## wpiea2022151-print-pdf

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---

### I. Introduction — Context and research questions
- The COVID-19 pandemic has extended a multi-year housing boom across advanced economies and emerging markets.
- Examples:
  - Nominal owner-occupied house prices in Turkey have more than doubled between 2016Q1 and 2021Q4.
  - In the U.S., nominal house prices have risen by more than 60 percent between 2016Q1 and 2022Q1 and are recently growing at a rate higher than that during the pre-GFC period.
- Motivations: concerns about financial, macroeconomic, and social stability linked to sharp rises and high levels of house prices.
- Central questions addressed:
  - Does high headline inflation follow high growth in owner-occupied housing prices?
  - Which methods perform best in forecasting inflation in rents and (if applicable) owner-occupied housing costs with housing prices?
  - How much do inflation in housing components (rent and owner-occupied housing cost) directly contribute to headline inflation, ignoring general equilibrium effects and policy responses?

### Key stylized findings (overview)
- Conceptual ambiguity: higher housing prices can affect headline inflation through multiple channels (demand for housing space, shifts between renting and owning, wealth channel, credit channel); net effect depends on shock type and country-specific structural factors.
- Empirical suggestion: house price growth appears to be a leading indicator of headline inflation in the U.S. and some selected countries.
- Forecasting performance: for eight of the nine countries analyzed, country-specific machine-learning models outperform the vector autoregression (VAR) model in out-of-sample forecast performance comparisons.
- Direct contribution dynamics:
  - During 2020, the direct contribution of housing components to headline inflation in most studied countries was disproportionally higher than their weights in headline inflation because rent and owner-occupied housing cost decreased more slowly than headline inflation.
  - The contribution dropped significantly in 2021 as rent and owner-occupied housing cost started catching up with rapid housing price growth experienced in 2020, and non-housing components (e.g., supply chain disruptions) dominated headline inflation.
  - Forecasts suggest that due to lagged responses of rent and owner-occupied housing cost to recent rapid housing price growth, the contribution of housing components to headline inflation will rise over the medium term; in some cases they could contribute to more than half of headline inflation projected by the WEO.
- Methodological scope: focuses on direct effect of housing price growth on headline inflation and does not account for general equilibrium effects, de-anchoring of inflation expectations, policy responses, or feedback from headline inflation to housing prices.

### II. Literature positioning
- Related literatures:
  1. Interaction between housing price and headline inflation (wealth and credit channels; house prices predictive of CPI inflation).
  2. Link between house prices and housing cost components in headline inflation (price-to-rent literature; acknowledged lags).
     - Zhou and Dolmas (2021): house price growth led rent inflation and OER inflation in the U.S. by somewhat less than two years.
     - Brescia (2021): house price gains historically lead changes in CPI shelter measures by about five quarters in the U.S.
     - IMF (2021a) WEO chapter: a one-percentage-point, year-on-year increase in nominal house prices in the quarter ahead is associated with a cumulative increase of 1.4 percentage points in annual rent inflation over two years.
  3. Inflation forecasting and macroeconomic forecasting literature, including recent machine-learning applications.
- Contributions:
  - Uses machine-learning models and selects best-performing models via back-testing.
  - Covers multiple countries with rapid house price growth using country-specific forecasting models.

### III. The U.S. case — Stylized facts and mechanisms
- House price growth leads inflation in the U.S.; headline inflation reached its highest level in four decades in the sample period.
- Transmission channels:
  - Rents and owners’ equivalent rent (OER) transmit owner-occupied housing price changes to headline inflation.
  - Combined weight in CPI and PCE:
    - PCE: Rent 3.6; Owners' equivalent rent 11.4; Total 15.0.
    - CPI: Rent 7.5; Owners' equivalent rent 23.8; Total 31.3.
- Timing and measurement frictions:
  - Contract rents adjust slowly (lease durations, legal/behavioral reluctance).
  - OER data collected every six months, contributing to sluggish recorded responses.
- Empirical caution: stylized facts may reflect correlations rather than causation; forecasting with these relationships remains informative for policy.

### IV. Methodology and data — Empirical strategy
- Two primary empirical goals:
  1. Identify effective ways to incorporate owner-occupied housing prices into headline inflation forecasts by comparing machine-learning models (Lasso, Elastic Net, Random Forest) to a reduced-form VAR model using out-of-sample RMSE.
  2. Quantify the direct contribution of housing components (rent and OER) to headline inflation by taking the weighted sum of rent inflation forecasts and OER inflation forecasts and comparing that sum with IMF U.S. team’s WEO forecasts of headline inflation (excluding general equilibrium effects).
- Two-step machine-learning forecasting approach:
  - Step 1: Forecast rent inflation and OER inflation with a two-year forecasting horizon.
    - Features include: nominal GDP growth; disposable income growth; M2 growth; change of policy interest rate; contemporaneous and lagged year-on-year nominal housing price growth (1-quarter, 2-quarter, 3-quarter, 4-quarter, and 8-quarter lags).
    - Robustness checks include rental vacancy rate and inflation expectations.
  - Step 2: Compute weighted sum of rent and OER forecasts using CPI (and alternatively PCE) weights and compare with WEO headline inflation forecasts.
- Model selection:
  - Time-split K-fold cross-validation on training set to select hyperparameters minimizing average RMSE; back-testing on 2020Q1-2021Q4 to choose best-performing model based on RMSE.

### V. U.S. back-testing and forecasting results (summary)
- Back-testing period: 2020Q1-2021Q4.
- Back-testing selection:
  - In main specification, VAR (allowing 1st-8th lags) selected as best-performing for both rent and OER forecasting.
  - All four models had much lower RMSEs than the simple constant model.
  - Robustness checks (adding inflation expectations and rental vacancy rate) selected Elastic Net (1st-4th & 8th lags) as best-performing for both rent and OER; in robustness back-testing machine-learning models significantly outperformed VAR.
- Forecasts (2022Q1-2023Q4):
  - Rent inflation:
    - Continues sharply rising trend started in 2021Q3.
    - Peaks in 2023Q2 at 6.7 percent year-on-year, then hovers around 6.5 percent in 2023Q3-Q4.
  - OER inflation:
    - Continues rising trend started in 2021Q2.
    - Peaks in 2023Q1 at 4.7 percent year-on-year, then drops to 4.1 percent in 2023Q4.
  - Weighted housing cost inflation and contribution to headline CPI (CPI weights):
    - Housing components’ contribution peaked at 231 percent in 2020Q2 and 69 percent in 2020Q3 (actual data).
    - Forecasted share rises again in 2022Q2 and reaches 68 percent in 2023Q4, compared with a 31 percent combined housing weight in CPI.
  - Using PCE weights:
    - Housing components’ share reached 76 percent in 2020Q2 and 33 percent in 2020Q3 (actual data).
    - Forecasted contribution rises to 23 percent in 2023Q4, compared with a 15 percent weight of housing costs in PCE.
- Policy implication: Persistent housing-cost-driven inflation could make headline inflation persistent and complicate monetary policymaking.

### VI. Robustness checks (U.S.)
- Adding inflation expectations and rental vacancy rate led to lower forecasts of rent and OER growth compared with the main model, but the pattern remains: housing cost inflation peaks after expected peak of headline inflation.
- Robustness-weighted housing cost inflation still projects a contribution to headline CPI and PCE substantially larger than housing weights.

### VII. Stylized facts and cross-country coverage
- Country coverage beyond the U.S.: Brazil, Canada, Iceland, Korea, Luxembourg, Mexico, Sweden, U.K.
- OOHC estimation approaches vary:
  - Rental equivalence used by U.S., Mexico, Sweden (modified) and others.
  - User cost approach used by Canada, U.K., Iceland.
  - Korea and Luxembourg do not include OOHC in CPI.
- Combined housing weights in CPI (as of 2021Q4):
  - U.S.: OOHC weight 23.8; Rent weight 7.5; Total weight 31.3.
  - U.K.: OOHC weight 18.5; Rent weight 9.4; Total weight 27.9.
  - Canada: OOHC weight 19.7; Rent weight 6.5; Total weight 26.2.
  - Iceland: OOHC weight 16.0; Rent weight 4.4; Total weight 20.4.
  - Sweden: OOHC weight 6.9; Rent weight 7.3; Total weight 14.2.
  - Mexico: OOHC weight 12.0; Rent weight 2.2; Total weight 14.2.
  - Korea: OOHC weight 0.0; Rent weight 9.8; Total weight 9.8.
  - Luxembourg: OOHC weight 0.0; Rent weight 6.7; Total weight 6.7.
  - Brazil: OOHC proxied by condo cost 1.6; Rent weight 3.6; Total weight 5.2.
- Stylized lagged responses (selected examples):
  - U.S.: house price deceleration starting 2006Q1; rent deceleration lag 5 quarters; OOHC deceleration lag 4 quarters. House price acceleration in 2020Q3; rent acceleration lag 4 quarters; OOHC acceleration lag 3 quarters.
  - U.K.: house price deceleration starting 2007Q3; rent deceleration lag 4 quarters; OOHC deceleration lag 4 quarters. House price acceleration in 2020Q3; rent acceleration lag 5 quarters; OOHC acceleration lag 2 quarters.
  - Canada, Iceland, Korea show similar multi-quarter lags in rent/OOHC responses.

### VIII. Model selection and forecasting results for non-U.S. countries
- Back-testing indicates machine-learning models outperform VAR/constant models in many non-U.S. cases.
- Selected best-performing models (summary from source):
  - U.K.: Rent — Lasso (1-4 & 8 lags); OOHC — Random Forest (1-4 lags).
  - Canada: Rent — Elastic Net (1-4 lags); OOHC — Elastic Net (1-4 lags).
  - Iceland: Rent — Random Forest (1-4 lags); OOHC — Elastic Net (1-4 lags).
  - Korea: Rent — Random Forest (1-4 lags); OOHC — N.A.
  - Mexico: Rent — Elastic Net (1-4 lags); OOHC — Elastic Net (1-4 lags).
  - Brazil: Rent — Random Forest (1-4 & 8 lags); OOHC — Lasso (1-4 & 8 lags).
  - Sweden: Rent — Random Forest (1-4 & 8 lags); OOHC — Lasso (1-4 & 8 lags).
  - Luxembourg: Rent — Random Forest (1-4 lags); OOHC — N.A.
- Forecast patterns (selected outcomes):
  - U.K.: Housing components peak in 2023Q1 (three quarters after IMF U.K. WEO peak); contribution to headline CPI projected to rise to 42 percent in 2023Q4 (housing weight 28 percent).
  - Canada: Housing components peak one quarter after WEO headline peak; contribution reached 404 percent in 2020Q2 and 110 percent in 2020Q3 (actual data); forecasted rise to 50 percent in 2023Q2 (housing weight 26 percent).
  - Iceland: Housing components peak in 2023Q3 (six quarters after WEO headline peak); contribution reached 244 percent in 2021Q3 (actual data); forecasted rise to about 150 percent in 2023Q4.
  - Korea: Rent inflation peaks in 2022Q4 (four quarters after WEO headline peak); contribution reached 44 percent in 2020Q2 and 12 percent in 2022Q4 (actuals); forecasted rise to 13.6 percent in 2023Q4 (housing weight 9.8 percent).
  - Mexico, Brazil, Sweden, Luxembourg: Similar patterns of housing components peaking in 2022-2023 after expected headline peaks; Brazil results after 2023Q2 become counter-intuitive/negative likely due to small sample.

### IX. Robustness checks across countries
- Robustness checks add inflation expectations and rental vacancy rate where available.
- For many countries, adding these variables leads to selection of different best-performing machine-learning models and often improves back-testing performance.
- Robustness results generally maintain the main qualitative conclusion: inflation of housing components tends to peak after headline inflation peaks and their contribution to headline inflation can rise to levels substantially above housing CPI weights.

### X. Heatmap for Ten More Countries with Rapid House Price Growth (method and simple analysis)
- Heatmap objective: preliminary assessment of additional inflation pressure via rent responses to house price growth where machine-learning models are not readily applicable.
- Country selection: top ten countries by average quarterly year-on-year house price growth rate since 2020Q1, excluding the nine analyzed previously.
- Calculations:
  - Deviation of latest house price growth rate from the average year-on-year growth rate right before the pandemic (2016-2019).
  - Deviation of latest rent growth from the pre-pandemic average rent growth.
  - "Pressure Index" = (ratio of latest house price growth to its pre-pandemic average) divided by (ratio of latest rent growth to its pre-pandemic average).
  - Ratings: "High" if pressure index exceeds 1.50; "Medium" if between 1.25 and 1.50; "Low" if below 1.25.
- Caveats:
  - Does not account for de-anchoring of inflation expectations, spillovers to non-housing inflation, policy responses.
  - Does not rule out a structural break (e.g., permanent household shift from renting to owning).
- Table 11 rows (preserving source strings):
  - Turkey129.69.050.29.414.33.7High
  - Russia220.24.622.81.98.91.1Low
  - New Zealand317.06.927.62.43.82.5High
  - Czech 412.29.222.02.54.21.4Medium
  - Australia511.42.123.70.60.418.8High
  - Lithuania610.47.118.96.18.02.0High
  - Netherlands710.27.316.72.10.76.5High
  - Poland89.55.29.03.37.80.7Low
  - Estonia99.25.817.46.914.51.4Medium
  - Germany109.06.512.01.41.41.8High
- Example interpretation preserved:
  - Turkey: latest year-on-year house price growth (30.2 percent as of 2021Q2) more than triples its average year-on-year growth of 9.0 percent observed right before the pandemic (2016-2019); latest year-on-year rent growth (10.3 percent) is more or less the same as the pre-pandemic average — suggesting potential upward pressure on rent and thus headline inflation in Turkey in the coming years.

### XI. Conclusions, operational implications, and policy recommendations
- Stylized results:
  - Headline inflation generally lags house price growth in nine AEs and EMs analyzed (U.S., U.K., Canada, Iceland, Korea, Mexico, Brazil, Sweden, Luxembourg).
  - Machine-learning forecasts show housing components (rent and OOHC/OER) in CPI (PCE) are expected to:
    - Peak after the expected peak of headline inflation in WEO forecasts.
    - Have contributions to headline inflation that were disproportionally higher than the housing weight in headline inflation in 2020-2021, dropped significantly afterward, but are expected to keep rising over the medium term.
  - For eight out of nine analyzed countries, machine-learning models outperform the VAR model.
- Operational recommendations for forecasters:
  - Carefully incorporate housing prices into headline inflation forecasts.
  - Use a granular approach: forecast different housing cost components (rent, OOHC/OER) separately and aggregate with respective weights.
  - Machine-learning methodology provides a complementary approach focusing on direct impact on housing components and can be used to cross-check other forecasting approaches.
- Monetary policy implications:
  - More analysis using structural and general equilibrium models is needed to capture feedback loops among house price growth, inflation, and monetary policy (e.g., introducing an endogenous monetary policy response function).
  - Two-sided considerations:
    - Rising housing prices can increase household expectations of headline inflation and spillovers to non-housing inflation.
    - Monetary tightening can slow house price or rent growth, mitigating inflation impact.
  - Highlighted risk: keeping a loose monetary policy for long may fuel continued house price growth, leading to higher rent and OOHC, and ultimately higher headline inflation.
- Measurement implications:
  - Debate about incorporating owner-occupied housing prices into inflation measures (rental equivalence approach vs. net acquisition approach).
  - ECB’s Strategy Review (July 2021) decided ECB should incorporate owner-occupied housing prices and plan to use the “net acquisition approach”.
  - Appropriately incorporating housing costs increases CPI representativeness.

### XII. Key caveats and interpretation
- Methodology does not account for general equilibrium effects, including:
  - spillovers of housing inflation to non-housing sectors;
  - potential de-anchoring of inflation expectations;
  - monetary policy responses and feedback from headline inflation to housing prices.
- Because of omitted general equilibrium channels, the estimates are likely a lower bound of the contribution of housing price increases to headline inflation; however, policy responses and feedbacks could bias results in either direction, so the overall direction of bias is unclear.

### XIII. Data sources (as listed)
- Indicators and frequencies:
  - Rent — Quarterly — Haver
  - Weight of rent in headline inflation — Quarterly — Haver
  - OOHC — Quarterly — Haver
  - Weight of OOHC in headline inflation — Quarterly — Haver
  - Headline inflation — Quarterly — Haver, WEO
  - Housing price — Quarterly — BIS
  - Nominal GDP — Quarterly — IFS
  - M2 — Quarterly — Haver
  - Policy rate — Quarterly — IFS, Federal Reserve Economic Data, CEIC
  - (Gross) Household disposable income — Quarterly — DataStream, CEIC
  - Inflation expectation — Quarterly — Consensus Forecast
  - Rental vacancy rate — Quarterly — Haver

*Source: wpiea2022151-print-pdf - References.....................................................................................................44*

### References.....................................................................................................44

### References (Content unit: wpiea2022151-print-pdf - References.....................................................................................................44)

### I. Introduction — Context and research questions
- The COVID-19 pandemic has extended a multi-year housing boom across advanced economies and emerging markets.
- Examples cited:
  - Nominal owner-occupied house prices in Turkey have more than doubled between 2016Q1 and 2021Q4.
  - In the U.S., nominal house prices have risen by more than 60 percent between 2016Q1 and 2022Q1 and are recently growing at a rate higher than that during the pre-GFC period.
- Motivations: concerns about financial, macroeconomic, and social stability linked to sharp rises and high levels of house prices.
- Three central questions addressed:
  - Does high headline inflation follow high growth in owner-occupied housing prices?
  - Which methods perform best in forecasting inflation in rents and (if applicable) owner-occupied housing costs with housing prices?
  - How much do inflation in housing components (rent and owner-occupied housing cost) directly contribute to headline inflation, ignoring general equilibrium effects and policy responses?

### Key stylized findings (from Introduction and overview)
- Conceptual ambiguity: higher housing prices can affect headline inflation through multiple channels (demand for housing space, shifts between renting and owning, wealth channel, credit channel), and the net effect depends on shock type and country-specific structural factors.
- Empirical suggestion: house price growth appears to be a leading indicator of headline inflation in the U.S. and some selected countries.
- Forecasting performance: for eight of the nine countries analyzed, country-specific machine-learning models outperform the vector autoregression (VAR) model in out-of-sample forecast performance comparisons.
- Direct contribution dynamics:
  - During 2020, the direct contribution of housing components to headline inflation in most studied countries was disproportionally higher than their weights in headline inflation because rent and owner-occupied housing cost decreased more slowly than headline inflation.
  - The contribution dropped significantly in 2021 as rent and owner-occupied housing cost started catching up with rapid housing price growth experienced in 2020, and non-housing components (e.g., supply chain disruptions) dominated headline inflation.
  - Forecasts suggest that due to lagged responses of rent and owner-occupied housing cost to recent rapid housing price growth, the contribution of housing components to headline inflation will rise over the medium term; in some cases they could contribute to more than half of headline inflation projected by the WEO.
- Methodological scope: the paper focuses on the direct effect of housing price growth on headline inflation and does not account for general equilibrium effects, de-anchoring of inflation expectations, policy responses, or feedback from headline inflation to housing prices.

### II. Literature review — Related strands and positioning
- Three related literatures:
  1. Interaction between housing price and headline inflation (theory: wealth and credit channels; empirical: house prices predictive of CPI inflation).
  2. Link between house prices and housing cost components in headline inflation (price-to-rent ratio literature; acknowledged lags due to market frictions).
     - Empirical lag evidence:
       - Zhou and Dolmas (2021): house price growth led rent inflation and OER inflation in the U.S. by somewhat less than two years.
       - Brescia (2021): house price gains historically lead changes in CPI shelter measures by about five quarters in the U.S.
       - IMF (2021a) WEO chapter: a one-percentage-point, year-on-year increase in nominal house prices in the quarter ahead is associated with a cumulative increase of 1.4 percentage points in annual rent inflation over two years.
  3. Inflation forecasting and macroeconomic forecasting literature, including recent machine-learning applications improving prediction in data-rich or data-poor environments.
- Paper’s contributions relative to prior work:
  - Uses machine-learning models and selects best-performing models via back-testing.
  - Covers multiple countries with rapid house price growth using country-specific forecasting models (as opposed to single cross-country models).

### III. The U.S. case — Stylized facts and mechanisms
- House price growth leads inflation in the U.S.; headline inflation reached its highest level in four decades in the sample period.
- Transmission channels to headline inflation:
  - Rents and owners’ equivalent rent (OER) transmit owner-occupied housing price changes to headline inflation.
  - Combined weight in CPI: rent and OER account for a combined weight of nearly one third in U.S. CPI measures (see Table 1).
  - Combined weight in PCE inflation: 15.0 percent of total.
- Table 1 (weights of Rent and OER in major inflation measures; Percent; as of 2021Q4):
  - PCE
    - Rent 3.6
    - Owners' equivalent rent 11.4
    - Total 15.0
  - CPI
    - Rent 7.5
    - Owners' equivalent rent 23.8
    - Total 31.3
  - Sources: Haver and authors’ calculations.
- Timing and measurement reasons for lags:
  - Contract rents adjust slowly due to lease durations and legal or behavioral reluctance to raise rents sharply at renewal.
  - OER data are collected every six months, contributing to sluggish recorded responses.
- Empirical caution: stylized facts may reflect correlations rather than causal relationships; nevertheless, forecasting headline inflation using these relationships is informative for policy.

### IV. Methodology and data — Empirical strategy summary
- Two primary empirical goals:
  1. Identify effective ways to incorporate owner-occupied housing prices into headline inflation forecasts by comparing machine-learning models (drawn from recent macroeconomic forecasting literature) to a reduced-form VAR model using out-of-sample RMSE as the comparison metric.
  2. Quantify the direct contribution of housing components (rent and OER) to headline inflation by taking the weighted sum of rent inflation forecasts and OER inflation forecasts and comparing that sum with IMF U.S. team’s WEO forecasts of headline inflation (noting this provides a suggestive comparison and excludes general equilibrium effects).

### V. Operational implications (brief)
- Machine-learning country-specific forecasting models are recommended as tools macroeconomic forecasters can explore to predict inflation of rents and owner-occupied housing costs and thereby calculate contributions to headline inflation.
- Importance of modeling housing-component inflation carefully: lagged adjustments in rent and OER imply housing-driven inflationary pressures can persist and complicate monetary policymaking even after non-housing supply disruptions ease.

*Source: wpiea2022151-print-pdf - References.....................................................................................................44*

### conclusion because our results do not account for general equilibrium effects, whereas the WEO

### wpiea2022151-print-pdf - conclusion because our results do not account for general equilibrium effects, whereas the WEO

### Key caveats and interpretation
- The methodology does not account for general equilibrium effects, including:
  - spillovers of housing inflation to non-housing sectors;
  - potential de-anchoring of inflation expectations;
  - monetary policy responses and feedback from headline inflation to housing prices.
- Because of omitted general equilibrium channels, the estimates are likely a lower bound of the contribution of housing price increases to headline inflation; however, policy responses and feedbacks could bias results in either direction, so the overall direction of bias is unclear.

### Implementation: two-step machine learning forecasting approach
- Step 1: Forecast rent inflation (year-on-year growth of rent) and OER inflation using machine-learning models with a two-year forecasting horizon.
  - Features used include: nominal GDP growth; disposable income growth; M2 growth; change of policy interest rate; contemporaneous year-on-year nominal housing price growth; lagged nominal housing price growth (1-quarter, 2-quarter, 3-quarter, 4-quarter, and 8-quarter lags).
  - Robustness checks also include rental vacancy rate and inflation expectations.
- Candidate forecasting models: VAR, Lasso, Elastic Net, Random Forest.
  - Model selection: time-split K-fold cross-validation on training set to select hyperparameters minimizing average RMSE; back-testing on 2020Q1-2021Q4 to choose best-performing model based on RMSE.
- Step 2: Compute weighted sum of rent and OER forecasts using CPI (and alternatively PCE) weights to measure contribution of housing components to headline inflation, and compare with IMF U.S. team WEO headline inflation forecasts.

### Back-testing and model selection (U.S.)
- Back-testing period: 2020Q1-2021Q4.
- For the U.S., the VAR model (allowing 1st-8th lags) was selected as best-performing for both rent and OER forecasting in the main specification.
  - All four models (VAR, Lasso, Elastic Net, Random Forest) had much lower RMSEs than the simple constant model.
- Robustness checks (adding inflation expectations and rental vacancy rate) selected Elastic Net (1st-4th & 8th lags) as best-performing for both rent and OER; in robustness back-testing machine-learning models significantly outperformed VAR.

### U.S. forecasting results (2022Q1-2023Q4)
- Rent inflation forecast:
  - Continues sharply rising trend started in 2021Q3.
  - Peaks in 2023Q2 at 6.7 percent year-on-year, then hovers around 6.5 percent in 2023Q3-Q4.
- OER inflation forecast:
  - Continues rising trend started in 2021Q2.
  - Peaks in 2023Q1 at 4.7 percent year-on-year, then drops to 4.1 percent in 2023Q4.
- Weighted housing cost inflation and contribution to headline CPI (using CPI weights):
  - Housing components’ contribution peaked at 231 percent in 2020Q2 and 69 percent in 2020Q3 (based on actual data).
  - Forecasted share rises again in 2022Q2 and reaches 68 percent in 2023Q4, compared with a 31 percent combined housing weight in CPI.
- Using PCE weights:
  - Housing components’ share reached 76 percent in 2020Q2 and 33 percent in 2020Q3 (actual data).
  - Forecasted contribution rises to 23 percent in 2023Q4, compared with a 15 percent weight of housing costs in PCE.
- Policy implication: Persistent housing-cost-driven inflation could make headline inflation persistent and complicate monetary policymaking.

### Robustness checks (U.S. findings)
- Adding inflation expectations and rental vacancy rate led to lower forecasts of rent and OER growth compared with the main model, but the pattern of housing cost inflation peaking after the expected peak of headline inflation remains.
- Robustness-weighted housing cost inflation still projects a contribution to headline CPI and PCE that is substantially larger than housing weights.

### Stylized facts and cross-country coverage
- Country coverage beyond the U.S.: Brazil, Canada, Iceland, Korea, Luxembourg, Mexico, Sweden, U.K.
- OOHC estimation approaches vary:
  - Rental equivalence used by U.S., Mexico, Sweden (modified) and others.
  - User cost approach used by Canada, U.K., Iceland.
  - Some countries (Korea, Luxembourg) do not include OOHC in CPI.
- Combined housing weights in CPI (as of 2021Q4) include:
  - U.S.: OOHC weight 23.8, Rent weight 7.5, Total weight 31.3.
  - U.K.: OOHC weight 18.5, Rent weight 9.4, Total weight 27.9.
  - Canada: OOHC weight 19.7, Rent weight 6.5, Total weight 26.2.
  - Iceland: OOHC weight 16.0, Rent weight 4.4, Total weight 20.4.
  - Sweden: OOHC weight 6.9, Rent weight 7.3, Total weight 14.2.
  - Mexico: OOHC weight 12.0, Rent weight 2.2, Total weight 14.2.
  - Korea: OOHC weight 0.0, Rent weight 9.8, Total weight 9.8.
  - Luxembourg: OOHC weight 0.0, Rent weight 6.7, Total weight 6.7.
  - Brazil: OOHC proxied by condo cost 1.6, Rent weight 3.6, Total weight 5.2.
- Stylized lagged responses (selected examples):
  - U.S.: house price deceleration starting 2006Q1; rent deceleration lag 5 quarters; OOHC deceleration lag 4 quarters. House price acceleration in 2020Q3; rent acceleration lag 4 quarters; OOHC acceleration lag 3 quarters.
  - U.K.: house price deceleration starting 2007Q3; rent deceleration lag 4 quarters; OOHC deceleration lag 4 quarters. House price acceleration in 2020Q3; rent acceleration lag 5 quarters; OOHC acceleration lag 2 quarters.
  - Canada, Iceland, Korea show similar multi-quarter lags in rent/OOHC responses to house price movements.

### Model selection and forecasting results for non-U.S. countries
- Back-testing indicates machine-learning models outperform VAR/constant models in many non-U.S. cases.
- Selected best-performing models (summary):
  - U.K.: Rent — Lasso (1-4 & 8 lags); OOHC — Random Forest (1-4 lags).
  - Canada: Rent — Elastic Net (1-4 lags); OOHC — Elastic Net (1-4 lags).
  - Iceland: Rent — Random Forest (1-4 lags); OOHC — Elastic Net (1-4 lags).
  - Korea: Rent — Random Forest (1-4 lags); OOHC — N.A.
  - Mexico: Rent — Elastic Net (1-4 lags); OOHC — Elastic Net (1-4 lags).
  - Brazil: Rent — Random Forest (1-4 & 8 lags); OOHC — Lasso (1-4 & 8 lags).
  - Sweden: Rent — Random Forest (1-4 & 8 lags); OOHC — Lasso (1-4 & 8 lags).
  - Luxembourg: Rent — Random Forest (1-4 lags); OOHC — N.A.
- Forecast patterns (selected outcomes):
  - U.K.: Housing components peak in 2023Q1 (three quarters after IMF U.K. WEO peak); contribution to headline CPI projected to rise to 42 percent in 2023Q4 (housing weight 28 percent).
  - Canada: Housing components peak one quarter after WEO headline peak; contribution reached 404 percent in 2020Q2 and 110 percent in 2020Q3 (actual data); forecasted rise to 50 percent in 2023Q2 (housing weight 26 percent).
  - Iceland: Housing components peak in 2023Q3 (six quarters after WEO headline peak); contribution reached 244 percent in 2021Q3 (actual data); forecasted rise to about 150 percent in 2023Q4.
  - Korea: Rent inflation peaks in 2022Q4 (four quarters after WEO headline peak); contribution reached 44 percent in 2020Q2 and 12 percent in 2022Q4 (actuals); forecasted rise to 13.6 percent in 2023Q4 (housing weight 9.8 percent).
  - Mexico, Brazil, Sweden, Luxembourg: Similar patterns of housing components peaking in 2022-2023 after expected headline peaks; Brazil results after 2023Q2 become counter-intuitive/negative likely due to small sample.

### Robustness checks across countries
- Robustness checks add inflation expectations and rental vacancy rate where available.
- For many countries, adding these variables leads to selection of different best-performing machine-learning models and often improves back-testing performance.
- Robustness results generally maintain the main qualitative conclusion: inflation of housing components tends to peak after headline inflation peaks and their contribution to headline inflation can rise to levels substantially above housing CPI weights.

*Source: wpiea2022151-print-pdf (conclusion and related sections).*

### Appendix Table 1.

### Appendix Table 1.

### Model selection and forecasting approach
- Two-step procedure:
  - First select the best forecasting models for rent inflation and OOHC inflation.
  - Then take the weighted sum of the forecasts of these two components using their respective weights in headline CPI inflation.
- Forecast horizon using selected models: 2022Q1 to 2023Q4.
- Comparison benchmark: IMF country teams’ forecasts of headline CPI inflation (WEO forecasts).
- Robustness-check finding: for countries with available robustness check results, the weighted housing cost inflation:
  - Would peak after the expected peak of the headline CPI inflation in the WEO forecasts.
  - Its contribution to the headline CPI would rise during 2022Q1-2023Q3, although by a somewhat less extent than in the case without considering the additional two variables.

### Selected models for non-U.S. countries (Table 10)
- General observation: all of the best-performing models are machine-learning models, both for rent forecasting and for OOHC forecasting.
- Table 10 entries (Country — Rent — OOHC) preserved as in source:
  - U.K. — Random Forest (1-4 lags) — Random Forest (1-4 lags)
  - Canada — Random Forest (1-4 & 8 lags) — Random Forest (1-4 & 8 lags)
  - Iceland — N.A. — N.A.
  - Korea — Random Forest (1-4 & 8 lags) — N.A.
  - Mexico — Random Forest (1-4 lags) — Lasso (1-4 lags)
  - Brazil — Random Forest (1-4 & 8 lags) — Lasso (1-4 & 8 lags)
  - Sweden — Random Forest (1-4 & 8 lags) — Lasso (1-4 & 8 lags)
  - Luxembourg — N.A. — N.A.
- Source note: Authors’ calculations.

### Robustness-check projections and pattern
- Using best-performing models to forecast rent inflation and OOHC inflation and aggregating by weights in headline CPI:
  - Weighted housing cost inflation displays a similar pattern as in the main analysis: peaks after headline CPI peak in WEO.
  - Contribution to headline CPI rises during 2022Q1-2023Q3 but to a somewhat lesser extent when including the additional two variables in robustness checks.
- Appendix Figures 9-14 present country-specific results (figures referenced in source).

### Heatmap for Ten More Countries with Rapid House Price Growth (method)
- Objective: preliminary assessment of additional inflation pressure via rent responses to house price growth where machine-learning models are not readily applicable.
- Country selection: top ten countries by average quarterly year-on-year house price growth rate since 2020Q1, excluding the nine countries analyzed previously.
- Calculations:
  - Deviation of latest house price growth rate from the average year-on-year growth rate right before the pandemic (2016-2019).
  - Deviation of latest rent growth from the pre-pandemic average rent growth.
  - "Pressure Index" = (ratio of latest house price growth to its pre-pandemic average) divided by (ratio of latest rent growth to its pre-pandemic average).
  - Ratings assigned using judgment-based thresholds: "High" if pressure index exceeds 1.50; "Medium" if it lies between 1.25 and 1.50; "Low" if it falls below 1.25.
- Caveats explicitly noted:
  - Analysis does not account for potential de-anchoring of inflation expectations, spillovers to non-housing inflation, or policy responses.
  - Does not rule out possibility of a structural break (e.g., permanent household shift from renting to owning).
  - Intended as suggestive preliminary evidence and a first step for more rigorous analyses.

### Simple analysis (Table 11) — preserved rows as in source
- Header notes:
  - 1/ Ranked based on the average yoy house price growth since 2020Q1, excluding countries analyzed in the machine-learning section.
  - 2/ As of 2021Q3, except Turkey and Australia (both 2021Q4).
  - 3/ As of 2022Q1, except New Zealand and Australia (both 2021Q4).
  - 4/ Equals the ratio of the latest house price growth to its pre-pandemic average, divided by the ratio of the latest rent growth to its pre-pandemic average.
  - 5/ "High" if pressure index exceeds 1.50; "Medium" if it lies between 1.25 and 1.50; "Low" if it falls below 1.25.
- Table 11 rows (preserving numeric strings exactly as in source):
  - Turkey129.69.050.29.414.33.7High
  - Russia220.24.622.81.98.91.1Low
  - New Zealand317.06.927.62.43.82.5High
  - Czech 412.29.222.02.54.21.4Medium
  - Australia511.42.123.70.60.418.8High
  - Lithuania610.47.118.96.18.02.0High
  - Netherlands710.27.316.72.10.76.5High
  - Poland89.55.29.03.37.80.7Low
  - Estonia99.25.817.46.914.51.4Medium
  - Germany109.06.512.01.41.41.8High
- Example interpretation preserved from source:
  - Turkey: latest year-on-year house price growth (30.2 percent as of 2021Q2) more than triples its average year-on-year growth of 9.0 percent observed right before the pandemic (2016-2019); latest year-on-year rent growth (10.3 percent) is more or less the same as the pre-pandemic average — suggesting potential upward pressure on rent and thus headline inflation in Turkey in the coming years.
- Source: OECD and authors' calculations.

### Conclusions and operational implications
- Stylized facts and machine-learning forecasts:
  - Headline inflation generally lagging house price growth in nine AEs and EMs (U.S., U.K., Canada, Iceland, Korea, Mexico, Brazil, Sweden, Luxembourg).
  - Machine-learning forecasts show housing components (rent and OOHC/OER) in CPI (PCE) are expected to:
    - Peak after the expected peak of headline inflation in WEO forecasts.
    - Have contributions to headline inflation that were disproportionally higher than the housing weight in headline inflation in 2020-2021, dropped significantly afterward, but are expected to keep rising over the medium term.
  - For eight out of the nine analyzed countries, machine-learning models outperform the VAR model.
- Operational recommendations for forecasters:
  - Carefully incorporate housing prices into headline inflation forecasts.
  - Use a granular approach: forecast different housing cost components (rent, OOHC/OER) separately and aggregate with respective weights.
  - Machine-learning methodology provides a complementary approach focusing on direct impact on housing components and can be used to cross-check other forecasting approaches.
- Monetary policy implications:
  - More analysis using structural and general equilibrium models is needed to capture feedback loops among house price growth, inflation, and monetary policy (e.g., introducing an endogenous monetary policy response function).
  - Two-sided considerations:
    - Rising housing prices can increase household expectations of headline inflation and spillovers to non-housing inflation.
    - Monetary tightening can slow house price or rent growth, mitigating inflation impact.
  - Highlighted risk: keeping a loose monetary policy for long may fuel continued house price growth, leading to higher rent and OOHC, and ultimately higher headline inflation.
- Measurement and indexation implications:
  - Debate about incorporating owner-occupied housing prices into inflation measures (rental equivalence approach vs. net acquisition approach).
  - ECB’s Strategy Review (July 2021) decided ECB should incorporate owner-occupied housing prices and plan to use the “net acquisition approach” (as noted in source).
  - Appropriately incorporating housing costs increases CPI representativeness and better reflects household expenditures.

### Data sources (Appendix Table 1)
- Indicators and frequencies (as listed in source):
  - Rent — Quarterly — Haver
  - Weight of rent in headline inflation — Quarterly — Haver
  - OOHC — Quarterly — Haver
  - Weight of OOHC in headline inflation — Quarterly — Haver
  - Headline inflation — Quarterly — Haver, WEO
  - Housing price — Quarterly — BIS
  - Nominal GDP — Quarterly — IFS
  - M2 — Quarterly — Haver
  - Policy rate — Quarterly — IFS, Federal Reserve Economic Data, CEIC
  - (Gross) Household disposable income — Quarterly — DataStream, CEIC
  - Inflation expectation — Quarterly — Consensus Forecast
  - Rental vacancy rate — Quarterly — Haver
- Source: Authors.

*Source: wpiea2022151-print-pdf - Appendix Table 1.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2022/english/wpiea2022151-print-pdf.pdf_