## _wp08278

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---

### Introduction and Objectives
- Study structure:
  - Part one: small quarterly projection model of the US economy to illustrate model use for understanding and forecasting.
  - Part two: expands the US model to include financial-real linkages.
- Longer-term goals:
  - Develop a Small Quarterly Global Projection Model (GPM) integrating a series of small country models into a single global model.
  - Analyze differences between models with and without financial-real linkages.
  - Assess relative importance of real cross-border linkages and financial cross-border linkages in producing international business cycle commonalities.

### Sample, Narrative, and Background
- Sample periods for estimation:
  - 1994Q1 to 2008Q1 (the long period)
  - 2001Q1 to 2007Q4 (the short period)
- Rationale for samples:
  - Simplify estimation by ignoring longer-run structural changes; availability constraints for extended/global models; use priors to address weak identification in short samples; financial variables stronger in recent decade.
- Key narrative developments (1994–2007):
  - Fed raised rates post-1994 recovery; 1996–1999 rapid growth, low unemployment; apparent NAIRU decline from the 6% range to 5% or lower.
  - Late 1990s: oil price increases and inflation concerns; Fed raised rates through 1999–2000.
  - 2001 onward: GDP slowdown, sharp inflation decline by mid-2001; 9/11 exacerbated weak demand; Fed cut fed funds rate to 1% in mid-2003 and held low rates until deflation risk subsided.
  - From mid-2004 Fed began removing stimulus; "interest rate conundrum": long-term real rates remained low despite increases in short-term rates.
  - Low policy rates supported residential construction and consumer spending; housing price boom important.
  - Unemployment: declined from about 6% in 2003 to about 4 1/2%.

### Benchmark Model Specification (without financial-real linkages)
- Observable variables (4):
  - Real GDP (Y defined as 100 times the log of real GDP).
  - Unemployment rate (U and the NAIRU, ØU).
  - CPI inflation (quarterly rate  defined as 400 times first difference of log CPI; year-on-year 4 as 100 times difference of log CPI from four quarters earlier).
  - Federal funds rate.
- Key definitions and identities:
  - Output gap: y = Y - ØY.
  - Unemployment gap: u = U - ØU.
  - Real interest rate: rr_t = rs_t - _{t+1} (equation 5).
  - Real interest rate gap: rrgap_t = rr_t - rr_t (equation 6).
  - Equilibrium real interest rate: rr_t =  rr_ss + (1-) rr_{t-1} + "rr_t (equation 7).
- Selected behavioral equations (as specified):
  - Output gap: y_t = 1 y_{t-1} + 2 y_{t+1} - 3 rrgap_{t-1} + "y_t (equation 8).
  - Inflation: _t = 1 4_{t+4} + (1-1) 4_{t-1} + 2 y_{t-1} - "_t (equation 9).
  - Policy (Taylor-type): rs_t = (1-1)  rr_t + 4_{t+3} + 2(4_{t+3}-_{tar}) + 4 y_t + 1 rs_{t-1} + "rs_t (equation 10).
  - Okun’s law (unemployment gap): u_t = 1 u_{t-1} + 2 y_t + "u_t (equation 11).
- Latent stochastic processes:
  - Potential output level: ØY_t = ØY_{t-1} + gY_t/4 + "Y_t (equation 1).
  - Growth of potential GDP: gY_t =  gYss + (1-) gY_{t-1} + "gY_t (equation 2).
  - NAIRU level and growth follow analogous specifications (equations 3 and 4).
- Model features:
  - More stochastic shocks than observables; permanent level and persistent growth shocks to potential output and NAIRU allowed.
  - Cross-equation dynamics include forward-looking and backward-looking elements.

### Bayesian Estimation Approach and Diagnostics
- Bayesian benefits:
  - Combines priors and data; tightness of priors determines relative weight.
  - Useful for small-sample macro contexts and simultaneity.
  - Produces plausible dynamics and sensible forecasting properties; integrates judgmental near-term forecasts.
- Evaluation criteria:
  - Posterior coefficients relative to priors.
  - Impulse response functions compatibility with researcher views.
  - Relative log data density and RMSEs for model comparison.
- Posterior diagnostics (base model 1994–2007):
  - Output gap equation: more weight on lagged and lead output gap, less on real interest rate vs priors.
  - Inflation equation: posterior places more weight on forward-looking element, less on backward-looking element vs priors.
  - Posterior SDs: unemployment and interest rate shocks smaller than priors; inflation and two of three output equation shocks substantially higher than priors.
- Limitation noted:
  - Model had difficulty generating a downturn absent a breakout of inflation, motivating addition of a financial variable.

### Extended Model with Financial-Real Linkages (BLT)
- BLT definition:
  - Unweighted average of net responses to four Fed Senior Loan Officer Opinion Survey questions (C&I loans to large/middle-market firms; C&I loans to small firms; commercial real estate loans; mortgage loans to purchase homes), each weighted by one quarter.
  - Net tightening = percent “tightened considerably” + percent “tightened somewhat” minus percent “eased somewhat” + percent “eased considerably”.
  - Noted bias: net tightening responses outweigh net easing on average by about 5% over the sample.
- BLT dynamics:
  - BLT_t = BLT_{t-1} -  y_{t+4} + "BLT_t (equation 12).
  - BLT equilibrium: BLT = BLT_{t-1} + "BLT_t (equation 13).
  - Banks’ lending conditions respond to expected economic conditions 4 quarters ahead.
- BLT enters output gap as a distributed lag:
  - y_t = 1 y_{t-1} + 2 y_{t+1} - 3 rrgap_{t-1} -  _t + "y_t (equation 14).
  - _t weighted distributed lag of "BLT innovations (equation 15) with coefficients for lags t-1 through t-9:
    - 0:04, 0:08, 0:12, 0:16, 0:20, 0:16, 0:12, 0:08, 0:04.
- Interpretation and modeling issues:
  - BLT may capture exogenous tightening/loosening in bank lending affecting access to funds and spending.
  - BLT may function as a leading indicator reflecting lending officers’ views.
  - Considerations: asymmetry of BLT shocks; threshold tests (zeroing BLT values with absolute value less than 15 reduced ); BLT may not capture all financial-real linkages—other proxies (risky spreads, asset prices) are candidates.

### Cross-Correlations of Disturbances
- Two introduced cross-correlations:
  - Positive correlation between "gY (shock to potential output growth) and "y (output gap shock): persistent positive potential growth shock raises expected permanent income and spending, increasing output gap before potential rises.
  - Positive correlation between "Y (shock to level of potential output) and " (inflation shock with negative sign in equation): positive supply shock to potential output puts downward pressure on costs/prices, producing a positive correlation between these disturbances.
- Purpose: mimic DSGE IRFs and embed DSGE insights into a smaller semi-structural model.

### Results from the Extended Model (with BLT)
- Structural changes with BLT:
  - Output gap equation: substantial reduction in weights on lagged and lead output gap terms; slight increase in weight on real interest rate.
  - Unemployment gap equation: significant increase in coefficient on lagged dependent variable.
  - Standard deviations of structural shocks changed only modestly with BLT inclusion.
- Impulse response summaries:
  - Downward inflation shock → decline in nominal and real policy interest rate → increase in output gap and decline in unemployment gap; effect amplified by easing of bank lending terms.
  - Positive output gap shock → increase in output gap, decline in unemployment gap, increase in inflation and policy rate.
  - Policy interest rate shock → reduces output, increases unemployment, downward pressure on inflation.
  - BLT tightening shock → sizable hump-shaped decline in output, rise in unemployment, decline in inflation and policy rate.
  - Growth rate of potential output shock → larger effects than level shock; growth shock increases demand and output gap via cross-correlation, raising inflation and policy rates.
  - Equilibrium real interest rate shock → changes nominal interest rate with very little effect on other variables.
- Forecasting and fit improvements:
  - Adding BLT markedly improves model functioning.
  - RMSEs: sharp decline in RMSE on the output gap at all horizons and on 4-quarter inflation at 4- and 8-quarter ahead forecasts when moving from base model to BLT model.
  - Some deterioration in short-term NAIRU forecasts with BLT inclusion.
- Contribution of shocks (variance decompositions):
  - Innovations in BLT account for about 70 percent of the variation in the output and unemployment gaps.
  - BLT accounts for about 40 percent of the variation in year-on-year GDP growth and inflation.
  - Shocks to the fed funds rate make a very small contribution to variability in the fed funds rate, indicating most variation resulted from Fed reactions to information rather than exogenous policy shocks.
- In-sample tracking:
  - Model with BLT tracks unemployment gap and output gap moderately well; more difficulty tracking output growth and inflation.
  - Both models tend to have interest rates rising in 2003 more than a year before the Fed raised rates; model lacks mechanism to capture concern about price deflation and the zero lower bound.

### Robustness and Extensions
- Short vs long sample (2001–2007 short sample vs 1994–2007 long sample):
  - Output gap: lagged gap coefficient appreciably larger in short sample.
  - Larger coefficient on financial variable in short sample → financial variable played stronger role in influencing output gap in the 2000s.
  - RMSEs: 4-, 8-, and 12-quarter ahead forecasts for one-quarter and four-quarter output growth much lower for the shorter sample.
- Core CPI vs headline CPI:
  - Replacing headline with core CPI:
    - Posterior SD of structural shock in inflation equation fell sharply: from about 1.35 to 0.4 in the base model and from about 1.25 to 0.4 in the BLT model.
    - Inflation equation became more backward looking with core inflation.
    - Policy reaction to core inflation increases stronger than to headline inflation increases.
- Suggested further development priorities:
  - Include other financial variables (risky spreads, asset prices).
  - Develop two-country and multicountry versions to assess spillovers via financial linkages.
  - Explore threshold/asymmetric specifications, satellite models, and regime-switching features.

### Key Empirical Findings and Select Statistics
- NAIRU path (1994–2007): decline from just above 6% to just above 4 1/4%, then increase to above 4 1/2%.
- BLT construction and properties:
  - Unweighted average of four Senior Loan Officer survey net tightening responses (each weighted by 1/4).
  - Net tightening responses biased about 5% toward tightening on average.
  - BLT distributed-lag coefficients for _t (lags t-1 through t-9): 0:04, 0:08, 0:12, 0:16, 0:20, 0:16, 0:12, 0:08, 0:04.
- BLT importance (variance shares):
  - About 70 percent of variation in output and unemployment gaps attributable to BLT innovations.
  - About 40 percent of variation in year-on-year GDP growth and inflation attributable to BLT innovations.
- Posterior modes and selected SDs (Base Case Model, Table 1 & Table 2 selected entries):
  - us1 beta: Posterior mode 0.7453, s.d. 0.0581
  - gamm (us2): Posterior mode 0.1711, s.d. 0.0310
  - beta (us3): Posterior mode 0.3339, s.d. 0.1931
  - norm (gYss us): Posterior mode 2.6016, s.d. 0.2360
  - norm (rr us): Posterior mode 1.8221, s.d. 0.1729
  - "u_us": Posterior mode 0.0943, s.d. 0.0146
  - "y_us": Posterior mode 0.3567, s.d. 0.0585
  - "gY_us": Posterior mode 0.3486, s.d. 0.1326
  - "_us": Posterior mode 1.3598, s.d. 0.1440
  - "rs_us": Posterior mode 0.4643, s.d. 0.0605
- Selected BLT model posterior modes and SDs (Tables 4–6, selected entries):
  - us1 beta: Posterior mode 0.8710, s.d. 0.0484
  - us3 beta: Posterior mode 0.5175, s.d. 0.2724
  - gYss us: Posterior mode 2.6227, s.d. 0.2323
  - "y_us": Posterior mode 0.3490, s.d. 0.0416
  - "Y_us": Posterior mode 0.0230, s.d. 0.0094
  - "gY_us": Posterior mode 0.3319, s.d. 0.0856
  - "_us": Posterior mode 1.2353, s.d. 0.1189
  - "rs_us": Posterior mode 0.4712, s.d. 0.0556
  - "BLT_us" posterior modes: 0.8082 (s.d. 0.3342) and 0.0928 (s.d. 0.0384)
  - Correlation "y_us ; gY_us": Posterior mode 0.1944, s.d. 0.0928
  - Correlation "Y_us ; _us": Posterior mode 0.0422, s.d. 0.0187
- RMSE comparisons (selected horizons):
  - Base case (Table 3) y_us: 1 Q Ahead 0.63, 4 Q Ahead 0.91, 8 Q Ahead 1.3, 12 Q Ahead 1.4
  - BLT case (Table 7) y_us: 1 Q Ahead 0.43, 4 Q Ahead 0.58, 8 Q Ahead 0.82, 12 Q Ahead 0.93
  - Base case 4_us: 1 Q Ahead 0.36, 4 Q Ahead 1.0, 8 Q Ahead 0.89
  - BLT case 4_us: 1 Q Ahead 0.34, 4 Q Ahead 0.83, 8 Q Ahead 0.76
- Inflation shock posterior SD changes when using core CPI:
  - Base model: from about 1.35 to 0.4.
  - BLT model: from about 1.25 to 0.4.

### Policy and Modeling Implications
- Inclusion of a financial variable (BLT) substantially improves model dynamics and forecasting for output and unemployment, underscoring importance of financial-real linkages for explaining recent macro behavior.
- Financial-real linkages can operate as:
  - Direct exogenous supply-side constraints on credit (affect lending supply), and
  - Leading indicators of future real activity via lending officers’ expectations.
- Fed behavior interpretation:
  - Most variation in the fed funds rate reflects Fed reactions to information rather than exogenous policy shocks in model results.
- Recommended further work:
  - Extend model to include additional financial variables (risky spreads, asset prices).
  - Build two-country and multicountry versions to assess spillovers via financial linkages.
  - Explore threshold/asymmetric specifications, satellite models, and regime-switching features.

*Source: _wp08278 - References (IMF working paper content as provided in the supplied document).*

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

### _wp08278 - References..............................................................................................................

### Appendix and Figures/Tables Inventory
- Appendix: Data Definitions (page 30)
- Figure No. 1. US Historical Data (page 31)
- Table No. 1 Results from Posterior Maximization (parameters) Base Code Model (page 32)
- Table No. 2 Results from Posterior Maximization (standard deviation of structural Shocks) Base Case Model (page 33)
- Figure No. 2 Unemployment and Model-Consistent NAIRU (page 34)
- Figure No. 3. GDP and Model-Consistent Potential GDP (page 35)
- Table No. 3. Base Case Root Mean Squared Errors (page 36)
- Figure No. 4 (page 37)
- Table No. 4. Results from Posterior Maximization (parameters) BLT Model (page 38)
- Table No. 5. Results from Posterior Maximization (standard deviation of structural Shocks) BLT Model (page 39)
- Table No. 6. Results from posterior parameters (correlation of structural shocks) BLT Model (page 40)
- Figure No. 5 IRF Supply Shock (page 41)
- Figure No. 6 IRF Demand Shock (page 42)
- Figure No. 7 IRF Policy Rate Shock (page 43)
- Figure No. 8 IRF BLT Shock (page 44)
- Figure No. 9. IRF Equilibrium GDP Growth Shock (page 45)
- Figure No. 10 IRF Equilibrium GDP Level Shock (page 46)
- Table No. 7. BLT Root Mean Squared Errors (page 47)
- Table No. 8. Variance Decompositions (page 48)
- Figure No. 11. Y-O-Y GDP Growth Rate Dynamic Forecast (Base Case Model) (page 49)
- Figure No. 12. Y-O-Y GDP Growth Rate Dynamic Forecast (BLT Model) (page 49)
- Figure No. 13. Q-O-Q GDP Growth Rate Dynamic Forecast (Base Case Model) (page 50)
- Figure No. 14. Q_O_Q GDP Growth Rate Dynamic Forecast (BLT Model) (page 50)
- Figure No. 15. Inflation Dynamic Forecast (Base Case Model) (page 51)
- Figure No. 16. Inflation Dynamic Forecast (BLT Model) (page 51)
- Figure No. 17. Interest Rate Dynamic Forecast (Base Case Model) (page 52)
- Figure No. 18. Interest Rate Dynamic Forecast (BLT Model) (page 52)
- Figure No. 19. Unemployment Rate Dynamic Forecast (Base Case Model) (page 53)
- Figure No. 20. Unemployment Rate Dynamic Forecast (BLT Model) (page 53)
- Figure No. 21. Output GAP Dynamic Forecast (Base Case Model) (page 54)
- Figure No. 22. Output GAP Dynamic Forecast (BLT Model) (page 54)

### I  Introduction — A. Objectives
- The study has two parts:
  - Part one: sets out a small quarterly projection model of the US economy to illustrate how such models can be used to understand economic developments and to forecast future developments.
  - Part two: expands the US model to include financial-real linkages that have become prominent in recent years.
- Purposes and longer-term goals:
  - Develop a Small Quarterly Global Projection Model (GPM) integrating a series of small country models into a single global model.
  - Analyze differences between models with and without financial-real linkages.
  - Assess the relative importance of real cross-border linkages and financial cross-border linkages in producing international business cycle commonalities.

### I  Introduction — B. The US Economy Over the Sample Period
- Sample periods for estimation:
  - 1994Q1 to 2008Q1 (the long period)
  - 2001Q1 to 2007Q4 (the short period)
- Reasons for choosing these sample periods:
  - Simplify estimation by ignoring changes in underlying inflation objectives and other structural changes over longer samples.
  - Some variables in extended/global models are unavailable before these periods.
  - Demonstrate the use of priors to address weak identification with short samples.
  - Financial variables appear considerably stronger in the recent decade, motivating the shorter period for models with financial-real linkages.
- Narrative of key developments (1990ñ2007, Figure 1 reference):
  - 1994: After recovery from the 1990ñ1991 recession and rising inflation concerns, the Fed raised its policy interest rate toward a more neutral, less stimulative level.
  - 1996–1999: Rapid growth, unemployment fell to multi-decade lows; concerns about excess demand and inflationary pressures.
    - Alternative view: spread of computer-based technology as a positive supply shock increasing potential growth.
  - Apparent decline in NAIRU from the widely accepted 6% range to 5% or lower; explanations include improved worker-job matching, increased immigration, and rapid growth in Chinese and Southeast Asian economies reducing US labor bargaining power.
  - Late 1990s: Increased concerns about inflation as demand was perceived as high relative to increased potential; oil price increases fed into headline CPI and raised inflation-expectation concerns; core CPI showed upward tendency.
  - Response: Fed gradually raised interest rates through 1999 into 2000.
  - Mid-2000 onward: GDP growth slowed, partly due to high-tech slowdown and stock market weakness; inflation declined sharply from about mid-2001.
  - 9/11 accentuated ongoing weak demand and uncertainty.
  - Fed reduced policy rate to levels not seen since the early 1960s; with inflation falling to about 1% year-on-year headline CPI in mid-2002 and year-on-year core CPI in late 2003, deflation fears emerged.
  - Fed lowered the fed funds rate to 1% in mid-2003 and committed to hold rates at very low levels until deflation risk dissipated.
  - From mid-2004 the Fed began removing monetary stimulus by gradually raising interest rates toward neutral levels.
    - Period labeled the "interest rate conundrum": long-term real rates remained low despite significant increase in short-term nominal and real rates.
  - Low policy rates reinvigorated the economy, supporting strong residential construction and consumer-led expenditures; housing price boom played an important role.
  - Unemployment declined from a peak of about 6% in 2003 to a trough of about 4 1/2% (4 1/2% formatting preserved).

*Source: _wp08278 - References..............................................................................................................*

### 2006. Finally, over the past few months, the end of the housing price boom, the inability of many

### _wp08278 - 2006. Finally, over the past few months, the end of the housing price boom, the inability of many

### Background and purpose
- Presents a small quarterly projection model of the U.S. economy estimated with Bayesian techniques to analyze output, unemployment, inflation, and the federal funds rate.
- Motivations:
  - Replicate combination of supply and demand shocks, policy responses, and dynamics that drove actual movements in output, inflation, and interest rates.
  - Provide a tractable framework that can be extended to include financial-real linkages and integrated into a Global Projection Model (GPM).
- Two model types used by the IMF: DSGE models and small quarterly projection models. Small models:
  - Use four or five behavioral equations focusing on key macro variables.
  - Are easy to use and comprehensible to policymakers.
- Two important extensions described:
  - Use of Bayesian techniques to estimate parameters for the U.S. economy.
  - Plan to integrate country small models into a small quarterly Global Projection Model (GPM).

### Benchmark model specification (without financial-real linkages)
- Observable variables (benchmark model has only 4 observable variables):
  - Real GDP (Y defined as 100 times the log of real GDP).
  - Unemployment rate (U and the NAIRU, ØU).
  - CPI inflation (quarterly rate  defined as 400 times first difference of log CPI; year-on-year 4 as 100 times difference of log CPI from four quarters earlier).
  - Federal funds rate.
- Key definitions and identities:
  - Output gap: y = Y - ØY.
  - Unemployment gap: u = U - ØU.
  - Real interest rate: rr_t = rs_t - _{t+1} (equation 5).
  - Real interest rate gap: rrgap_t = rr_t - rr_t (equation 6).
  - Equilibrium real interest rate follows rr_t =  rr_ss + (1-) rr_{t-1} + "rr_t (equation 7).
- Behavioral equations (selected):
  - Output gap: y_t = 1 y_{t-1} + 2 y_{t+1} - 3 rrgap_{t-1} + "y_t (equation 8).
  - Inflation (quarterly at annual rates): _t = 1 4_{t+4} + (1-1) 4_{t-1} + 2 y_{t-1} - "_t (equation 9).
  - Taylor-type reaction function for short-term nominal interest rate (policy rate): rs_t = (1-1)  rr_t + 4_{t+3} + 2(4_{t+3}-_{tar}) + 4 y_t + 1 rs_{t-1} + "rs_t (equation 10).
  - Dynamic Okun’s law for unemployment gap: u_t = 1 u_{t-1} + 2 y_t + "u_t (equation 11).
- Stochastic processes for latent variables:
  - Potential output level: ØY_t = ØY_{t-1} + gY_t/4 + "Y_t (equation 1).
  - Growth rate of potential GDP: gY_t =  gYss + (1-) gY_{t-1} + "gY_t (equation 2).
  - NAIRU level and growth follow analogous specifications (equations 3 and 4).
- Model features:
  - Allows more stochastic shocks than observables; permits permanent level and persistent growth shocks to potential output and NAIRU.
  - Cross-equation dynamics include forward-looking and backward-looking elements (lead and lag terms) in demand and inflation equations.

### Bayesian estimation approach
- Bayesian estimation provides a middle ground between classical estimation and calibration:
  - Allows incorporation of priors and data; the tightness of priors (e.g., standard deviation) adjusts relative weight.
  - Helpful in small-sample macro contexts and for handling simultaneity.
- Criteria for evaluating Bayesian-estimated models:
  - Posterior coefficients close to priors despite data weight indicates prior consistency.
  - Impulse response functions (IRFs) compatibility with researcher views.
  - Relative magnitudes of log data density and RMSEs useful in comparing model variants.
- Advantages:
  - Produces plausible dynamics and sensible forecasting properties.
  - Allows flexible stochastic processes and model-consistent latent variable estimates.
  - Can be combined with judgmental near-term forecast inputs for improved medium-term projections.

### Confronting the benchmark model with data (1994–2007)
- Balanced model treats both demand and supply shocks as important.
- Key empirical patterns reproduced:
  - NAIRU declined from just above 6% to just above 4 1/4% in the late 1990s, then rose to above 4 1/2% (figure referenced).
  - Pickup in potential growth in the second half of the 1990s, slowing thereafter; excess demand in much of the former period and excess supply in much of the latter.
- Estimation diagnostics (summary):
  - Posterior coefficient shifts: output gap equation puts more weight on lagged and lead output gap, less on real interest rate than priors; inflation equation posterior places more weight on forward-looking element and less on backward-looking element than priors.
  - Standard deviations: posteriors for shocks in unemployment and interest rate equations are considerably smaller than priors; posteriors for inflation and two of three output equations are substantially higher than priors.
- Model limitation noted:
  - Difficulty generating a downturn absent a breakout of inflation; need for additional dynamics—motivating addition of a financial variable.

### Extended model with financial-real linkages — motivation
- Recent downturns (early 2000s, current) not preceded primarily by inflationary pressures and interest rate increases; financial developments played a central role.
- Financial-real linkages include:
  - Financial institution behavior (e.g., changes in bank willingness to lend, capital positions).
  - Financial market dysfunction (e.g., liquidity freezes, valuation uncertainty).
  - Episodes referenced: Regulation Q era, early 1990s U.S. “financial headwinds,” 1998 LTCM episode, and the rise/fall of the U.S. subprime mortgage market (including liquidity freezing in asset-backed commercial paper markets and writedowns of structured financial instruments).
- Modeling questions:
  - Whether to incorporate financial-real linkages in central macro model or as satellite models.
  - Whether linkages should operate continuously or only when thresholds are crossed (regime shifts).
  - How to proxy linkages (e.g., bank lending survey variables, risky spreads, asset prices).

### Extended model specification — financial-real linkages (BLT)
- Introduces financial variable BLT:
  - BLT is an unweighted average of the net responses to four questions in the Fed’s Senior Loan Officer Opinion Survey (C&I loans to large/middle-market firms; C&I loans to small firms; commercial real estate loans; mortgage loans to purchase homes).
  - Net tightening: percent “tightened considerably” + percent “tightened somewhat” minus percent “eased somewhat” + percent “eased considerably”; each of four questions weighted by one quarter to form BLT.
  - Noted bias: net tightening responses outweigh net easing on average over the sample period, indicating a bias of about 5% in the variable.
- BLT dynamics:
  - BLT_t = BLT_{t-1} -  y_{t+4} + "BLT_t (equation 12).
  - BLT equilibrium follows BLT = BLT_{t-1} + "BLT_t (equation 13).
  - Banks’ lending conditions respond to expected economic conditions 4 quarters ahead.
- BLT enters output gap equation as a distributed lag (equations 14–15):
  - y_t = 1 y_{t-1} + 2 y_{t+1} - 3 rrgap_{t-1} -  _t + "y_t (equation 14).
  - _t is a weighted distributed lag of "BLT innovations:
    - _t = 0:04 "BLT_{t-1} + 0:08 "BLT_{t-2} + 0:12 "BLT_{t-3} + 0:16 "BLT_{t-4} + 0:20 "BLT_{t-5} + 0:16 "BLT_{t-6} + 0:12 "BLT_{t-7} + 0:08 "BLT_{t-8} + 0:04 "BLT_{t-9} (equation 15).
  - Interpretation options:
    - BLT captures exogenous tightening/loosening in bank lending that can directly affect access to funds and spending.
    - BLT can function as a leading indicator reflecting lending experts’ views on future economic/financial conditions.
  - Additional considerations:
    - Possible asymmetry between positive and negative BLT shocks.
    - Threshold effects tested by setting BLT values with absolute value less than 15 to zero (this reduced , contrary to expectation).
    - BLT may not capture all financial-real linkages; other proxies (risky spreads, asset prices) may be needed.

### Cross correlations of disturbances
- Two cross-correlations introduced:
  - Positive correlation between "gY (shock to potential output growth) and "y (output gap shock): expected persistent positive shock to potential growth raises expected permanent income and spending, increasing output gap before potential output rises.
  - Positive correlation between "Y (shock to level of potential output) and " (inflation shock with negative sign in equation): a positive supply shock to potential output puts downward pressure on costs/prices, producing a positive correlation between these disturbances.
- These correlations help mimic IRFs from DSGE models and embed DSGE insights into the smaller semi-structural model.

### Results from the extended model (with BLT)
- Major structural changes when BLT is added:
  - Output gap equation: substantial reduction in weights on lagged and lead output gap terms, slight increase in weight on real interest rate.
  - Unemployment gap equation: significant increase in coefficient on lagged dependent variable.
  - Standard deviations of structural shocks change only modestly with financial variable inclusion.
- Impulse response functions (high-level summary):
  - Downward shock to inflation → decline in nominal and real policy interest rate → increase in output gap and decline in unemployment gap; effect amplified by easing of bank lending terms.
  - Positive shock to output gap → increase in output gap, decline in unemployment gap, increase in inflation and policy rate.
  - Shock to policy interest rate → reduces output, increases unemployment, puts downward pressure on inflation.
  - Shock to BLT (tightening in bank lending) → sizable decline in output (hump-shaped), rise in unemployment, decline in inflation and policy rate.
  - Shock to growth rate of potential output → larger effects than shock to level of potential output; growth shock increases demand and output gap via cross-correlation, raising inflation and policy rates.
  - Shock to equilibrium real interest rate → change in nominal interest rate with very little effect on other variables.
- Forecasting and fit:
  - Adding BLT markedly improves model functioning.
  - RMSEs: sharp decline in RMSE on the output gap at all horizons and on 4-quarter inflation in the 4- and 8-quarter ahead forecasts when going from base model to model with BLT (Tables 3 and 7 referenced).
  - Some deterioration in short-term NAIRU forecasts with BLT inclusion.
- Contribution of shocks (Table 8 summary):
  - Innovations in BLT account for about 70 percent of the variation in the output and unemployment gaps.
  - BLT accounts for about 40 percent of the variation in year-on-year GDP growth and inflation.
  - Shocks to the fed funds rate make a very small contribution to variability in the fed funds rate, indicating most variation resulted from Fed reactions to information rather than exogenous policy shocks.
- In-sample tracking and forecasts:
  - Model with BLT tracks unemployment gap and output gap moderately well, has more difficulty tracking output growth and inflation.
  - Both models (with and without BLT) show tendency for interest rates to rise in 2003, more than a year before the Fed raised rates. Model lacks mechanism to capture concern about price deflation and the zero lower bound.

### Extensions and robustness
- Short vs long sample (2001–2007 short sample vs 1994–2007 long sample):
  - Output gap equation: lagged gap coefficient appreciably larger in small sample.
  - Much larger coefficient on financial variable in output gap equation in short sample → financial variable played a stronger role in influencing the output gap in the 2000s than earlier.
  - RMSEs for 4-, 8-, and 12-quarter ahead forecasts of one-quarter and four-quarter output growth are much lower for the shorter sample than for the longer sample (consistent with smoother growth in the current decade and lower structural shock SD in potential output growth).
- Core CPI replacement:
  - Replacing headline CPI with core CPI had limited effect on most results, but:
    - Posterior SD of structural shock in inflation equation fell sharply: from about 1.35 to 0.4 in the base model and from about 1.25 to 0.4 in the model with the financial variable.
    - Inflation equation became more backward looking with core inflation than with headline inflation.
    - Reaction function showed substantially stronger response of policy interest rate to core inflation increases than to headline inflation increases.

### Key empirical and model findings (concise bullets)
- Benchmark model observable variables: real GDP, unemployment rate, CPI inflation (headline or core), and federal funds rate.
- NAIRU: decline from just above 6% to just above 4 1/4%, then increase to above 4 1/2% (sample 1994–2007).
- BLT construction:
  - Unweighted average of four Senior Loan Officer survey net tightening responses (each weighted by 1/4).
  - Net tightening responses biased about 5% toward tightening over the sample.
  - BLT distributed-lag coefficients in  equation: 0:04, 0:08, 0:12, 0:16, 0:20, 0:16, 0:12, 0:08, 0:04 (lags t-1 through t-9 respectively).
- Importance of BLT:
  - Accounts for about 70 percent of variation in output and unemployment gaps.
  - Accounts for about 40 percent of variation in year-on-year GDP growth and inflation.
- Inflation shock posterior SD falls sharply when using core CPI: from about 1.35 to 0.4 (base model) and from about 1.25 to 0.4 (with financial variable).

### Policy and modeling implications
- Inclusion of a financial variable (BLT) substantially improves model dynamics and forecasting for output and unemployment, suggesting financial-real linkages are important for explaining recent macro behavior.
- Financial-real linkages can operate both as:
  - Direct exogenous supply-side constraints on credit (affecting lending supply), and
  - Leading indicators of future real activity via lending officers’ expectations.
- Model suggests that in recent episodes most variation in interest rates reflected Federal Reserve reaction to information rather than exogenous policy shocks.
- Further model development priorities:
  - Extend the model to include other financial variables (risky spreads, asset prices).
  - Develop two-country and multicountry versions to assess spillovers through financial linkages.
  - Explore threshold/asymmetric specifications for financial-real linkages and include satellite models or regime-switching features if appropriate.

*Source: IMF working paper content as provided in the supplied document.*

### References:

### _wp08278 - References:

### References (selected)
- Argov, E., N. Epstein, P. Karam, D. Laxton, and D. Rose, 2007, ìEndogenous Monetary Policy Credibility in a Small Macro Model of Israel,î IMF Working Paper 07/207 (August), available at www.imf.org.
- Bayoumi, T. and A. Swiston, 2007, ìForeign Entanglements: Estimating the Source and Size of Spillovers Across Industrial Countries,î IMF Working Paper No. 07/182 (July), available at www.imf.org.
- Bayoumi, T. and O. Melander, 2008, ìCredit Matters: Empirical Evidence on U.S. Macro-Financial Linkages,î IMF Working Paper No. 08/169 (July), available at www.imf.org.
- Berg, A., P. Karam, and D. Laxton, 2006a, ìA Practical Model-Based Approach to Monetary Policy AnalysisóOverview,î IMF Working Paper 06/080 (April), available at www.imf.org.
- Berg, A., P. Karam, and D. Laxton, 2006b, ìPractical Model-Based Monetary Policy AnalysisóA How-to Guide,î IMF Working Paper 06/081 (April), available at www.imf.org.
- Bernanke, B. S., and M. Gertler, 1995, ìInside the Black Box: The Credit Channel of Monetary Policy Transmission,î Journal of Economic Perspectives (Fall), pp. 27ñ48.
- Botman, D., P. Karam, D. Laxton, and D. Rose, 2007, ìDSGE Modeling at the Fund: Applications and Further Developments,î IMF Working Paper 07/200 (August), available at www.imf.org.
- Coats, W., D. Laxton, and D. Rose, 2003, ìThe Czech National Bank's Forecasting and Policy Analysis System,î (Prague, Czech Republic: Czech National Bank).
- Epstein, N., D. Laxton, P. Karam, and D. Rose, 2006, ìA Simple Forecasting and Policy Analysis System for Israel: Structure and Applications,î in Israel: Selected Issues, IMF Country Report No. 06/121 (March), available at www.imf.org.
- Juillard, M., O. Kamenik, M. Kumhof, and D. Laxton, 2007, ìMeasures of Potential Output from An Estimated DSGE Model of the United States,î paper presented at a workshop on Issues in Measuring Potential Output (Ankara Turkey).
- Juillard, M., O. Kamenik, D. Laxton, and M. Kumhof, 2008, ìOptimal Price Setting and Inflation Inertia in a Rational Expectations Model,î (forthcoming) Journal of Economic Dynamics and Control.
- Laidler D., 2003, ìThe Price Level, Relative Prices and Economic Stability: Aspects of the Interwar Debate,î BIS Working Papers No. 136 (September), available at www.bis.org.
- Lown, C., D. Morgan, and S. Rohatgi, 2000, ìListening to Loan Officers: The Impact of Commercial Credit Standards on Lending and Output,î Federal Reserve Bank of New York Economic Policy Review (July), pp. 1ñ16.
- Lown, C. and D. Morgan, 2002, ìCredit Effects in the Monetary Mechanism,î Federal Reserve Bank of New York Economic Policy Review (May), pp. 217ñ35.
- Lown, C., D. Morgan, 2006, ìThe Credit Cycle and the Business Cycle: New Findings Using the Loan Officer Opinion Survey,î Journal of Money, Credit, and Banking, Vol. 38 (September), pp. 1575ñ97.
- Meyer L., 2000, ìThe Economic Outlook and the Challenges Facing Monetary Policy,î Remarks at the Century Club Breakfast Series (Washington University, St. Louis: Missouri), available at www.federalreserve.gov.
- Orphanides, A., 2003, ìHistorical Monetary Policy Analysis and The Taylor Rule,î Journal of Monetary Economics (July), pp. 983ñ1022.
- Swiston, A., 2008, ìA U.S. Financial Conditions Index: Putting Credit Where Credit is Due,î IMF Working Paper No. 08/161 (June), available at www.imf.org.

### Appendix: Data Definitions (United States)
- GDP U.S.: Gross Domestic Product (SAAR, Bil.Chn.2000.Dollars)
- Interest rates Federal Open Market Committee: Fed Funds Target Rate (percent) (period average)
- CPI U.S.: Consumer Price Index (SA, 1982-84=100)
- Core CPI U.S.: CPI-U: All Items Less Food and Energy (SA, 1982-84=100)
- Unemployment U.S.: Civilian Unemployment Rate (SA, percent)
- Bank lending tightening (BLT) Average of:
  - FRB Sr Ofcers Survey: Banks Tightening C.I Loans to Large Firms (percent)
  - FRB Sr Ofcers Survey: Banks Tightening C.I Loans to Small Firms (percent)
  - FRB Sr Loan Off Survey: Tightening Standards for Commercial Real Estate (percent)
  - FRB Sr Loan Survey: Res Mortgages: Net Share, Banks Tightening (Haver Est, percent)

### Key Tables and Model Results (selected figures and statistics)
- Table 1: Results From Posterior Maximization (parameters) Base Case Model (selected posterior modes and s.d.):
  - us1 beta: Posterior mode 0.7453, s.d. 0.0581
  - gamm (us2): Posterior mode 0.1711, s.d. 0.0310
  - beta (us3): Posterior mode 0.3339, s.d. 0.1931
  - norm (gYss us): Posterior mode 2.6016, s.d. 0.2360
  - norm (rr us): Posterior mode 1.8221, s.d. 0.1729
  - beta (us) later entries: Posterior mode 0.9239, s.d. 0.0462; Posterior mode 0.0768, s.d. 0.0389
  - Additional parameter posterior modes: 0.8523 (s.d. 0.0817), 0.1674 (s.d. 0.0971), 0.1270 (s.d. 0.0290), 0.7272 (s.d. 0.0613), 0.1937 (s.d. 0.0382), 0.7087 (s.d. 0.0365), 1.2679 (s.d. 0.2271), 0.2192 (s.d. 0.0563)
- Table 2: Results From Posterior Maximization (standard deviation of structural shocks) Base Case Model (selected posterior modes and s.d.):
  - "u_us": Posterior mode 0.0943, s.d. 0.0146
  - "U_us": Posterior mode 0.0466, s.d. 0.0193
  - "gU_us": Posterior mode 0.0455, s.d. 0.0166
  - "y_us": Posterior mode 0.3567, s.d. 0.0585
  - "Y_us": Posterior mode 0.0483, s.d. 0.0218
  - "gY_us": Posterior mode 0.3486, s.d. 0.1326
  - "_us": Posterior mode 1.3598, s.d. 0.1440
  - "rs_us": Posterior mode 0.4643, s.d. 0.0605
  - "rr_us": Posterior mode 0.0934, s.d. 0.0393
- Table 3: Base Case Root Mean Squared Errors (selected horizons)
  - y_us: 1 Q Ahead 0.63, 4 Q Ahead 0.91, 8 Q Ahead 1.3, 12 Q Ahead 1.4
  - 4_us: 1 Q Ahead 0.36, 4 Q Ahead 1.0, 8 Q Ahead 0.89, (third value appears as 0.78)
  - rs_us: 1 Q Ahead 0.43, 4 Q Ahead 1.4, 8 Q Ahead 1.8
  - U_us: 1 Q Ahead 0.15, 4 Q Ahead 0.39, 8 Q Ahead 0.74, 12 Q Ahead 1
  - Y_us differences and multiple entries: 4(Y_us - Y_us; -1) 1.92 2.12; Y_us - Y_us;4 0.53 1.2 1.4 1.4; additional series 0.4 0.65 0.8 0.88
- Table 4: Results From Posterior Maximization (parameters) BLT Model (selected posterior modes and s.d.):
  - us1 beta: Posterior mode 0.8710, s.d. 0.0484
  - us2 gamm: Posterior mode 0.1688, s.d. 0.0279
  - us3 beta: Posterior mode 0.5175, s.d. 0.2724
  - gYss us: Posterior mode 2.6227, s.d. 0.2323
  - rr us: Posterior mode 1.8121, s.d. 0.1754
  - Other posterior modes: 0.9240 (s.d. 0.0462), 0.0813 (s.d. 0.0373), 0.6840 (s.d. 0.0559), 0.0495 (s.d. 0.0525), 0.1360 (s.d. 0.0303), 0.7091 (s.d. 0.0590), 0.2224 (s.d. 0.0381), 0.7762 (s.d. 0.0254), 1.2993 (s.d. 0.2399), 0.2102 (s.d. 0.0546), gamm 20.0000 (Posterior mode 19.9943, s.d. 0.4956), gamm 1.0000 (Posterior mode 1.2824, s.d. 0.5621)
- Table 5: Results From Posterior Maximization (standard deviation of structural shocks) BLT Model (selected posterior modes and s.d.):
  - "u_us": Posterior mode 0.0989, s.d. 0.0161
  - "U_us": Posterior mode 0.0473, s.d. 0.0200
  - "gU_us": Posterior mode 0.0445, s.d. 0.0161
  - "y_us": Posterior mode 0.3490, s.d. 0.0416
  - "Y_us": Posterior mode 0.0230, s.d. 0.0094
  - "gY_us": Posterior mode 0.3319, s.d. 0.0856
  - "_us": Posterior mode 1.2353, s.d. 0.1189
  - "rs_us": Posterior mode 0.4712, s.d. 0.0556
  - "rr_us": Posterior mode 0.0934, s.d. 0.0391
  - "BLT_us" (two entries): Posterior modes 0.8082 (s.d. 0.3342) and 0.0928 (s.d. 0.0384)
- Table 6: Results from posterior parameters (correlation of structural shocks) BLT Model (selected posterior modes and s.d.):
  - "y_us ; gY_us": Posterior mode 0.1944, s.d. 0.0928
  - "Y_us ; _us": Posterior mode 0.0422, s.d. 0.0187
- Table 7: BLT Root Mean Squared Errors (selected horizons)
  - y_us: 1 Q Ahead 0.43, 4 Q Ahead 0.58, 8 Q Ahead 0.82, 12 Q Ahead 0.93
  - 4_us: 1 Q Ahead 0.34, 4 Q Ahead 0.83, 8 Q Ahead 0.76, 12 Q Ahead 0.75
  - rs_us: 1 Q Ahead 0.46, 4 Q Ahead 1.1, 8 Q Ahead 1.5, 12 Q Ahead 1.7
  - U_us: 1 Q Ahead 0.15, 4 Q Ahead 0.39, 8 Q Ahead 0.68, 12 Q Ahead 0.9
  - Additional Y series: 4(Y_t - Y_t-1) 1.82 2.2 2.1; Y_t - Y_t;4 0.54 1.2 1.6 1.5; Y_t - Y_t;4 0.32 0.61 0.88 1
- Table 8: Variance Decompositions (Mean, Std. Dev. and shares; entries presented as in source)
  - y_t Mean 0.0 Std. Dev. 1.0 5    1   22   2    70
  - _t Mean 2.5 Std. Dev. 1.6 2    0   2   75   22
  - 4_t Mean 2.5 Std. Dev. 1.13 0   3   53   41
  - rs_t Mean 4.3 Std. Dev. 1.613 3   0   3   10   73
  - 4(Y_t - Y_t-1) Mean 2.6 Std. Dev. 2.13 21  52   0    24
  - (Y_t - Y_t-4) Mean 2.6 Std. Dev. 1.43 35  20   0    41
  - u_t Mean 0.0 Std. Dev. 0.86 0   14   2    71

### Figures and Forecasts (listed)
- Figures include: US Historical data; Unemployment and Model-Consistent NAIRU; GDP and Model-Consistent Potential GDP; IRFs for Supply Shock ("_us"), Demand Shock ("y_us"), Policy Rate Shock ("rs_us"), BLT Shock ("BLT_us"), Equilibrium GDP Growth Shock ("gY_us"), Equilibrium GDP Level Shock ("Y_us"); Dynamic Forecasts for Y-O-Y GDP Growth Rate, Q-O-Q GDP Growth Rate, Inflation, Interest Rate, Unemployment Rate, and Output Gap for both Base Case Model and BLT Model.

*Content derived from _wp08278 - References: (IMF Working Paper PDF).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08278.pdf_