euro area GDP 100.0, ROW GDP 0.0, U.S. GDP 0.0, euro area slope 0.00, euro area stock market 0.0, U.S. slope 0.0
  - horizon 4: Euro area GDP 75.14, ROW GDP 0.55, U.S. GDP 11.66, euro area slope 0.23, euro area stock market 11.05, U.S. slope 0.35, U.S. stock market 1.00
  - horizon 8: Euro area GDP 47.36, ROW GDP 2.11, U.S. GDP 25.19, euro area slope 5.73, euro area stock market 17.66, U.S. slope 1.19, U.S. stock market 0.76
  - horizon 12: Euro area GDP 31.42, ROW GDP 2.21, U.S. GDP 37.02, euro area slope 9.77, euro area stock market 12.72, U.S. slope 5.78, U.S. stock market 1.10
  - horizon 24: Euro area GDP 13.39, ROW GDP 1.16, U.S. GDP 45.82, euro area slope 10.12, euro area stock market 5.52, U.S. slope 20.29, U.S. stock market 3.68
- Table 2 — R^2 of regression of Δlog GDP on its counterfactual (selected values, full-sample)
  - U.S. column (full sample): U.S. 0.9, euro area 0.14, R.o.W 0.21
  - euro area column (full sample): U.S. 0.04, euro area 0.8, row 0.14
  - row column (full sample): U.S. 0.01, euro area 0.1, row 0.61
  - Decadal examples for U.S. column:
    - 1970s: 0.7 0.23 0.27
    - 1980s: 0.81 0.21 0.42
    - 1990s: 0.87 0.25 0.46
    - 2000s: 0.89 0.36 0.29
- Table 3 — Unconditional out-of-sample RMSE (selected model minima)
  - RW horizon 1..12: 0.45 0.44 0.45 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47
  - BiVARC 2 gdp coint. horizon 1..12: 0.43 0.41 0.41 0.40 0.40 0.40 0.40 0.40 0.41 0.42 0.42 0.43
  - TriVARC 3 gdp coint. horizon 1..12: 0.42 0.42 0.43 0.42 0.41 0.42 0.43 0.44 0.44 0.45 0.45 0.45
  - Panel C summary:
    - minimum all: 0.42 0.41 0.41 0.40 0.40 0.40 0.40 0.41 0.42 0.42 0.43 0.43
    - minimum fin: 0.47 0.43 0.48 0.47 0.45 0.44 0.45 0.45 0.43 0.44 0.44 0.44
    - relative gap: 0.05 0.02 0.07 0.07 0.05 0.04 0.05 0.04 0.01 0.02 0.02 0.01
    - % gap: 12.43 4.34 16.66 16.86 11.88 11.18 12.75 8.87 2.48 3.73 3.67 2.32
- Table 4 — Conditional RMSE (selected minima and gaps)
  - Panel A minimum: 0.49 0.47 0.45 0.53 0.53 0.51 0.50 0.49 0.47 0.44 0.44 0.44
  - Panel A % gap: 17.1 13.2 11.6 32.2 33.1 28.0 25.4 18.0 12.9 4.9 1.6 1.1
  - Panel B minimum: 0.50 0.48 0.50 0.54 0.55 0.51 0.51 0.50 0.44 0.44 0.43 0.44
  - Panel B % gap: 17.6 17.4 23.0 34.2 37.5 27.9 27.4 21.5 6.5 5.3 0.6 1.1
- Table 5 — Monthly-information RMSE minima (Panels A–C)
  - Panel A minimum: 0.50 0.46 0.47 0.47 0.45 0.42 0.43 0.45 0.42 0.43 0.44 0.44
  - Panel B minimum: 0.47 0.46 0.46 0.48 0.45 0.42 0.43 0.44 0.42 0.43 0.44 0.44
  - Panel C minimum: 0.47 0.45 0.44 0.48 0.46 0.42 0.44 0.44 0.43 0.43 0.44 0.43
- Table 6 — GW conditional predictive ability test (methodology and selected outcomes)
  - GW test p-values and conditional-choice counts indicate models with financial variables would have been preferred in several episodes; FiVar1D, FiVar2D and models including Fama-French factors or C&I loans show low p-values (often < 0.05) in the GW test.

*Content extracted from _wp09241 - References (source PDF: _wp09241 - REFERENCES).*

### References .............................................................................................................

### References

### I. INTRODUCTION

- Context and motivation
  - Large bank losses and financial turbulences are direct consequences of the subprime mortgages crisis that erupted in the United States after July 2007.
  - Two years later, financial turmoil and the global recession have renewed focus on macro-linkages and the role of financial factors as amplifiers of international transmission of real shocks.

- Research goal
  - Study determinants of quarterly euro area GDP in the context of financial turbulences originated in the U.S.
  - Assess whether considering financial variables helps track observed linkages between the U.S. and the euro area.

- Key literature and channels of transmission discussed
  - Trade channel: U.S. imports represent around 15% of euro area exports; euro area exports contribute for only 10% to its GDP growth.
  - Third-country effects (Dees and Vansteenkiste, 2007) may cause bilateral trade statistics to underestimate linkages.
  - Commodity prices channel considered but found not consequential by Bayoumi and Swiston (2007).
  - Financial sector/global financial conditions argued as a central channel (Dees et al., 2005; Bayoumi and Swiston, 2007).
    - Dees, di Mauro, Smith and Pesaran (2005): a 4 percent fall in U.S. real equity prices reduces U.S. output by 0.4 percent within a year, depresses European financial markets by around 4 percent and euro area GDP growth by 0.4 percent in the second year after the shock.
  - Financial accelerator and credit-quantity channels (Bernanke and Gertler, 1989; Carlson et al., 2008; Goodhart et al., 2006).
    - Carlson et al. (2008): one standard deviation shock to an aggregate index of distance to default of financial institutions leads to a cumulative decrease in investments of about 2% over the subsequent two years (in-sample result).
  - Forward-looking nature of asset prices and forecasting literature (Ang, Piazzesi and Wei, 2006; Stock and Watson, 2003; Liew and Vassalou, 2000; Gilchrist et al., 2008).
  - Evidence on predictive value for the euro area is limited (Forni et al., 2003).

- Main empirical findings (in-sample)
  - Impulse responses support a relationship between financial variables and real activity both domestically and internationally.
  - Forecast error variance decomposition: half of the variance of euro area GDP can be explained by U.S. and ‘financial’ shocks eight-quarters ahead.
  - Sub-sample analysis suggests linkages have become stronger after 1985.
  - Counterfactual experiments: including financial variables in addition to GDP leads to simulated GDP values much closer to actual GDP figures.
  - The United States have had a leading role in transmission of shocks since the 70s.

- Main empirical findings (out-of-sample)
  - ‘Unconditional’ out-of-sample GDP forecasts (traditional forecasts for time t+k conditional on time t):
    - A model including the GDPs of the two or three economic areas has the best performance in terms of forecast Root Mean Square Error (RMSE) across the eight VAR models considered.
    - Adding various combinations of financial variables worsens out-of-sample performance at short horizons; the gap tends to shrink when forecasting 2 to 3 years ahead.
  - ‘Conditional’ forecasts (future values of financial variables assumed known for next 1 or 2 quarters) do not change the above conclusion.
  - Rolling RMSE and the Giacomini and White (2006; GW) conditional predictive ability test:
    - GW test shows financial variables would have improved forecast for euro area GDP between 1999 and 2002.
    - Historical decomposition indicates financial shocks had a prominent role in that period.

- Interpretation and hypotheses
  - Financial shocks may be infrequent, making average predictive power marginal over long samples.
  - Financial prices may affect real activity nonlinearly, reducing predictive power in linear frameworks.
  - Support from other studies: financial prices help fit recessionary periods out-of-sample (Fornari and Mele, 2009; Fornari and Lemke, 2009); threshold VAR models (Balke, 2000) give some support to nonlinear effects.

### II. THE VAR MODELS

- Data
  - Quarterly seasonally adjusted real GDP for three economic areas observed between 1970q1 and 2007q4: U.S., euro area, Rest of the World (ROW).
  - Rest of the World: weighted aggregate of seven countries (Australia, Canada, Denmark, Norway, New Zealand, Sweden and Switzerland) with weights being the 1995 GDP expressed in U.S. dollars; results similar with un-weighted averages.
  - Figure 1: Rates of Growth of Real GDP in the Three Economic Areas (quarter-on-quarter) shows commonality and episodes where the U.S. leads the euro area (e.g., after 1990 recession).
  - Financial data: stock market indices, dividend yields, 10-year and 3-month yields for all sample countries; dividend yield used with Government bond yield to construct a disequilibrium measure (the ‘Fed’ model).
  - Stock market returns used to generate time-varying volatilities as 4-quarter backward-looking moving averages of absolute values.
  - Slope of yield curve: difference between 10-year government bond and 3-month T-Bill; euro area slope relies on German data.
  - Monthly financial variables collected between March 1970 and March 2008; monthly transformations mirror quarterly transformations (12-month moving averages for monthly data).
  - To limit VAR size, only two financial variables per economic area are included at once; largest VAR has 9 variables.

- Specifications
  - VAR models with four lags; rationale:
    - Standard lag choice tests (AIC, SIC) suggest one lag but are known to underestimate dependence; likelihood ratio test and quarterly frequency motivated fixing lag length at 4.
    - Slope of yield curve and stock market volatility predict business cycles at 12 to 24 months horizons; short lags would limit measured predictability.
  - Variable transformations:
    - VARs with GDP variables only are specified in levels with or without cointegration.
    - Models with financial variables are also estimated in log-difference to limit the impact of higher volatility of financial variables relative to real GDP.
  - Cointegration:
    - Trace statistic (Johansen, 1988) finds evidence of at most one cointegrating vector among the three economic areas.
    - Cointegration model estimated with a 2-step procedure; cointegrating vector λ links dynamics of the two or three GDPs.
    - Authors do not investigate full Vector Error Correction models for financial variables due to synchronization and near-integration concerns.
  - General model form (cointegration model):
    - y_t and fin_t form vector Y_t; equation:
      - y_t = A_1 y_{t-1} + A_2 y_{t-2} + A_3 y_{t-3} + C·λ·y_{t-4} + ε_t
      - (paper expresses VAR with four lags and cointegrating vector λ; matrices A_0,...,A_3, C estimated by OLS; λ estimated in preliminary step)
  - Model classes estimated:
    - Two VARs include measures of real activity only (GDP).
    - Remaining models include three combinations of financial variables, estimated in log-differences where appropriate.
  - Estimation details:
    - Matrices A_0,...,A_3, C are estimated through OLS; cointegrating vector λ estimated in a preliminary step and imposed via 2-step procedure.
    - ε_t is a vector of error terms (dimensions range from 2×1 to 9×1) assumed normally distributed with covariance matrix Σ.

- Modeling choices and caveats
  - Authors avoid forcing cointegration among nearly integrated financial variables; acknowledge potential misspecification for stationary models but note level specifications are superconsistent in presence of cointegration.
  - Choice of lag length and transformations aim to capture longer-horizon predictive relationships (12–24 months) of financial predictors.

*Source: _wp09241 - References .............................................................................................................*

### 1.      A 2-country model of the U.S. and euro area log GDP (estimated unconstrained -

### 1.      A 2-country model of the U.S. and euro area log GDP (estimated unconstrained -

### Overview of benchmark models
- Model 0: the random walk for the GDP growth rate (benchmark against which other specifications are tested).
- BiVARL: 2-country BiVAR estimated in levels (unconstrained).
- BiVARC: 2-country BiVAR with cointegration.

### Alternative multivariate specifications described
- 2-country specification
  - BiVARL and BiVARC (U.S. and euro area log GDP in levels; BiVARC includes cointegration).
  - Together with Model 0 (random walk for GDP growth rate) these constitute the benchmark set for model comparison.

- 3-country specifications
  - TriVar model: 3-country model of the U.S., the euro area and the Rest of the World (ROW) log GDP in levels with cointegration.
  - FiVAR1 family: 3-country model for log GDP in levels with cointegration, plus stock market volatility and the slope.
    - FiVAR1D: model estimated in log-difference.
    - FiVAR1C: cointegrating VAR.
    - FiVAR1L: level VAR.
  - FiVAR2 family: 3-country model including log GDP in levels with cointegration, plus the stock market index (level) and the slope (level).
    - FiVAR2D: the log-difference model.
    - FiVAR2C: cointegrating VAR.
    - FiVAR2L: level VAR.
  - FiVAR3L: 3-country model for log GDP plus the dividend yield, the bond yield and the slope (level VAR).

### Purpose and structure
- Use of multiple model forms (levels, log-differences, and cointegrating VARs) to assess robustness of dynamics and cross-country linkages among U.S., euro area, and ROW GDP, and to incorporate financial variables (stock market volatility, stock market index, dividend yield, bond yield, slope) as extensions to the core GDP system.

*Source: _wp09241 - 1.      A 2-country model of the U.S. and euro area log GDP (estimated unconstrained -*

### 6.      A 3-country model for the log-difference of the GDP plus the stock market disequilibria

### 6.      A 3-country model for the log-difference of the GDP plus the stock market disequilibria and the change in the slope (FiVAR3D)

### III. CHARACTERIZING THE MODELS — IRFs and Pre-1985 and Post-1985 Evidence
- Model setup, identification, and estimation
  - Reduced-form VARs identified by Choleski ordering separating slow-moving (real) from fast-moving (financial) variables; ordering: euro area GDP first, Rest of the World (ROW) second, U.S. last.
  - VARs estimated between 1970Q1 and 2007Q4 with four lags.
  - Confidence bands reported at 68%.
  - Orthogonalized IRFs computed; error bands based on 500 Monte-Carlo draws from the posterior distributions of the VAR parameters and the covariance matrix.

- Main in-sample IRF findings
  - U.S. GDP adjusts faster to shocks and leads other areas (consistent with Giannone et al., 2008).
  - Spillovers:
    - Some U.S.–ROW spillovers.
    - U.S.–euro area spillovers appear one-way, coming from the U.S.
  - Financial variables’ marginal impact:
    - Including stock market volatility (sm) and slope of the yield curve (sl) suggests sm and sl affect GDP growth, but financial variables contribute only to a small extent to future GDP growth; significance is borderline in most cases and sample-dependent (pre/post-1985).
    - Literature benchmark: an 8% increase in the U.S. stock market index boosts U.S. and euro area activity by around 0.2% quarter-on-quarter during the first year after the shock (Dees et al., 2007).

- Sub-sample (Great Moderation) comparisons: 1970–1984 vs 1985–2007
  - Amplitude of IRFs decreased after 1985; linkages across variables changed.
  - Specific changes after 1985:
    - Response of euro area and ROW to U.S. GDP shocks flattened significantly at short horizons; long-term effects remain similar.
    - Synchronization between ROW and U.S. strengthened; not observed for the euro area.
    - U.S. started to respond positively to a GDP shock in ROW after 1985.
  - Linkages with slope of the yield curve:
    - Increased and more stable in latest 25 years.
    - In first sub-sample, IRFs were negative over short horizons and imprecise; post-1985 they have become positive and significant at all horizons in the U.S. and euro area.
    - ROW GDP response to U.S. slope: almost always insignificant until the 2-year horizon.
  - Role of U.S. stock market volatility post-1985:
    - A 1% positive volatility shock would have lowered GDP by about 1% annualized in the U.S. and the euro area within 8 quarters.
    - Effect for the Rest of the World is half a percentage point at the same horizon and is also significant.

### B. Linkages and the Role of Financial Shocks — Forecast Error Variance Decomposition and Counterfactuals
- Forecast error variance decomposition (for euro area GDP) computed at 1-, 4-, 8-, 12- and 24-quarter horizons from a model with the 3 GDPs plus U.S. and euro area slope and stock market index.
  - At long horizons the U.S. GDP and U.S. slope explain the majority of movements in euro area GDP.
  - At short horizons domestic variables matter more.
  - Euro area cycles have little effect on U.S. cycles.

- Counterfactual VAR experiments (restricting cross-country propagation)
  - Trivariate VARs estimated with restrictions so that each country, in turn, is the sole shock propagator; generate ‘counterfactual’ series assuming historical shocks to other countries’ GDP equations are zero.

- Key quantified counterfactual / explanatory results
  - Across the whole sample:
    - The United States would have explained about 15% of euro area GDP growth rates and 10% of ROW GDP growth.
    - Euro area and ROW explain only a very limited fraction of U.S. GDP growth.
  - Decadal/sub-sample variation:
    - On average, U.S.-originating shocks explained about 23% of euro area GDP growth between 1970 and 2000; this percentage rose to 36% since that year.
  - Including financial variables:
    - U.S. and ROW real shocks alone would have explained 12% and 8% of euro area GDP growth rates across the whole sample.
    - These percentages rise to 18% and 16% when financial shocks are also considered.

- Historical decomposition insights for euro area GDP
  - 1974 recession worsened by negative U.S. and ROW cycles.
  - Early 1980s growth hurt by restrictive monetary policy, especially in the U.S.
  - 1992 long contraction followed German reunification — not explained by international or financial factors.
  - Financial factors mattered in 2002 recession and the current episode (sample end).
  - U.S. stock market shocks did not play a major role in U.S. recessions until 2001; since 2001 they significantly affected activity.
  - The slope of the yield curve was particularly sizeable between 1979 and 1983, but marginal afterwards.

### IV. OUT-OF-SAMPLE EVIDENCE — Forecast Evaluation and Predictive Ability
- Forecast evaluation framework and statistics
  - Three main statistics: Root Mean Square Error (RMSE) for out-of-sample forecast errors between 1 and 12 quarters ahead; rolling RMSEs over 12-quarter moving windows; conditional predictive ability test of Giacomini and White (GW, 2006).
  - GW test re-estimates models on fixed-length rolling windows (minimum practical window length noted as 48 quarters for VAR estimation in practice).

- A. ‘Unconditional’ Forecast Evaluation (RMSE)
  - Table 3 summary results:
    - Except 1-step-ahead forecast, model 1 (VAR with two GDPs) has best performance across most horizons.
    - Performance of model 1 very close to the VAR including three GDPs and to the VAR with GDPs complemented by stock market volatility and slope.
    - Random walk model never a winning choice.
    - Adding other combinations of financial variables beyond slope and stock market volatility worsens forecasts at horizons shorter than one year; at longer horizons forecasts return near the global minimum.
  - Interpretation: Either long-horizon comovements are driven by implicit cointegration among GDPs unaffected by financial dynamics, or noisy financial information is smoothed out at long horizons.

- B. Conditional Forecast Evaluation (conditioning on more recent financial data)
  - Short-term forecaster setup:
    - Forecasts for period t+1 and beyond using financial data up to t+1, but most recent GDP known refers to period t.
    - Conditional forecasts: forecasts between t+1 and t+12 conditional on financial data as of t+1 and GDP as of t.
  - Table 4 findings:
    - Up to the 8th step ahead, forecasting performance deteriorates for all models with financial variables by between 15 and 35%.
    - Between the 2- and the 3-year ahead horizon, RMSE gets close to the overall minimum from unconditional exercise.
    - Panel B (GDP known only to t-1 while financials known to t and t+1): similar picture to panel A — optimal forecast need not use the most recent quarterly financial data.
  - Monthly financial data conditioning (Table 5):
    - Conditioning on monthly financial variables dated t+1/3, t+2/3, t+3/3 of a quarter generally worsens forecasting ability for models m4 to m6.
    - For model 3 (three GDPs plus stock market volatility and slope) unconditional and conditional forecast errors are similar at long horizons.
    - Some improvements observed for model 7 at h=8, 9, 10 (conditioning on first month and second month data) and at h=9 (conditioning on third month data).
  - Overall:
    - GDP-only models consistently beat the random walk over horizons for the euro area.
    - Models with 2 or 3 GDPs, including stock market volatility and slope, consistently improve forecasts; adding other financial variables tends to worsen predictions, but losses are small at long horizons (1.5 to 3 years ahead).
    - Conditional forecasts worsen significantly at short horizons in many cases.
    - The 2-GDP model performs best overall; 3-GDP model only slightly worse.

- C. Additional Explanatory Factors (non-price and firm-specific price info)
  - Alternative financial indicators tested: Fama and French factors (hml, smb), distance to default and its interquartile range, Consumer and Industrial (C&I) bank loans, consumer credit loans, real estate loans.
  - Stationarity / differencing notes:
    - Fama and French factors are stationary (yields).
    - Distance to default and interquartile range found stationary (ADF with 4 lags).
    - Three types of bank loans are I(1) and considered in first differences.
    - GDPs used in first logarithmic differences; all financial variables transformed to stationarity as needed.
  - Forecasting results:
    - These measures produce some improvement relative to models with price-related financial information but produce worse predictions relative to VARs with only 2 or 3 GDPs.

### V. CONDITIONAL EVALUATION — Rolling RMSEs and Giacomini–White Tests
- A. Rolling RMSEs (12-quarter windows)
  - Rolling RMSEs at 4- and 8-quarters-ahead horizons show time variation in predictive performance.
  - Between March 1996 and March 1999 and between 2002 and 2005 monthly information improved forecasting performance over the unconditional forecast.
  - Dramatic loss in forecasting ability when using quarterly information; substantial gain when using monthly releases, especially the second month of the quarter for 4-step-ahead, and the first month for 8-step-ahead.
  - VARs including slope, stock market volatility, and distance to default (which depends on equity volatilities) are particularly successful in these episodes.

- B. Giacomini–White (GW) conditional predictive ability test
  - GW test applied for horizons τ = 1, 4 and 8 quarters; the test examines whether past differences in forecast performance predict future differences.
  - Test computed using fixed-length rolling windows (60 quarters used in this analysis).
  - Test results:
    - First three columns in Table 6: GW test shows that differences in forecasting performance between financial models and random walk or GDP-only models can often be predicted (p-values lower than 0.05) for several models (FiVar1D, FiVar2D, model including Fama-French factors, C&I loans model).
    - Choice functions (Figures 10–12) indicate when a model with financial variables would have been preferred; number of quarters each model would have been chosen is tabulated.
  - Key conditional-choice takeaways:
    - Random walk preferred only in a significant fraction of quarters compared to model 1 (two GDPs) and less frequently to model 2 (three GDPs); random walk is by far surpassed by nearly all models with financial variables.
    - VAR with 2 GDPs, despite strong RMSE performance, would frequently be outperformed by the VAR that includes stock market volatility and yield curve slope beyond the 3 GDPs.
    - Models with financial variables performed best in 1999 and between 2001 and 2003 — periods when historical decomposition attributes large revisions to financial shocks.

### VI. CONCLUSIONS
- In-sample evidence: financial shocks matter for euro area real activity.
- Out-of-sample RMSE assessment: in line with Stock and Watson (2003), financial variables do not help forecasting real activity on average, even accounting for timeliness.
- Conditional predictive ability perspective: financial variables play a role in predicting euro area GDP in particular episodes (notably 1999 and 2001–2003), aligning with historical decomposition findings.
- Caveat and directions for future research:
  - Analysis conducted within linear models; financial variables may have nonlinear impacts on macroeconomic variables.
  - Nonlinear frameworks (e.g., Markov-Switching) can reveal forecasting gains from financial variables for turning points (e.g., Fornari and Lemke (2009)).
  - Potential larger forecasting power of financial variables during broadband negative movements in financial indicators is an important avenue for future research.

*Source: _wp09241 - 6.      A 3-country model for the log-difference of the GDP plus the stock market disequilibria and the change in the slope (FiVAR3D).*

### REFERENCES

### _wp09241 - REFERENCES

### References cited
- Ang, A., M. Piazzesi, and M. Wei, 2006, “What Does the Yield Curve Tell U.S. About GDP Growth?,” Journal of Econometrics, Vol. 131, pp. 359–403.
- Balke, N. S., 2000, “Credit and Economic Activity: Credit Regimes and Nonlinear Propagation of Shocks,” Review of Economics and Statistics, Vol. 82, pp. 344–49.
- Bayoumi, T., and A.J. Swiston, 2007, “Foreign Entanglements: Estimating the Source and Size of Spillovers Across Industrial Countries,” IMF Working Paper 07/182 (Washington: International Monetary Fund).
- Bernanke, B.S., and M. Gertler, 1989, “Agency Costs, Net Worth, and Business Fluctuations,” American Economic Review, Vol. 79, Issue 1, pp. 14–31.
- Bloom, N., 2008, “The Impact of Uncertainty Shocks: Firm Level Estimation and a 9/11 Simulation,” forthcoming Econometrica.
- Carlson, M.A., T. B. King, and K. F. Lewis, 2008, “Distress in the Financial Sector and Economic Activity,” Federal Reserve Board Working Paper 2008–43 (Washington: Federal Reserve Board).
- Dees S., F. di Mauro, M.H. Pesaran, and L.V. Smith, 2007, “Exploring the International Linkages of the Euro Area: A Global VAR Analysis,” Journal of Applied Econometrics, Vol. 22, pp. 1–38.
- Dees, S., and I. Vansteenkiste, 2007, “The Transmission of U.S. Cyclical Developments to the Rest of the World,” ECB Working Paper 798 (Frankfurt: European Central Bank).
- Diebold, F.X., and R.S. Mariano, 1995, “Comparing Predictive Accuracy,” Journal of Business and Economic Statistics, Vol. 13, pp. 253–63.
- Fagan, G., J. Henry, and R. Mestre, 2001, “An Area-wide Model (AWM) for the euro area,” ECB Working Paper 42 (Frankfurt: European Central Bank).
- Fama, E.F., and K.R. French, 1993, “Common Risk Factors in the Returns of Stocks and Bonds,” Journal of Financial Economics, Vol. 33, pp. 3–56.
- Favero, C., and F. Giavazzi, 2008, “Should the Euro Area Be Run as a Closed Economy?,” American Economic Review, Vol. 98, pp. 138–45.
- Fornari, F., and A. Mele, 2009, “Financial Volatility and Economic Activity,” London School of Economics, mimeo (London: London School of Economics and Political Sciences).
- Fornari, F., and W. Lemke, 2009, “A Simple Model for Predicting Economic Activity in Main Economic Areas”, ECB mimeo (Frankfurt: European Central Bank).
- Forni, M., M. Lippi, M. Hallin, and L. Reichlin, 2003, “Do Financial Variables Help Forecasting Inflation and Real Activity in the Euro Area?,” Journal of Monetary Economics, Vol. 50, pp. 1243–55.
- Giacomini, R., and H. White, 2006, “Tests of Conditional Predictive Ability”, Econometrica, Vol. 74, pp. 1545–78.
- Giannone, D., and L. Reichlin, 2004, “Euro area and U.S. recessions: 1970–2003,” in L. Reichlin (editor), The Euro Area Business Cycle: Stylized Facts and Measurement Issues, pp. 83–93 (London: Center for Economic Policy Research).
- Giannone, D., L. Reichlin, and D. Small, 2005, “Nowcasting GDP and Inflation: The Real Time Informational Content of Macroeconomic Data Releases,” CEPR Discussion Paper 5178 (London: Center for Economic Policy Research).
- Giannone, D., M. Lenza and L. Reichlin, 2009, “Business Cycles in the Euro Area,” in A. Alesina and F. Giavazzi (editors), Europe and the Euro, Chicago: University of Chicago Press forthcoming.
- Goodhart, C., P. Sunirand, and D. Tsomocos, 2006, “A Time Series Analysis of Financial Fragility in the UK Banking System,” Annals of Finance, Vol. 1, pp. 197–224.
- IMF, 2008, “Financial Stress and Economic Downturns,” in World Economic Outlook, October 2008: A survey by the Staff of the International Monetary Fund, World Economic and Financial Surveys (Washington).
- Liew, J., and M. Vassalou, 2000, “Can Book-to-Market Size and Momentum Be Risk Factors that Predict Economic Growth?,” Journal of Financial Economics, Vol. 57, pp. 221–45.
- Stock, J.H., and M.W. Watson, 2003, “Forecasting Output and Inflation: The Role of Asset Prices,” Journal of Economic Literature, Vol. 41, pp. 788–829.
- Swiston, A., 2008, “A U.S. Financial Condition Index: Putting Credit where Credit Needs is Due”, IMF Working Paper 08/61 (Washington: International Monetary Fund).

### Table 1 — Variance Decomposition of GDP in the Three Areas (selected entries)
- VAR model includes 7 variables in order: euro area GDP, Row GDP, U.S. GDP, euro area slope and stock market, U.S. slope and stock market.
- Euro area GDP attribution (percent of total variance) at horizons:
  - horizon 1: Euro area GDP 100.0, ROW GDP 0.0, U.S. GDP 0.0, euro area slope 0.00, euro area stock market 0.0, U.S. slope 0.0
  - horizon 4: Euro area GDP 75.14, ROW GDP 0.55, U.S. GDP 11.66, euro area slope 0.23, euro area stock market 11.05, U.S. slope 0.35, U.S. stock market 1.00
  - horizon 8: Euro area GDP 47.36, ROW GDP 2.11, U.S. GDP 25.19, euro area slope 5.73, euro area stock market 17.66, U.S. slope 1.19, U.S. stock market 0.76
  - horizon 12: Euro area GDP 31.42, ROW GDP 2.21, U.S. GDP 37.02, euro area slope 9.77, euro area stock market 12.72, U.S. slope 5.78, U.S. stock market 1.10
  - horizon 24: Euro area GDP 13.39, ROW GDP 1.16, U.S. GDP 45.82, euro area slope 10.12, euro area stock market 5.52, U.S. slope 20.29, U.S. stock market 3.68
- ROW GDP attribution (selected horizons):
  - horizon 1: ROW GDP 5.63, U.S. GDP 94.38
  - horizon 4: ROW GDP 3.65, U.S. GDP 79.91, euro area stock market 12.83
  - horizon 24: ROW GDP 3.80, U.S. GDP 30.82, euro area GDP 33.25, U.S. slope 13.62, U.S. stock market 12.21
- U.S. GDP attribution (selected horizons):
  - horizon 1: U.S. GDP 89.47, ROW GDP 8.34, euro area GDP 2.19
  - horizon 4: U.S. GDP 80.88, ROW GDP 5.57, euro area GDP 3.48, euro area stock market 1.97
  - horizon 24: U.S. GDP 50.11, ROW GDP 2.81, euro area GDP 0.79, euro area stock market 9.25, U.S. slope 22.94, U.S. stock market 11.92

### Table 2 — R^2 of Regression of Δlog GDP on its Counterfactual (selected values)
- Note: VARs estimated in levels without imposed cointegration between 1970q1 and 2007q4, with four lags. Regression Δlog GDP = α + β Δlog GDP_hat where GDP_hat are counterfactuals from VAR with only given region shocks.
- PANEL A: full sample counterfactual R2 (selected entries):
  - U.S. column: U.S. 0.9, euro area 0.14, R.o.W 0.21
  - euro area column: U.S. 0.04, euro area 0.8, row 0.14
  - row column: U.S. 0.01, euro area 0.1, row 0.61
- PANEL B: across decades (selected entries)
  - U.S. in 1970s: 0.7 0.23 0.27
  - U.S. in 1980s: 0.81 0.21 0.42
  - U.S. in 1990s: 0.87 0.25 0.46
  - U.S. in 2000s: 0.89 0.36 0.29
  - euro area 1970s: 0.03 0.45 0.01
  - euro area 1980s: 0 0.86 0
  - euro area 1990s: 0.23 0.89 0.6
  - euro area 2000s: 0.18 0.95 0.31
  - row 1970s: 0 0.1 0.55
  - row 1980s: 0 0.21 0.22
  - row 1990s: 0.23 0.12 0.51
  - row 2000s: 0.08 0.25 0.8

### Table 3 — Unconditional Out-of-Sample RMSE (selected model minima and comparisons)
- Panel A: RMSE 1 to 12 quarters for many models; selected entries:
  - RW (Random walk) horizon 1..12: 0.45 0.44 0.45 0.46 0.46 0.46 0.46 0.47 0.47 0.47 0.47 0.47
  - BiVARC 2 gdp coint. horizon 1..12: 0.43 0.41 0.41 0.40 0.40 0.40 0.40 0.40 0.41 0.42 0.42 0.43
  - TriVARC 3 gdp coint. horizon 1..12: 0.42 0.42 0.43 0.42 0.41 0.42 0.43 0.44 0.44 0.45 0.45 0.45
  - FIVAR1C var slope cointegrated horizon 1..12: 0.49 0.43 0.48 0.47 0.45 0.44 0.45 0.45 0.43 0.44 0.44 0.44
  - Panel B examples: MDS median dist, slope horizon 1..12: 0.50 0.44 0.49 0.54 0.50 0.51 0.52 0.50 0.47 0.46 0.46 0.45; BL Bank loans horizon 1..12: 0.54 0.48 0.52 0.59 0.58 0.61 0.61 0.64 0.60 0.57 0.53 0.49
- Panel C summary lines:
  - minimum all: 0.42 0.41 0.41 0.40 0.40 0.40 0.40 0.41 0.42 0.42 0.43 0.43
  - minimum fin: 0.47 0.43 0.48 0.47 0.45 0.44 0.45 0.45 0.43 0.44 0.44 0.44
  - relative gap: 0.05 0.02 0.07 0.07 0.05 0.04 0.05 0.04 0.01 0.02 0.02 0.01
  - % gap: 12.43 4.34 16.66 16.86 11.88 11.18 12.75 8.87 2.48 3.73 3.67 2.32
- Note: RMSE obtained estimating models on expanding windows starting 1970Q1 to 1986Q4; shaded areas identify model classes. ‘MDS’ and ‘MDIS’ include slope and distance-to-default measures; ‘C&I’ are Commercial and Industrial Loans; ‘BL’ include Commercial and Industrial Loans, Real Estate Loans and Consumer Credit Loans.

### Table 4 — Out-of-Sample RMSE (conditional on financial variables information timing)
- Panel A: estimation up to t, forecasts conditional on time t+1 information — selected minima:
  - minimum: 0.49 0.47 0.45 0.53 0.53 0.51 0.50 0.49 0.47 0.44 0.44 0.44
  - gain/loss over unco: 0.07 0.05 0.05 0.13 0.13 0.11 0.10 0.07 0.05 0.02 0.01 0.00
  - % gap: 17.1 13.2 11.6 32.2 33.1 28.0 25.4 18.0 12.9 4.9 1.6 1.1
- Panel B: estimation up to t-1, forecasts conditional on time t and t+1 information — selected minima:
  - minimum: 0.50 0.48 0.50 0.54 0.55 0.51 0.51 0.50 0.44 0.44 0.43 0.44
  - gain/loss over unco: 0.07 0.07 0.09 0.14 0.15 0.11 0.11 0.09 0.03 0.02 0.00 0.00
  - % gap: 17.6 17.4 23.0 34.2 37.5 27.9 27.4 21.5 6.5 5.3 0.6 1.1
- Selected model example values:
  - FIVAR1C var slope coint. Panel A horizon 1..12: 0.51 0.49 0.54 0.61 0.70 0.68 0.63 0.64 0.57 0.60 0.60 0.57
  - C&I Loans Panel A horizon 1..12: 0.49 0.47 0.46 0.53 0.53 0.53 0.53 0.54 0.51 0.48 0.47 0.46

### Table 5 — Out-of-Sample RMSE with monthly financial information (three timing panels)
- Panel A: estimation up to t, forecasts conditional on month t+1/3 information — minimum: 0.50 0.46 0.47 0.47 0.45 0.42 0.43 0.45 0.42 0.43 0.44 0.44
  - gain/loss over unco: 0.08 0.05 0.06 0.07 0.05 0.02 0.03 0.03 0.00 0.01 0.01 0.01
  - % gap: 18.2 11.2 14.8 17.3 12.5 5.6 8.2 8.0 1.2 2.4 3.0 2.3
- Panel B: estimation up to t, forecasts conditional on month t+2/3 information — minimum: 0.47 0.46 0.46 0.48 0.45 0.42 0.43 0.44 0.42 0.43 0.44 0.44
  - gain/loss over cond Q: 0.05 0.05 0.05 0.08 0.05 0.02 0.03 0.03 0.01 0.01 0.01 0.01
  - % gap: 11.9 12.5 12.7 19.5 13.7 4.7 8.0 7.0 1.7 2.8 3.1 1.7
- Panel C: estimation up to t, forecasts conditional on month t+3/3 information — minimum: 0.47 0.45 0.44 0.48 0.46 0.42 0.44 0.44 0.43 0.43 0.44 0.43
  - gain/loss over cond Q: 0.05 0.04 0.03 0.08 0.06 0.02 0.04 0.03 0.01 0.01 0.01 0.00
  - % gap: 12.6 10.0 8.1 20.4 15.2 5.3 8.8 7.9 2.7 1.9 2.6 0.5
- Model examples (Panel A): FIVAR1C 0.52 0.50 0.47 0.47 0.45 0.42 0.43 0.45 0.42 0.43 0.44 0.44; FIVAR2D 0.51 0.46 0.47 0.57 0.56 0.54 0.51 0.51 0.47 0.46 0.47 0.47

### Table 6 — Conditional Choice Between Models at Selected Horizons (methodology and outcomes)
- First three columns report Giacomini and White (2006) conditional predictive ability test p-values (chi-square with 2 degrees of freedom). For the conditional test, values larger than 0.05 indicate the model in the first row would not be surpassed by the model in the first column.
  - Example p-values (all-sample conditional test): BiVarC vs others 0.34; BiVarL 0.11 0.53; TriVarC 0.05 0.06; FiVar1D 0.00 0.00 0.00 (rows correspond to various models listed).
- Other columns (h = 4, h = 8, h = 12) show counts of times that RW, BiVarC, and TriVarC would have been chosen over the full set of models at those horizons per Giacomini and White’s methodology. Selected counts:
  - Cases (total comparisons per model): 3838, 36, 3030, 28, 24, 24, 24
  - Example choices at h=4: RWBiVarC vs many models — numbers include 20, 9, 1, 7, 6, 1114, 3, 9, etc.
  - Example choices at h=8 and h=12: large counts for some models (e.g., 2626, 2223, 1722) and smaller counts for others.
- Note: Low values below half the corresponding cell in the last row indicate models with financial variables are preferred to the random walk or to VARs with 2 or 3 GDPs only. Definitions: ‘MDS’ and ‘MDIS’ include slope and distance-to-default measures (Carlson et al., 2008), ‘C&I’ are U.S. Commercial and Industrial Loans, ‘BL’ include Commercial and Industrial Loans, Real Estate Loans and Consumer Credit Loans.

*Italic: Content extracted from _wp09241 - REFERENCES (source PDF: _wp09241 - REFERENCES).*

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