## ch3onlineannex — EXECUTIVE SUMMARY

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---

### Data sources and variable definitions
- Macroeconomic and financial variables sourced from Refinitiv Datastream, IMF World Economic Outlook, Bloomberg, Bank for International Settlements, Trepp, MSCI Real Estate, Real Capital Analytics, IMF iMaPP database, BIS Macroprudential Database, ESRB Macroprudential Measures Database, Leo Krippner, CBOE, Moody’s, Call Reports, FDIC (2012), and IMF staff calculations.
- Key variable definitions:
  - Bank Stock Returns: Refinitiv Datastream's bank sector return index.
  - Broad Money: Broad money, seasonally adjusted.
  - Break Even Inflation: 10-years break even inflation rate.
  - Capital Inflows: Sum of portfolio investment and foreign direct investment.
  - CRE and CMBS Delinquency Rates: percentage of CRE and CMBS loans within a financial institution's loan portfolio whose payments are delinquent.
  - CRE Capitalization rate: Net Operating Income per CRE value.
  - CRE Investments: Investments in commercial real estate.
  - CRE Prices: Asset value index.
  - CRE Vacancy Rates: Total market rental value in vacant units / total market rental value.
  - Financial Condition Index: Positive values indicate tighter-than-average financial conditions (methodology in Annex 3.2 of October 2017 GFSR).
  - Global Liquidity Indicator: sum of bank loans to non-banks and debt securities issuance by non-banks.
  - Long-Term Nominal Interest Rate: 10-years government bond yield.
  - Net Operating Income Yield: Total net operating income for the period in percent of CRE value.
  - Liquidity Ratio: (Cash and balances due from depository institutions + securities + federal funds sold and securities purchased under agreements to resell) / total assets.
  - Community Bank: defined consistent with FDIC (2012) with thresholds and criteria preserved as in source.
  - Commercial Real Estate Loans: sum of construction, land development, and other land loans and loans secured by multifamily (5 or more) residential properties and loans secured by nonfarm nonresidential properties.
  - Corporate variables (Accumulated Depreciation, Capital Expenditures, Cash, Long-Term Debt, Short-Term Debt, Return on Assets, Price-to-Book Ratio, Property, Plant, and Equipment, Rental and Lease Properties, Age, Location) sourced from Refinitiv Datastream and IMF staff calculations where noted.

### Methodology — Price-to-NOI structural model and misalignment measurement
- Conceptual approach:
  - Campbell-Shiller decomposition expresses CRE prices in terms of current and expected growth of Net Operating Income (NOI) and current and expected total returns (equation (1)).
  - Total returns = real 3-month short-term interest rate + spread of total returns over the real 3-month rate.
- SVAR specification:
  - General form: A y_t = B0 + B(L) y_{t-1} + u_t (equation (2)).
  - Variables are detrended and demeaned; output gap estimated by HP-filtering GDP with smoothing parameter 1600.
  - Credit-to-GDP gap from Bank for International Settlements.
- Detrending and misalignment:
  - log(Price) = log(Price-to-NOI) + log(NOI) (equation (4)).
  - Target series: log Price-to-NOI and NOI detrended with Hodrick–Prescott filter.
  - Misalignment P_t defined as component of detrended log Price-to-NOI not expected to be driven by fundamentals (equations (5) and (6)).
  - Interpretation: positive P_t = overconfidence/overpricing; negative P_t = underpricing; P_t may capture model mis-specification, numerical errors, parameter uncertainty, market interventions.

### SVAR identification, priors, sample, and estimation choices
- Model extension includes vacancy rate (inverse logit-transformation) to capture CRE-specific demand shocks (equation (7)).
- Sign identification follows Baumeister and Hamilton (2015, 2018) summarized in Online Annex Table 3.2.1.
- Priors:
  - Contemporaneous matrix A prior: truncated t-distribution to satisfy sign restrictions.
  - Shock magnitudes: inverse Gamma distribution for standard deviation of Σ.
  - Lagged structural coefficients B(L): Minnesota priors, assumed normal.
- Lag order and robustness:
  - Companion-form transformation with S = 2 chosen based on robustness and explanatory power.
- Country-level sample:
  - Country-by-country analysis over 2001:Q2 to 2019:Q4 for Australia, Canada, Denmark, Germany, Italy, Portugal, South Africa, Spain, Sweden, United Kingdom, and United States.

### Historical decomposition and illustrative findings
- Decomposition:
  - Any SVAR variable written as sum of past structural shocks (equation (8)); log price decomposed into fundamental shocks and misalignments (equation (9)).
  - Using fair value model and estimated SVAR, CRE prices decomposed into underlying economic shocks and misalignments.
- U.S. example:
  - In 2020 the CRE fair price is below the actual price (Figure 3.6 in main text).
  - Main drivers: a large adverse demand shock from COVID-19 reduced fair value; declines in aggregate supply and loose monetary policy (proxied by broad money-to-output) helped lift fair values.

### Segment analysis
- Valuation model applied to office and retail segments where data allow.
- Segment analysis for a narrower country subset reported in Online Annex Figure 3.2.1.
- Shock calibration example: vacancy rate increases on average by 5 percentage points in next 10 years (used in Figure 3.6 panel 4).
- Graphical summaries reported include one standard error band, Average (2018H2-19H2), interquartile range, Median, Optimistic, and Pessimistic paths for Office and Retail across 2005–2019.

---

### Estimated misalignments in office and retail segments — snapshots and simulations

### Simulation approach for CRE-specific demand shocks
- Contemporaneous parameters identified; model simulated by adding a one standard deviation permanent shock to the vacancy rate.
- Impulse response (IPS) = simulated path with shock (Rvvpv...,t = 1σ) minus path without shock (Rvvpv...,t = 0).
- Expectations computed using companion form yt� = M0 + Myt�−1 + Rt� and equation (5); Price-to-NOI and NOI simulated by forward iteration.
- Linear model allows shock rescaling; calibration for Figure 3.6 panel 4: vacancy rate calibrated to increase on average by 5 percentage points in the next 10 years.

### Calibration and reported graphical elements (Office and Retail)
- Shock size example: 5 percentage points vacancy increase over 10 years.
- Reported graphical elements: one standard error band; Average (2018H2-19H2); Interquartile range; Median; Optimistic and Pessimistic paths for Office and Retail (2005–2019).

---

### Macro-financial effects of CRE prices — Growth-at-Risk framework

### Model and estimation
- Objective: assess amplification of CRE price misalignment on downside risks to real GDP growth.
- Panel quantile local projections:
  - Δh YP,t,τ = αP,τh + βτh · CRE Misalignment i,t−1 + θτh · CCIRRPIIs P,t−1 + εP,t,τh
  - Δh YP,t,τ: (average) percentage change in real GDP growth in country P from quarter R to R+ h at quantile τ (focus on 5th percentile).
  - CRE Misalignment indicator: sign-inverted deviation of log capitalization rate from historical trend.
  - Controls: lag GDP growth, financial condition index (purged of CRE price variation), credit-to-GDP gap, house price growth.
- Data:
  - Unbalanced panel for 30 economies (23 advanced and 7 emerging market economies) from 2000:Q1 to 2019:Q4.
- Robustness:
  - Alternative estimator: Machado and Santos Silva (2019).
  - Estimation on smaller country sample using misalignment from Online Annex 3.2.
  - Results broadly consistent.

---

### Bank-level analysis — exposure, identification, and findings

### Empirical specification
- Data: MSA-level CRE price data and U.S. Bank Call Reports (2001:Q1–2020:Q3).
- Main estimating equation captures interactions of banks’ CRE exposure with CRE price changes and asymmetry for price declines:
  - Yb,t l outcomes include:
    - (i) non-performing CRE loans (90+ days overdue)-to-total CRE loans ratio,
    - (ii) charged off CRE loans (net of recoveries)-to total CRE loans ratio,
    - (iii) log change in pre-provision net revenues (PPNR),
    - (iv) log change in total regulatory capital.
  - CRE_Exposure_b,t−k l = bank b’s CRE loans at t-k / total assets.
  - ΔP t,t−k l = (log) change in average CRE price index in MSA l (MSCI Real Estate Portal).
  - I(ΔP < 0) indicator captures asymmetry (declines trigger LTV constraints).
  - Controls: capital ratio, liquidity ratio, log total assets, and interactions; fixed effects μb (bank) and η l,t (MSA x quarter).

### Estimation details and sample coverage
- Estimation via weighted least squares; weight = log of bank total assets.
- Standard errors double clustered at bank and quarter level.
- Identification and coverage:
  - Sample restricted to MSAs with multiple banks (robust to inclusion of single-bank MSAs; 4 MSAs have a single bank headquarter).
  - Broad sample includes all banks submitting FFIEC 031 and 051 Call Reports.
  - Coverage: total of 10,796 banks over entire sample period; 5,116 reporting banks in 2020:Q3.
  - Focus on banks in 69 major MSAs for which CRE price indices are available (on average cover more than 50 percent of total banking sector assets).
  - Robustness: expanded sample using state- or Census Bureau region averages of MSA-level CRE prices yields qualitatively similar results.

### Measurement notes and limitations
- Disaggregated segment-level CRE price indices exist, but bank loan data by segment not available; therefore average CRE prices used.
- Banks assumed exposed to CRE price changes in their headquarter MSAs; over 95 percent of US banks are small/community banks and geographically concentrated.
- Potential mismeasurement of CRE locations/prices likely induces attenuation bias.

---

### Capital loss scenarios and stress calculations

### Scenario definitions (CRE price paths)
- Mild adverse scenario:
  - CRE prices implied by a 1.15 percent permanent increase in the vacancy rate.
  - Implies a cumulative drop in CRE prices by 16 percent after 8 quarters (Online Annex Figure 3.3.2).
- Alternative valuation-model scenario:
  - Permanent increase in vacancy rates by 5 percentage points (as projected by valuation model).
  - Implies about 30 percent decline in CRE prices in the long run.
- Assumption: common CRE price path across MSAs due to lack of MSA-specific CRE price forecasts.

### Translating sensitivities into dollar capital impacts (procedure)
- Estimate equation (12) with dependent variable (ii) net CRE loan charge-off rate; forward the estimated equation by k periods to obtain Yb,t+k l = (αk� + βk� * CRE_Exposure_b,t l * ΔP t+k,t l).
- Assume total outstanding CRE loans decline by 2 percent quarterly for each bank.
- Multiply projected charge-off rates by projected CRE loan balances to obtain dollar CRE loan losses by bank and horizon.
- Allowance for Loan & Lease Losses (ALLL) due to CRE loan exposure assumed equal to four quarters of projected net CRE loan charge-offs; provision expenses calculated accordingly (CLASS Model assumptions referenced).
- Estimate PPNR percentage changes from equation (12) with dependent variable (iii) and apply to PPNR in 2020:Q3 to obtain PPNR dollar losses by horizon k and bank.
- Sum CRE-driven provision expenses and PPNR losses and divide by pre-shock total risk weighted assets (2020:Q3) to obtain capital impact.

### Methodological notes
- Procedure follows related top-down stress-test literature (Hirtle and others 2015) but is not a full top-down stress test — it estimates marginal impact of a decline in CRE prices on bank capital via credit and revenue channels under given regulatory rules.
- Extensions can incorporate macroeconomic effects by including location x quarter fixed effects in forecast horizon and assuming a path for those effects for k = 1, 2, ... 8.

---

### Impact of CRE prices on corporate investment

### Baseline firm-level investment model and key variables
- Empirical specification (conceptual):
  - Investment rate (capital expenditures / lagged PPE) regressed on RE_Value_i,baseline / lagged PPE interacted with ΔP t c / P baseline, controls, firm and city-sector-year fixed effects.
- Definitions:
  - IRIEsRPerR P,t: ratio of capital expenditures of firm i in year t normalized by lagged PPE.
  - RE_Value_i,baseline: market value of firm i’s real estate holdings in baseline year normalized by lagged PPE (estimated following Chaney and others (2012)).
  - ΔP t c / P baseline: change in CRE prices in city c (firm headquarters) from baseline to year t.
  - Controls: current cash flows / lagged PPE, lagged market-to-book ratio, firm characteristics (size, age, return on assets), and interactions.

### Robustness and identification
- Results robust across sample periods: 2004-2007; 2008-2009; 2010-2019.
- Results hold for small firms within cities (firms with total assets < 25th percentile of city firms).
- Alternative dependent variables produce consistent results: change in PPE net of change in book value of real estate assets; three-year forward-looking investment; firm-level investment adjusted by sector peers.
- Baseline year choices (2004, 2008, 2010) do not alter main findings.

### Limitations and IV approach
- Limitation: lack of exact data on firms’ real estate holdings locations; assumption that holdings concentrated in headquarters city may induce attenuation bias.
- Instrumental-variable (US-only first stage):
  - First-stage: P t c = αc + δt + γ · [LandSupplyConstraints × 30-year Treasury rate] + ε t c
  - First-stage estimate: γ = 0.0155 (p-value: 0.0017); adjusted R2 = 0.95; N = 880.
  - Instrumented CRE prices from first stage used in second-stage regressions yield strongly robust estimates for β.

---

### Policy analysis — Impact of policies on CRE prices (Online Annex 3.4)

### Sample and objective
- Unbalanced panel for 30 economies (23 advanced and 7 emerging market economies) from 2000:Q1 to 2019:Q4.
- Objective: assess impact of policy measures (macroprudential and capital flow management) on downside risks to CRE prices.
- Outcome variable: Δ_h Y_P,t,τ — (average) percentage change in real CRE prices in country P from quarter R to R+ h at quantile τ (focus on 5th percentile).

### Estimation approach and controls
- Panel quantile regression with country fixed effects α_P,h and controls: lagged real GDP growth, changes in credit-to-GDP ratio, capital inflows-to-GDP ratio, VIX index.
- Macroprudential policy change variable ΔMP_P,t captures change in macroprudential stance; monetary policy shock MP_P,t captured as residual from policy rate regression.
- Macroprudential and capital flow measures purged of credit-to-GDP and capital flows-to-GDP variations where specified to address endogeneity.

### Macroprudential policy categorizations and construction
- CRE-specific (targeted) measures:
  - Categorical variable: -1 = loosening action, 0 = no change, 1 = tightening action in a quarter.
  - Measures directly limit borrower access to CRE credit or increase cost of CRE lending (e.g., CRE-specific LTV, DSR, higher risk weights, sectoral capital buffers).
- Borrower-based measures:
  - Two-year rolling sum of individual measures with +1 = tightening, 0 = no change, -1 = loosening; includes residential measures potentially affecting CRE indirectly.
- Both sets purged of credit-to-GDP to mitigate endogeneity.

### Monetary policy shock treatment
- Policy shock = residual from regression of policy rate on contemporaneous and lagged macro variables (real GDP, inflation, stock returns) and quadratic time trend (Iacoviello and Navarro (2019) approach).
- For selected countries (US, Euro Area, UK, Japan, Switzerland, Canada, Australia, New Zealand) use Leo Krippner shadow rate to capture unconventional policy.
- Robustness: alternatives include actual policy rate and Wu and Xia (2016) shadow rate.

### Capital flow management measures
- Replace ΔMP with ΔCFM to evaluate association between capital flow management and downside CRE price risks.
- Capital flow measures: overall capital inflow restrictions index or real-estate-specific capital inflow restriction index from Fernández and others (2017), updated.
- Constructed as two-year rolling sum (+1 tightening, 0 no change, -1 loosening) and purged of capital flows-to-GDP variations.

### Examples of CRE-specific macroprudential measures (selected)
- Denmark, Jun. 2003: 60% LTV limit on recreational dwellings, office properties and retailing properties, industrial properties and craftsman's properties, collective energy-supply plants.
- Hong Kong SAR, Feb. 2013: 10 pp lower LTV limit on mortgage loans for all commercial and industrial properties.
- Hong Kong SAR, May 2017: Lower DSR limit by 10 percentage points for certain borrowers.
- Indonesia: multiple LTV adjustments across Jun. 2012, Jun. 2015, Aug. 2016, Jun. 2018 affecting office/shop house and property loans.
- Ireland, Jan. 2007 and Jan. 2014: minimum risk weight on commercial property lending increased from 50% to 100%.
- Norway, Sep. 2014: Risk weight of 100% on CRE lending for banks using standardized approach.
- Poland, Jan. 2005; Jun. 2014; Dec. 2017: various risk weight and LTV rules on commercial property.
- Singapore, Jan. 2013; Jun. 2013: seller's stamp duties for industrial properties; TDSR applied to residential and nonresidential property.
- Sweden, Jan. 2014: 100% risk-weight floor for commercial mortgages under standardized approach.
- United Kingdom, Jan. 2014 and Oct. 2014: stricter criteria and eligibility for risk-weight treatment on CRE lending.
- United States, Dec. 2006; Jan. 2015; Dec. 2016: guidance to banks on CRE concentration; 150% risk weight on HVCRE; implementation of 5 percent risk retention rule for securitizations.

*Source: ch3onlineannex - EXECUTIVE SUMMARY and Online Annexes (International Monetary Fund staff calculations; data sources cited in original).*

### EXECUTIVE SUMMARY

### EXECUTIVE SUMMARY — Commercial Real Estate (Online Annexes)

### Data sources and variable definitions
- Macroeconomic and financial variables sourced from Refinitiv Datastream, IMF World Economic Outlook, Bloomberg, Bank for International Settlements, Trepp, MSCI Real Estate, Real Capital Analytics, IMF iMaPP database, BIS Macroprudential Database, ESRB Macroprudential Measures Database, Leo Krippner, CBOE, Moody’s, Call Reports, FDIC (2012), and IMF staff calculations.
- Key variable definitions preserved as in the source:
  - Bank Stock Returns: Refinitiv Datastream's bank sector return index.
  - Broad Money: Broad money, seasonally adjusted.
  - Break Even Inflation: 10-years break even inflation rate.
  - Capital Inflows: Sum of portfolio investment and foreign direct investment.
  - CRE and CMBS Delinquency Rates: percentage of CRE and CMBS loans within a financial institution's loan portfolio whose payments are delinquent.
  - CRE Capitalization rate: Net Operating Income per CRE value.
  - CRE Investments: Investments in commercial real estate.
  - CRE Prices: Asset value index.
  - CRE Vacancy Rates: Total market rental value in vacant units / total market rental value.
  - Financial Condition Index: Positive values indicate tighter-than-average financial conditions (methodology in Annex 3.2 of October 2017 GFSR).
  - Global Liquidity Indicator: sum of bank loans to non-banks and debt securities issuance by non-banks.
  - Long-Term Nominal Interest Rate: 10-years government bond yield.
  - Net Operating Income Yield: Total net operating income for the period in percent of CRE value.
  - Liquidity Ratio: (Cash and balances due from depository institutions + securities + federal funds sold and securities purchased under agreements to resell) / total assets.
  - Community Bank: defined consistent with FDIC (2012): (i) total assets less than $1 billion (in 2010 terms), or (ii) if total assets higher than $1 billion (in 2010 terms), then loan-to-assets ratio > 33%, core deposits-to-total assets > 50%, and number of states with offices ≤ three; banks with no loans or no core deposits or foreign deposits-to-total deposits ratio > 10% are labeled non-community banks.
  - Commercial Real Estate Loans: sum of construction, land development, and other land loans and loans secured by multifamily (5 or more) residential properties and loans secured by nonfarm nonresidential properties.
  - Corporate variables (Accumulated Depreciation, Capital Expenditures, Cash, Long-Term Debt, Short-Term Debt, Return on Assets, Price-to-Book Ratio, Property, Plant, and Equipment, Rental and Lease Properties, Age, Location) sourced from Refinitiv Datastream and IMF staff calculations where noted.

### Methodology — Price-to-NOI structural model and misalignment measurement
- Campbell-Shiller decomposition is used to express CRE prices in terms of current and expected growth of Net Operating Income (NOI) and current and expected total returns on CRE holdings (equation (1) in source).
- Total returns are expressed as the sum of the real 3-month short-term interest rate and the spread of total returns over the real 3-month rate.
- A structural vector autoregression (SVAR) links CRE price, NOI, returns and fundamentals:
  - General form: A y_t = B0 + B(L) y_{t-1} + u_t (equation (2)).
  - Variables include detrended and demeaned series; output gap is estimated by HP-filtering GDP with smoothing parameter 1600.
  - Credit-to-GDP gap is taken from the Bank for International Settlements.
- Detrending and misalignment:
  - The logarithm of CRE price decomposed into log(Price-to-NOI) + log(NOI) (equation (4)).
  - Targeted series for misalignment are the logarithm of Price-to-NOI and NOI detrended with the Hodrick–Prescott filter.
  - Misalignment P_t is defined as the component of the detrended log Price-to-NOI ratio not expected to be driven by economic fundamentals (equations (5) and (6)).
  - Interpretation: positive P_t = overconfidence/overpricing relative to fundamentals; negative P_t = underconfidence/underpricing; P_t may also capture mis-specification, numerical errors, parameter uncertainty, market interventions.

### SVAR identification, priors, and sample
- Model extension to include the vacancy rate (inverse logit-transformation) to capture CRE-specific demand shocks (equation (7)).
- Sign identification follows Baumeister and Hamilton (2015, 2018) as summarized in Online Annex Table 3.2.1 (sign assumptions across supply, demand, conventional monetary policy, spread, NOI growth, credit-to-output, broad money-to-output, capital flow-to-output, vacancy rate).
- Priors:
  - Contemporaneous matrix A prior set by truncated t-distribution to satisfy sign restrictions.
  - Shock magnitudes (standard deviation of Σ) given by inverse Gamma distribution.
  - Lagged structural coefficients B(L) assumed normal and set by Minnesota priors.
- Lag order and robustness:
  - Companion-form transformation and S = 2 chosen based on robustness and explanatory power.
- Sample (country-level analysis): performed country-by-country over the period 2001:Q2 to 2019:Q4 for Australia, Canada, Denmark, Germany, Italy, Portugal, South Africa, Spain, Sweden, United Kingdom, and United States.

### Historical decomposition and illustrative findings
- Any variable in the SVAR can be written as the sum of past structural shocks (equation (8)), allowing decomposition of log price into contributions from fundamental shocks and misalignments (equation (9)).
- Using the fair value model and estimated SVAR, CRE prices are decomposed into underlying economic shocks and misalignments.
- U.S. example finding:
  - In 2020 the CRE fair price is below the actual price (Figure 3.6 in main text).
  - Main drivers: a large adverse demand shock from the COVID-19 pandemic reduced fair value; declines in aggregate supply and loose monetary policy (proxied by broad money-to-output) helped lift fair values.

### Segment analysis
- The valuation model is applied to estimate misalignments for CRE office and retail segments.
- Segment analysis is performed for a narrower universe of countries due to data availability.
- Results are reported in Online Annex Figure 3.2.1.

*Source: ch3onlineannex - EXECUTIVE SUMMARY*

### 1. Estimated misalignments in the office and retail segments –

### 1. Estimated misalignments in the office and retail segments – snapshots before the COVID-19 pandemic

### Simulating CRE prices and measuring misalignments
- Misalignments are based on the estimated residuals of the fair-price model applied to the real CRE price deviations from trend.
- Simulation approach:
  - Contemporaneous parameters identified; model simulated by adding a one standard deviation permanent shock to the vacancy rate representing a CRE-specific demand shock in the structural shock vector.
  - The impulse response (IPS) is defined as the deviation of the simulated path of prices forecasted under the shock (Rvvpv...,t = 1σ) from the one forecasted without shocks (Rvvpv...,t = 0).
  - Expectations computed using the companion form yt� = M0 + Myt�−1 + Rt� and equation (5).
  - Price-to-NOI and NOI simulated by forward iteration. Because the model is linear, shocks can be rescaled.
  - In panel 4 of Figure 3.6 (Chapter 3), the shock size is calibrated so the vacancy rate would gradually increase on average by 5 percentage points in the next 10 years.

### Calibration and graphical summaries (as reported)
- Shock calibration example:
  - Vacancy rate increases on average by 5 percentage points in the next 10 years (used in Figure 3.6 panel 4).
- Graphical elements reported in source include:
  - One standard error band and Average (2018H2-19H2) for Office and Retail (before COVID-19).
  - Interquartile range, Median, Optimistic, Pessimistic paths for Office and Retail across years 2005–2019.

*Italic note: Sources for figures and data: Bloomberg, L.P., Haver, MSCI Real Estate; and IMF Staff calculations.*

---

### 2. Macro-financial effects of CRE prices

### Growth-at-Risk model (local projections with panel quantile regression)
- Objective: assess amplification of CRE price misalignment on downside risks to real GDP growth.
- Model specification (panel quantile estimation following Canay (2011) and local projections):
  - Δh YP,t,τ = αP,τh + βτh · CRE Misalignment i,t−1 + θτh · CCIRRPIIs P,t−1 + εP,t,τh
  - Δh YP,t,τ denotes the (average) percentage change in real GDP growth in country P from base quarter R to R+ h (h = 1, 2, ..., 16) at quantile τ (5th percentile).
  - CRE Misalignment indicator: sign-inverted deviation of log capitalization rate from a historical trend.
  - Controls: lag GDP growth, financial condition index (purged of CRE price variation), credit-to-GDP gap, and house price growth.
- Data:
  - Unbalanced panel for 30 economies (23 advanced and 7 emerging market economies) from 2000:Q1 to 2019:Q4.
- Robustness:
  - Alternative panel quantile estimator following Machado and Santos Silva (2019).
  - Estimation on a smaller country sample using misalignment measure from Online Annex 3.2.
  - Results broadly consistent.

---

### 3. Bank-level analysis

### Empirical strategy and model
- Data combined: MSA-level CRE price data and U.S. Bank Call Reports (2001:Q1–2020:Q3).
- Main estimating equation (summary of structure):
  - Yb,t l = αk · CRE_Exposure_b,t−k l * ΔP t,t−k l · I(ΔP t,t−k l < 0) + βk · CRE_Exposure_b,t−k l * ΔP t,t−k l + Controls_b,t−k + μb + η l,t + εb,t l
  - Yb,t l denotes one of:
    - (i) non-performing CRE loans (90+ days overdue)-to-total CRE loans ratio at t;
    - (ii) charged off CRE loans (net of recoveries)-to total CRE loans ratio at t;
    - (iii) log change in pre-provision net revenues from t-k to t;
    - (iv) log change in total regulatory capital from t-k to t.
  - CRE_Exposure_b,t−k l: bank b’s exposure to CRE loans at t-k (total CRE loans by US-domiciled offices divided by total assets).
  - ΔP t,t−k l: (log) change in average CRE price index in MSA l from t-k to t (MSCI Real Estate Portal).
  - I(ΔP < 0) indicator to capture asymmetry (declines likely to trigger LTV constraints).
  - Controls include capital ratio, liquidity ratio, (log) total asset size, and interactions of these with ΔP and CRE exposure.
  - Fixed effects: bank fixed effects (μb) and location (MSA) x quarter fixed effects (η l,t).

### Estimation details and identification
- Estimation via weighted least squares (WLS); weight = log of bank total assets.
- Standard errors double clustered at bank and quarter level.
- Identification:
  - Sample restricted to MSAs with multiple banks (robust to including single-bank MSAs; 4 MSAs have a single bank headquarter).
  - Broad sample includes all banks submitting FFIEC 031 and 051 Call Reports.
  - Coverage: total of 10,796 banks over entire sample period; 5,116 reporting banks in the last available quarter (2020:Q3).
  - Focus on banks in 69 major MSAs for which CRE price indices are available (on average cover more than 50 percent of total banking sector assets).
  - Robustness: expanded sample using state- or Census Bureau region averages of MSA-level CRE prices yields qualitatively similar results.

### Measurement notes and limitations
- Disaggregated segment-level CRE price indices (office, retail, industrial, lodging) exist, but disaggregated bank loan data by segment is not available; therefore average CRE prices used.
- Banks assumed exposed to CRE price changes in their headquarter MSAs; over 95 percent of US banks are small/community banks and geographically concentrated.
- Potential mismeasurement of CRE locations/prices likely induces attenuation bias.

---

### 4. Capital loss scenarios and stress calculations

### Scenario definitions (CRE price paths)
- Mild adverse scenario:
  - CRE prices implied by a 1.15 percent permanent increase in the vacancy rate.
  - Implies a cumulative drop in CRE prices by 16 percent after 8 quarters (Online Annex Figure 3.3.2).
- Alternative (valuation-model) scenario:
  - Permanent increase in vacancy rates by 5 percentage points (as projected by valuation model).
  - Implies about 30 percent decline in CRE prices in the long run.
- Assumption for transparency: a common CRE price path across MSAs (due to lack of MSA-specific CRE price forecasts).

### Translating estimated sensitivities into dollar capital impacts
- Procedure:
  - Estimate equation (12) with dependent variable (ii) net CRE loan charge-off rate; forward the estimated equation by k periods to obtain Yb,t+k l = (αk� + βk� * CRE_Exposure_b,t l * ΔP t+k,t l).
  - Total outstanding CRE loans assumed to decline by 2 percent quarterly for each bank.
  - Multiply projected charge-off rates by projected CRE loan balances to obtain dollar CRE loan losses at each horizon and bank.
  - Allowance for Loan & Lease Losses (ALLL) due to CRE loan exposure assumed equal to four quarters of projected net CRE loan charge-offs; provision expenses calculated accordingly (CLASS Model assumptions referenced).
  - Estimate PPNR (pre-provision net revenues) percentage changes by estimating equation (12) with dependent variable (iii) and apply estimated changes to PPNR in 2020:Q3 to obtain PPNR losses in dollar amounts (for each horizon k and bank).
  - Sum CRE-driven provision expenses and PPNR losses and divide by pre-shock total risk weighted assets (2020:Q3) to obtain capital impact.

### Additional methodological notes
- The procedure follows related top-down stress-test literature (Hirtle and others 2015) but is not a full top-down stress test — it estimates the marginal impact of a decline in CRE prices on bank capital through credit and revenue losses for a given macroeconomic scenario and regulatory capital rules.
- Extensions can incorporate macroeconomic effects by including location x quarter fixed effects in the forecast horizon and assuming a path for those effects for k = 1, 2, ... 8.

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### 5. Impact of CRE prices on corporate investment

### Baseline firm-level investment model
- Empirical specification (conceptual form):
  - IRIEsRPerR P,t = β · RE_Value_i,baseline / lagged PPE · ΔP t c / P baseline + γ · controls + ΣRk · Xk,baseline · ΔP t c / P baseline + k[CCIRRPIIs] P,t + firm and city-sector-year fixed effects + ε
- Key variables and definitions:
  - IRIEsRPerR P,t: ratio of capital expenditures of firm i in year t normalized by lagged properties, plant and equipment (PPE).
  - RE_Value_i,baseline: market value of real estate holdings of firm i in baseline year normalized by lagged PPE (estimated following Chaney and others (2012) procedures).
  - ΔP t c / P baseline: change in CRE prices in city c (location of firm i’s headquarters) from baseline year to year t.
  - Xk,baseline: firm-level characteristics (size, age, return on assets) measured in the baseline year.
  - Controls: ratio of current cash flows to lagged PPE, lagged market-to-book ratio, interactions of controls with CRE price changes.
  - Fixed effects: firm and city-sector(1-digit)-year.

### Robustness checks and identification
- Robustness:
  - Results hold across sample periods: 2004-2007; 2008-2009; 2010-2019.
  - Results hold for small firms within cities (firms with total assets less than the 25th percentile of city firms).
  - Alternative dependent variables used: change in PPE net of change in book value of real estate assets; three-year forward-looking investment (average capital expenditures current year and next 2 years); firm-level investment adjusted by overall investment of firms within same 1-digit sector.
  - Results robust to choice of baseline year (including 2004, 2008, 2010).

### Limitations and instrumental-variable approach
- Limitations:
  - No data on exact location of firms’ real estate holdings; assumption that firms hold most of their real estate in the city of their headquarters can induce attenuation bias (estimates likely stronger with exact-location data).
  - Potential reverse causality from investment to market value of real estate holdings mitigated by fixing firms’ real estate holdings at a baseline year and inflating via location-specific CRE prices.
  - Large firms could still affect local CRE prices; robustness checks address this by focusing on small firms.
- Instrumental-variable strategy (US-only first stage):
  - First-stage regression: P t c = αc + δt + γ · [LandSupplyConstraints × 30-year Treasury rate] + ε t c
  - Interpretation: larger effect of a drop in interest rates in cities where land supply is more constrained.
  - First-stage result: estimate of γ = 0.0155 (p-value: 0.0017); adjusted R2 = 0.95; N = 880.
  - Using estimated P t c from first-stage as instrumented CRE prices in second-stage regression for market value of real estate yields strongly robust results for β (coefficient on the focus variable).

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*Italic: Source: ch3onlineannex - 1. Estimated misalignments in the office and retail segments – (PDF chapter/section). International Monetary Fund staff calculations; data sources cited: Bloomberg, L.P., Haver, MSCI Real Estate.*

### 0.033 to 0.031 while preserving its significance at the 0.01 level.

### Online Annex 3.4. The Impact of Policies on CRE Prices

### Methodology
- Sample: unbalanced panel data for 30 economies (23 advanced and 7 emerging market economies) from 2000:Q1 to 2019:Q4.
- Objective: assess the impact of policy measures (macroprudential and capital flow management measures) on downside risks to CRE prices.
- Outcome variable: Δ_h Y_P,t,τ — the (average) percentage change in real CRE prices in country P from quarter R to quarter R+ h (h = 1, 2, ..., H) at a specific quantile τ. The analysis focuses on the 5th percentile of the distribution of future changes in CRE prices.
- Estimation approach: panel quantile regression with country fixed effects α_P,h and control variables (lagged real GDP growth, changes in credit-to-GDP ratio, capital inflows-to-GDP ratio, the VIX index). Error term denoted ε_P,t,τ,h.
- Macroprudential policy change variable: ΔMP_P,t captures change in macroprudential policy stance. Monetary policy shock: MP_P,t (predicted residual of a regression of the policy rate on contemporary and lagged macro variables and a quadratic time trend).
- Endogeneity treatment: macroprudential indicators and capital flow management indices are purged of credit-to-GDP and variations in capital flows-to-GDP where specified.

### Macroprudential policy categorizations
- Two categorizations used:
  - CRE-specific (targeted) measures: apply specifically to the CRE sector and directly limit borrowers’ access to bank credit or increase cost of CRE lending (examples: CRE-specific LTV, DSR, higher risk weights, sectoral capital buffers).
    - Defined as a categorical variable taking values -1, 0, or 1 if there was a loosening action, no change, or a tightening action respectively in a quarter.
    - Indicators purged of credit-to-GDP to address potential endogeneity concerns.
  - Borrower-based measures: include measures targeting the residential segment that could have an indirect effect on CRE; constructed as a two-year rolling sum of individual measures with +1 = tightening, 0 = no change, -1 = loosening. These measures are also purged of credit-to-GDP.

### Monetary policy shock
- Captured as the predicted residual from a regression of the policy rate on contemporaneous and lagged macro variables (real GDP, inflation, stock returns) and a quadratic time trend, following Iacoviello and Navarro (2019).
- For selected countries (US, Euro Area, UK, Japan, Switzerland, Canada, Australia, New Zealand), the shadow rate by Leo Krippner is used as the policy rate to capture unconventional monetary policy.
- Robustness: alternative specifications considered using the actual policy rate and the shadow rate by Wu and Xia (2016).

### Capital flow management measures
- Model specification replacing ΔMP with ΔCFM (change in capital flow management measures) to evaluate association between capital flow management measures and downside risks to CRE prices.
- Capital flow management measure sources: overall capital inflow restrictions index or real-estate-specific capital inflow restriction index from Fernández and others (2017) updated with recent policy announcements.
- Construction: indices based on a two-year rolling sum of individual measures (+1 = tightening, 0 = no change, -1 = loosening) and purged from variations in capital flows-to-GDP.

### Examples of CRE-Specific Macroprudential Policies (selected entries from Online Annex Table 3.4.1.)
- Denmark, Jun. 2003: 60% LTV limit on recreational dwellings, office properties and retailing properties, industrial properties and craftsman's properties, collective energy-supply plants.
- Hong Kong SAR, Feb. 2013: 10 pp lower LTV limit on mortgage loans for all commercial and industrial properties.
- Hong Kong SAR, May 2017: Lower the applicable DSR limit by 10 percentage points for mortgage to borrowers whose income is mainly derived from outside of Hong Kong SAR.
- Indonesia, Jun. 2012: LTV limit of 70% on 2nd loan for an office/shop house; 60% for 3rd or more loans for an office/shop house.
- Indonesia, Jun. 2015: Lifting LTV ratio for property (including office houses) loans.
- Indonesia, Aug. 2016: Lifting LTV limit on office houses based on banks’ internal policy (first loan), 85% (second loan), 80% (third loan or more).
- Indonesia, Jun. 2018: Lifting regulatory limits on the first mortgage on home stores/home offices.
- Ireland, Jan. 2007: Minimum risk weight on commercial property lending increased from 50% to 100%.
- Ireland, Jan. 2014: Minimum risk weight applied to commercial property lending was increased to 100% from 50%.
- Norway, Sep. 2014: Risk weight of 100% on CRE lending for banks using the standardized approach.
- Poland, Jan. 2005: 100% risk weight on non-residential property.
- Poland, Jun. 2014: 75% or 80% LTV limit on CRE loans if the part above 75% is insured or collateralized with funds on bank account, government or NBP securities.
- Poland, Dec. 2017: For banks using the Standardized Approach to determine capital requirement: 100% risk weight on exposures secured by commercial immovable property located in Poland.
- Singapore, Jan. 2013: Seller's stamp duties for industrial properties.
- Singapore, Jun. 2013: Total Debt Servicing Ratio (TDSR) to the loan applied for both residential and nonresidential property (e.g., industrial and commercial property), and covers property both in- and outside of Singapore.
- Sweden, Jan. 2014: Risk-weight floor framework for commercial mortgages at 100% for exposures calculated according to the standardized approach for credit risk.
- United Kingdom, Jan. 2014: Stricter criterion requirement for firms to determine whether the annual average loss rates for lending secured by mortgage on commercial real estate in the UK did not exceed 0.5% over a representative period.
- United Kingdom, Oct. 2014: Stricter criteria for the eligibility of the 50% risk weight (RW) exposures fully and completely secured by mortgages on commercial real estate located in non-EEA country entered into force.
- United States, Dec. 2006: Guidance to banks with high CRE risk concentrations to tighten managerial controls.
- United States, Jan. 2015: 150% risk weight on High-Volatility Commercial Real Estate (HVCRE) exposure held by a banking organization.
- United States, Dec. 2016: Implementation of risk retention rule. The risk retention rules require that at least one sponsor of a securitization (or its majority owned affiliate) retain a 5 percent interest in the credit risk of the securitized assets.

*Online Annex 3.4, GLOBAL FINANCIAL STABILITY REPORT—Commercial Real Estate, International Monetary Fund | April 2021*

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_Source: https://www.imf.org/-/media/files/publications/gfsr/2021/april/english/ch3onlineannex.pdf_