## _wp15233

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---

### Overview and purpose
- Potential output defined as the level of output (or GDP) compatible with stable inflation or sustainable output an economy can produce over the medium term in the absence of imbalances.
- Potential and sustainable output are economic constructs, not observables; difficult to identify in real time because overlapping shocks (including financial booms and busts) can temporarily lift or depress GDP without immediately affecting inflation.
- Analysis focuses on how financial variables (credit, house prices, borrowing costs) can inform estimates of sustainable and potential output, applied to euro area countries, notably Greece, Ireland, Italy, Portugal, and Spain.

### Methods compared for estimating potential/sustainable output
- Aggregate univariate filtering methods (e.g., Hodrick-Prescott (HP) filter)
  - Assume potential output is a smooth trend; advantages: simplicity; drawbacks: sensitivity to smoothing, endpoint/reversion issues, limited insight into drivers.
  - Example: For Greece, Ireland, Italy, Portugal, and Spain in 2000–07, a standard HP filter would have suggested a level of potential output closer to actual GDP than a much less flexible linear trend (HP filter λ=6.25 for a trend estimated over 1982-99 in the text figure).
- Production-function models
  - Construct potential output from labor, capital inputs, total factor productivity, and utilization rates; require timely micro-level data and filtering of short-term fluctuations.
- Structural multivariate approaches
  - Use economic theory (e.g., Phillips curve, Okun’s law) to identify potential output; narrow definition to output available absent price and wage rigidities while allowing for real frictions.
- Dynamic stochastic general equilibrium (DSGE) models
  - Model demand and supply including financial frictions (credit, asset markets, banks, housing); can distinguish sustainable changes linked to reductions in financial frictions from credit-fueled temporary growth.

### Multivariate filter (MVF) approach used in the paper
- MVF features and specification
  - MVF incorporates fluctuations in financial variables (credit, house prices), inflation, and capacity utilization to improve estimates of the non-cyclical component of GDP.
  - Observed GDP decomposed: y_t = y_t* + c_t; Δy_t* = ε_t**; Var(c_t)/Var(ε_t**) ≡ λ.
  - With quarterly data, conventional λ = 1600 (potential output captures output movement at frequencies above 8 years).
  - Current output gap allowed to depend on lagged values and up to four observables x_t: credit growth, house price inflation, consumer price inflation, and capacity utilization.
  - Dynamic specification: y_t - y_t* = ρ (y_{t-1} - y_{t-1}*) + β x_{t-1} + ε_t.
  - Pre-filtering: additional variables x_t pre-filtered to exclude movements at frequencies of 20 years or longer using HP filter with λ = 63,500 for financial-cycle variables.
- Three methodological departures from Borio, Disyatat, and Juselius (2013)
  - Use maximum likelihood estimation (MLE) rather than Bayesian approach.
  - Two-step estimation of persistence parameters: ρ estimated from HP output gap then substituted into equation (4) and β estimated by MLE.
  - Pre-filtering to remove very low-frequency movements (20+ years) to avoid misinterpreting permanent financial deepening as cyclical.
- MVF empirical tendencies
  - Conventional estimates may overestimate sustainable output during credit booms and underestimate it during busts.
  - MVF tends to show larger positive output gaps before the crisis and more negative output gaps after the crisis in countries with a financial cycle.
  - MVF restricts financial-variable information to higher frequencies to avoid treating permanent financial deepening as transitory.

### MVF empirical findings for euro-area groups
- GIIPS (Greece, Ireland, Italy, Portugal, Spain)
  - Actual output started to exceed estimated sustainable output prior to the crisis; MVF gap peaks earlier (2005) and stays high until about 2007, then turns significantly negative after the crisis.
  - Differences between MVF and HP predominantly driven by deviations of house price and credit growth from longer-term trends; CPI inflation contributes relatively little compared to house prices and credit growth.
  - Country-level notes:
    - Spain, Portugal, Greece: including financial variables notably changes estimated output gap for the full sample.
    - Ireland: MVF–HP differences pronounced only after 2005.
    - Italy: MVF-implied output gap exceeds HP until about 2005 due to moderate but uninterrupted house price growth.
- Germany and France
  - Where a financial cycle was lacking, MVF output gap is fairly similar to HP filter.
- Real-time use
  - MVF models perform best when estimated over a complete boom-and-bust episode; using only data until 2007 HP and MVF estimate similar gaps that turn negative around 2005, but applying MVF estimated from full sample to 2007 data points to a significantly positive output gap.
  - Alternatives: exploit cross-country variation or structural modeling when sample length limited.

### Robustness, sensitivity, and data requirements
- Results robust to a number of alternative specifications; small to moderate variations in persistence do not change results significantly.
- Treatment of non-stationary additional variables matters:
  - Pre-treatment (removing very long-term trends) important; simple de-meaning of x_t produces results closer to HP.
  - Including credit-boom related explanatory variables jointly or individually gives broadly similar results, though pre-treatment affects estimated sustainable output levels.
- Estimation requires time series long enough to capture pre-crisis states; limited sample length impedes coefficient identification.

### DSGE model with financial frictions: structure and estimation
- Framework and agents
  - Two-region, two-sector, two-agent general equilibrium model for the euro area with housing and non-durable consumption, monopolistic competition, nominal rigidities; housing non-tradable.
  - Two household types: savers and borrowers; borrowers more impatient leading to equilibrium credit demand.
  - Single central bank with flexible inflation targeting stabilizing union-wide consumer inflation and real GDP growth.
- Financial frictions and mechanisms
  - BGG (1999)-type collateral constraint: borrowers post houses as collateral; house values subject to idiosyncratic valuation shocks; variance of valuation shocks varies over time via housing “risk” shocks (σ_t^w) following AR(1).
  - Housing accelerator: house demand raises prices → improves net worth → increases credit availability and residential investment → further raises house prices; leverage and LTV amplify effects.
- Definition and construction of potential output
  - Potential output = counterfactual output under fully flexible prices and wages and absence of mark-up shocks; nominal rigidities and “inefficient” mark-up shocks removed; real and financial frictions retained.
  - Construction steps: solve model at posterior mode; obtain smoothed shocks; solve model with price/wage rigidity parameters set to zero; feed smoothed shocks (except price mark-up shocks) to obtain potential output.
- Data and estimation
  - Quarterly data 2000:Q1–2013:Q4 aggregated into two regions: (1) France and Germany; (2) Greece, Ireland, Italy, Portugal, Spain.
  - Regional variables: GDP, household consumption, residential investment, HICP inflation, house prices, household credit (logged and first-differenced).
  - ECB repo rate used for euro-area common monetary policy.
  - Bayesian estimation for most parameters; some parameters calibrated (e.g., default probability).
  - Fraction of savers estimated at 0.57.
  - Price stickiness: average duration roughly ten quarters in nondurable sector; two quarters in durable sector. Wage-setting durations range four to six quarters.

### DSGE model key findings and decompositions
- Credit dynamics
  - GIIPS: favorable financial shocks after euro lowered financial frictions and improved credit access; credit surge around 2003 driven by housing demand and housing-accelerator feedback; post-2008 reverse explains much of credit drop.
  - Germany and France: credit less volatile and generally reduced by falling housing demand for most of the sample.
- Output drivers
  - GIIPS: financial shocks (country risk premia and housing market risk) and housing demand were main drivers of output; other aggregate demand and supply shocks minor except 2008–09. Single monetary policy mildly pro-cyclical in 2002–05 and countercyclical overall but insufficient to offset housing-driven boom-bust.
  - Germany and France: output fluctuations milder and linked to aggregate demand shocks; monetary policy countercyclical and increasingly expansionary toward end of sample.
- Output gap behavior
  - GIIPS: actual output exceeded potential prior to crisis—initially from improved financial conditions after euro, later housing demand contributed; fiscal policy supported growth in 2008 but reversed financial conditions pushed output gap negative afterwards.
  - Germany and France: output gap oscillated around zero, driven mostly by external demand and productivity shocks.
- Financial frictions and potential output
  - Including financial frictions increases estimated pre-crisis output gap for GIIPS by between one and three times compared with a model without credit frictions.
  - HP filter produced misleading signals in mid-2000s and end of sample for GIIPS; for Germany and France differences between models with and without financial frictions small and HP delivered same signal.
- Financial wedge
  - Difference between output gap with financial frictions and without identifies a financial wedge; leverage and lending spreads amplify the housing accelerator in booms and reverse in busts.

### Policy relevance and recommendations
- Fiscal sustainability
  - Financial variables purged of long-term trend provide valuable information for sustainable/potential output estimates; during credit/house price upswings conventional cyclically adjusted fiscal balances will be too rosy → policymakers should aim for less expansionary budgets during the boom and more expansionary policies afterwards.
  - Improved measurement can help avoid fiscal “debt bias” by identifying temporary revenue gains from booming sectors so spending is not raised permanently and fiscal buffers can be built.
- Monetary and macroprudential policy
  - If financial variables imply greater overheating, the optimal response depends on instrument effectiveness: higher interest rates could help, but macroprudential measures that reduce credit demand at the source should be prioritized when monetary policy cannot effectively target sectoral/region-specific credit booms.
  - Central banks should re-adjust view of the output gap to take financial frictions into account; this can justify more assertive tightening during credit-fueled overheating.
- Structural reforms and growth
  - Estimates that account for financial variables better inform medium- and long-term growth expectations and guide labor and product market reforms, which act with lags.
- Use in real time
  - MVF and DSGE can serve as a “fire alarm” highlighting shortcomings of conventional potential output measures, but substantial judgment remains required in real time.

### Caveats, limitations, and areas for further work
- Model sensitivity and estimation complexity
  - Findings sensitive to underlying assumptions; different models can produce different output gaps.
  - DSGE models require substantial estimation and calibration; complexity may hinder deployment for all countries.
- Data and sample requirements
  - Multivariate models perform better when estimated over periods that include boom-bust episodes or using cross-country experience; limited sample length reduces identification.
- Extensions
  - Embedding multivariate approaches in a production function framework can help interpretation.
  - More elaborate models including a fuller set of policy instruments are needed to map directly the impact of different policy measures on potential or sustainable output.

### Appendix I: MVF estimation highlights (selected statistical findings)
- MVF estimated by maximum likelihood in state-space; parameters enter observation equation determining GDP gap.
- Most parameter estimates significant, except real credit growth for France and Germany.
- Point estimates (impact on output gap):
  - France and Germany:
    - Real HPI growth: 0.4202; Std. Error: 0.1305; p-value: 0.001
    - Real credit growth: 0.0497; Std. Error: 0.2604; p-value: 0.849
    - CPI inflation: 0.7317; Std. Error: 0.2383; p-value: 0.002
  - Greece, Ireland, Italy, Portugal, and Spain:
    - Real HPI growth: 0.2067; Std. Error: 0.0979; p-value: 0.035
    - Real credit growth: 0.1666; Std. Error: 0.0629; p-value: 0.008
    - CPI inflation: 0.7285; Std. Error: 0.1918; p-value: 0.000
- Statistical comparison MVF vs HP:
  - For France and Germany: HP gap contained within MVF 2-standard-deviation error band (modest credit-cycle impact).
  - For GIIPS: HP gap estimates lie well outside MVF confidence interval during the “great expansion” (large economic impact of credit cycle).
- Practical implication: MVF preferred when credit cycle large; when credit cycle minor MVF ≈ HP.

### Appendix II: DSGE calibration and selected posterior estimates (selected values)
- Calibrated parameters (selected)
  - β (Discount factor savers): 0.99
  - ω (Steady-State loan-to-value ratio): 0.7
  - F (Default rate on loans): 0.025
  - ωσ (Steady state risk): 0.1742
  - μ (Proportion of housing value paid to debt-collection agency): 0.2
  - Bβ (Discount factor borrowers): 0.985
  - δ (Depreciation rate): 0.0125
  - σ (Elasticity of substitution between intermediate goods): 10
  - Lσ (Elasticity of substitution between labor types): 10
  - n (Size of economies Germany and France): 0.6
  - g (Fraction of exogenous demand in GDP): 0.3
  - 1-τ (Fraction of imported goods from GIIPS to France/Germany): 0.06
  - 1-τ* (Fraction of imported goods from France/Germany to GIIPS): 0.09
  - α (Size of non-durable sector in GDP): 0.94
- Selected posterior structural parameter estimates (posterior mean; 90% C.S. where reported)
  - λ (Fraction of savers): Posterior mean 0.57; 90% C.S. [0.50,0.64]
  - ε (Habit formation savers): Posterior mean 0.71; 90% C.S. [0.65,0.78]
  - εB (Habit formation borrowers): Posterior mean 0.63; 90% C.S. [0.52,0.73]
  - φ (Labor disutility): Posterior mean 1.14; 90% C.S. [0.75,1.53]
  - ιC (Elasticity of substitution between goods): Posterior mean 1.50; 90% C.S. [0.86,2.17]
  - ιL (Labor reallocation costs): Posterior mean 0.66; 90% C.S. [0.42,0.83]
  - ψ (Investment adjustment costs): Posterior mean 1.94; 90% C.S. [1.31,2.55]
  - γπ (Taylor rule reaction to inflation): Posterior mean 1.34; 90% C.S. [1.16,1.50]
  - γy (Reaction to real growth): Posterior mean 0.29; 90% C.S. [0.19,0.41]
  - γr (Interest rate smoothing): Posterior mean 0.84; 90% C.S. [0.81,0.87]
  - κB (International risk premium): Posterior mean 0.006; 90% C.S. [0.002,0.009]
  - θC (Calvo, price non-durables): Posterior mean 0.87; 90% C.S. [0.82,0.92]
  - θC* (Calvo non-durables GIIPS): Posterior mean 0.93; 90% C.S. [0.89,0.97]
  - θD (Calvo, price durables): Posterior mean 0.50; 90% C.S. [0.39,0.61]
  - θD* (Calvo durables GIIPS): Posterior mean 0.43; 90% C.S. [0.31,0.54]
  - φC (Indexation, price non-durables): Posterior mean 0.16; 90% C.S. [0.03,0.28]
  - φC* (Indexation non-durables GIIPS): Posterior mean 0.30; 90% C.S. [0.13,0.47]
  - θW,C (Calvo, wage non-durables): Posterior mean 0.69; 90% C.S. [0.62,0.77]
  - θW,C* (Calvo, wage non-durables GIIPS): Posterior mean 0.83; 90% C.S. [0.79,0.87]
  - θW,D (Calvo, wage durables): Posterior mean 0.78; 90% C.S. [0.71,0.85]
  - θW,D* (Calvo, wage durables GIIPS): Posterior mean 0.77; 90% C.S. [0.72,0.82]
  - φW,C (Indexation, wage non-durables): Posterior mean 0.26; 90% C.S. [0.06,0.47]
  - φW,C* (Indexation wage non-durables GIIPS): Posterior mean 0.29; 90% C.S. [0.06,0.51]
  - φW,D (Indexation, wage durables): Posterior mean 0.27; 90% C.S. [0.06,0.47]
  - φW,D* (Indexation wage durables GIIPS): Posterior mean 0.28; 90% C.S. [0.06,0.48]

*Source: _wp15233 - REFERENCES (IMF staff appendices and reference list).*

### REFERENCES .............................................................................................................

### _wp15233 - REFERENCES

### Overview and purpose
- Potential output is defined as the level of output (or GDP) compatible with stable inflation or, equivalently, the absence of price rigidities; an alternative definition is sustainable output, the level of GDP that an economy can sustainably produce over the medium term in the absence of imbalances.
- The paper emphasizes that potential and sustainable output are economic constructs, not observables, and are difficult to identify in real time because overlapping shocks (including financial booms and busts) can temporarily lift or depress GDP without immediately affecting inflation.
- The analysis focuses on how financial variables (credit, house prices, borrowing costs) can inform estimates of sustainable and potential output, with application to euro area countries, notably Greece, Ireland, Italy, Portugal, and Spain.

### Methods compared for estimating potential/sustainable output
- Aggregate univariate filtering methods (e.g., the Hodrick-Prescott (HP) filter)
  - Assume potential output is a smooth trend around which GDP fluctuates.
  - Advantages: simplicity.
  - Drawbacks: sensitivity to statistical choices (degree of smoothing), endpoint/reversion issues, limited insight into drivers of potential output.
  - Example: For Greece, Ireland, Italy, Portugal, and Spain in 2000–07, a standard HP filter would have suggested a level of potential output closer to actual GDP than a much less flexible linear trend (note: HP filter λ=6.25 for a trend estimated over 1982-99 in the text figure).
- Production-function models
  - Construct potential output from labor, capital inputs, total factor productivity, and utilization rates.
  - Used by institutions such as the European Commission and the Congressional Budget Office.
  - Require timely micro-level data and filtering of short-term fluctuations, facing problems similar to univariate filters.
- Structural multivariate approaches
  - Use economic theory (e.g., Phillips curve, Okun’s law) to identify potential output and focus on supply-side shocks that matter for potential over the longer term.
  - Narrow the definition to output available absent price and wage rigidities while allowing for real frictions.
  - Sensitive to specification of partial-equilibrium relationships and may not capture all imbalances that affect medium-term sustainability.
- Dynamic stochastic general equilibrium (DSGE) models
  - Model both demand and supply sides and can include financial frictions (credit, asset markets, banks, housing).
  - Can distinguish sustainable changes in output linked to reductions in financial frictions from credit-fueled temporary growth.
  - Example literature: Smets and Wouters (2003); Andrés, López-Salido, and Nelson (2005); Christiano, Motto, and Rostagno (2014); Furlanetto, Gelain and Taheri Sanjani (2014).

### Multivariate filter (MVF) approach used in the paper
- MVF in the spirit of Borio, Disyatat, and Juselius (2013) incorporates fluctuations in financial variables (credit, house prices), inflation, and capacity utilization to improve estimates of the non-cyclical component of GDP.
- Key MVF features:
  - Identifies episodes of particularly high or low GDP growth as cyclical deviations based on co-movements with credit, house prices, inflation, and capacity utilization.
  - Restricts information from financial variables to higher frequencies to avoid misinterpreting permanent shifts (e.g., financial deepening) as transitory.
- MVF implications and empirical tendencies:
  - Conventional estimates may overestimate sustainable output during credit booms and underestimate it during busts.
  - MVF tends to deviate markedly from univariate HP filters in countries that experienced a “financial cycle,” providing a clearer distinction between sustainable and transitory GDP movements driven by credit and housing price movements.
  - As a consequence, MVF output gaps tend to show:
    - Larger positive output gaps before the crisis (indicating more severe overheating).
    - More negative output gaps after the crisis (indicating more excess capacity).
  - MVF models “learn” how financial data impacts sustainable output estimates; where time series alone are insufficient, cross-country approaches or structural models can help.

### DSGE model with financial frictions: role and findings
- The paper uses a two-region DSGE model with housing and financial frictions (leverage and credit risk) to provide theoretical foundations consistent with MVF findings.
- Model insights:
  - Distinguishes sustainable increases in potential output caused by reductions in financial frictions (e.g., persistent decline in risk premia) from temporary, credit-fueled booms.
  - Example for Greece, Ireland, Italy, Portugal, and Spain:
    - Introduction of the euro led to significantly improved credit access and falling interest rates and country risk premia, which the model interprets as a persistent decline in risk premia that raised GDP and potential output.
    - Subsequently, some countries experienced housing and credit booms that created large positive output gaps; the crisis reversed much of these gains, increasing risk premia, generating a credit bust, and producing large negative output gaps.
    - For the rest of the euro area, the output gap remained relatively flat after the 2008–09 turmoil.
- The DSGE structural approach and MVF produce broadly consistent messages: financial variables matter for assessing sustainable/potential output and associated output gaps.

### Policy relevance and implications
- Improved measurement of sustainable output that accounts for financial cycles may:
  - Help avoid fiscal “debt bias” by identifying temporary revenue gains from booming sectors (e.g., housing) so spending is not raised permanently and fiscal buffers can be built.
  - Make it easier to assess the impact of structural reforms on medium- and long-term growth.
- Monetary and macroprudential policy implications:
  - If financial variables imply greater overheating than conventional measures, the optimal policy response depends on instruments’ effectiveness—higher interest rates could help, but macroprudential measures may be more useful and should be prioritized.
- Caveats and research needs:
  - MVF requires practical choices that affect findings and need further scrutiny.
  - DSGE model outcomes depend on structural assumptions; both approaches are complementary and further research is warranted.

### Figures and appendices referenced (as listed)
- Figures listed include: 1. Euro Area: Output Gaps from a MVF Model; 2. Euro Area: Greece/Ireland/Italy/Portugal/Spain—Output Gaps Estimates at Different Years; 3. Euro Area: Shock Decomposition; 4. Euro Area: Output Gaps with and without Financial Friction; 5. Euro Area: Financial Wedge.
- Appendices listed: I. MVF Estimate and Comparison with HP Filter; II. DSGE Model and Estimation—An Overview.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15233.pdf*

### Section IV briefly points out preliminary implications of these findings for policymakers.

### _wp15233 - Section IV briefly points out preliminary implications of these findings for policymakers.

### A multivariate filtering (MVF) empirical approach
- MVF models augment traditional aggregate univariate filtering methods by using additional information to help identify transitory movements in economic activity.
- Observed GDP is decomposed into unobservable cycle and trend (sustainable) components:
  - y_t = y_t* + c_t  (equation (1) as presented)
  - Δy_t* = ε_t**  (equation (2) as presented)
  - Var(c_t)/Var(ε_t**) ≡ λ  (equation (3) as presented)
- The model mirrors the HP filter by constraining the variance ratio λ to ensure desired spectral properties. With quarterly data, the conventional value for λ is 1600, which implies that potential output will capture output movement at frequencies above 8 years.

### Incorporating additional observable variables x_t
- The current output gap is allowed to depend on lagged values and a set of observable variables x_t (up to four): credit growth, house price inflation, consumer price inflation, and a survey-based measure of capacity utilization where available.
- Dynamic specification (as presented):
  - y_t - y_t* = ρ (y_{t-1} - y_{t-1}*) + β x_{t-1} + ε_t  (equation (4) as presented)
  - The variance ratio Var*(Δy)/Var(y - y*) is constrained to match that implied by equations (1)-(3) and implicitly the frequency characteristics of the HP filter.

### Three methodological departures from Borio, Disyatat, and Juselius (2013)
- First: Maximum likelihood estimation (MLE) is used rather than a Bayesian approach to avoid selection of priors and facilitate application across many countries.
- Second: Persistence parameters ρ and β are estimated in a two-step procedure rather than jointly:
  - ρ is estimated from the output gap obtained from the original HP filter and substituted into equation (4), which is then estimated using MLE. 12
  - This bypasses numerical joint estimation issues and lets the data determine persistence. Results are noted as not very sensitive to moderate changes in ρ. 13
- Third: Additional variables x_t are pre-filtered to exclude movements at frequencies of 20 years or longer, preventing longer-term trends in x_t being misinterpreted as cyclical. 14
  - Practical implementation: A HP filter with λ equal to 63,500 is used for pre-filtering financial-cycle variables; AR-model extensions are used to mitigate the endpoint problem.

### Key empirical findings for euro-area country groups
- Applying MVF to Greece, Ireland, Italy, Portugal, and Spain indicates actual output started to exceed estimated sustainable output prior to the crisis, producing a large positive output gap.
  - The MVF gap measure peaks earlier, in 2005, and stays at a high level until about 2007, then turns significantly negative after the crisis as actual output fell.
- Differences between MVF and HP filter results are predominantly driven by deviations of house price and credit growth from their longer-term trends; CPI inflation contributes relatively little weight compared to house prices and credit growth.
- For the rest of the euro area (approximated by Germany and France), where a financial cycle was lacking, the MVF output gap is fairly similar to the HP filter.

### Robustness, sensitivity, and data requirements
- Results are fairly robust to a number of alternative specifications; small to moderate variations in the persistence of the output gap in the MVF do not change results significantly.
- Treatment of non-stationary additional variables matters:
  - Pre-treatment (longer-term stationarity) of x_t is important; simple de-meaning of x_t produces results much closer to the HP filter.
  - Including individual credit-boom related explanatory variables or including them jointly (e.g., house prices and credit cycle variables) gives broadly similar results, though pre-treatment can affect estimated sustainable output levels.
- Estimation requires time series long enough to capture pre-crisis states; limited sample length can impede coefficient identification.

### Real-time use and country-level application
- MVF models perform best when estimated across a complete “boom and bust” episode because identification exploits variation of financial and other variables around their longer-term trend.
- Using only data until 2007, HP and MVF estimate fairly similar output gaps that turn negative around 2005. However, applying the MVF model estimated from the full sample to the data available in 2007 points to a significantly positive output gap—suggesting MVF can inform policymakers in “real time” when long enough series are used.
- Alternatives less sensitive to sample-length include exploiting cross-country variation in estimating MVF models or turning to structural modeling (see Section III).
- Country-level findings among Greece, Ireland, Italy, Portugal, and Spain:
  - Spain, Portugal, and Greece: Including financial variables notably changes the estimated output gap for the full sample, resembling aggregate outcomes.
  - Ireland: MVF–HP differences become more pronounced only after 2005, reflecting timing of house price inflation and accelerated credit growth.
  - Italy: MVF-implied output gap exceeds HP until about 2005, likely due to moderate but uninterrupted house price growth relative to long-term trends.

### Cautionary notes and practical implications for policymakers
- Ensuring longer-term stationarity of additional variables is crucial to avoid misinterpreting long-lasting financial deepening or reductions in financial frictions as cyclical (which would raise potential output and lower the output gap).
- The MVF approach can prevent mistaking boom-and-bust-induced output increases for permanent increases in potential, thereby affecting judgments on overheating and policy stance.
- Mechanistic application of MVF can be misleading in some cases; careful pre-treatment, long enough samples, and consideration of country-specific contexts are important.

*Source: _wp15233 - Section IV briefly points out preliminary implications of these findings for policymakers.*

### Section IV.

### _wp15233 - Section IV.

### Structural modeling approach (DSGE with financial frictions)
- Framework: Two-region, two-sector, two-agent general equilibrium model for the euro area with housing and non-durable consumption produced under monopolistic competition and nominal rigidities; non-durables traded across regions, housing non-tradable.
- Agents: In each region there are savers and borrowers; borrowers prefer to consume early, creating equilibrium credit demand.
- Monetary policy: Single central bank with a flexible inflation targeting regime stabilizing union-wide consumer inflation and real GDP growth; monetary policy cannot address sector- or region-specific shocks alone.
- Financial frictions: Based on Bernanke, Gertler and Gilchrist (BGG) (1999) applied to households—borrowers post houses as collateral; house values subject to idiosyncratic valuation shocks. Variance of valuation shocks varies over time via housing “risk” shocks, increasing house price volatility, mortgage default risk, and lending-deposit spreads.
- Mechanisms: Housing accelerator—house demand raises prices → improves household net worth → increases credit availability and residential investment → further raises house prices. Leverage and loan-to-value ratios amplify effects.
- Definition of potential output: Counterfactual output under fully flexible prices and wages and absence of mark-up shocks; nominal rigidities and “inefficient” mark-up shocks removed; real and financial frictions retained along with technology, preference, demand and financial shocks; firms maintain constant monopoly power and mark-ups at steady state.
- Estimation: Model estimated for euro area regions (Greece, Ireland, Italy, Portugal, Spain grouped; Germany and France grouped) using Bayesian methods with quarterly data between 2000:Q1 and 2013:Q4. Some parameters calibrated (e.g., probability of credit defaults) to back out risk levels.

### Key model-based findings and decompositions
- Credit dynamics:
  - For Greece, Ireland, Italy, Portugal, and Spain (GIIPS group): favorable financial shocks after the euro lowered financial frictions and improved access to credit; credit surge around 2003 largely driven by rapidly increasing housing demand and the housing-accelerator feedback loop. Post-2008 the same factors in reverse explain much of the credit drop.
  - For Germany and France: credit was an order of magnitude less volatile and generally reduced by falling housing demand for most of the sample.
- Output drivers:
  - In GIIPS: financial shocks (country risk premia and housing market risk) and housing demand were the main drivers of output; other aggregate demand shocks (household consumption, government spending, net-exports) and supply-side shocks (technology and mark-ups) played a comparatively minor role except in 2008–09. Single monetary policy had a mildly pro-cyclical effect in 2002–05 and was countercyclical overall but insufficient to offset housing-driven boom-bust.
  - In Germany and France: output fluctuations were milder and more linked to aggregate demand shocks; common monetary policy had a countercyclical effect and became increasingly expansionary toward the end of the sample.
- Output gap behavior:
  - In GIIPS: actual output consistently exceeded potential prior to the crisis. Until 2002 this reflected improving financial conditions after the euro; later housing demand contributed to the output gap. Fiscal policy supported growth in 2008 but faltering housing demand and reversed financial conditions pushed the output gap negative afterwards.
  - In Germany and France: estimated output gap oscillated around zero, driven mostly by external demand and productivity shocks.
- Financial frictions and potential output:
  - Including financial frictions increases the estimated pre-crisis output gap for GIIPS by between one and three times compared with a model without credit frictions.
  - The HP filter produced misleading signals in mid-2000s and at the end of the sample for GIIPS; for Germany and France the difference between models with and without financial frictions was much smaller and the HP filter delivered the same signal.
- Financial wedge and drivers:
  - Difference between output gap with financial frictions and without identifies a financial wedge. Leverage matters via the housing accelerator; financial shocks change the mortgage lending spread vs risk-free rate, directly affecting the efficiency frontier.
  - In early 2000s for GIIPS the boom was amplified by diminishing financial risks; around 2003 accelerator-driven housing demand lifted output and output gap; post-2008 a reverse financial accelerator deepened the recession.

### Policy implications and recommendations
- General:
  - Financial variables (credit, house prices purged of long-term trend) provide valuable information for estimates of potential or sustainable output, especially where boom-bust episodes occurred.
  - Multivariate models incorporating financial variables tend to show more stable sustainable output during boom-bust periods than univariate HP filter estimates.
- Fiscal sustainability:
  - If sustainable/potential output moves more steadily than suggested by conventional measures during financial booms and busts, fiscal policy should avoid debt bias.
  - During credit/house price upswings: conventional cyclically adjusted fiscal balances will be too rosy → policymakers should aim for less expansionary budgets during the boom and more expansionary policies afterwards.
- Structural reforms:
  - Estimates that account for financial variables will better inform medium- and long-term growth expectations and guide labor and product market reforms, which act with lags.
- Macroeconomic stabilization:
  - Policy choice depends on whether instruments affect the output gap once financial variables are accounted for.
  - If adjusted output gap is more positive (larger overheating), raising interest rates may be appropriate if monetary policy effectively addresses the credit/housing boom; otherwise, macroprudential measures reducing credit demand at the source should be the first line of defense.
  - Real-time judgments remain difficult (e.g., whether a persistent decline in credit risk is fundamental or a market misperception).
- Optimal monetary policy:
  - Central banks should re-adjust their view of the output gap to take financial frictions into account; this can justify more assertive tightening during credit-fueled overheating.
  - Presence of financial frictions introduces new trade-offs for monetary policymakers if those frictions cannot be addressed by other means.

### Caveats, limitations, and areas for further work
- Model sensitivity:
  - Findings sensitive to underlying assumptions; different models can produce different output gaps.
  - DSGE models require substantial estimation and calibration; complexity may hinder deployment for all countries.
- Data and estimation:
  - Multivariate models perform better when estimated over periods that include boom-bust episodes or using cross-country experience.
- Extensions and future research:
  - Embedding multivariate approaches in a production function framework (e.g., IMF (2015)) can help interpretation.
  - More elaborate models including a fuller set of policy instruments are needed to map directly the impact of different policy measures on potential or sustainable output.
- Practical use:
  - Existing models can serve as a “fire alarm” highlighting shortcomings of conventional potential output measures, but substantial judgment is still required in real time.

*Source: _wp15233 - Section IV.*

### REFERENCES

### _wp15233 - REFERENCES

### Key methodological findings (Appendix I: MVF estimate and comparison with HP filter)
- MVF model estimated by maximum likelihood in state-space; economically interesting parameters enter the observation equation determining the GDP gap.
- Most parameter estimates significant, except real credit growth for France and Germany.
- Real house price growth has a positive and significant impact on the output gap in both regional groups; point estimates:
  - France and Germany:
    - Real HPI growth: 0.4202; Std. Error: 0.1305; p-value: 0.001
    - Real credit growth: 0.0497; Std. Error: 0.2604; p-value: 0.849
    - CPI inflation: 0.7317; Std. Error: 0.2383; p-value: 0.002
  - Greece, Ireland, Italy, Portugal, and Spain:
    - Real HPI growth: 0.2067; Std. Error: 0.0979; p-value: 0.035
    - Real credit growth: 0.1666; Std. Error: 0.0629; p-value: 0.008
    - CPI inflation: 0.7285; Std. Error: 0.1918; p-value: 0.000
- Statistical comparison MVF vs HP gaps:
  - For France and Germany: the HP gap is entirely contained within the MVF 2-standard-deviation error band, implying modest economic impact of credit-cycle variables on the output gap.
  - For Greece, Ireland, Italy, Portugal, and Spain: during the “great expansion” HP gap estimates lie well outside the MVF confidence interval, indicating a large economic impact of the credit cycle.
- Practical implication:
  - Use MVF as preferred method: when credit cycle is minor/nonexistent MVF ≈ HP; when credit cycle is large only MVF produces correct estimates.
- Notes on estimation details:
  - Standard errors of the estimated GDP gap calculated by means of the Kalman filter.
  - Figure A.1 compares HP and MVF output gaps (units percent/100); MVF estimates are statistically significantly different from HP estimates during the run up and aftermath of the recession.

### Model structure and estimation (Appendix II: DSGE model and estimation—overview)
- Model architecture:
  - Two-country, two-agent, two-sector DSGE in a currency union with a common central bank reacting to union-wide HICP inflation and real GDP growth.
  - Both economies produce differentiated nondurable consumption goods (tradable) and housing (non-tradable); production under monopolistic competition with nominal rigidities.
  - Two household types per country: savers and borrowers (borrowers more impatient → credit equilibrium).
  - Financial intermediaries: domestic (take deposits, grant loans, issue bonds) and international (trade bonds, charge risk premium depending on net foreign asset position and spread shock).
  - Lending-deposit spread depends on housing market conditions and borrowers’ balance sheets via a BGG (1999)-type accelerator: S(Loan-to-Value, σ_t^w) increasing in both arguments; lending rate L_tR minus deposit rate tR equals S(.). Risk shock σ_t^w follows AR(1).
  - Defaults arise from idiosyncratic household housing-value shocks; higher leverage → higher default probability → higher lending spreads → amplifier between house prices and household debt.
- Frictions and shocks:
  - Nominal frictions: staggered price setting (firms), staggered wage setting with indexation, monopolistic competition on labor.
  - Real frictions: habit formation in consumption, residential investment adjustment costs, costly labor reallocation across sectors.
  - Shocks included: productivity (each country and sector), preference shocks (each good and country), monetary policy shocks, financial shocks (risk and country spread), price mark-up shocks, and aggregate demand shocks (business investment, external demand, fiscal policy captured as part of aggregate demand shock).
- Data and estimation:
  - Estimated using quarterly data 2000:Q1–2013:Q4 with thirteen macroeconomic time series aggregated into two regions: (1) France and Germany; (2) Greece, Ireland, Italy, Portugal, and Spain.
  - For each region variables: GDP, household consumption, residential investment, HICP inflation, house prices, household credit (all logged and first-differenced).
  - ECB repo rate used to capture euro-area common monetary policy.
  - Bayesian estimation used for most parameters; some parameters calibrated (e.g., default probability).
  - Fraction of savers estimated at 0.57.
  - Price stickiness and wage-setting durations:
    - Prices more sticky in nondurable sector: average duration roughly ten quarters in both areas.
    - Durable sector: average duration roughly two quarters in both areas.
    - Wage-setting heterogeneity smaller: average durations ranging from four to six quarters.

### Construction of counterfactual potential output (DSGE-based)
- Steps:
  - Solve model using calibration at the posterior mode.
  - Obtain smoothed shocks from state-space solution plus data via the Kalman filter (series of shocks that explain the data through the model).
  - Solve model with prices and wages fully flexible (set price and wage rigidity parameters to zero).
  - Feed smoothed shocks (except price mark-up shocks) into the flexible-price-wage model; resulting counterfactual output series = potential output.

### Calibrated parameters (Table A2.1)
- β (Discount factor savers): 0.99
- ω (Steady-State loan-to-value ratio): 0.7
- F (Default rate on loans): 0.025
- ωσ (Steady state risk): 0.1742
- μ (Proportion of housing value paid to debt-collection agency): 0.2
- Bβ (Discount factor borrowers): 0.985
- δ (Depreciation rate): 0.0125
- σ (Elasticity of substitution between intermediate goods): 10
- Lσ (Elasticity of substitution between labor types): 10
- n (Size of economies Germany and France): 0.6
- g (Fraction of exogenous demand in GDP): 0.3
- 1-τ (Fraction of imported goods from Greece, Ireland, Italy, Portugal, and Spain to France and Germany economies): 0.06
- 1-τ* (Fraction of imported goods from France and Germany to Greece, Ireland, Italy, Portugal, and Spain economies): 0.09
- α (Size of non-durable sector in GDP): 0.94

### Selected posterior structural parameter estimates (Table A2.2, prior → posterior summaries)
- λ (Fraction of savers): Prior Beta mean 0.5 SD 0.05 → Posterior mean 0.57; 90% C.S. [0.50,0.64]
- ε (Habit formation savers): Prior Beta mean 0.5 SD 0.15 → Posterior mean 0.71; 90% C.S. [0.65,0.78]
- εB (Habit formation borrowers): Prior Beta mean 0.5 SD 0.15 → Posterior mean 0.63; 90% C.S. [0.52,0.73]
- φ (Labor disutility): Prior Gamma mean 1 SD 0.5 → Posterior mean 1.14; 90% C.S. [0.75,1.53]
- ιC (Elasticity of subst. between goods): Prior Gamma mean 1.5 SD 0.5 → Posterior mean 1.50; 90% C.S. [0.86,2.17]
- ιL (Labor reallocation costs): Prior Gamma mean 1 SD 0.5 → Posterior mean 0.66; 90% C.S. [0.42,0.83]
- ψ (Investment adjustment costs): Prior Gamma mean 2 SD 1 → Posterior mean 1.94; 90% C.S. [1.31,2.55]
- γπ (Taylor rule reaction to inflation): Prior Normal mean 1.5 SD 0.1 → Posterior mean 1.34; 90% C.S. [1.16,1.50]
- γy (Taylor rule reaction to real growth): Prior Gamma mean 0.2 SD 0.05 → Posterior mean 0.29; 90% C.S. [0.19,0.41]
- γr (Interest rate smoothing): Prior Beta mean 0.66 SD 0.15 → Posterior mean 0.84; 90% C.S. [0.81,0.87]
- κB (International risk premium): Prior Gamma mean 0.005 SD 0.002 → Posterior mean 0.006; 90% C.S. [0.002,0.009]
- θC (Calvo lottery, price non-durables): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.87; 90% C.S. [0.82,0.92]
- θC* (Calvo lottery, price non-durables for GIIPS): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.93; 90% C.S. [0.89,0.97]
- θD (Calvo lottery, price durables): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.50; 90% C.S. [0.39,0.61]
- θD* (Calvo lottery, price durables for GIIPS): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.43; 90% C.S. [0.31,0.54]
- φC (Indexation, price non-durables): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.16; 90% C.S. [0.03,0.28]
- φC* (Indexation, price non-durables GIIPS): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.30; 90% C.S. [0.13,0.47]
- φD (Indexation, price durables): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.14; 90% C.S. [0.02,0.25]
- φD* (Indexation, price durables GIIPS): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.20; 90% C.S. [0.03,0.36]
- θW,C (Calvo lottery, wage non-durables): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.69; 90% C.S. [0.62,0.77]
- θW,C* (Calvo lottery, wage non-durables GIIPS): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.83; 90% C.S. [0.79,0.87]
- θW,D (Calvo lottery, wage durables): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.78; 90% C.S. [0.71,0.85]
- θW,D* (Calvo lottery, wage durables GIIPS): Prior Beta mean 0.75 SD 0.15 → Posterior mean 0.77; 90% C.S. [0.72,0.82]
- φW,C (Indexation, wage non-durables): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.26; 90% C.S. [0.06,0.47]
- φW,C* (Indexation, wage non-durables GIIPS): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.29; 90% C.S. [0.06,0.51]
- φW,D (Indexation, wage durables): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.27; 90% C.S. [0.06,0.47]
- φW,D* (Indexation, wage durables GIIPS): Prior Beta mean 0.33 SD 0.15 → Posterior mean 0.28; 90% C.S. [0.06,0.48]

*Source: _wp15233 - REFERENCES (IMF staff appendices and reference list).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15233.pdf_