## wpiea2020265-print-pdf - References

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---

### Introduction — key findings and observed facts
- Housing accounts for 65.3 percent of Chinese households’ assets, compared with 36.0 percent in the US.
- Since the housing market reform in 1998, house prices in China have exhibited a rising trend that persisted through the COVID-19 shock (nominal series illustrated for July 2017-October 2020).
- COVID-19 era anecdotes and milestones:
  - In March 2020, 288 apartments in a Shenzhen neighborhood sold out online in less than eight minutes.
  - In July 2020, China’s average residential house price surpassed 10,000 RMB/sq.m for the first time.
  - New regulation issued on September 28, 2020: new housing-related loans should not exceed 30 percent of total bank loans; yet housing prices continued to rise in October 2020.
- Household behavior during COVID-19: lower consumption and higher saving increased speculative house purchases, particularly among multiple-property owners; quote from Professor Gan Li: “Speculative demand is on the rise because [people] view housing as a safer asset than the stock market or overseas assets... Because of the pandemic they’re actually consuming less, and saving more. So they’ll actually have more money available to invest. That will create an even larger housing problem.”
- Financial market structure and frictions in China:
  - Bank-dominated financial market: financing via the second-board stock market about 1-2 percent of bank loans; small-and-medium board market about 3-5 percent of bank loans.
  - More than 75 percent of corporate bonds are held by banks (as of end-2018).
  - Strict restrictions on “illegal fund-raising” and constraints on overseas investment (rule cited: from February 1, 2019, holding foreign exchange more than RMB 5 million may lead to criminal penalties).
- Central question: Is financial market incompleteness the underlying force linking high housing prices, abundant household savings, unmet SME financing demand, and bank-dominated markets?

### Analytical contribution and mechanisms
- Core contribution: unified framework emphasizing financial market incompleteness as a slow-moving structural determinant of housing prices, developed in a stylized DSGE model with heterogeneous households (rich investors vs. poor renters).
- Two main channels through which incomplete financial markets raise housing demand and prices:
  - Rich households channel: Lack of alternative profitable or “safe” investment opportunities leads rich households to allocate “hot money” into housing, raising demand, prices, and potentially wealth inequality.
  - Poor households channel: Poor households effectively have only bank deposits as a saving channel; abundant deposits push down interest rates, stimulating borrowing demand for housing.
- Supply-side amplification: Low interest rates stimulate real estate developer borrowing to build housing; constrained local land supply implies demand effects dominate supply effects, yielding higher equilibrium prices and resource crowding-out from productive industries.
- Policy implication emphasized: addressing high housing prices requires developing financial markets and deploying “non-housing policies”; without addressing financial market incompleteness, higher household savings and government stimulus (especially in the COVID era) may fuel housing bubbles and future crises.

### Stylized empirical evidence motivating the model
- Household deposits-to-GDP ratio:
  - Broad rising trend from a little over 60 percent in 1998 to 90 percent in 2020 (2020 ratio calculated using stock of deposits in Q3 and nominal GDP of RMB 100,000 billion; official estimate released on October 31, 2020).
  - Exception: 2007 drop of more than 10 percentage points, likely due to a stock market boom.
  - Negative correlation observed between household deposit ratio and stock price index.
- Household mortgage and developer loan ratios (to GDP):
  - Residential housing mortgage loan-to-GDP ratio rose from close to 0 (1998) to more than 30 percent in 2020.
  - Real estate development loan-to-GDP ratio also rose, but at a slower rate than the mortgage loan-to-GDP ratio.
- Cross-checked data caveats: 2020 figures use third-quarter stocks and official GDP estimate; numbers in Figures 3 and 4 cross-checked against other published numbers.

### Model structure and key elements
- Model type: DSGE with heterogeneous households and financial market incompleteness; extends Iacoviello (2005) by including renters, housing investors, real estate developers, and incomplete financial markets.
- Household types and key equations:
  - Renters (“poor” households):
    - Account for φ fraction of population; inelastic labor supply of one unit each; cannot afford down payments or access mortgage market; can only deposit surplus funds with banks.
    - Renters maximize E_t ∑_{t=0}^∞ β_{R,t} U_{R,t}(c^R_t,h^R_t) subject to c^R_t + p^r_t h^R_t + d^R_t = (1+i_{t-1}) d^R_{t-1} + Y_t/N_t.
    - Euler condition: U_{R,t,c^R}(.) = E_t[β_{R,t} U_{R,t+1,c^R}(.)] (1+i_t).
    - Intra-temporal condition: U_{R,t,h^R}(.) = p^r_t U_{R,t,c^R}(.).
    - Renters assumed more patient than investors (β_{R,t} > β_{I,t}).
  - Investors (“rich” households):
    - Account for 1−φ fraction; inelastic labor supply; own one real estate developer; borrow and buy houses, choose housing for own living and for rental.
    - Investors maximize E_t ∑_{t=0}^∞ β_{I,t} U_{I,t}(c^I_t,h^I_t) subject to c^I_t + p^h_t(h^I_t + h^{RI}_t) + (1+i_{t-1}) b^I_{t-1} = p^r_t h^{RI}_t + b^I_t + p^h_t(1−δ)(h^I_{t-1} + h^{RI}_{t-1}) + Y_t/N_t + π_t.
    - Collateral constraint: b^I_t ≤ m_t p^h_t(h^I_t + h^{RI}_t).
    - First-order conditions include inter-temporal and intra-temporal conditions and a borrowing FOC linking consumption marginal utility to shadow price μ_t.
- Equilibrium intuition:
  - Appendix 1 shows investors always borrow up to the collateral limit: b_I_t = m_t p_h_t (h_I_t + h_RI_t) (equation (19)).
  - Renters’ steady state implies β_R/(1+i) = 1, so with β_R > β_I investors are more impatient and optimally borrow to the limit.

### Developer, production, and market-clearing conditions
- Developer flow of funds: b_Dev_t = W_t n_Dev_t + p_l_t l_t (20).
- Production of new houses: y_h_t = A_t (n_Dev_t)^γ (l_t)^{1−γ} (21).
- No-default requirement: (1+i_t) b_Dev_t ≤ E_t [ A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{1−γ} ] (22).
- Developer collateral constraint binds ex ante; realized profit π_{t+1} = A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{1−γ} − b_Dev_t (1+i_t) (28).
- Non-housing production: Y_t = A_t (N_G_t)^α (29); non-housing sector assumed not to borrow.
- Market-clearing conditions determine prices and allocations:
  - Housing market (31), rental market (32), bond market (33), labor market (34), land market with fixed per-period land flow L̄ (35).

### Calibration and parameter values (China-specific where available)
- Key calibrated parameter values:
  - φ_ss Share of renters in households population 0.255
  - β_R,ss Discount factor of the renters 0.976
  - β_I Discount factor of the investors 0.85
  - δ Depreciation rate of houses 0.025
  - γ Share of labor in housing production 0.0574
  - α Share of labor in goods production 2/3
  - L Constant supply of new land 1
  - j Weight on housing services by renters 0.06
  - κ Weight on housing services by investors 0.12
- Calibration targets and procedures:
  - β_R,ss set by matching steady-state interest rate to average one-year benchmark deposit rate in China from 2000 to 2018, which equals 2.42 percent.
  - Housing GDP share target set to equal 0.05 given φ_ss = 0.255.
  - γ = 5.74 percent computed from firm-level labor cost shares for five large developers over 2010-2019.
  - δ follows Iacoviello (2005); β_I and α follow Gete (2020).
  - j and κ chosen so model-generated housing value-added share equals 0.05.

### Impulse response results and mechanisms
- Shock analyzed: temporary positive shock to φ (share of renters) — φ increases by 1 percentage point at time 0 then gradually returns to original level.
- Main dynamics:
  - Increase in renters raises aggregate deposits and lowers the interest rate.
  - Lower interest rate:
    - Stimulates higher mortgage borrowing and higher housing demand by investors.
    - Encourages developers to borrow more and produce more houses.
  - Due to rationed land supply, demand-side effect dominates → equilibrium housing price increases.
  - Wealth concentration: wealthy able to afford down payments may buy larger or multiple houses, worsening wealth inequality.
- Crowding-out effects:
  - Developers hire more labor and use more land, increasing wages and reducing labor available to non-housing sectors, lowering non-housing output.
- Dynamic margins in IRF:
  - Time 1: extensive margin dominates (deposit below steady state, interest rate above steady state).
  - From time 2: intensive margin dominates; all indicators return to steady state because shock is temporary. A permanent shock would produce persistent effects similar to initial responses.
- Alternative shock: higher renter discount factor produces similar responses to higher financial market incompleteness.

### Policy analysis and recommendations
- Financial market incompleteness identified as a slow-moving structural vulnerability contributing to higher housing prices and crowding-out of non-housing sectors.
- Two complementary policy approaches to depress housing demand and contain prices:
  - Directly block fund inflows to housing using macroprudential tools (limits on loan-to-value ratio, debt-to-income ratio, etc.).
  - Open up new outlets for funds via financial market reforms to divert funds away from real estate (indirectly depress housing demand and mitigate supply-side resource misallocation).
- Key reform objective:
  - Transition from a bank-dominated system to a well-regulated multi-layer financial system (banks, bond markets, multi-layer stock markets) to accommodate diverse risk preferences and reduce risk mismatches.
  - Suggested measures (aligned with IMF (2019) direction): targeted reserve ratio cuts for lending to MSEs; increase lending to MSEs by 30 percent; private enterprises to receive at least 50 percent of new loans.
- Complementary structural reforms:
  - Strengthen medical insurance, social security, and other measures to reduce household precautionary savings.
- Regulatory safeguards:
  - While expanding non-bank channels, maintain strict regulation and monitoring to limit fraud in P2P markets and excess risk-taking; include mechanisms for managers to have skin in the game.

### Appendix 1 — Investor and Developer Behavior; Model Equilibrium
- Investor borrowing result:
  - b_I_t = m_t p_h_t (h_I_t + h_RI_t) (equation (19)).
- Proof outline:
  - Kuhn-Tucker condition: μ_t [ m_t p_h_t ( h_I_t + h_RI_t ) − b_I_t ] = 0.
  - If constraint not binding then μ_t = 0 and investor FOC implies β_I (1+i) = 1 at steady state.
  - Renters’ steady state implies β_R (1+i) = 1 and with β_R > β_I this is inconsistent unless μ_t > 0.
  - Therefore constraint binds and μ_t > 0.
- Developer FOCs under binding constraint:
  - Labor demand: E_t [ γ A_t p_h_{t+1} (n_Dev_t)^{γ−1} (l_t)^{1−γ} ] = W_t (1+i_t) (25).
  - Land demand: E_t [ (1−γ) A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{−γ} ] = p_l_t (1+i_t) (26).
  - Binding collateral constraint implies ex ante expected profit zero; realized developer profits flow to investor budget.

### Appendix 2 — System of Steady-State Conditions
- Steady-state conditions (selected equations listed exactly):
  - c_R + p_r h_R = Y_N + id_R  (43)
  - U_R h_R ( c_R, h_R ) = p_r t U_R c_R ( c_R, h_R )  (44)
  - U_R n_R ( c_R, h_R ) = − W U_R c_R ( c_R, h_R )  (45)
  - 1 = β_R (1+i)  (46)
  - c_I + p_h δ ( h_I + h_RI ) + i b_I t = Y_N + I + p_r h_RI  (47)
  - [1 − β_I (1−δ)] U_I c_I ( c_I, h_I ) / p_h = U_I h_I ( c_I, h_I ) + μ m p_h  (48)
  - [1 − β_I (1−δ)] U_I c_I ( c_I, h_I ) / p_h = U_I c_I ( c_I, h_I ) / p_r + μ m p_h  (49)
  - [1 − β_I (1+i)] U_I c_I ( c_I, h_I ) = μ  (50)
  - b_I = m p_h h_I  (51)
  - b_Dev = W n_Dev + p_l l  (52)
  - Y_h = A ( n_Dev )^γ ( l )^(1−γ)  (53)
  - W = γ A p_h ( n_Dev )^(γ−1) ( l )^(1−γ) / (1+i)  (54)
  - p_l = (1−γ) A p_h ( n_Dev )^γ ( l )^(−γ) / (1+i)  (55)
  - Y = A ( N_G )^α  (56)
  - W = A α ( N_G )^(α−1)  (57)
  - δ ( h_I + h_RI ) = y_h  (58)
  - (1−φ) h_RI = φ h_R  (59)
  - (1−φ) b_Dev + (1−φ) b_I = φ d_R  (60)
  - N_G + (1−φ) N n_Dev = N  (61)
  - (1−φ) Nl = L  (62)
- Notation: system links consumption, housing stocks, prices, labor allocations, borrowing, and multiplier μ; equations (46) and (50) connect discount factors to the interest rate and μ; equation (51) restates investor borrowing binding condition.

### Appendix 3 — Parameter Calibration
- Calibration targets and exact values:
  - β_R,ss calibrated to match average one-year benchmark deposit rate in China (2000-2018) = 2.42 percent.
  - Housing GDP share target set to 0.05 given φ_ss = 0.255.
  - γ calibrated to 5.74 percent from firm-level labor cost shares for five large developers (2010-2019).
  - δ set as in Iacoviello (2005); β_I and α from Gete (2020).
- Calibration procedure notes:
  - β_R,ss set via observed average deposit rate (2.42 percent).
  - j and κ chosen so model-generated housing value-added share equals 0.05 given φ_ss = 0.255.
  - γ computed as weighted-average labor cost share across five developers and averaged across years to obtain 5.74 percent.

*Source — wpiea2020265-print-pdf (IMF working paper content provided).*

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

### wpiea2020265-print-pdf - References

### Introduction — key findings and observed facts
- Housing accounts for 65.3 percent of Chinese households’ assets, compared with 36.0 percent in the US.
- Since the housing market reform in 1998, house prices in China have exhibited a rising trend that persisted through the COVID-19 shock (nominal series illustrated for July 2017-October 2020).
- Illustrative COVID-19 era anecdotes and milestones:
  - In March 2020, 288 apartments in a Shenzhen neighborhood sold out online in less than eight minutes.
  - In July 2020, China’s average residential house price surpassed 10,000 RMB/sq.m for the first time.
  - New regulation issued on September 28, 2020: new housing-related loans should not exceed 30 percent of total bank loans; yet housing prices continued to rise in October 2020.
- Household behavior during COVID-19: lower consumption and higher saving increased speculative house purchases, particularly among multiple-property owners; quote from Professor Gan Li: “Speculative demand is on the rise because [people] view housing as a safer asset than the stock market or overseas assets... Because of the pandemic they’re actually consuming less, and saving more. So they’ll actually have more money available to invest. That will create an even larger housing problem.”
- Financial market structure and frictions in China:
  - Bank-dominated financial market: financing via the second-board stock market about 1-2 percent of bank loans; small-and-medium board market about 3-5 percent of bank loans.
  - More than 75 percent of corporate bonds are held by banks (as of end-2018).
  - Strict restrictions on “illegal fund-raising” and constraints on overseas investment (rule cited: from February 1, 2019, holding foreign exchange more than RMB 5 million may lead to criminal penalties).
- Central question posed: Is financial market incompleteness the underlying force linking high housing prices, abundant household savings, unmet SME financing demand, and bank-dominated markets?

### Analytical contribution and mechanisms
- Core contribution: unified framework emphasizing financial market incompleteness as a slow-moving structural determinant of housing prices, developed in a stylized DSGE model with heterogeneous households (rich investors vs. poor renters).
- Two main channels through which incomplete financial markets raise housing demand and prices:
  - Rich households channel: Lack of alternative profitable or “safe” investment opportunities leads rich households to allocate “hot money” into housing, raising demand, prices, and potentially wealth inequality.
  - Poor households channel: Poor households effectively have only bank deposits as a saving channel; abundant deposits push down interest rates, stimulating borrowing demand for housing.
- Supply-side amplification: Low interest rates also stimulate real estate developer borrowing to build housing; constrained local land supply implies demand effects dominate supply effects, yielding higher equilibrium prices and resource crowding-out from productive industries.
- Policy implication emphasized: addressing high housing prices requires developing financial markets and deploying “non-housing policies”; without addressing financial market incompleteness, higher household savings and government stimulus (especially in the COVID era) may fuel housing bubbles and future crises.

### Stylized empirical evidence motivating the model
- Household deposits-to-GDP ratio:
  - Broad rising trend from a little over 60 percent in 1998 to 90 percent in 2020 (2020 ratio calculated using stock of deposits in Q3 and nominal GDP of RMB 100,000 billion; official estimate released on October 31, 2020).
  - Exception: 2007 drop of more than 10 percentage points, likely due to a stock market boom.
  - Negative correlation observed between household deposit ratio and stock price index.
- Household mortgage and developer loan ratios (to GDP):
  - Residential housing mortgage loan-to-GDP ratio rose from close to 0 (1998) to more than 30 percent in 2020.
  - Real estate development loan-to-GDP ratio also rose, but at a slower rate than the mortgage loan-to-GDP ratio.
- Cross-checked data caveats: 2020 figures use third-quarter stocks and official GDP estimate; numbers in Figures 3 and 4 cross-checked against other published numbers.

### Model structure and key elements
- Model type: DSGE with heterogeneous households and financial market incompleteness; extends Iacoviello (2005) by including renters, housing investors, real estate developers, and incomplete financial markets.
- Household types:
  - Renters (“poor” households): account for φ fraction of population; inelastic labor supply of one unit each; cannot afford down payments or access mortgage market; can only deposit surplus funds with banks; deposits are passed to housing investors and real estate developers (banks treated passively). Higher φ implies more incomplete financial markets.
    - Renters maximize expected lifetime utility E_t ∑_{t=0}^∞ β_{R,t} U_{R,t}(c^R_t,h^R_t) subject to budget constraint c^R_t + p^r_t h^R_t + d^R_t = (1+i_{t-1}) d^R_{t-1} + Y_t/N_t.
    - Euler condition: U_{R,t,c^R}(.) = E_t[β_{R,t} U_{R,t+1,c^R}(.)] (1+i_t).
    - Intra-temporal condition: U_{R,t,h^R}(.) = p^r_t U_{R,t,c^R}(.).
    - Renters assumed more patient than investors (β_{R,t} > β_{I,t}).
  - Investors (“rich” households): account for 1−φ fraction; inelastic labor supply; own one real estate developer; borrow and buy houses, choose housing for own living and for rental.
    - Investors maximize E_t ∑_{t=0}^∞ β_{I,t} U_{I,t}(c^I_t,h^I_t) subject to budget constraint c^I_t + p^h_t(h^I_t + h^{RI}_t) + (1+i_{t-1}) b^I_{t-1} = p^r_t h^{RI}_t + b^I_t + p^h_t(1−δ)(h^I_{t-1} + h^{RI}_{t-1}) + Y_t/N_t + π_t.
    - Collateral constraint: b^I_t ≤ m_t p^h_t(h^I_t + h^{RI}_t), where m_t is loan-to-value ratio.
    - First-order conditions yield:
      - Inter-temporal condition for owner-occupied housing (equation (15) in source), showing marginal benefit components including extra borrowing capacity μ_t m_t p^h_t and expected resale value β_I E_t[(1−δ)p^h_{t+1} U_{I,t+1,c^I}(.))].
      - Intra-temporal condition equating marginal utility of renting out one unit with marginal utility of living in one unit: U_{I,t,c^I}(.) p^r_t = U_{I,t,h^I}(.).
      - Borrowing FOC (equation (18) in source) linking marginal utility of consumption to borrowing shadow price μ_t and expected marginal utility next period.

### Policy analysis and recommendations (as stated)
- Root-cause focus: Eradication of high housing price problem likely requires developing financial markets to reduce incompleteness rather than relying solely on housing-targeted regulations.
- Non-housing policies: Reforms to financial market structure and social security systems are important levers; the DSGE framework can quantify impacts of such reforms on housing prices and macrofinancial indicators.
- COVID-era warning: Without addressing financial market incompleteness, higher household savings and fiscal/monetary stimulus risk fueling housing bubbles that could sow seeds for future crises.

*Italic: Source — wpiea2020265-print-pdf (IMF working paper content provided).*

### Appendix 1 shows that the investor will always want to borrow up to the limit, that is:

### Appendix 1 — Investor and Developer Behavior; Model Equilibrium and Policy Implications

### Investor borrowing behavior and equilibrium intuition
- Appendix 1 shows that the investor will always want to borrow up to the limit, that is:
  - b_I_t = m_t p_h_t (h_I_t + h_RI_t) (19)
- Intuition:
  - Renters’ intra-temporal optimality condition in steady state: β_R/(1+i) = 1, hence steady state interest rate i = 1/β_R − 1.
  - Renters are more patient than investors (β_R > β_I), so this interest rate is lower than the rate implied by investors’ intra-temporal condition; investors therefore optimally borrow as much as possible consistent with their greater impatience.
- Equilibrium determination:
  - The system uses the three optimality conditions (15), (16), (18), the investor’s budget constraint (10), and the binding collateral constraint (19) to determine c_I_t, h_I_t, h_RI_t, b_I_t, and μ_t.

### Real estate developer (firm side) — setup and equilibrium conditions
- Developer flow of funds:
  - b_Dev_t = W_t n_Dev_t + p_l_t l_t (20)
- Production function of new houses:
  - y_h_t = A_t (n_Dev_t)^γ (l_t)^{1−γ} (21)
- No-default requirement (expectation):
  - (1+i_t) b_Dev_t ≤ E_t [ A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{1−γ} ] (22)
- Developer maximization problem (expectation of profits), Lagrangian includes multiplier λ_t; since developer is owned by investor (more impatient), the collateral constraint binds (λ_t > 0).
- First-order condition for labor demand (n_Dev_t) under binding constraint:
  - E_t [ γ A_t p_h_{t+1} (n_Dev_t)^{γ−1} (l_t)^{1−γ} ] = W_t (1+i_t) (25)
- Land demand (l_t):
  - E_t [ (1−γ) A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{−γ} ] = p_l_t (1+i_t) (26)
- Using (25) and (26) in (20) implies:
  - b_Dev_t (1+i_t) = E_t [ A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{1−γ} ] (27)
  - Developer’s collateral constraint binds and ex ante expected profit is zero; ex post realized profit:
    - π_{t+1} = A_t p_h_{t+1} (n_Dev_t)^γ (l_t)^{1−γ} − b_Dev_t (1+i_t) (28)
  - Realized developer profits become investor revenue in the investor budget constraint.

### Non-housing consumption production
- Aggregate production:
  - Y_t = A_t (N_G_t)^α (29)
- Non-housing sector does not borrow (assumption for tractability and to capture empirical fact that housing is more interest-sensitive and involves more borrowing).
- Zero-profit condition in equilibrium implies wage:
  - W_t = A_t α (N_G_t)^{α−1} (30)

### Market-clearing conditions (determine prices and allocations)
- Housing market clearing (determines p_h_t):
  - [ (1−φ_t) N_t h_I_t + (1−φ_t) N_t h_RI_t ] − (1−δ) [ (1−φ_{t−1}) N_{t−1} h_I_{t−1} + (1−φ_{t−1}) N_{t−1} h_RI_{t−1} ] = (1−φ_t) N_t y_h_t (31)
- Rental market clearing (determines p_r_t):
  - φ_t N_t h_R_t = (1−φ_t) N_t h_RI_t (32)
- Bond market clearing (determines i_t):
  - (1−φ_t) N_t b_Dev_t + (1−φ_t) N_t b_I_t = φ_t N_t d_R_t (33)
- Labor market clearing (determines W_t):
  - N_G_t + (1−φ_t) N_t n_Dev_t = N_t (34)
- Land market clearing (determines p_l_t), with fixed per-period land flow L̄:
  - (1−φ_t) N_t l_t = L̄ (35)
  - Land supply per period is constant (L̄ = 1 in calibration), implying land stock increases over time at a constant rate.

### Summary of equilibrium objects and exogenous variables
- Key endogenous objects: c_R, h_R, d_R, c_I, h_I, h_RI, b_I, μ, b_Dev, y_h, n_Dev, l, Y, N_G, p_h, p_r, i, W, p_l determined by equations (2), (8), (6), (10), (15), (16), (18), (19), (20), (21), (25), (26), (29), (30), (31), (32), (33), (34), (35).
- Exogenous variables (shockable in analysis):
  - N Total population of households
  - m Loan-to-value ratio
  - A TFP
  - φ Renter population share
  - β_R Renter discount factor
- Utility functional forms (Iacoviello (2005) style):
  - U_R_t(c_R_t,h_R_t) = ln c_R_t + j ln h_R_t (36)
  - U_I_t(c_I_t,h_I_t) = ln c_I_t + κ ln h_I_t (37)
  - Marginal utilities:
    - U_{R_t,c_R} = 1 / c_R_t (38)
    - U_{R_t,h_R} = j / h_R_t (39)
    - U_{I_t,c_I} = 1 / c_I_t (40)
    - U_{I_t,h_I} = κ / h_I_t (41)

### Calibration and parameter values (China-specific where available)
- Calibration choices and some data sources noted in text (e.g., renter share derived from Chinese urban home-ownership averages).
- Specific parameter values:
  - φ_ss Share of renters in households population 0.255
  - β_R,ss Discount factor of the renters 0.976
  - β_I Discount factor of the investors 0.85
  - δ Depreciation rate of houses 0.025
  - γ Share of labor in housing production 0.0574
  - α Share of labor in goods production 2/3
  - L Constant supply of new land 1
  - j Weight on housing services by renters 0.06
  - κ Weight on housing services by investors 0.12

### Impulse response results and mechanisms
- Shock analyzed: temporary positive shock to φ (share of renters) — φ increases by 1 percentage point at time 0 then gradually returns to original level.
- Main dynamics and channels:
  - An increase in renters raises aggregate deposits and lowers the interest rate.
  - Lower interest rate:
    - Stimulates higher mortgage borrowing and higher housing demand by housing investors.
    - Encourages real estate developers to borrow more and produce more houses.
  - Due to rationed land supply, demand-side effect dominates supply-side effect → equilibrium housing price increases.
  - The wealthy who can afford down payments may buy larger or multiple houses, concentrating homeownership and worsening wealth inequality.
- Crowding-out effect on non-housing sector:
  - Developers borrow more and hire more labor (and land), increasing wages, reducing labor available to non-housing sectors, lowering non-housing output.
  - Even stronger crowding-out would occur if non-housing used land as an input.
- Dynamic interplay after time 1:
  - Extensive margin: smaller renter share reduces aggregate deposits and raises interest rate.
  - Intensive margin: higher interest rate at time t increases aggregate deposit at t+1 (via Equation 2), decreasing interest rate at t+1.
  - In the IRF, extensive margin dominates at time 1 (deposit below steady state, interest rate above steady state at time 1); intensive margin dominates from time 2 onwards.
  - Because the shock is temporary, all indicators return to steady state over time. A permanent shock would produce persistent effects similar to the initial time-0 responses.

### Alternative shock: higher renter discount factor
- An increase in renters’ discount factor (higher saving propensity) produces impulse responses very similar to higher financial market incompleteness:
  - Higher aggregate deposit, lower interest rate → higher investor borrowing and housing demand; developers borrow more and produce more houses → higher housing price and larger crowding-out effects.

### Conclusion and policy implications
- Financial market incompleteness is a slow-moving structural vulnerability that:
  - Has materially contributed to higher housing prices in China through both demand and supply channels.
  - Crowds out non-housing sectors and may worsen wealth inequality by enabling housing speculation by the wealthy.
- Two complementary policy approaches to depress housing demand and contain prices:
  - Directly block fund inflows to housing (macroprudential tools: limits on loan-to-value ratio, debt-to-income ratio, etc.).
  - Open up new outlets for funds via financial market reforms to divert funds away from real estate (indirectly depress housing demand and mitigate supply-side resource misallocation).
- Key reform objective:
  - Move from a bank-dominated system to a well-regulated multi-layer financial system (banks, bond markets, multi-layer stock markets) to accommodate diverse risk preferences and reduce risk mismatches between fund suppliers and demanders.
  - Suggested measures (aligned with IMF (2019) direction): targeted reserve ratio cuts for lending to MSEs; increase lending to MSEs by 30 percent; private enterprises to receive at least 50 percent of new loans.
- Complementary structural reforms:
  - Strengthen medical insurance, social security, and other measures to reduce household precautionary savings.
- Regulatory safeguards:
  - While expanding non-bank channels, maintain strict regulation and monitoring (e.g., to limit fraud in P2P markets and excess risk-taking), including mechanisms for managers to have skin in the game as in Rajan (2006).

*Source: wpiea2020265-print-pdf*

### Appendix 1: Proof of Investors’ Binding Borrowing Constraint

### Appendix 1: Proof of Investors’ Binding Borrowing Constraint

### Key logical steps and result
- Kuhn-Tucker condition for the collateral constraint:
  - μ_t [ m_t p_h_t ( h_I_t + h_RI_t ) − b_I_t ] = 0
- If (11) is not binding, then μ_t = 0.
- Investor’s FOC (Equation (18)) written as:
  - U_I t,c_I ( c_I_t, h_I_t, n_I_t ) = β_I E_t [ (1+i_t) U_I t+1,c_I ( c_I_t+1, h_I_t+1, n_I_t+1 ) ]  (42)
- At steady state:
  - β_I (1+i) = 1
- From (6) at steady state:
  - β_R (1+i) = 1
- With parameter restriction β_R > β_I, β_I (1+i) < 1, which contradicts β_I (1+i) = 1 if μ_t = 0.
- Therefore μ_t > 0 and the collateral constraint binds:
  - b_I_t = m_t p_h_t ( h_I_t + h_RI_t ).
- Conclusion: Q.E.D.

### Exact equilibrium implication
- The borrowing constraint for investors holds with μ_t strictly positive, yielding the equality b_I_t = m_t p_h_t ( h_I_t + h_RI_t ).

*Italicized source attribution line.*

### Appendix 2: System of Steady-State Conditions

### Steady-state equilibrium conditions (as listed)
- c_R + p_r h_R = Y_N + id_R  (43)
- U_R h_R ( c_R, h_R ) = p_r t U_R c_R ( c_R, h_R )  (44)
- U_R n_R ( c_R, h_R ) = − W U_R c_R ( c_R, h_R )  (45)
- 1 = β_R (1+i)  (46)
- c_I + p_h δ ( h_I + h_RI ) + i b_I t = Y_N + I + p_r h_RI  (47)
- [1 − β_I (1−δ)] U_I c_I ( c_I, h_I ) / p_h = U_I h_I ( c_I, h_I ) + μ m p_h  (48)
- [1 − β_I (1−δ)] U_I c_I ( c_I, h_I ) / p_h = U_I c_I ( c_I, h_I ) / p_r + μ m p_h  (49)
- [1 − β_I (1+i)] U_I c_I ( c_I, h_I ) = μ  (50)
- b_I = m p_h h_I  (51)
- b_Dev = W n_Dev + p_l l  (52)
- Y_h = A ( n_Dev )^γ ( l )^(1−γ)  (53)
- W = γ A p_h ( n_Dev )^(γ−1) ( l )^(1−γ) / (1+i)  (54)
- p_l = (1−γ) A p_h ( n_Dev )^γ ( l )^(−γ) / (1+i)  (55)
- Y = A ( N_G )^α  (56)
- W = A α ( N_G )^(α−1)  (57)
- δ ( h_I + h_RI ) = y_h  (58)
- (1−φ) h_RI = φ h_R  (59)
- (1−φ) b_Dev + (1−φ) b_I = φ d_R  (60)
- N_G + (1−φ) N n_Dev = N  (61)
- (1−φ) Nl = L  (62)

### Notation and interdependence
- The system lists general equilibrium relationships among consumption, housing stocks, prices, labor allocations, borrowing, and multiplier μ.
- Equations (46) and (50) link discount factors β_R and β_I to the interest rate and the multiplier μ in steady state.
- Equation (51) restates the binding borrowing condition for investors in steady state: b_I = m p_h h_I.

### Appendix 3: Parameter Calibration

### Calibration targets and exact values used
- The discount factor of the renters (β_R,ss) is calibrated by matching the steady-state interest rate to the average one-year benchmark deposit rate in China from 2000 to 2018 (People’s Bank of China), which equals 2.42 percent.
- The housing GDP as a share of total GDP target is set to:
  - (1−φ_ss) N y_h_ss p_h_ss + φ_ss N h_R p_R
    ------------------------------------------------- = 0.05
    (1−φ_ss) N y_h_ss p_h_ss + φ_ss N h_R p_R + Y_ss
  - Here φ_ss = 0.255.
  - y_h_ss, p_h_ss, h_R, p_R, Y_ss are general equilibrium objects that depend on j and κ.
- The share of labor in housing production (γ) is calibrated to match the average share of labor cost in total cost of real estate developers using firm-level data for five large developers across 2010-2019, yielding γ = 5.74 percent.
- The depreciation rate of houses (δ) takes the standard value from Iacoviello (2005).
- The discount factor of the investors (β_I) and share of labor in goods production (α) take values from Gete (2020).

### Calibration procedure notes
- β_R,ss is set via the observed average deposit rate (2.42 percent).
- j (weight on housing services by renters) and κ (weight on housing services by investors) are chosen so that the model-generated housing value-added share equals 0.05 given φ_ss = 0.255.
- γ was computed as the weighted-average labor cost share across five large real estate developers (China Overseas Land and Investment; China Vanke; China Evergrande Group; Country Garden; Sunac China Holdings) for years 2010-2019, and then averaged across years to obtain 5.74 percent.
- δ follows Iacoviello (2005); β_I and α follow Gete (2020).

*Italicized source attribution line.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020265-print-pdf.pdf_