## wpiea2020083-print-pdf - Section IV presents the results. Section V concludes.

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---

### Literature and motivation
- Standard monetary policy rules that react to inflation and output could lead to growing financial risks under financial frictions (such as collateral borrowing constraints); a monetary policy that also targets financial stability by “leaning against the wind” could be welfare improving in some DSGE models.
- Findings in the literature are mixed:
  - Some models strongly support leaning against the wind (example: Gambacorta and Signoretti 2014).
  - Other models find quantitatively small deviations from standard rules (example: Curdia and Woodford 2010).
  - The case for leaning against the wind may be weaker in small open economies because of international capital flow responses.
- Recent DSGE models (including the present model) typically find monetary and macroprudential policies are complements rather than substitutes, i.e., optimal to use together rather than relying on a single instrument (example: Angelini et al. 2014).
- The relationship between monetary and macroprudential policy is highly dependent on the nature of shocks and financial frictions; e.g., macroprudential tools tend to be favored after financial shocks, whereas after a positive productivity shock constraining credit may run counter to accommodative monetary policy unless bank lending endogenously increases systemic risk.

### Model structure and calibration
- Framework: New Keynesian DSGE model for small open economies with price rigidities and financial frictions, tailored to the Thai economy; incorporates a fully specified banking sector, household and corporate debt, and external borrowing.
- Model size: more than 50 equations with more than 80 parameters.
- Agents:
  - Two types of households: patient (lower intertemporal discount rate) and impatient. Patient households save (deposits and foreign bonds); impatient households borrow to consume and purchase houses.
  - Entrepreneurs borrow from domestic banks and abroad to purchase capital; they hire labor and produce goods sold to retailers in a monopolistically competitive environment.
  - Banks intermediate funds from patient to impatient households and entrepreneurs; banks can lend to government, entrepreneurs, or households; interest rates are sticky due to quadratic costs of changing rates; bank borrowing is subject to macroprudential measures.
- Policy instruments:
  - Monetary policy via a Taylor-type rule (two variants):
    - Standard Taylor rule: i = α1 × inflation gap + α2 × output gap.
    - Modified Taylor rule: i = α1 × inflation gap + α2 × output gap + α3 × credit gap (credit gap = actual stock of household credit minus steady-state level).
  - Macroprudential policy via either:
    - Cap on household loan-to-value (LTV) ratio, or
    - Minimum bank capital adequacy ratio (CAR).
  - Two variants for each macroprudential measure:
    - Constant LTV (or CAR) rule: cap (or minimum CAR) kept constant.
    - Countercyclical LTV (or CAR) rule: LTV cap decreases (or minimum CAR increases) as household (or bank) credit increases relative to steady state.
- Policy combinations evaluated (performance measured by volatilities of inflation, output gap, and housing loans):
  - (i) standard Taylor rule + constant LTV (or CAR)
  - (ii) standard Taylor rule + counter-cyclical LTV (or CAR)
  - (iii) modified Taylor rule + constant LTV (or CAR)
- Shocks considered: a negative world interest rate shock (monetary easing in advanced economies) and a positive shock to domestic housing demand.
- Note: Using alternative financial gaps (including a house price gap) does not change results substantively.

### Benchmark results (minus one percentage point world interest rate shock; responses expressed as percentage deviations from steady state)
- Shock specification: minus one percentage point shock to the world interest rate.
- Key benchmark outcomes:
  - The shock causes domestic currency appreciation pressure and domestic monetary easing, which can lead to housing market overheating.
  - Growth of housing loans is contained to a similar extent under both the counter-cyclical LTV cap and the modified Taylor rule.
  - The negative impact on inflation and output gap is much larger under the modified Taylor rule than under the counter-cyclical LTV rule.
  - Conclusion: counter-cyclical LTV rule performs better in stabilizing inflation, output, and housing loans than the modified Taylor rule in this scenario.
- Positive housing demand shock results:
  - Counter-cyclical LTV: contains housing loan growth without raising the nominal interest rate.
  - Modified Taylor rule: raising the interest rate causes a substantial decline in inflation and output gap while insufficiently containing housing loan growth.
- Overall benchmark implication: Monetary policy focused on inflation and output gap combined with macroprudential policy targeted at the source of financial instability yields better outcomes; asking monetary policy to also target financial stability leads to suboptimal inflation and growth outcomes.

### Robustness checks on monetary policy transmission
- Flatter Philips Curve experiment:
  - Parameter change: α in equation (34) of Appendix changed from 0.5 (benchmark case) to 0.8 (flattened Philips Curve case).
  - Result: Performance of the modified Taylor rule in stabilizing inflation gets closer to, but does not outperform, the counter-cyclical LTV rule.
  - In the flatter Philips Curve case, while the cost of the modified Taylor rule in terms of additional deviations from the inflation target is small, its benefit for financial stability is also small and does not exceed that of the counter-cyclical LTV rule.
  - For a positive housing demand shock with a flatter Philips Curve, the modified Taylor rule performs much worse than the counter-cyclical LTV rule — stabilizing housing loans with the modified Taylor rule comes at a huge cost in terms of the output gap.
- Imperfect monetary transmission:
  - Confirmed that some impairment of monetary policy transmission in the banking sector (e.g., lower pass-through to the loan interest rate) does not change the result that the counter-cyclical LTV rule outperforms the modified Taylor rule.

### Robustness checks on alternative macroprudential measures (counter-cyclical CAR vs targeted LTV)
- When targeted household LTV cap is not available and a broader counter-cyclical bank minimum CAR is used:
  - Negative world interest rate shock:
    - Counter-cyclical CAR “overkills” housing loan growth while stabilizing corporate loans, leading to a more severe reduction in output gap compared with the modified Taylor rule.
    - Therefore, counter-cyclical CAR performs worse than the modified Taylor rule for this shock.
  - Positive housing demand shock:
    - Counter-cyclical CAR does not necessarily overkill housing loans, but may overkill corporate loans and thus reduce output much more severely than the modified Taylor rule.
    - Comparison of rules becomes less clear and depends on the relative importance assigned to output, inflation, and financial stabilization objectives.
- Implication: Appropriateness of monetary policy reacting to financial stability concerns depends on availability of targeted macroprudential measures and the nature of shocks.

### Conclusions and policy implications
- Main finding: Well-targeted macroprudential measures can usefully complement monetary policy in the Thai context; active use of targeted macroprudential measures allows monetary policy to focus on inflation and output stabilization while effectively containing financial risks.
- Caveats and contextual limits:
  - Availability of targeted macroprudential measures may be limited by reliable data, resources for implementation, and jurisdictional constraints.
  - Cases of weak effectiveness or leakage of macroprudential measures are relatively uncertain and untested.
  - Different types of shocks beyond those considered (world interest rate and domestic housing demand) may change conclusions.
- Recommended further work: Further analysis of various types of macroprudential measures in response to a broader set of shocks is an important direction for future research.

### 1.4 Deposit/Loan Demand — key model mechanics
- Deposit demand (patient households):
  - Objective: ∫_0^1 i_t^d(i) D_t(i) di.
  - Aggregators: D_t = [∫_0^1 D_t(i)^(1+ε_d)/ε_d di]^(ε_d/(1+ε_d)); i_t^d = [∫_0^1 i_t^d(i)^(1+ε_d) di]^(1/(1+ε_d)).
  - Retail bank i-th deposit demand: D_t(i) = [ i_t^d(i) / i_t^d ]^(ε_d) D_t.
- Loan demand (impatient households) and entrepreneurs:
  - Impatient households minimize ∫_0^1 i_t^{lH}(i) B_t^H(i) di; B_t^H(i) = [ i_t^{lH}(i) / i_t^{lH} ]^(−ε_{lH}) B_t^H.
  - Entrepreneurs: B_t^E = q_t K_{t+1} − n_t; domestic borrowing L_t^d = ω̅ B_t^E at rate i_t^{lE}; foreign borrowing L_t^f = (1−ω̅) B_t^E at rate i_t^f.
  - Real costs of loans: Domestic: ω̅ π_t [1 + i_t^{lE} / π_{t+1}]; Foreign: (1−ω̅) π_t [1 + i_t^f / π_{t+1}^* (ε_{t+1}/ε_t)].
  - Entrepreneur loan demand: L_t^d(i) = [ i_t^{lE}(i) / i_t^{lE} ]^(−ε_{lE}) L_t^d.
- Entrepreneur external finance and returns:
  - Marginal external financing cost: π_t f_{t+1} = (1 + Γ_t) [ ϖ π_t [1 + i_t^l / π_{t+1}] + Θ(n_{t+1} / (q_t K_{t+1})) (1−ϖ) π_t [1 + i_t^f / π_{t+1}^* (ε_{t+1}/ε_t)] ].
  - External finance premium: Θ( n_{t+1} / (q_t K_{t+1}) ) = ( n_{t+1} / (q_t K_{t+1}) )^(−η).
  - Expected gross return on capital: π_t R_{t+1}^k = π_t [ r_{t+1}^k + (1−δ) q_{t+1} / q_t ].
  - Individual net worth: V_t = R_t^k q_{t−1} K_t − f_t B_t^E.
  - Aggregate net worth: n_t = ν V_t + (1−ν) H − ε_t^n.
  - Exiting entrepreneurs consumption: C_t^e = (1 − ν) ( V_t − H ).
- Capital producers and investment:
  - Capital accumulation: K_{t+1} = (1−δ) K_t + ϖ_{I,t+1} I_{t+1} − ζ/2 ( I_{t+1}/K_t − δ )^2 K_t.
  - Investment aggregator: I_t = [ γ^{1/ϖ} (I_{H,t})^{(ϖ−1)/ϖ} + (1−γ) (I_{F,t})^{(ϖ−1)/ϖ} ]^{ϖ/(ϖ−1)}.
  - Capital supply FOC: q_t [ ϖ_{I,t} − ζ ( I_t/K_{t−1} − δ ) ] = 1.
- Wholesale and retail sectors, Calvo pricing, and New Keynesian Phillips Curve are modeled with standard profit-maximization and pricing equations (see model equations referenced).

### Banking sector: structure, rate setting, and policy rules
- Banking structure:
  - Monopolistic competition with wholesale and retail branches; nominal rigidities in deposit and loan rate setting via quadratic adjustment costs.
- Retail branch optimal rates (symmetric equilibrium):
  - Deposit rate condition (see equations (33) and surrounding text).
  - Loan rates:
    - i_t^{lH} = ε_{lH} / (ε_{lH} − 1) i_t^b − φ_{i_{lH}} / (ε_{lH} − 1) ( i_t^{lH} / i_{t−1}^{lH} − 1 ) i_t^{lH} / i_{t−1}^{lH} + β φ_{i_{lH}} / (ε_{lH} − 1) E_t [ ( i_{t+1}^{lH} / i_t^{lH} − 1 ) i_{t+1}^{lH} / i_t^{lH} B_{t+1}^H / B_t^H ].
    - i_t^{lE} analogous with ε_{lE}, φ_{i_{lE}}, and L_t^d terms.
- Wholesale branch:
  - Holds CRR and SLR: α_t^s and α_t^d; balance sheet: (1 − α_t^s − α_t^d) D_t + Z_t = B_t^H + L_t^d.
  - Banks face capital-to-assets (leverage) ratio κ_t with quadratic cost for deviations.
  - Bank capital accumulation: Z_t = (1 − δ_b) Z_{t−1} + ω_b Π_{t−1}^B − ε_t^B.
  - Wholesale loan rate relation: i_t^b = i_t^s / (1 − α_t^s − α_t^d) − φ_z ( Z_t / ( B_t^H + L_t^d ) − κ_t ) ( Z_t / ( B_t^H + L_t^d ) )^2 − α_t^d / (1 − α_t^s − α_t^d) i_t^t.
  - With i_t^s = i_t^{SDA} and i_t^{SDA} = i_t, symmetric equilibrium expression for i_t^b given in source.
- Aggregate bank profits Π_t^B specified (see model expression).

### Public sector rules, market clearing, and shocks
- Central bank policy rate rule: i_t = γ_i i_{t−1} + (1 − γ_i) i + γ_π ( π_t − π ) + γ_Y ( Y_t − Y ) + ε_t^i.
- CRR and SLR rules: α_t^s and α_t^d follow AR(1)-type rules with responses to inflation and output.
- Macroprudential CAR rule: κ_t = (1 − ρ_κ) κ + (1 − ρ_κ) χ_κ ( B_t^H + L_t^d − B^H − L ) + ρ_κ κ_{t−1}.
- LTV ratio rule: m_t = (1 − ρ_m) m + (1 − ρ_m) ( B_t^H − B^H ) + ρ_m m_{t−1}.
- Resource constraint and balance of payments specified; foreign debt elastic risk premium closure: 1 + i_t^f = (1 + i_t^*)^(−χ) [ ( B_t^f + L_t^f ) − ( B^f + L^f ) ].
- Shocks: thirteen structural shocks including θ_t, ϖ_{I,t}, e_t^h, Γ_t, ε_t^n, ε_t^B, i_t^*, Y_t^*, G_t, α_t^s, α_t^d, i_t^t, ε_t^i; most follow AR(1) except specified i.i.d. shocks.

### Key parameter values (calibrated)
- σ = 2
- σ_h = 1
- b = 0.7
- φ = 2
- η = 0.05
- δ = 0.025
- ζ = 10
- ψ = 0.33
- α = 0.5
- v = 5
- ω_b = 0.8
- φ_{i_d} = 0.01
- φ_{i_{lH}} = 0.01
- φ_{i_{lE}} = 0.01

*Source: wpiea2020083-print-pdf - 1.4  Deposit/Loan Demand (IMF).*

### Section IV presents the results. Section V concludes.

### wpiea2020083-print-pdf - Section IV presents the results. Section V concludes.

### Literature and motivation
- Standard monetary policy rules that react to inflation and output could lead to growing financial risks under financial frictions (such as collateral borrowing constraints); a monetary policy that also targets financial stability by “leaning against the wind” could be welfare improving in some DSGE models.
- Findings in the literature are mixed:
  - Some models strongly support leaning against the wind (example: Gambacorta and Signoretti 2014).
  - Other models find quantitatively small deviations from standard rules (example: Curdia and Woodford 2010).
  - The case for leaning against the wind may be weaker in small open economies because of international capital flow responses.
- Recent DSGE models (including the present model) typically find monetary and macroprudential policies are complements rather than substitutes, i.e., optimal to use together rather than relying on a single instrument (example: Angelini et al. 2014).
- The relationship between monetary and macroprudential policy is highly dependent on the nature of shocks and financial frictions; e.g., macroprudential tools tend to be favored after financial shocks, whereas after a positive productivity shock constraining credit may run counter to accommodative monetary policy unless bank lending endogenously increases systemic risk.

### Model structure and calibration
- Framework: New Keynesian DSGE model for small open economies with price rigidities and financial frictions, tailored to the Thai economy; incorporates a fully specified banking sector, household and corporate debt, and external borrowing.
- Model size: more than 50 equations with more than 80 parameters (parameters calibrated based on data, previous studies, or judgment).
- Agents:
  - Two types of households: patient (lower intertemporal discount rate) and impatient. Patient households save (deposits and foreign bonds); impatient households borrow to consume and purchase houses.
  - Entrepreneurs borrow from domestic banks and abroad to purchase capital; they hire labor and produce goods sold to retailers in a monopolistically competitive environment.
  - Banks intermediate funds from patient to impatient households and entrepreneurs; banks can lend to government, entrepreneurs, or households; interest rates are sticky due to quadratic costs of changing rates; bank borrowing is subject to macroprudential measures.
- Policy instruments:
  - Monetary policy via a Taylor-type rule (two variants):
    - Standard Taylor rule: i = α1 × inflation gap + α2 × output gap (i is the policy interest rate).
    - Modified Taylor rule: i = α1 × inflation gap + α2 × output gap + α3 × credit gap (credit gap = actual stock of household credit minus steady-state level).
  - Macroprudential policy via either:
    - Cap on household loan-to-value (LTV) ratio, or
    - Minimum bank capital adequacy ratio (CAR).
  - Two variants for each macroprudential measure:
    - Constant LTV (or CAR) rule: cap (or minimum CAR) kept constant.
    - Countercyclical LTV (or CAR) rule: LTV cap decreases (or minimum CAR increases) as household (or bank) credit increases relative to steady state.
- Policy combinations evaluated (performance measured by volatilities of inflation, output gap, and housing loans):
  - (i) standard Taylor rule + constant LTV (or CAR)
  - (ii) standard Taylor rule + counter-cyclical LTV (or CAR)
  - (iii) modified Taylor rule + constant LTV (or CAR)
- Shocks considered: a negative world interest rate shock (monetary easing in advanced economies) and a positive shock to domestic housing demand.
- Note: Using alternative financial gaps (including a house price gap) does not change results substantively.

### Benchmark results (minus one percentage point world interest rate shock; responses expressed as percentage deviations from steady state)
- Shock specification: minus one percentage point shock to the world interest rate.
- Key benchmark outcomes:
  - The shock causes domestic currency appreciation pressure and domestic monetary easing, which can lead to housing market overheating.
  - Growth of housing loans is contained to a similar extent under both the counter-cyclical LTV cap and the modified Taylor rule.
  - The negative impact on inflation and output gap is much larger under the modified Taylor rule than under the counter-cyclical LTV rule.
  - Conclusion: counter-cyclical LTV rule performs better in stabilizing inflation, output, and housing loans than the modified Taylor rule in this scenario.
- Positive housing demand shock results:
  - Counter-cyclical LTV: contains housing loan growth without raising the nominal interest rate.
  - Modified Taylor rule: raising the interest rate causes a substantial decline in inflation and output gap while insufficiently containing housing loan growth.
- Overall benchmark implication: Monetary policy focused on inflation and output gap combined with macroprudential policy targeted at the source of financial instability yields better outcomes; asking monetary policy to also target financial stability leads to suboptimal inflation and growth outcomes.

### Robustness checks on monetary policy transmission
- Flatter Philips Curve experiment:
  - Parameter change: α in equation (34) of Appendix changed from 0.5 (benchmark case) to 0.8 (flattened Philips Curve case).
  - Result: Performance of the modified Taylor rule in stabilizing inflation gets closer to, but does not outperform, the counter-cyclical LTV rule.
  - In the flatter Philips Curve case, while the cost of the modified Taylor rule in terms of additional deviations from the inflation target is small, its benefit for financial stability is also small and does not exceed that of the counter-cyclical LTV rule.
  - For a positive housing demand shock with a flatter Philips Curve, the modified Taylor rule performs much worse than the counter-cyclical LTV rule — stabilizing housing loans with the modified Taylor rule comes at a huge cost in terms of the output gap.
- Imperfect monetary transmission:
  - Confirmed that some impairment of monetary policy transmission in the banking sector (e.g., lower pass-through to the loan interest rate) does not change the result that the counter-cyclical LTV rule outperforms the modified Taylor rule.

### Robustness checks on alternative macroprudential measures (counter-cyclical CAR vs targeted LTV)
- When targeted household LTV cap is not available and a broader counter-cyclical bank minimum CAR is used:
  - Negative world interest rate shock:
    - Counter-cyclical CAR “overkills” housing loan growth while stabilizing corporate loans, leading to a more severe reduction in output gap compared with the modified Taylor rule.
    - Therefore, counter-cyclical CAR performs worse than the modified Taylor rule for this shock.
  - Positive housing demand shock:
    - Counter-cyclical CAR does not necessarily overkill housing loans, but may overkill corporate loans and thus reduce output much more severely than the modified Taylor rule.
    - Comparison of rules becomes less clear and depends on the relative importance assigned to output, inflation, and financial stabilization objectives.
- Implication: Appropriateness of monetary policy reacting to financial stability concerns depends on availability of targeted macroprudential measures and the nature of shocks.

### Conclusions and policy implications
- Main finding: Well-targeted macroprudential measures can usefully complement monetary policy in the Thai context; active use of targeted macroprudential measures allows monetary policy to focus on inflation and output stabilization while effectively containing financial risks.
- Caveats and contextual limits:
  - Availability of targeted macroprudential measures may be limited by reliable data, resources for implementation, and jurisdictional constraints.
  - Cases of weak effectiveness or leakage of macroprudential measures are relatively uncertain and untested.
  - Different types of shocks beyond those considered (world interest rate and domestic housing demand) may change conclusions.
- Recommended further work: Further analysis of various types of macroprudential measures in response to a broader set of shocks is an important direction for future research.

*Source: wpiea2020083-print-pdf*

### 1.4  Deposit/Loan Demand

### 1.4  Deposit/Loan Demand

### Deposit demand (patient households)
- Patient households maximize interest payments from deposits:
  - Objective: ∫_0^1 i_t^d(i) D_t(i) di
- Deposit aggregators:
  - D_t = [∫_0^1 D_t(i)^(1+ε_d)/ε_d di]^(ε_d/(1+ε_d))
  - i_t^d = [∫_0^1 i_t^d(i)^(1+ε_d) di]^(1/(1+ε_d))
- First-order condition yields retail bank i-th deposit demand:
  - D_t(i) = [ i_t^d(i) / i_t^d ]^(ε_d) D_t
  - (equations (10)-(13) in source)

### Loan demand (impatient households) and entrepreneurs
- Impatient households minimize interest payments from loans:
  - Objective: ∫_0^1 i_t^{lH}(i) B_t^H(i) di
- Loan aggregators analogous to deposit side.
- Loan demand functional form for impatient households:
  - B_t^H(i) = [ i_t^{lH}(i) / i_t^{lH} ]^(−ε_{lH}) B_t^H
- Entrepreneurs:
  - Balance sheet identity for total borrowing B_t^E:
    - B_t^E = q_t K_{t+1} − n_t
  - Domestic borrowing (proportion ω̅):
    - L_t^d = ω̅ B_t^E at nominal rate i_t^{lE}
  - Foreign borrowing (proportion 1−ω̅):
    - L_t^f = (1−ω̅) B_t^E at rate i_t^f (assumed same as foreign-denominated bonds held by patient households)
  - Real costs of domestic and foreign loans:
    - Domestic: ω̅ π_t [1 + i_t^{lE} / π_{t+1}]  (as given)
    - Foreign: (1−ω̅) π_t [1 + i_t^f / π_{t+1}^* (ε_{t+1}/ε_t)]  (as given)
- Entrepreneur loan demand (minimizing interest payments) yields:
  - L_t^d(i) = [ i_t^{lE}(i) / i_t^{lE} ]^(−ε_{lE}) L_t^d
  - (equations (13)-(16) in source)

### Entrepreneur external finance and returns
- Marginal external financing cost for entrepreneurs:
  - π_t f_{t+1} = (1 + Γ_t) [ ϖ π_t [1 + i_t^l / π_{t+1}] + Θ(n_{t+1} / (q_t K_{t+1})) (1−ϖ) π_t [1 + i_t^f / π_{t+1}^* (ε_{t+1}/ε_t)] ]
  - Γ_t is a shock to cost of borrowing.
- External finance premium specification:
  - Θ( n_{t+1} / (q_t K_{t+1}) ) = ( n_{t+1} / (q_t K_{t+1}) )^(−η)
- Expected gross return on capital:
  - π_t R_{t+1}^k = π_t [ r_{t+1}^k + (1−δ) q_{t+1} / q_t ]
- Optimal loan contract condition (marginal return equals marginal cost):
  - π_t f_{t+1} = (1 + Γ_t) Θ( n_{t+1} / (q_t K_{t+1}) ) [ ϖ π_t (1 + i_t^l / π_{t+1}) + (1−ϖ) π_t (1 + i_t^f / π_{t+1}^* (ε_{t+1}/ε_t)) ]
- Entrepreneur individual net worth:
  - V_t = R_t^k q_{t−1} K_t − f_t B_t^E
- Aggregate net worth evolution:
  - n_t = ν V_t + (1−ν) H − ε_t^n
  - ε_t^n is zero mean i.i.d. shock to net worth.
- Survival and consumption of exiting entrepreneurs:
  - Proportion surviving: ν
  - Consumption of exiting entrepreneurs: C_t^e = (1 − ν) ( V_t − H )

### Capital producers and investment
- Capital accumulation with quadratic adjustment costs:
  - K_{t+1} = (1−δ) K_t + ϖ_{I,t+1} I_{t+1} − ζ/2 ( I_{t+1}/K_t − δ )^2 K_t
  - ϖ_{I,t} is shock to marginal efficiency of investment.
- Gross investment aggregate and foreign/domestic composition:
  - I_t = [ γ^{1/ϖ} (I_{H,t})^{(ϖ−1)/ϖ} + (1−γ) (I_{F,t})^{(ϖ−1)/ϖ} ]^{ϖ/(ϖ−1)}
  - Demand for domestic and imported investment goods:
    - I_{H,t} = γ (P_{H,t} / P_t)^(−ϖ) I_t
    - I_{F,t} = (1−γ) (P_{F,t} / P_t)^(−ϖ) I_t
- Capital producers maximize expected profits:
  - E_t [ q_t [ ϖ_{I,t} I_t − ζ/2 (I_t/K_t − δ)^2 K_t ] − I_t ]
- First-order condition (capital supply equation):
  - q_t [ ϖ_{I,t} − ζ ( I_t/K_{t−1} − δ ) ] = 1

### Wholesale sector (perfect competition)
- Wholesale production (CRS Cobb-Douglas):
  - Y_t = θ_t K_{t−1}^ψ [ (L_t^P)^μ (L_t^I)^{1−μ} ]^{1−ψ}
  - θ_t is total factor productivity shock.
- Factor demands (from profit maximization):
  - w_t^P = μ (1−ψ) mc_t Y_t / L_t^P
  - w_t^I = (1−μ) (1−ψ) mc_t Y_t / L_t^I
  - r_t^k = ψ mc_t Y_t / K_{t−1}
  - mc_t is real marginal cost.

### Retail sector (monopolistic competition, price stickiness)
- Domestic final goods aggregator:
  - Q_t^d = [ ∫_0^1 Q_t^d(s)^{(v−1)/v} ds ]^{v/(v−1)}
- Retailer demand for individual goods:
  - Q_t^d(s) = [ P_{H,t}(s) / P_{H,t} ]^(−v) Q_t^d
- Aggregate export demand (assumed):
  - Q_t^x = ( P_{X,t} / P_t^* )^(−ϖ_x) Y_t^*
  - Law of one price for export market: P_{x,t} = e_t P_{H,t}
- Calvo pricing: fraction able to reset prices each period is 1 − α.
- Retailers maximize expected discounted profits (stochastic discount factor λ_{t+s}):
  - E_t ∑_{s=0}^∞ (αβ)^s λ_{t+s} [ (P_{H,t+s}/P_{t+s})^{1−v} Y_{t+s} − mc_{t+s} (P_{H,t+s}/P_{t+s})^{−v} Y_{t+s} ]
- New Keynesian Phillips Curve relation (from profit maximization):
  - P_{H,t} = (1−α) (P_{H,t})^{1−v} + α (P_{H,t−1})^{1−v}
- Imported good prices set similarly.

### Banking sector: structure and rate setting
- Banking sector is monopolistically competitive with wholesale and retail branches.
- Nominal rigidities in interest rate setting: deposit and loan banks face quadratic adjustment costs when setting rates.

Retail branch
- Deposit bank profit maximization (retail deposit rate i_t^d):
  - Max E_t ∑ β^t [ i_t^s D_t(i) − i_t^d(i) D_t(i) − φ_{i_d}/2 ( i_t^d(i)/i_{t−1}^d(i) − 1 )^2 D_t ]
  - Subject to deposit demand (equation (13)).
- Symmetric-equilibrium optimal retail deposit rate:
  - 1 + ε_d / ε_d i_t^d = i_t^s − φ_{i_d} / ε_d ( i_t^d i_{t−1}^d^{−1} ) i_t^d i_{t−1}^d + β φ_{i_d} / ε_d E_t [ ( i_{t+1}^d / i_t^d − 1 ) i_{t+1}^d / i_t^d D_{t+1} / D_t ]
  - (as given; equations (33) and surrounding text)
- Loan banks maximize expected profits (retail loan rates i_t^{lH}, i_t^{lE}):
  - Max E_t ∑ β^t [ i_t^{lH}(i) B_t^H(i) + i_t^{lE}(i) L_t^d(i) − i_t^b(i) ( B_t^H(i) + L_t^d(i) ) − φ_{i_{lH}}/2 ( i_t^{lH}(i)/i_{t−1}^{lH}(i) − 1 )^2 B_t^H − φ_{i_{lE}}/2 ( i_t^{lE}(i)/i_{t−1}^{lE}(i) − 1 )^2 L_t^d ]
  - Subject to loan demand equations (14) and (16).
- Symmetric-equilibrium optimal retail loan rates:
  - i_t^{lH} = ε_{lH} / (ε_{lH} − 1) i_t^b − φ_{i_{lH}} / (ε_{lH} − 1) ( i_t^{lH} / i_{t−1}^{lH} − 1 ) i_t^{lH} / i_{t−1}^{lH} + β φ_{i_{lH}} / (ε_{lH} − 1) E_t [ ( i_{t+1}^{lH} / i_t^{lH} − 1 ) i_{t+1}^{lH} / i_t^{lH} B_{t+1}^H / B_t^H ]
  - i_t^{lE} = ε_{lE} / (ε_{lE} − 1) i_t^b − φ_{i_{lE}} / (ε_{lE} − 1) ( i_t^{lE} / i_{t−1}^{lE} − 1 ) i_t^{lE} / i_{t−1}^{lE} + β φ_{i_{lE}} / (ε_{lE} − 1) E_t [ ( i_{t+1}^{lE} / i_t^{lE} − 1 ) i_{t+1}^{lE} / i_t^{lE} L_{t+1}^d / L_t^d ]

Wholesale branch
- Wholesale branch holds CRR and SLR: α_t^s and α_t^d respectively.
  - Keeps α_t^s D_t(i) as cash; keeps α_t^d D_t(i) in government securities earning i_t^t.
- Wholesale branch balance sheet (combines bank capital Z_t with remaining deposits to make loans):
  - (1 − α_t^s − α_t^d) D_t + Z_t = B_t^H + L_t^d
- Banks face exogenously given capital-to-assets (leverage) ratio κ_t; quadratic cost when deviating from κ_t.
- Bank capital accumulation:
  - Z_t = (1 − δ_b) Z_{t−1} + ω_b Π_{t−1}^B − ε_t^B
  - ω_b fraction of bank profits used to accumulate capital; δ_b measures resources used in managing bank capital; ε_t^B is mean zero shock.
- Wholesale branch maximization (profit function with adjustment cost φ_z) yields relation linking wholesale loan rate i_t^b to deposits and leverage:
  - i_t^b = i_t^s / (1 − α_t^s − α_t^d) − φ_z ( Z_t / ( B_t^H + L_t^d ) − κ_t ) ( Z_t / ( B_t^H + L_t^d ) )^2 − α_t^d / (1 − α_t^s − α_t^d) i_t^t
- No-arbitrage between SDA facility and deposit market: i_t^s = i_t^{SDA} and policy rate–SDA rate identity implies i_t^{SDA} = i_t. In symmetric equilibrium:
  - i_t^b = i_t / (1 − α_t^s − α_t^d) − φ_z ( Z_t B_t^H + L_t^d − κ_t ) ( Z_t B_t^H + L_t^d )^2 − α_t^d / (1 − α_t^s − α_t^d) i_t^t
- Aggregate bank profits (after deleting intra-group transactions):
  - Π_t^B = i_t^{lH} B_t^H + i_t^{lE} L_t^d + i_t^t α_t^d D_t − i_t^d D_t − φ_{i_{lH}}/2 ( i_t^{lH} / i_{t−1}^{lH} − 1 )^2 B_t^H − φ_{i_{lE}}/2 ( i_t^{lE} / i_{t−1}^{lE} − 1 )^2 L_t^d − φ_{i_d}/2 ( i_t^d / i_{t−1}^d − 1 )^2 D_t − φ_z/2 ( Z_t B_t^H + L_t^d − κ_t )^2 Z_t

### Public sector: policy rules
- Central bank policy (Taylor-type rule for policy rate i_t):
  - i_t = γ_i i_{t−1} + (1 − γ_i) i + γ_π ( π_t − π ) + γ_Y ( Y_t − Y ) + ε_t^i
- Central bank sets CRR and SLR rules:
  - α_t^s = (1 − ρ_{αs}) α_s + ρ_{αs} α_{t−1}^s + γ_π ( π_t − π ) + γ_Y ( Y_t − Y ) + ε_t^{αs}
  - α_t^d = (1 − ρ_{αd}) α_d + ρ_{αd} α_{t−1}^d + ε_t^{αd}
- Macroprudential capital adequacy ratio rule (κ_t):
  - κ_t = (1 − ρ_κ) κ + (1 − ρ_κ) χ_κ ( B_t^H + L_t^d − B^H − L ) + ρ_κ κ_{t−1}
  - Described as analogous to Basel III counter-cyclical capital buffer: increase capital requirement when conditions are good, relax during downturns.
- LTV ratio rule for impatient households (m_t):
  - m_t = (1 − ρ_m) m + (1 − ρ_m) ( B_t^H − B^H ) + ρ_m m_{t−1}

### Market clearing, balance of payments, and small open economy closure
- Resource constraint:
  - Y_t = Q_t^d + Q_t^x
  - Q_t^d = C_{H,t} + C_{H,t}^e + I_{H,t} + G_t
- National income accounting:
  - ZZ_t = C_t + C_t^e + I_t + ( P_{H,t} / P_t ) G_t + ( P_{X,t} / P_t^* ) ε_t Q_t^x − ( P_{F,t} / P_t ) Q_t^m
- Aggregate housing stock fixed: h = h_t^P + h_t^I (housing investment not included in aggregate demand)
- Balance of payments:
  - ( P_{X,t} / P_t^* ) ε_t Q_t^x − ( P_{F,t} / P_t ) Q_t^m + i_t^f ( B_t^f + L_t^f ) = ( B_{t+1}^f + L_{t+1}^f ) − ( B_t^f + L_t^f )
- Foreign debt elastic risk premium (closure):
  - 1 + i_t^f = (1 + i_t^*)^(−χ) [ ( B_t^f + L_t^f ) − ( B^f + L^f ) ]
  - χ is degree of capital mobility.

### Stochastic processes (shocks)
- Model includes thirteen structural shocks:
  - θ_t (technology), ϖ_{I,t} (investment efficiency), e_t^h (housing demand), Γ_t (entrepreneur borrowing cost), ε_t^n (net worth), ε_t^B (bank capital), i_t^* (world interest rate), Y_t^* (foreign demand), G_t (government spending), α_t^s (CRR), α_t^d (SLR), i_t^t (T-bill rate), ε_t^i (monetary policy).
- Aside from monetary policy and net worth shocks (zero mean i.i.d. with standard deviations σ_i and σ_nw respectively), other shocks follow AR(1):
  - x_t = (1 − ρ_x) x + ρ_x x_{t−1} + ε_t^x
  - where x_t ∈ { θ_t, ϖ_{I,t}, e_t^h, Γ_t, i_t^*, Y_t^*, G_t, α_t^s, α_t^d, i_t^t }, x is steady state, ρ_x ∈ (−1,1), ε_t^x ~ N(0, σ_{xt})

### Key parameter values (calibrated)
- σ = 2; relative risk aversion with respect to consumption
- σ_h = 1; relative risk aversion with respect to housing
- b = 0.7; consumption habit persistence
- φ = 2; Frisch elasticity on labor supply
- η = 0.05; external finance premium for entrepreneurs
- δ = 0.025; capital depreciation ratio
- ζ = 10; cost of capital adjustment
- ψ = 0.33; capital share in production function
- α = 0.5; Calvo pricing share
- v = 5; elasticity of substitution between domestic goods
- ω_b = 0.8; fraction of bank profits used to accumulate bank capital
- φ_{i_d} = 0.01; deposit rate adjustment cost parameter
- φ_{i_{lH}} = 0.01; adjustment cost of loan rate for households
- φ_{i_{lE}} = 0.01; adjustment cost of loan rate for entrepreneurs

*Source: wpiea2020083-print-pdf - 1.4  Deposit/Loan Demand (IMF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020083-print-pdf.pdf_