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### Context and research question
- Following a decade-long increase in house prices in Canada, the COVID-19 pandemic brought house prices to new historical highs.
- Productivity growth in Canada has remained sluggish over the past decades.
- A negative correlation between lagged real house price growth and productivity growth is evident in Canada at the aggregate and provincial level, and in several other advanced economies, including Australia, the UK, and selected European countries.
- Relationship particularly strong in Canada and evident in almost all Canadian provinces except Manitoba.
- Research question: examines the relationship between house prices and productivity in Canada by empirically testing the collateral channel—whether increases in real-estate values, in the presence of financial frictions, disproportionately benefit firms holding such assets and lead to inefficient reallocation of resources toward firms holding more real estate assets.

### Approach and empirical strategy
- The paper outlines intuition using a highly stylized model and then implements a three-step empirical analysis with Compustat data on publicly traded Canadian firms:
  - Step 1: Examine relationship between firm productivity and real estate holdings.
  - Step 2: Test how changes in real estate prices affect firm-level investment.
  - Step 3: Test aggregate effect of the collateral channel at the industry level.
- Primary housing price series: MLS home price index published by CREA (preferred measure, used by Bank of Canada).
- Firm-level sample: Compustat annual data for firms headquartered in Canada; exclude finance and mining industries and firms operating less than two years; sample size: 7,091 firm-year observations spanning 2000 to 2023.
- Instrumental variable: municipality-level housing supply elasticity × aggregate long-term real mortgage interest rate; fixed effects: year, location, industry, industry#year; robust SEs clustered at city level.

### Key empirical finding (headline)
- Firms holding larger tangible assets on a gross basis at the beginning of the sample tend to be less productive (consistent with Doerr (2020) for the United States).

### Theoretical stylized model — mechanisms and analytical findings
- Setup: firms indexed by i have real estate holdings h_i ∈ [͞h, h], liquid funds ω_i, can borrow d_i at real interest rate R subject to collateral constraint R d_i ≤ θ [P* h_i + ω_i]; housing supply H_S = P^ε and demand H_D = (σ + B), equilibrium house price P* = (σ + B)^{1/ε}.
- Closed-form constrained equilibrium capital stock (equation (5)): k_i* = θ/R P* h_i + (1+ θ/R ) + ω_i (as presented).
- Finding 1: In a housing boom investment rates increase. Expression (equation (6)): k_i* = θ/R (∑_i h_i + B)^{1/ε} h_i + (1+ θ/R ) ω_i. Derivative (equation (7)): ∂k_i / ∂B = θ/(εR) (∑_i h_i + B)^{(1/ε -1)} h_i > 0.
- Finding 2: Firms with higher initial real estate assets increase capital investment relatively more when house prices rise. Interaction derivative (equation (8)) shows ∂(dk_i/dB)/∂h_i > 0.
- Finding 3: Average industry productivity decreases with real estate prices when less-productive firms are more collateral-rich. Two-type firm model yields weighted average industry productivity (equation (9)); derivative of TFP with respect to B is proportional to (A_1 − A_2) and is < 0 when A_1 < A_2.

### Data sources and identification specifics
- Primary data sources: Canadian Real Estate Association (CREA), Statistics Canada (StatCan), Compustat Financials.
- Housing price series: MLS home price index (CREA).
- Sample: 7,091 firm-year observations (2000–2023) after exclusions.
- Instrument: housing supply elasticity at municipality level × aggregate long-term real interest rate of home mortgages (subnational housing supply elasticity data for Canada courtesy of Nuno Marques da Paixao (Bank of Canada)).
- Rationale: reductions in long-term interest rates stimulate housing demand; local supply elasticity determines house price response (Saiz, 2010).
- Mitigation of confounders: inclusion of industry-time fixed effects to control for aggregate trends in interest rates and other macro factors.

### Empirical analysis — Step 1: Firm productivity and initial tangible assets (Table 1)
- Regression: y_{i,t} = α + β initial tangible assets_i + controls_{i,t−1} + controls_{i,t} + τ_t + φ_{j,t} + ω_k + ε_{i,t}.
- Productivity measures: labor productivity (log value added per employee), TFP (OP and LP); sales-based robustness checks.
- Selected coefficients (Table 1):
  - Initial Tangible Assets: -0.131* (Labor Productivity)
  - Initial Tangible Assets: -0.092*** (TFP (LP))
  - Initial Tangible Assets: -0.371*** (TFP (OP))
  - Firm Size: 0.038 (Labor Productivity); -0.022** (TFP (LP)); 0.177*** (TFP (OP))
  - No. of Obs.: 7,091 (Labor Productivity); 5,404 (TFP (LP)); 5,384 (TFP (OP))
  - R2: 0.490, 0.579, 0.571 respectively
- Conclusion: higher initial tangible asset ratio is associated with significantly lower productivity, robust across specifications.

### Empirical analysis — Step 2: Rising house prices and firm investment (Table 2)
- Regression: ΔSize_{i,t} = β_0 + β_1 ΔHP_{k,t−1} × Initial Tangible Assets_i + β_2 ΔHP_{k,t−1} + β_3 Initial Tangible Assets_i + controls + fixed effects + ε_{i,t}.
- Instrument for ΔHP_{k,t}: HSE_k × R_t (housing supply elasticity × aggregate long-term real interest rate).
- Key empirical results (Table 2):
  - ∆ln(Real House Price)*Initial Tangible Assets: 4.861*** (∆Firm Size)
  - ∆ln(Real House Price)*Initial Tangible Assets: 5.246*** (∆Gross Assets)
  - ∆ln(Real House Price): -1.985* (∆Firm Size)
  - ∆ln(Real House Price): -2.064* (∆Gross Assets)
  - Initial Tangible Assets: -0.206*** (∆Firm Size)
  - Initial Tangible Assets: -0.233*** (∆Gross Assets)
  - No. of Obs.: 4,288 (∆Firm Size); 4,209 (∆Gross Assets)
  - R2: 0.135 for both
- Interpretation: positive and significant interaction term implies housing price increases expand firm size and gross assets for firms with larger tangible assets; negative main effect of ∆ln(Real House Price) indicates house-price increases can reduce investment for firms with low tangible assets.

### Empirical analysis — Step 3: Aggregate industry-level effects (Table 3)
- Industry regression: y_{j,t} = α + β ΔHP_{k,t−1} × Initial Tangible Assets_j + γ ΔHP_{k,t−1} + δ Initial Tangible Assets_j + controls + fixed effects + ε_{j,t}.
- Selected coefficients (Table 3):
  - ∆ln(Real House Price)*Initial Tangible Assets: -52.370*** (Labor Productivity) — (17.919)
  - ∆ln(Real House Price)*Initial Tangible Assets: -5.005*** (TFP (LP)) — (1.487)
  - ∆ln(Real House Price)*Initial Tangible Assets: -13.311* (TFP (OP)) — (6.882)
  - ∆ln(Real House Price): 13.005*** (Labor Productivity) — (3.604)
  - ∆ln(Real House Price): 1.320*** (TFP (LP)) — (0.331)
  - ∆ln(Real House Price): 5.144 (TFP (OP)) — (3.483)
  - Initial Tangible Assets: 1.955* (Labor Productivity) — (1.143)
  - Initial Tangible Assets: 0.082 (TFP (LP)) — (0.082)
  - Initial Tangible Assets: 0.168 (TFP (OP)) — (0.354)
  - Firm Size: 0.186*** (Labor Productivity) — (0.012); 0.011*** (TFP (LP)) — (0.002); 0.035*** (TFP (OP)) — (0.008)
  - Firm Age: -0.086*** (Labor Productivity) — (0.015); -0.001 (TFP (LP)) — (0.008); 0.001 (TFP (OP)) — (0.017)
  - No. of Obs.: 1,782 (Labor Productivity); 1,896 (TFP (LP)); 1,891 (TFP (OP))
  - R2: 0.291, 0.414, 0.057 respectively
- Conclusion: rising house prices lead to larger productivity declines in industries with higher shares of initial tangible assets, consistent with reallocation where property-rich but less productive firms gain credit access while asset-light, more productive firms face capital constraints.

### Synthesis of findings
- Theoretical model and empirical evidence support a collateral-driven misallocation channel in Canada:
  - Housing booms increase aggregate investment but disproportionately favor firms with larger real estate holdings.
  - Firms with higher initial tangible assets are empirically less productive (negative association between initial tangible asset share and productivity).
  - Housing-price-driven reallocation toward real-estate-heavy firms reduces average industry productivity where such firms are less productive.
- Empirical highlights:
  - Firm-level interaction coefficients for ∆ln(Real House Price)*Initial Tangible Assets: 4.861*** and 5.246*** (Table 2).
  - Large negative industry-level interaction effect on Labor Productivity: -52.370*** (Table 3).

### Limitations and robustness considerations
- Causality efforts undertaken but results could be improved by using more robust instrumental variables.
- More nuanced real estate price data, including residential and commercial real estate, could enhance granularity.
- Sample limitations: publicly traded firms dataset is not fully representative of the entire spectrum of Canadian firms; small businesses (98% of all employer businesses and employing about two thirds of all employees in 2022) are typically not well represented.
- Potential endogeneity of housing supply elasticities noted; demand-side bias would work against finding a negative association, lending weight to the misallocation interpretation given consistently negative associations found.

### Broader interpretation and context
- Paper documents a novel collateral channel through which house price booms affect productivity via resource reallocation.
- Complementary factors contributing to slow productivity growth in Canada include:
  - low stock of capital investment (Voss, 2002),
  - investment climate (Lutz, Yang and Huang, 2024),
  - declining business dynamism (Diez et al., 2021),
  - presence of zombie firms (Amundsen, 2023).

_Conclusions — Housing Booms and Productivity Growth, Working Paper No. WP/2025/161_

### Introduction ...........................................................................................................

### Introduction

### Context and research question
- Following a decade-long increase in house prices in Canada, the COVID-19 pandemic brought house prices to new historical highs.
- Productivity growth in Canada has remained sluggish over the past decades.
- A negative correlation between lagged real house price growth and productivity growth is evident in Canada at the aggregate and provincial level, and in several other advanced economies, including Australia, the UK, and selected European countries.
- Compared to other advanced economies, the relationship appears particularly strong in Canada and is evident in almost all Canadian provinces except Manitoba (see Appendix I).
- The study examines the relationship between house prices and productivity in Canada by empirically testing the collateral channel: in the presence of financial frictions, increases in real-estate values may disproportionately benefit firms holding such assets, leading to inefficient reallocation of resources toward firms holding more real estate assets (see e.g., Rogoff and Yang, 2024a).

### Approach and empirical strategy
- The paper first outlines the intuition of the collateral channel using a highly stylized model.
- Empirical testing uses a three-step empirical analysis with Compustat data on publicly traded Canadian firms:
  - Step 1: Examine the relationship between firm productivity and real estate holdings.
  - Step 2: Test how changes in real estate prices affect firm-level investment.
  - Step 3: Test the aggregate effect of the collateral channel at the industry level.
- The document includes figures and tables supporting the analysis:
  - Figure 1: House price and productivity growth in Canada and selected advanced economies.
  - Figure 2: House price appreciation in Canada.
  - Figure 3: House price and productivity growth in Canadian provinces.
  - Stylized Model section.
  - Data section.
  - Empirical Analysis with Tables 1–3 corresponding to steps outlined above.
  - Annex I: House Price and Productivity Growth in Canadian Provinces (Figures I.1 and I.2).

### Key empirical finding (as reported)
- First main finding: Firms holding larger tangible assets on a gross basis (a proxy for real estate assets) at the beginning of the sample tend to be less productive. This finding is noted to be in line with Doerr (2020), who documented a similar relationship for the United States.

### Structure of remaining analysis (as presented)
- Step 1. Firm productivity and initial real estate (Table 1. Firm Productivity and Tangible Asset Holdings).
- Step 2. Rising house prices and firm investment (Table 2. Rising house prices and firm size).
- Step 3. Aggregate effects at the industry level (Table 3. Aggregate effects at the industry level).
- Conclusions section.
- Annex and References.

*Source: IMF Working Paper — Introduction (wpiea2025161-source-pdf).*

### Annex I summarizes the relationship between house price and productivity growth for several additional advanced economie

### Annex I — Relationship between house price and productivity growth (selected advanced economies) and Canada-focused analysis

### Key observations and motivation
- Aggregate-level negative relationship between house price growth and productivity growth in all countries except Germany, Japan and the US.
- Paper focus: relationship between housing booms, resource reallocation, and productivity with a focus on Canada using the same empirical methodology and dataset as in Doerr (2020).
- Three main channels from the literature explaining negative correlation between house prices and productivity:
  - Collateral channel: rising real estate values relax collateral constraints disproportionately for firms with large real estate holdings, reallocating resources toward lower-productivity, real-estate-heavy firms (Chaney, Sraer and Thesmar, 2012; Basco, Lopez-Rodriguez and Moral-Benito, 2023; Doerr, 2020).
  - Crowding-out channel: if bank credit supply is inelastic, mortgage demand during housing booms may crowd out commercial lending, hampering firm investment and productivity (Rogoff and Yang, 2020, 2021, 2024b, 2024c).
  - Labor mobility / ownership channel: housing supply constraints and price dynamics can limit worker mobility into high-productivity locations (Hsieh and Moretti, 2019; Bergy, 2010).
- Study concentrates on the collateral channel in Canada because:
  - "more than 73 percent of outstanding business credit held by banks in 2022."
  - SMEs prevalence: "more than 58 percent of small business, representing represent 98 percent of all Canadian businesses and employing 67.7 percent of the private sector labor force, were asked to pledge collateral to secure their loans in 2021."
  - A prolonged and robust housing boom has made housing a significant form of collateral.

### Theoretical stylized model — mechanism and analytical findings
- Model setup (partial equilibrium): firms indexed by i have real estate holdings h_i ∈ [͞h, h], liquid funds ω_i, can borrow d_i at real interest rate R subject to collateral constraint R d_i ≤ θ [P* h_i + ω_i]; housing supply H_S = P^ε and demand H_D = (σ + B), equilibrium house price P* = (σ + B)^{1/ε}. Firms maximize profits f(k_i) − R d_i + s_i subject to budget and collateral constraints.
- Closed-form constrained equilibrium capital stock (equation (5)):
  - k_i* = θ/R P* h_i + (1+ θ/R ) + ω_i (as presented).
- Finding 1: In a housing boom investment rates increase.
  - Expression for k_i* incorporating B (equation (6)): k_i* = θ/R (∑_i h_i + B)^{1/ε} h_i + (1+ θ/R ) ω_i.
  - Derivative (equation (7)): ∂k_i / ∂B = θ/(εR) (∑_i h_i + B)^{(1/ε -1)} h_i > 0.
- Finding 2: Firms with higher initial real estate assets increase capital investment relatively more when house prices rise.
  - Interaction derivative (equation (8)) shows ∂(dk_i/dB)/∂h_i > 0.
- Finding 3: Average industry productivity decreases with real estate prices when less-productive firms are more collateral-rich.
  - Model with two firm types (type 1: real estate holdings only, A_1 < A_2; type 2: liquid assets only) yields weighted average industry productivity (equation (9)).
  - Derivative of TFP with respect to B (presented) is proportional to (A_1 − A_2) and is < 0, demonstrating decline in average industry productivity as B increases.

### Data sources and identification
- Primary data sources: Canadian Real Estate Association (CREA), Statistics Canada (StatCan), Compustat Financials.
- Housing price series chosen: MLS home price index published by CREA (preferred measure, used by Bank of Canada).
- Firm-level sample: Compustat annual data for firms headquartered in Canada; exclude finance and mining industries and firms operating less than two years; sample size: 7,091 firm-year observations spanning 2000 to 2023.
- Instrumental variable strategy for identification:
  - Instrument: housing supply elasticity multiplied by long-term interest rates (municipality-level housing supply elasticity × aggregate long-term real interest rate of home mortgages).
  - Rationale: reductions in long-term interest rates stimulate housing demand; local supply elasticity determines house price response (Saiz, 2010).
  - Mitigation of confounders: inclusion of industry-time fixed effects to control for aggregate trends in interest rates and other macro factors.
  - Note on potential endogeneity of housing supply elasticities: demand-side factors may bias toward a positive association between house prices and productivity; the consistently found negative association strengthens interpretation of a misallocation/collateral channel.

### Empirical analysis — three-step approach and results
- Step 1: Relation between firms’ initial real estate holdings and their productivity.
  - Regression specification: y_{i,t} = α + β initial tangible assets_i + controls_{i,t−1} + controls_{i,t} + τ_t + φ_{j,t} + ω_k + ε_{i,t}.
  - Productivity measures: labor productivity (log value added per employee), TFP (control-function Olley-Pakes (OP) and Levinsohn-Petrin (LP)); sales-based measures used as robustness.
  - Controls include log total assets and firm age; fixed effects: year, location, industry, industry#year; robust SE clustered at city level.
  - Table 1 (selected coefficients):
    - Initial Tangible Assets: -0.131* (Labor Productivity), -0.092*** (TFP (LP)), -0.371*** (TFP (OP))
    - Firm Size: 0.038 (Labor Productivity), -0.022** (TFP (LP)), 0.177*** (TFP (OP))
    - No. of Obs.: 7,091 (Labor Productivity), 5,404 (TFP (LP)), 5,384 (TFP (OP))
    - R2: 0.490, 0.579, 0.571 respectively
  - Empirical conclusion: higher initial tangible asset ratio is associated with significantly lower productivity, robust across specifications.
  - Qualitative implications: property ownership ties firms to locations, may reduce relocation/restructuring and divert managerial focus and capital toward real estate as speculative asset rather than productivity-enhancing activities.

- Step 2: How housing price increases affect firm investment conditional on real estate holdings.
  - Regression specification for firm expansion: ΔSize_{i,t} = β_0 + β_1 ΔHP_{k,t−1} × Initial Tangible Assets_i + β_2 ΔHP_{k,t−1} + β_3 Initial Tangible Assets_i + controls + fixed effects + ε_{i,t}.
  - Instrument for ΔHP_{k,t}: HSE_k × R_t (housing supply elasticity × aggregate long-term real interest rate).
  - Key empirical results (Table 2):
    - ∆ln(Real House Price)*Initial Tangible Assets: 4.861*** (∆Firm Size), 5.246*** (∆Gross Assets)
    - ∆ln(Real House Price): -1.985* (∆Firm Size), -2.064* (∆Gross Assets)
    - Initial Tangible Assets: -0.206*** (∆Firm Size), -0.233*** (∆Gross Assets)
    - No. of Obs.: 4,288 (∆Firm Size), 4,209 (∆Gross Assets)
    - R2: 0.135 for both
  - Interpretation: positive and significant interaction term implies housing price increases expand firm size and gross assets for firms with larger tangible assets, consistent with the collateral channel. Negative main effect of Δln(Real House Price) suggests house-price increases can reduce investment for firms with low tangible assets.

- Step 3: Aggregate industry-level effects (resource reallocation → productivity)
  - Industry-level regression: y_{j,t} = α + β ΔHP_{k,t−1} × Initial Tangible Assets_j + γ ΔHP_{k,t−1} + δ Initial Tangible Assets_j + controls + fixed effects + ε_{j,t}.
  - Dependent variable: industry-average initial tangible assets as share of total assets (averaged controls: firm assets and age).
  - Table 3 (selected coefficients):
    - ∆ln(Real House Price)*Initial Tangible Assets: -52.370*** (Labor Productivity), -5.005*** (TFP (LP)), -13.311* (TFP (OP))
      - Standard errors (reported parenthetically): (17.919) for Labor Productivity, (1.487) for TFP (LP), (6.882) for TFP (OP)
    - ∆ln(Real House Price): 13.005*** (Labor Productivity), 1.320*** (TFP (LP)), 5.144 (TFP (OP))
      - Standard errors: (3.604), (0.331), (3.483)
    - Initial Tangible Assets: 1.955* (Labor Productivity), 0.082 (TFP (LP)), 0.168 (TFP (OP))
      - Standard errors: (1.143), (0.082), (0.354)
    - Firm Size: 0.186*** (Labor Productivity), 0.011*** (TFP (LP)), 0.035*** (TFP (OP))
      - Standard errors: (0.012), (0.002), (0.008)
    - Firm Age: -0.086*** (Labor Productivity), -0.001 (TFP (LP)), 0.001 (TFP (OP))
      - Standard errors: (0.015), (0.008), (0.017)
    - No. of Obs.: 1,782 (Labor Productivity), 1,896 (TFP (LP)), 1,891 (TFP (OP))
    - R2: 0.291, 0.414, 0.057 respectively
  - Empirical conclusion: rising house prices lead to larger productivity declines in industries with higher shares of initial tangible assets, consistent with a reallocation/crowding-out mechanism where property-rich but less productive firms gain credit access while asset-light, more productive firms are starved of capital.

### Synthesis of findings
- Theoretical model and empirical evidence consistently support a collateral-driven misallocation channel in Canada:
  - Housing booms increase aggregate investment but disproportionately favor firms with larger real estate holdings.
  - Firms with higher initial tangible assets are empirically less productive (negative association between initial tangible asset share and productivity).
  - Housing-price-driven reallocation toward real-estate-heavy firms reduces average industry productivity where such firms are less productive.
- Empirically observed patterns:
  - Positive interaction coefficients at the firm level for ∆ln(Real House Price)*Initial Tangible Assets (Table 2: 4.861*** and 5.246***).
  - Large negative interaction effects at industry level for ∆ln(Real House Price)*Initial Tangible Assets on Labor Productivity: -52.370*** (Table 3).

### Data and methodological notes (salient specifics)
- Firm-level sample: 7,091 firm-year observations (2000–2023), after excluding finance and mining and firms with less than two years of operation.
- Primary housing series: MLS home price index (CREA).
- Instrumental variable: municipality-level housing supply elasticity × aggregate long-term real mortgage interest rate; subnational housing supply elasticity data for Canada courtesy of Nuno Marques da Paixao (Bank of Canada).
- Fixed effects strategy: year, location, industry, industry#year (industry-time) fixed effects included across specifications; robust SEs clustered at city level reported.

*Source: IMF Working Paper — Housing Booms and Productivity Growth (Annex I and accompanying sections, as provided).*

### Conclusions

### Conclusions

### Main findings
- Presented a stylized theoretical framework outlining a channel linking house price booms and productivity at the aggregate level.
- Empirical evidence supports the theoretical prediction that firms with lower productivity benefit disproportionately from real estate booms because:
  - they typically hold more real estate assets, and
  - they can secure greater lending from banks following an increase in collateral values (i.e. tangible assets).
- The three empirical steps in the study confirm the existence of a collateral-induced misallocation of capital in Canada.

### Limitations and robustness
- Efforts were made to establish causality, but results could be improved by using more robust instrumental variables.
- Using more nuanced real estate price data, including both residential and commercial real estate, could enhance granularity and comprehensiveness.
- Dataset contains a rich set of information on publicly traded firms but:
  - is not fully representative of the entire spectrum of Canadian firms,17
  - outcomes may not be directly generalizable to all firms or industries.
- Footnote note: Small businesses, which comprised 98% of all employer business and employed about two thirds of all employees in 2022, are typically not well represented. This distinction should be taken into account when interpreting findings.

### Interpretation and context
- The paper provides evidence for a novel channel through which house price booms affect productivity (the collateral channel and resulting misallocation).
- Slow productivity growth observed in Canada during past decades has also been attributed to complementary factors, including:
  - the low stock of capital investment (Voss, 2002),
  - the investment climate (Lutz, Yang and Huang, 2024),
  - declining business dynamism (Diez et al., 2021),
  - the existence of zombie firms (Amundsen, 2023).
- These factors are viewed as complementary contributors to low aggregate productivity growth.

_Conclusions — Housing Booms and Productivity Growth, Working Paper No. WP/2025/161_

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025161-source-pdf.pdf_