## _wp15109

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---

### I. Introduction — focus and motivation
- Temporary asset price movements can exert a large fiscal impact through:
  - build-up of contingent fiscal risks in the financial sector, and
  - direct impact on revenues (taxes on capital transactions and wealth effects).
- Paper focus:
  - adjust structural fiscal balances (SFBs) for the cyclical revenue impact of asset prices.
- Operational steps emphasized:
  - date asset price cycles,
  - measure synchronization between asset price cycles and the business cycle,
  - estimate responsiveness of government revenues and the overall fiscal balance to business and asset price cycles using elasticity and semi-elasticity approaches.
- Asset classes considered: equities and residential housing.
- Key pre-crisis quantified effect (average across 20 OECD countries):
  - Excluding asset price cycles overestimated the underlying fiscal balance by about 2 percentage points of GDP.
  - Contribution breakdown:
    - ¾ percentage point of GDP owing to the impact of house price cycles.
    - 1¼ percentage points of GDP owing to the impact of equity price cycles.
- Larger fiscal impacts in economies with extensive and persistent asset price rises, including Ireland and Spain.

### II. Literature review — prior approaches and findings
- Empirical focus: OECD and other advanced economies.
- Common findings:
  - Government revenues and fiscal balance are significantly affected by asset prices.
  - Property prices tend to have a larger elasticity than stock prices.
- Typical empirical approaches cited:
  - Fixed-effects OLS for contemporaneous relationships.
  - Error-correction mechanisms for short- and long-run relationships.
  - Elasticity and semi-elasticity estimation frameworks to adjust beyond the business cycle.
- Asset price cycle measurement methods reviewed:
  - Hodrick-Prescott (HP) filter.
  - Detrending relative to equilibrium or fundamentals (median ratios, Gordon model, user cost/price-to-rent).
- Identified gap: no cited study assesses the impact of not accounting for asset price cycles on the pre-crisis fiscal stance in OECD countries.

### III. Empirical methodology — data, steps, and conceptual framework
- Two-step correction approach:
  1. Identify asset price cycle measures and estimate synchronization with the business cycle.
  2. Estimate coefficients for sensitivity of fiscal variables to business and asset price cycles and adjust SFB calculations beyond the business cycle.
- Data and sample:
  - Quarterly sample period: 1980Q1–2012Q4.
  - Sample: 20 OECD countries (AUS, BEL, CAN, DNK, FIN, FRA, DEU, GRC, IRL, ITA, JPN, KOR, NLD, NOR, NZL, ESP, SWE, CHE, GBR, USA).
  - Fiscal and real variables from OECD analytical database; real house prices from IMF database incorporating BIS and national sources; national stock price indices (MSCI) from DataStream.
- Channels:
  - Direct: taxes on capital and financial transactions.
  - Indirect: wealth effects raising consumption and output — unobserved directly and estimated econometrically.

### IV. Dating cycles and measuring synchronization — algorithms and metrics
- Cycle dating:
  - Harding and Pagan (2002a) extension of Bry and Boschan (1971) BB algorithm used to identify turning points by searching for local maxima and minima.
  - Censoring rules:
    - (i) duration of a complete cycle must be at least five quarters;
    - (ii) duration of each phase must be at least two quarters.
  - Peak/trough conditions for series xt preserved verbatim in the source.
  - Detrended real asset prices and output used to eliminate common price factors when dating cycles.
- Synchronization metric:
  - Concordance index (Harding and Pagan (2002b)) measures fraction of time two series are in the same phase; index equals unity if perfectly procyclical and zero if perfectly countercyclical.
  - Concordance index supplemented with simple correlation statistics.
- Empirical finding:
  - Historical output and asset prices are not fully synchronized, motivating adjustment beyond the business cycle when asset price cycles affect fiscal variables.

### V. Measuring asset price cycles — methods reviewed
- Hodrick-Prescott (HP) filter:
  - Applied with smoothing parameters: 1600 (real GDP), 74300 (equity), 36573 (housing).
  - Operationally simple; vulnerable to end-point bias and understates mis-valuations during extreme episodes.
  - HP filter is the least preferred empirical proxy for asset price gaps.
- Intrinsic valuation (IV) models:
  - Gordon growth model for equities: (P/E)* = (1+g)/(r+σ−g).
  - Poterba model for housing: price-to-rent equilibrium related to user cost with inputs including real GDP growth, nominal 10-year government bond yield, spreads, property tax rates, 4 percent recurring holding costs, and expected capital gain approximated by a 5-year moving-average of the consumer inflation rate.
  - Theoretically robust but sensitive to input choices and can generate counter-intuitive gaps.
- Fundamental valuation ratios:
  - Deviations from historical mean (1980–2012 average where available); operationally attractive due to data availability.

### VI. Estimation frameworks
- Elasticity approach:
  - Revenue and expenditure elasticities (ε_R, ε_E): 1-percent change in nominal output → ε_R (ε_E) percent change in nominal revenues (expenditures).
  - Pooled mean-group (PMG) estimator used (long-run coefficients homogeneous; short-run and adjustment speeds can vary).
  - PMG allows long-run and short-run elasticities and speed-of-adjustment estimation; computationally intensive (maximum likelihood).
- Semi-elasticity approach:
  - Semi-elasticity η of overall balance ratio relative to the output gap: cab = overall balance ratio adjusted by η times output gap (expression preserved).
  - A 1-percent change in nominal output relative to potential leads to an η-percentage point change in overall balance-to-output ratio.
  - η estimated by regressing overall balance-to-GDP ratio on output gap (fixed-effects panel); asset price corrections included analogously with asset price gaps and elasticity coefficients (ε_F^R, ε_F^E).

### VII. Empirical results — elasticity approach (highlights)
- Long-run revenue elasticity with respect to output: long-run elasticity ≈ 1 (unitary).
- Short-run revenue elasticity to real GDP: short-run elasticity ≈ 0.62 (temporary 1-percent increase in output → 0.62 percent increase in total revenues).
- Speed of adjustment: 2.5 percent per quarter; half of deviations adjusted in 34 quarters.
- Asset price long-run elasticities (when added):
  - Revenues to real house prices: long-run elasticity 0.166.
  - Revenues to real stock prices: long-run elasticity 0.095.
  - Short-run elasticities: real house prices 0.14; real stock prices 0.01.
- Observations and sample sizes vary by specification (e.g., Obs.: 1,460 to 2,083; Countries: 20).

### VIII. Empirical results — semi-elasticity approach (Table 3 summary)
- Output gap semi-elasticity declines when asset price cycles included:
  - From 0.83 (Column 1) to 0.58 (Column 4) when asset price cycles are included.
- Semi-elasticity coefficients (full specification, Column 4):
  - Output gap: 0.583***.
  - Housing price gap: 0.053***.
  - Equity price gap: 0.036***.
- Interpretation:
  - Semi-elasticity 0.58 corresponds to an elasticity of about 1½ (based on revenue and expenditure ratios).
- Estimation details:
  - Dependent variable: overall balance-to-GDP ratio (in percent).
  - Output gap estimated using HP filter (in percent); housing gap: de-trended price-to-rent ratio; equity gap: demeaned price-to-book ratio.
  - Estimator: fixed effects with robust t-statistics.
  - Example sample detail: Obs. 2,082; Countries 18; Adjusted R-squared for full specification: 0.292.

### IX. Robustness checks and sensitivity
- Robustness exercises: alternative asset gap measures, sample composition/time periods, omitted variables, simultaneity bias, non-linear specifications, instrumental variables/dynamics, and other checks.
- Selected robustness findings:
  - Alternative proxies:
    - IV methods sometimes produce incorrect signs.
    - HP filter keeps housing and equity gaps significant but yields smaller magnitudes.
    - Fundamental valuation ratios used in benchmark.
  - Sample selection:
    - Pre-GFC sample: semi-elasticity with respect to output lower than benchmark; housing coefficient higher.
    - Non-GIIS sample (excluding Greece, Ireland, Italy, Spain): semi-elasticity of output larger; housing coefficient smaller.
  - Emerging markets:
    - Elasticity of fiscal balance to output cycle is lower at 0.36 for emerging markets (sample includes 20 OECD countries plus the listed emerging economies).
    - Average expenditure-to-GDP ratio in emerging-market sample about 0.35.
  - Omitted variables:
    - Adding credit growth and market capitalization does not materially change benchmark results.
  - Non-linearity:
    - Modest evidence of non-linearity in equity price gap; overall semi-elasticity pattern broadly unchanged.
  - Instrumental variables / dynamics:
    - System GMM and dynamic specifications broadly confirm benchmark pattern; equity price gap impact remains consistent.
  - Additional robustness:
    - Semi-elasticity of overall fiscal balance with respect to equity cycles remains stable between 0.035 and 0.045 across specifications.
    - Four-quarter lagged housing price gap not significant; contemporary impact stronger.
- Selected coefficient table excerpts (Appendix II Table 2 and Table 3 preserved values):
  - Output gap coefficients across specifications:
    - Benchmark: 0.583***; With 4-qtr lagged asset price gaps: 0.680***; With banking crisis dummy: 0.541***; with CAPE: 0.651***; with 4-qtr smoothed gaps: 0.630***; dummy for expansion: 0.611**.
  - Price-to-Rent gap (%) coefficients (selected): Benchmark: 0.053***; With 4-qtr lagged asset price gaps: 0.009; With banking crisis dummy: 0.043***; with CAPE: 0.032; with 4-qtr smoothed gaps: 0.039**.
  - Price-to-Book gap (%) coefficients (selected): Benchmark: 0.036***; With 4-qtr lagged asset price gaps: 0.032***; With banking crisis dummy: 0.034***; with CAPE: 0.040***.

### X. Fiscal impact of asset price cycles — magnitudes and examples
- Average OECD effects (benchmark semi-elasticity with fundamental valuation ratios, pre-crisis):
  - Housing cycles ≈ 1 percent of GDP.
  - Equity cycles ≈ 1¼ percent of GDP.
  - Combined average fiscal impact ≈ 2 percent of GDP.
- Illustrative country-specific pre-crisis impacts:
  - Ireland housing impact ≈ 3 percent of GDP pre-crisis.
  - United Kingdom housing impact ≈ 1 percent of GDP pre-crisis.
  - United States housing impact ≈ 1¼ percent of GDP pre-crisis.
  - Spain overall pre-crisis fiscal impact above 4 percent of GDP, mainly due to equity price misalignment.
- Dot-com equity bubble late 1990s:
  - Pronounced fiscal impact, especially in Spain and the United States, with estimated impact about 4 percent of GDP.
- Method differences:
  - Elasticity approach with HP-filtered asset cycles yields smaller estimated fiscal impacts than semi-elasticity approach using fundamental valuation ratios.

### XI. Synchronization of cycles — empirical patterns
- Appendix II Table 1 (2000Q1–2012Q4) highlights:
  - Stock prices troughed in late 1998 and early 2009 and peaked in late 2000 and 2007 in most countries.
  - Housing prices peaked in many countries during late 2007 and early 2008.
- Concordance between de-trended output, equity, and house prices:
  - Cycles synchronized roughly 45 to 70 percent of the time depending on country and cycle type.
  - Median correlation between cycles about 0.45 to 0.5 with significant variation by country.
  - Concordance index between de-trended equity and house prices ranged between 0.4 and 0.7 with a median of 0.59.
- Note on metrics:
  - Bivariate correlations affected by amplitude/level shifts and can be misleading; concordance focuses on duration of co-movement.

### XII. Conclusions and policy implications
- Methodology:
  - Operational approach presented to adjust fiscal balances for asset-price cycles using HP filter, intrinsic valuation, and fundamental valuation; each approach has trade-offs and requires practitioner judgment.
  - More disaggregated data could improve identification of revenue components sensitive to asset price cycles.
- Key findings:
  - Economic and asset price cycles are not fully synchronized; corrections for asset prices are necessary to avoid pro-cyclical bias in SFB calculations.
  - Asset price cycles are quantitatively important for fiscal balances and revenues.
  - Average fiscal impact of asset price cycles in OECD sample about 2 percent of GDP pre-crisis; can reach at least 4 percentage points of GDP during large mis-valuation episodes.
- Policy recommendation:
  - Correcting fiscal balances for asset price cycles is important to prevent cyclical revenues being converted into recurrent expenditures that create pro-cyclical fiscal stances and insufficient buffers for future revenue declines.

*Source: _wp15109 - REFERENCES (IMF working paper content provided).*

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

### _wp15109 - References .............................................................................................................

### I. Introduction — focus and motivation
- Temporary asset price movements can exert a large fiscal impact through:
  - build-up of contingent fiscal risks in the financial sector, and
  - direct impact on revenues (taxes on capital transactions and wealth effects).
- This paper focuses on adjusting structural fiscal balances (SFBs) for the cyclical revenue impact of asset prices.
- Conventional SFB calculations adjust for the business cycle and one-time transactions but may miss the revenue effects of asset price cycles.
- Key operational focus:
  - date asset price cycles,
  - measure synchronization between asset price cycles and the business cycle,
  - estimate responsiveness of government revenues and the overall fiscal balance to business and asset price cycles using elasticity and semi-elasticity approaches.
- Asset classes considered: equities and residential housing.
- Sample context:
  - OECD business and asset price cycles are not fully synchronized.
  - Excluding asset price cycles can lead to misleading SFBs and reinforce pro-cyclical fiscal policy by passing temporary revenue gains into recurring expenditures.
- Quantified effect (pre-crisis, average across 20 OECD countries):
  - SFB excluding asset price cycles overestimated the underlying fiscal balance by about 2 percentage points of GDP.
  - Contribution to the 2 percentage points:
    - ¾ percentage point of GDP owing to the impact of house price cycles.
    - 1¼ percentage points of GDP owing to the impact of equity price cycles.
- Larger fiscal impacts occurred in economies with extensive and persistent asset price rises, including Ireland and Spain.

### II. Literature review — prior approaches and findings
- Studies mostly focus on OECD and other advanced economies due to asset market importance and data availability.
- Common findings:
  - Government revenues and fiscal balance are significantly affected by asset prices.
  - Property prices tend to have a larger elasticity than stock prices.
- Typical empirical approaches:
  - Fixed-effects OLS to capture contemporaneous relationships (e.g., Eschenbach and Schuknecht (2004); Farrington and others (2008)).
  - Error-correction mechanisms to capture short- and long-run relationships (e.g., Price and Dang (2011)).
  - Elasticity and semi-elasticity estimation frameworks to adjust beyond the business cycle.
- Methods to measure asset price cycles:
  - Hodrick-Prescott (HP) filter (widely used, consistent with output gap estimation).
  - Detrending relative to equilibrium or fundamentals (e.g., median ratio of real house prices to real disposable per capita income; Gordon model for equity valuation; models anchoring long-term equilibrium house prices via user cost and price-to-rent).
- Gap in the literature: none of the cited studies assesses the impact of not accounting for asset price cycles on the pre-crisis fiscal stance in OECD countries.

### III. Empirical methodology — data, steps, and conceptual framework
- Two-step approach to correct SFBs for asset price cycles:
  1. Identify asset price cycle measures and estimate synchronization with the business cycle. High synchronization could justify conventional output-cycle adjustments alone.
  2. Estimate coefficients for sensitivity of fiscal variables to business and asset price cycles and adjust SFB calculations beyond the business cycle.
- Data and sample:
  - Quarterly sample period: 1980Q1–2012Q4.
  - Sample: 20 OECD countries (AUS, BEL, CAN, DNK, FIN, FRA, DEU, GRC, IRL, ITA, JPN, KOR, NLD, NOR, NZL, ESP, SWE, CHE, GBR, USA).
  - Fiscal variables and real variables from OECD analytical database.
  - Real house prices from an IMF database incorporating BIS and national sources.
  - National stock price indices (MSCI) from DataStream.
- Direct and indirect channels:
  - Direct: taxes on capital and financial transactions (chart referenced: "Taxes on Financial and Capital Transactions, 1990–2012"; pre-crisis outcome in 2006 is highlighted).
  - Indirect: wealth effects raising consumption and output — unobserved directly and estimated econometrically.

### IV. Dating cycles and measuring synchronization — algorithms and metrics
- Cycle dating algorithm:
  - Use Harding and Pagan (2002a) algorithm (an extension of Bry and Boschan (1971) "BB" algorithm) to identify turning points by searching for local maxima and minima.
  - Censoring rules:
    - (i) the duration of a complete cycle must be at least five quarters; and
    - (ii) the duration of each phase must be at least two quarters.
  - For a series xt:
    - a cyclical peak occurs at quarter t if:
      {[(x_t --- x_{t-2})>0, (x_t --- x_{t-1})>0] and [(x_{t+2} --- x_t)<0, (x_{t+1} --- x_t)<0]}
    - a cyclical trough occurs at time t if:
      {[(x_t --- x_{t-2})<0, (x_t --- x_{t-1})<0] and [(x_{t+2} --- x_t)>0, (x_{t+1} --- x_t)>0]}
  - For the paper’s purposes, detrended real asset prices and output are used to eliminate common price factors when dating cycles.
- Synchronization metric:
  - Concordance index (Harding and Pagan (2002b)):
    - CI_xy measures the fraction of time two series x and y are in the same phase of their respective cycles over t = 1,...,T.
    - Index equals unity if series are perfectly procyclical and zero if perfectly countercyclical.
  - Concordance index is supplemented with simple correlation statistics.
- Empirical finding:
  - Historical output and asset prices are not fully synchronized in the data, motivating adjustment beyond the business cycle when asset price cycles affect fiscal variables.

### V. Key empirical insights and operational implications
- Practical implementation:
  - Estimate elasticity or semi-elasticity of revenues and fiscal balance to asset price cycles.
  - Apply those coefficients to cyclical components of asset prices to derive beyond-the-business-cycle adjustments to SFBs.
- Operational result (average across 20 OECD countries, pre-crisis):
  - Excluding asset price cycles leads to an overestimation of the underlying fiscal balance by about 2 percentage points of GDP.
  - Breakdown:
    - ¾ percentage point of GDP from house price cycles.
    - 1¼ percentage points of GDP from equity price cycles.
- Policy implications:
  - Conventional cyclical adjustment that ignores non-synchronized asset price cycles can:
    - Provide misleading signals on the underlying fiscal stance.
    - Reinforce pro-cyclical fiscal policy by converting temporary revenue gains into recurring expenditures.
    - Undermine incentives or assessments for building fiscal buffers to cushion future revenue declines when asset prices correct.

*Source: _wp15109 - References (IMF working paper content provided).*

### Appendix II Table 1 illustrates peaks and troughs of the cycles in real GDP, stock prices and

### _wp15109 - Appendix II Table 1 illustrates peaks and troughs of the cycles in real GDP, stock prices and

### Synchronization of cycles
- Appendix II Table 1 covers 20 countries from 2000Q1 to 2012Q4 and shows global cycle influence: stock prices troughed in late 1998 and early 2009 and peaked in late 2000 and 2007 in most countries; housing prices peaked in many countries during late 2007 and early 2008.
- Concordance between de-trended output, equity, and house prices:
  - Cycles are synchronized roughly 45 to 70 percent of the time depending on country and type of cycle.
  - Median correlation between cycles is about 0.45 to 0.5 with significant variation by country.
- Concordance index vs. bivariate correlations:
  - Bivariate correlations are affected by amplitude/level shifts and can be misleading; concordance focuses on duration of co-movement.
  - Concordance index between de-trended equity and house prices ranged between 0.4 and 0.7 with a median of 0.59.

### Measuring asset price cycles (three approaches)
- Hodrick-Prescott (HP) filter:
  - Applied to real GDP, equity and housing series using smoothing parameters: 1600 (underlying real GDP), 74300 (equity), and 36573 (housing).
  - Operationally simple; generates symmetric expansion/contraction phases.
  - Vulnerable to end-point bias and understates mis-valuations during extreme episodes (e.g., tech bubble).
  - HP filter is the least preferred empirical proxy for asset price gaps.
- Intrinsic valuation (IV) models:
  - Gordon growth model for equities: relates (P/E)* to g, r, and σ via (P/E)* = (1+g)/(r+σ−g) (presentation preserved as in source).
  - Poterba model for housing: price-to-rent equilibrium related to user cost; inputs used in empirical exercise include real GDP growth, nominal 10-year government bond yield, spread between U.S. AAA corporate bond and U.S. Treasury 10-year bond yields, 10-year government bond yields as after-tax mortgage rate, property tax rates from Girourd and others (2006), 4 percent recurring holding costs, and expected capital gain approximated by a 5-year moving-average of the consumer inflation rate.
  - Theoretically robust but sensitive to input choices and can generate counter-intuitive gaps.
- Fundamental valuation ratios:
  - Long tradition (Graham and Dodd; Shiller’s CAPE); derive gaps as deviation from long-run mean.
  - Historical mean in empirical work calculated as average between 1980 and 2012, subject to data availability.
  - Operationally attractive due to data availability.

### Estimation framework
- Elasticity approach:
  - Define revenue and expenditure elasticity coefficients (ε_R, ε_E) where a 1-percent change in nominal output leads to ε_R (ε_E) percent change in nominal revenues (expenditures).
  - Use pooled mean-group (PMG) estimator for panel (long-run coefficients homogeneous; short-run and adjustment speeds can vary).
  - PMG advantages: does not require proxy of potential output for estimation; allows long-run and short-run elasticities and speed-of-adjustment estimation; computationally intensive (maximum likelihood).
- Semi-elasticity approach:
  - Define semi-elasticity η of overall balance ratio relative to the output gap: cab = overall balance ratio adjusted by η times output gap (expression preserved as in source).
  - A 1-percent change in nominal output relative to potential leads to an η-percentage point change in overall balance-to-output ratio.
  - η can be estimated by regressing overall balance-to-GDP ratio on output gap (fixed-effects panel); variables generally stationary.
  - Semi-elasticity related to revenue and expenditure elasticities via equation (9) (as in source).
  - Asset price corrections included analogously with asset price gaps (F relative to its fundamental value) and elasticity coefficients (ε_F^R, ε_F^E).

### Empirical results — elasticity approach
- Long-run revenue elasticity with respect to output:
  - Long-run elasticity ≈ 1 (unitary), interpreted as a 1-percent permanent increase in output → ~1-percent permanent increase in total revenues in the long run.
- Short-run revenue elasticity to real GDP:
  - Short-run elasticity ≈ 0.62 (temporary 1-percent increase in output → 0.62 percent increase in total revenues).
- Speed of adjustment:
  - 2.5 percent per quarter adjustment; half of deviations adjusted in 34 quarters.
- Asset price long-run elasticities (when added):
  - Revenues to real house prices: long-run elasticity 0.166.
  - Revenues to real stock prices: long-run elasticity 0.095.
  - Short-run elasticities: real house prices 0.14; real stock prices 0.01.
- Observations and sample:
  - Obs.: varying by specification: e.g., 1,460 to 2,083 observations; Countries: 20.

### Empirical results — semi-elasticity approach (Table 3 summary)
- Semi-elasticity of overall balance ratio:
  - Output gap semi-elasticity declines from 0.83 (Column 1) to 0.58 (Column 4) when asset price cycles are included.
  - Inclusion of asset price cycles implies business and asset cycles are not fully synchronous.
  - Semi-elasticity coefficients:
    - Output gap: 0.583*** (Column 4) with robust t-statistics reported in table.
    - Housing price gap: 0.053*** (when included).
    - Equity price gap: 0.036*** (when included).
  - Interpretation: semi-elasticity 0.58 corresponds to an elasticity of about 1½ (based on revenue and expenditure ratios).
- Statistical details:
  - Dependent variable: overall balance-to-GDP ratio (in percent).
  - Output gap estimated using HP filter (in percent); housing gap: de-trended price-to-rent ratio; equity gap: demeaned price-to-book ratio.
  - Estimator: fixed effects with robust t-statistics; sample Obs. range and Countries vary by column (e.g., Obs. 2,082; Countries 18 in Column 4).
  - Adjusted R-squared increases when asset gaps included (e.g., 0.292 for full specification).

### Robustness checks and sensitivity
- Robustness exercises include alternative asset gap measures, sample composition/time periods, omitted variables, simultaneity bias, non-linear specifications, and additional checks.
- Key robustness findings:
  - Alternative proxies: IV methods sometimes produce incorrect signs; HP filter keeps housing and equity gaps significant but yields smaller magnitudes; fundamental valuation ratios used in benchmark.
  - Sample selection:
    - Pre-GFC sample: semi-elasticity with respect to output lower than benchmark; housing coefficient higher.
    - Non-GIIS sample (excluding Greece, Ireland, Italy, Spain): semi-elasticity of output larger than benchmark; housing coefficient smaller.
  - Emerging market economies:
    - Elasticity of fiscal balance to output cycle is lower at 0.36 for emerging markets (sample includes Argentina, Brazil, Chile, China, Colombia, Hong Kong SAR, Hungary, India, Indonesia, Malaysia, Mexico, Peru, Philippines, Poland, Singapore, South Africa, Taiwan P.o.C., Thailand, Venezuela, Vietnam, and 20 OECD countries).
    - Average expenditure-to-GDP ratio in emerging-market sample about 0.35.
  - Omitted variables:
    - Adding credit growth (annual growth of banking credit to private sector) and market capitalization (proxy for financial development) does not materially change benchmark results.
  - Non-linearity:
    - Modest evidence of non-linearity in equity price gap; overall pattern for semi-elasticities broadly unchanged.
  - Instrumental variables / dynamics:
    - System GMM and dynamic specifications broadly confirm benchmark pattern; equity price gap impact remains consistent.
  - Additional robustness:
    - Tests including duration of asset price cycle, four-quarter lagged asset gaps, banking crisis dummies, cyclically-adjusted CAPE, and four-quarter smoothing show little change.
    - Semi-elasticity of overall fiscal balance with respect to equity cycles remains stable between 0.035 and 0.045 across specifications.
    - Four-quarter lagged housing price gap not significant; contemporary impact stronger.

### Fiscal impact of asset price cycles
- Illustrative country comparisons (Ireland, Spain, United Kingdom, United States):
  - Adjusting for asset price cycles suggests SFBs were over-estimated in years preceding the global financial crisis by about 3 percentage points of GDP on average compared to conventional cyclically-adjusted fiscal balance.
  - Dot-com equity bubble late 1990s: pronounced fiscal impact, especially in Spain and the United States, with estimated impact about 4 percent of GDP.
- Average OECD effects (benchmark semi-elasticity with fundamental valuation ratios):
  - Average fiscal impact in OECD of housing cycles ≈ 1 percent of GDP pre-crisis.
  - Average fiscal impact in OECD of equity cycles ≈ 1¼ percent of GDP pre-crisis.
  - Combined average fiscal impact in OECD ≈ 2 percent of GDP pre-crisis.
- Country-specific pre-crisis impacts:
  - Ireland housing impact ≈ 3 percent of GDP pre-crisis.
  - United Kingdom housing impact ≈ 1 percent of GDP pre-crisis.
  - United States housing impact ≈ 1¼ percent of GDP pre-crisis.
  - Spain overall pre-crisis fiscal impact above 4 percent of GDP, mainly due to equity price misalignment.
- Method differences:
  - Elasticity approach with HP-filtered asset cycles yields smaller estimated fiscal impacts than semi-elasticity approach using fundamental valuation ratios.

### Conclusions and policy implications
- Methodology:
  - Provides operational approach to adjust fiscal balances for asset-price cycles using HP filter, intrinsic valuation, and fundamental valuation; each has pros and cons and requires practitioner judgment.
  - More disaggregated data could improve identification of revenue components sensitive to asset price cycles.
- Key findings:
  - Economic and asset price cycles are not fully synchronized; corrections for asset prices are necessary to avoid pro-cyclical bias in SFB calculations.
  - Asset price cycles are quantitatively important for fiscal balances and revenues.
  - Average fiscal impact of asset price cycles in OECD sample about 2 percent of GDP pre-crisis; can reach at least 4 percentage points of GDP during large mis-valuation episodes.
- Policy recommendation:
  - Correcting fiscal balances for asset price cycles is important to prevent cyclical revenues being converted into recurrent expenditures that create pro-cyclical fiscal stances and insufficient buffers for future revenue declines.

*Source: IMF staff estimates and analysis as presented in the referenced chapter/appendix.*

### REFERENCES

### _wp15109 - REFERENCES

### Key references cited
- Agnello, L. and R. Sousa, 2011, "Fiscal Policy and Asset Prices," Bulletin of Economic Research, Vol. 65(2): pp. 154---77.
- André, C., 2010, "A Bird’s Eye View of OECD Housing Markets," OECD Economic Department Working Papers No. 746.
- Benetrix, A. and P. Lane, 2011, "Financial Cycles and Fiscal Cycles," Unpublished Manuscript.
- Bornhorst, F., G. Dobrescu, A. Fedelino, J. Gottschalk, and T. Nakata, 2011, "When and How to Adjust Beyond the Business Cycle? A Guide to Structural Fiscal Balances," Technical Guidance Note, Fiscal Affairs Department (Washington: International Monetary Fund).
- Bry, G. and C. Boschan, 1971, "Cyclical Analysis of Economic Time Series: Selected Procedures and Computer Programs," NBER Technical Working Paper No. 20.
- Cashin, P., 2004, "Caribbean Business Cycles," IMF Working Paper No. 04/136.
- Claessens, S., A. Kose, and M. Terrones, 2011a, "Financial Cycles: What? How? When?" IMF Working Paper No. 11/76.
- Claessens, S., A. Kose, and M. Terrones, 2011b, "How Do Business and Financial Cycles Interact?" IMF Working Paper No. 11/88.
- Cochrane, J., 2011, "Presidential Address: Discount Rates," The Journal of Finance, Vol. LXVI, No. 4, August.
- Driscoll, J.C., and A.C. Kraay, 1998, "Consistent Covariance Matrix Estimation with Spatially Dependent Panel Data," Review of Economics and Statistics 80: 549---560.
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### Appendix I — Dynamic adjustment using long-run and short-run elasticity coefficients (summary)
- Scope:
  - Example applies to government revenues; approach is adaptable to government expenditures.
  - Variables expressed in logarithms (real terms): r = real government revenue, y = real output, s = real stock price index, h = real house price index.
- Long-run elasticities interpretation:
  - A 1-percent change in real output/equity/house prices leads to α1 / α2 / α3 percent change in real revenue.
- Dynamic (ARDL(1,1)) specification:
  - Expression (A.2) is an ARDL(1,1) representation allowing for dynamic effects and beyond-the-cycle (equity and house price gap) effects.
- Deviation-from-potential and exponentiated specification:
  - Taking differences with the steady state yields expression (A.3).
  - Exponentiating yields specification (A.4), where deviations of government revenues from potential depend on:
    - Its deviation in the previous period,
    - Output/equity/house price gaps in current and previous periods.
  - Elasticities α0–α6 needed for cyclical adjustment can be obtained from the error-correction specification.
- Error-correction estimation steps (summary of algebraic manipulations in the text):
  - Subtract r_{t-1} from both sides of (A.2).
  - Add and subtract α1 y_{t-1}, α2 s_{t-1}, and α3 h_{t-1} on the RHS.
  - Rearrange to generate the error-correction term.
- Error-correction model (A.6) interpretation:
  - β1/β2/β3 are short-run elasticities of revenue with respect to output/equity/house prices.
  - β5/β6/β7 are long-run elasticities of revenue with respect to output/equity/house prices.
  - β4 is the speed of adjustment coefficient.
  - After estimating β1–β7, derive α0–α6 needed for cyclical adjustment in (A.4) via the algebraic relations shown in the appendix.

### Appendix II — Empirical dating, robustness checks, and SFB comparisons (highlights)
- Cycle dating methodology:
  - Source: IMF staff estimates based on Harding and Pagan (2002a).
  - Estimations performed for detrended real GDP (GDP), detrended real house price (HP), and detrended real stock price (SP) variables.
  - Detrending was done using the HP filter with smoothing parameter 1600.
  - "P" indicates the quarter in which the series reached its peak; "T" denotes the quarter of trough.
  - A tabular/sequence listing shows peak/trough labels by quarter and country identifiers (e.g., 20001P T T P P P ... and country codes: CAN BEL AUS DEU CHE USA SWE NZL NLD NOR KOR JPN FIN ESP DNK ITA IRL GRC GBR FRA).
- Appendix II, Table 2 — Additional robustness checks (selected coefficient estimates and statistics; values preserved exactly):
  - Output gap coefficients across specifications:
    - Benchmark: 0.583***
    - With 4-qtr lagged asset price gaps: 0.680***
    - With banking crisis dummy: 0.541***
    - with Shiller cyclically adjusted price-to-earning gaps (CAPE): 0.651***
    - with 4-qtr smoothed gaps: 0.630***
    - With dummy for expansion in output and assets: 0.611**
  - Price-to-Rent gap (%) coefficients:
    - Benchmark: 0.053***
    - With 4-qtr lagged asset price gaps: 0.009
    - With banking crisis dummy: 0.043***
    - with CAPE: 0.032
    - with 4-qtr smoothed gaps: 0.039**
    - With dummy for expansion in output and assets: 0.043
    - With 4-qtr lagged output gap column: 0.064***
  - Price-to-Book gap (%) coefficients:
    - Benchmark: 0.036***
    - With 4-qtr lagged asset price gaps: 0.032***
    - With banking crisis dummy: 0.034***
    - with CAPE: 0.040***
    - with 4-qtr smoothed gaps: 0.042**
    - With dummy for expansion in output and assets: 0.041***
  - Interaction and other reported values:
    - Output gap*crisis: 0.069 [0.416]
    - Intercept values (selected): Benchmark -2.361*** [0.012]; With 4-qtr lagged asset price gaps -2.381*** [0.015]; With banking crisis dummy -2.317*** [0.096]; with CAPE -1.806*** [0.076].
    - Observations (Obs.): columns report 2082, 2082, 2014, 2082, 1757, 2031, 2082, 2034 (as displayed).
    - Countries: 18 in each column.
    - Adjusted R-squared: 0.292, 0.253, 0.300, 0.242, 0.295, 0.295 (as displayed).
    - Log likelihood values: -5,400; -5,300; -5,400; -4,600; -5,300; -5,400; -5,300.
  - Notes:
    - 1/ Banking crises dummies come from Laeven and Valencia (2012).
    - 2/ The equity cycles are calculated following techniques introduced in Shiller (2000).
    - 3/ Periods are defined as output (asset) expansion if the output (asset price) gaps are positive.
    - 4/ The duration dummy indicates the persistence of the expansion/contraction periods for business and asset cycles.
    - 5/ Concordance indices were checked but results were not significant and not presented.
- Appendix II, Table 3 — Robustness to different asset price measures (selected estimates; values preserved exactly):
  - Output gap:
    - Valuation Ratio: 0.583***
    - HP Filter: 0.471***
    - Intrinsic Valuation: 0.989***
  - Housing price gap (%):
    - Valuation Ratio: 0.053***
    - HP Filter: 0.067**
    - Intrinsic Valuation: -0.013**
  - Equity price gap (%):
    - Valuation Ratio: 0.036***
    - HP Filter: 0.043***
    - Intrinsic Valuation: 0
  - Intercept:
    - Valuation Ratio: -2.361***
    - HP Filter: -2.231***
    - Intrinsic Valuation: -2.198***
  - Observations (Obs.): 2082; 2427; 1707 (columns respectively).
  - Countries: 18; 20; 18.
  - Adjusted R-squared: 0.292; 0.196; 0.162.
  - Log likelihood: -5400; -6,400; -4,500.
  - Note (verbatim from table): The dependent variable is the overall balance/GDP ratio (in percent). Output gap is estimated using the HP filter (in percent). Estimations are performed using the fixed effects estimator. Robust t-statistics are in parentheses. *, **, and *** denote significance at 10, 5, and 1 percent confidence level, respectively. All variables are tested for unit root.
- Appendix II, Figure 1 — Comparison of Structural Fiscal Balance (SFB) estimates (description preserved):
  - Figure panels display, for multiple countries (Australia, Belgium, Canada, Denmark, Finland, France, Germany, Italy, Japan, Netherland, New Zealand, Norway, South Korea, Sweden, Switzerland), time series plots of:
    - Fiscal Balance
    - Cyclically-adjusted Fiscal Balance (overall balance adjusted for output cycles)
    - Structural Balance with Asset Price Correction (overall balance adjusted for output, housing and equity price cycles)
  - Vertical axis labeled "In percent of GDP"; horizontal axis sample ticks include 1995Q4, 1997Q4, 1999Q4, 2001Q4, 2003Q4, 2005Q4, 2007Q4, 2009Q4, 2011Q4 as shown in the figure.
  - Caption note: IMF staff estimates. Fiscal balance refers to overall fiscal balance for general government. Cyclically-adjusted fiscal balance is the overall balance adjusted for output cycles. Structural balance with asset price correction is the overall balance adjusted for output, housing and equity price cycles. The estimates do not account for one-off items.

*Italic: Source: _wp15109 - REFERENCES (content unit provided).*

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