## Financial Conditions Indexes for the United States and Euro Area

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### Introduction
- Financial conditions indexes (FCIs) for the United States and the euro area are developed using a wide range of financial indicators and a dynamic factor model (DFM).
- Key advantages of the DFM: can estimate FCIs when some indicators are missing due to publication lags, allowing timely use of all available information.
- Sample period for the FCIs begins in 1994.

### Methodology
- Each standardized indicator y_t is decomposed into a common component and an idiosyncratic component:
  - y_t = φ_t + ε_t; ε_t ~ N(0, Ψ)
  - φ_t = Λ F_t and Ψ is assumed diagonal (relaxed for backdating).
- The common factor F_t (the FCI) follows an autoregressive process:
  - F_t = Σ_{i=1}^p ρ_i F_{t−i} + η_t; η_t ~ N(0, I_q)
- Lag length p selected using the Swartz-Bayesian information criteria (SBC).
- Quarterly series are linearly interpolated; daily series converted to monthly averages; non-stationary series transformed (quarterly log differences where appropriate). Indicators not transformed remain as-is.

### Data Description and Results
- Indicators drawn from spreads, prices, quantities, and survey (SLOS) categories; most series are monthly, some daily or quarterly.
- Indicators not available for the full sample (e.g., some euro-area survey data) are backdated using the DFM prior to estimation.
- Factor loadings (Λ) reflect whether higher indicator values imply tightening (positive loading) or easing (negative loading).
  - Examples of high positive loadings: SLOS series (positive = tightening); BAA/10-year government bond spread (United States); high-yield corporate/10-year government bond spread (euro area).
  - Prices categories generally have negative loadings (prices tend to rise when financial conditions ease).
- Estimated FCI dynamics:
  - Both FCIs show easing in the years preceding the global financial crisis.
  - Financial conditions tightened significantly just prior to the crisis, peaking around the beginning of 2009.
  - According to the FCIs, financial conditions only began to ease around the beginning of 2010 despite extremely accommodative monetary policy settings in both economies.

### Forecasting Performance
- Baseline forecasting model: quarterly closed economy VAR with output gap, headline inflation, and a real short-term interest rate.
- Real-time out-of-sample forecast evaluation: forecasts from 2004:Q1 onward; FCI estimated using data available at the beginning of the third month of each quarter; forecasts evaluated two- and four-quarters ahead using RMSEs relative to an AR benchmark.
- Key comparative RMSE results (RMSEs Relative to AR):
  - United States:
    - Baseline VAR: 1.23 (2Qtrs Ahead), 1.05 (4 Qtrs Ahead)
    - Baseline VAR augmented with FCI: 0.84 (2Qtrs Ahead), 0.79 (4 Qtrs Ahead)
    - AR (RMSE): 1.09 (2Qtrs Ahead), 2.01 (4 Qtrs Ahead)
  - Euro Area:
    - Baseline VAR: 1.07 (2Qtrs Ahead), 1.02 (4 Qtrs Ahead)
    - Baseline VAR augmented with FCI: 0.89 (2Qtrs Ahead), 0.85 (4 Qtrs Ahead)
    - AR (RMSE): 1.19 (2Qtrs Ahead), 2.14 (4 Qtrs Ahead)
- Results summary:
  - For the United States, the VAR augmented with the FCI outperforms the AR and all other VAR forecasts considered.
  - For the euro area, the VAR augmented with the FCI is at least as accurate as almost all other models; the VAR augmented with SLOS indicators is an exception in some comparisons.

### Real-Time Properties
- Revisions to FCIs are generally small relative to overall variance across the sample.
- Figure 2 analysis: monthly real-time FCI estimates (made each month of the out-of-sample period) are compared with estimates using data up to March 2011.
- Few 'false signals' where an initial estimate of easing/tightening is later reversed; exception: the period around 2008 in the euro area (real-time estimates indicated easing that were later estimated as tightening).
- Practical real-time implementation note: in the forecasting experiment, the most recent vintage of data is used to simulate data availability each quarter (real-time data vintages not available for the experiment). Real-time output gaps and short-term real interest rates are truncated from the most recent GPM estimates.

### Conclusion
- FCIs estimated with a DFM using a broad set of financial indicators provide useful summary measures of financial conditions for the United States and the euro area.
- Augmenting simple baseline closed economy VARs with the estimated FCIs improves short-horizon forecasting performance relative to a range of alternative specifications.
- The FCIs display generally good revision properties over the sample period and offer timely information on the evolution of economic activity in real time.

*Source: IMF Working Paper WP/11/93, "Financial Conditions Indexes for the United States and Euro Area", Troy Matheson, April 2011.*

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