## 9. Uniform LSTI, α = 30 Percent of after-tax household income

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### Major assumptions and model setup
- Static borrowing-capacity (SBC) approach: households allocate a portion α of income Yt at loan origination to service mortgage payments, At = α Yt, with the baseline α = 30 percent of after-tax median household income in the uniform-LSTI scenario.
- Mortgage assumptions:
  - median-income households take 25-year mortgages with interest rates fixed for 5-year intervals;
  - baseline loan-to-value (LTV) ratio = 80 percent.
- Data sources:
  - RPS Real Property Solutions (2005:Q1—2019:Q1 spliced back to 2000:Q1 using Teranet);
  - CMHC five-year conventional mortgage lending rate used for mortgage calculations;
  - Long-Range Consensus Forecast used for expected GDP/CPI/10-year bond yields.
- Pricing and valuation frameworks:
  - SBC pricing formula: PPPt = 1/LTV × f(im, Nt m) × α Yt (formula (4) in text).
  - Investment (NPV) approach: present value of net rent flow discounted by cost of equity, with steady-state form sensitive to the “i − g” differential (formula (6) in text).
- Interest-rate mapping: 10-year bond yields adjusted by an average premium of 180 bps to approximate the 5-year mortgage-rate path used in valuation exercises.

### Key empirical findings (aggregate and regional)
- General result:
  - In most of the 11 CMAs analyzed, house prices can be explained by household median income dynamics and mortgage-rate declines; attainable house prices (SBC) closely track observed prices in most CMAs.
- Exceptions (evidence of overvaluation):
  - Hamilton, Toronto, and Vancouver (HTV) show significant deviations from fundamentals beginning in early 2016.
  - Pricing gap in 2018: approximately 50 percent for Toronto and Vancouver, and almost 60 percent for Hamilton.
  - Implied adjustment: house prices would have to drop by roughly 30 percent to align with current fundamentals in these three markets.
- Historical precedent:
  - Calgary and Edmonton experienced overvaluation cycles (Edmonton peak overvaluation estimated at 60 percent at 2007:Q3) that normalized by 2012 via moderate price declines, income growth, and lower mortgage rates.
- Interest-rate effect on borrowing capacity:
  - Example SBC implication: households allocating 30 percent of income to mortgage payments could borrow around 3 times income in 2000 and nearly 5 times income by 2016 due to mortgage-rate declines (from 8 percent to less than 4 percent).
  - The LTI–interest-rate relation is non-linear and sensitive to mortgage maturity; longer maturities increase sensitivity.
- Contribution decomposition (example Edmonton):
  - decline in mortgage rates since 2001 accounted for a large portion of the increase in attainable house prices (e.g., added C$100,000 out of a C$400,000 house in 2017 under SBC decomposition).
- Affordability and down payments:
  - With stable LTV and declining mortgage rates, down payments as a share of income rise, increasing the time required to save for down payments and reducing affordability.
- Required income growth to keep attainable prices non-declining (conditional on interest-rate forecasts):
  - At early 2019 and using Consensus Forecast 10-year bond yields (adjusted by 180 bps), the median income growth required to prevent house-price declines is at least 3 percent in 2019 and around 1.5 percent until 2025.
  - If interest rates stop increasing, zero house-price growth is consistent with zero income growth; required growth rates are sensitive to mortgage-rate changes.

### Investment (NPV) approach results and limitations
- Findings:
  - The investment approach helps explain valuation spikes in 2005 and 2016 where the narrowing of the expected long-run interest rate minus expected long-run nominal growth (“i − g”) raised NPV valuations.
  - Even under the investment approach with Consensus-based expectations, aggregate house prices in HTV remain overvalued.
- Limitations:
  - The NPV approach can significantly overvalue markets in some periods (e.g., 2016:Q4), making it insufficient alone to explain price increases.
  - Valuation is sensitive to long-run continuation-value assumptions and to the assumed constant risk premium added to bond yields to obtain cost of equity.

### Macro-financial risks and transmission
- Increasing price-to-income, price-to-rent, and loan-to-income ratios are predominantly driven by mortgage-rate declines and households keeping debt-service-to-income (DSTI) stable at origination.
- Higher LTI ratios for new borrowers raise household sector leverage and increase exposure to shocks in income, unemployment, interest rates, or house-price corrections.
- The flow of new credit (new loans) is most relevant for assessing house-price dynamics; the stock of mortgage credit mixes vintages and delays transmission.

### Policy implications and recommendations
- Policies that increase households’ borrowing capacity or lower effective mortgage costs are likely to raise house prices in tight-supply markets:
  - Measures such as extending mortgage amortization, introducing or increasing interest-expense tax deductibility, providing direct borrower subsidies, or relaxing macroprudential DSTI/LTI limits will likely put upward pressure on prices unless housing supply is exceptionally elastic in the short run.
- Most durable improvements in housing affordability are likely to come from:
  - Policies focused on increasing housing supply.
  - Reducing tax benefits associated with mortgage debt.
- Loan-to-income (LTI) limits are an effective macroprudential tool:
  - when binding, further declines in nominal interest rates translate largely into lower debt service rather than higher borrowing, thus constraining household indebtedness growth.

*Source: wpiea2019248-print-pdf — https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019248-print-pdf.pdf*

### 1. Observed Aggregate House Prices in Canada vs. ................................................................13

### 1. Observed Aggregate House Prices in Canada vs.

### Section inventory and page references
- "1. Observed Aggregate House Prices in Canada vs." — page 13
- "2. Implied share of debt-service to after-tax median household income" — page 14
- "3. Attainable House Prices – Income vs. Interest Rate Contribution" — page 15
- "4. Interest Rate Effect on LTI" — page 15
- "5. Nominal Income Growth Consistent with Non-Declining House Prices (Conditioned on Interest Rate Forecast)" — page 16
- "6. Investment Approach Results" — page 18
- "7. Long-Run Expectations of Interest Rates and Growth (Percent)" — page 18
- "8. House Prices: Aggregate, Condos, and Single-Detached Family House" — page 23

*Source: wpiea2019248-print-pdf — https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019248-print-pdf.pdf*

### 9. Uniform LSTI, α = 30 Percent of a fter-ta x ho use hold inco m ..............................................23

### 9. Uniform LSTI, α = 30 Percent of after-tax household income

### Major assumptions and model setup
- Static borrowing-capacity (SBC) approach: households allocate a portion α of income Yt at loan origination to service mortgage payments, At = α Yt, with the baseline α = 30 percent of after-tax median household income in the uniform-LSTI scenario.
- Mortgage assumptions: median-income households take 25-year mortgages with interest rates fixed for 5-year intervals; baseline loan-to-value (LTV) ratio = 80 percent.
- Data sources: RPS Real Property Solutions (2005:Q1—2019:Q1 spliced back to 2000:Q1 using Teranet), CMHC five-year conventional mortgage lending rate used for mortgage calculations, Long-Range Consensus Forecast used for expected GDP/CPI/10-year bond yields.
- Pricing and valuation frameworks:
  - SBC pricing formula: PPPt = 1/LTV × f(im, Nt m) × α Yt (formula (4) in text).
  - Investment (NPV) approach: present value of net rent flow discounted by cost of equity, with steady-state form sensitive to the “i − g” differential (formula (6) in text).
- Interest-rate mapping: 10-year bond yields adjusted by an average premium of 180 bps to approximate the 5-year mortgage-rate path used in valuation exercises.

### Key empirical findings (aggregate and regional)
- General result: In most of the 11 CMAs analyzed, house prices can be explained by household median income dynamics and mortgage-rate declines; attainable house prices (SBC) closely track observed prices in most CMAs.
- Exceptions (evidence of overvaluation): Hamilton, Toronto, and Vancouver (HTV) show significant deviations from fundamentals beginning in early 2016.
  - Pricing gap in 2018: approximately 50 percent for Toronto and Vancouver, and almost 60 percent for Hamilton.
  - Implied adjustment: house prices would have to drop by roughly 30 percent to align with current fundamentals in these three markets.
- Historical precedent: Calgary and Edmonton experienced overvaluation cycles (Edmonton peak overvaluation estimated at 60 percent at 2007:Q3) that normalized by 2012 via moderate price declines, income growth, and lower mortgage rates.
- Interest-rate effect on borrowing capacity:
  - Example SBC implication: households allocating 30 percent of income to mortgage payments could borrow around 3 times income in 2000 and nearly 5 times income by 2016 due to mortgage-rate declines (from 8 percent to less than 4 percent).
  - The LTI–interest-rate relation is non-linear and sensitive to mortgage maturity; longer maturities increase sensitivity.
- Contribution decomposition (example Edmonton): decline in mortgage rates since 2001 accounted for a large portion of the increase in attainable house prices (e.g., added C$100,000 out of a C$400,000 house in 2017 under SBC decomposition).
- Affordability and down payments:
  - With stable LTV and declining mortgage rates, down payments as a share of income rise, increasing the time required to save for down payments and reducing affordability.
- Required income growth to keep attainable prices non-declining (conditional on interest-rate forecasts):
  - At early 2019 and using Consensus Forecast 10-year bond yields (adjusted by 180 bps), the median income growth required to prevent house-price declines is at least 3 percent in 2019 and around 1.5 percent until 2025.
  - If interest rates stop increasing, zero house-price growth is consistent with zero income growth; required growth rates are sensitive to mortgage-rate changes.

### Investment (NPV) approach results and limitations
- The investment approach helps explain valuation spikes in 2005 and 2016 where the narrowing of the expected long-run interest rate minus expected long-run nominal growth (“i − g”) raised NPV valuations.
- Even under the investment approach with Consensus-based expectations, aggregate house prices in HTV remain overvalued.
- Limitations:
  - The NPV approach can significantly overvalue markets in some periods (e.g., 2016:Q4), making it insufficient alone to explain price increases.
  - Valuation is sensitive to long-run continuation-value assumptions and to the assumed constant risk premium added to bond yields to obtain cost of equity.

### Macro-financial risks and transmission
- Increasing price-to-income, price-to-rent, and loan-to-income ratios are predominantly driven by mortgage-rate declines and households keeping debt-service-to-income (DSTI) stable at origination.
- Higher LTI ratios for new borrowers raise household sector leverage and increase exposure to shocks in income, unemployment, interest rates, or house-price corrections.
- The flow of new credit (new loans) is most relevant for assessing house-price dynamics; the stock of mortgage credit mixes vintages and delays transmission.

### Policy implications and recommendations
- Policies that increase households’ borrowing capacity or lower effective mortgage costs are likely to raise house prices in tight-supply markets:
  - Measures such as extending mortgage amortization, introducing or increasing interest-expense tax deductibility, providing direct borrower subsidies, or relaxing macroprudential DSTI/LTI limits will likely put upward pressure on prices unless housing supply is exceptionally elastic in the short run.
- Most durable improvements in housing affordability are likely to come from:
  - Policies focused on increasing housing supply.
  - Reducing tax benefits associated with mortgage debt.
- Loan-to-income (LTI) limits are an effective macroprudential tool: when binding, further declines in nominal interest rates translate largely into lower debt service rather than higher borrowing, thus constraining household indebtedness growth.

*Source: IMF Working Paper chapter "9. Uniform LSTI, α = 30 Percent of after-tax household income" (content from wpiea2019248-print-pdf).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019248-print-pdf.pdf_