## 2.   The Model

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---

### 2.1 Households
- Objective and preferences:
  - Representative infinitely lived household maximizes:
    - E_0 Σ_{t=0}^∞ β^t 1/(1−ψ) (C_t − H_t^{1+φ}/(1+φ))^{1−ψ}
  - Parameters and interpretations:
    - 0<β<1
    - ψ>0 is the inverse of the intertemporal elasticity of substitution
    - φ>0 is the inverse elasticity of labour supply
    - Utility allows for Greenwood, Hercowitz and Huffman (GHH, 1988) preferences (eliminates wealth effects from labor supply).
- Consumption and preferences over domestic vs imported goods:
  - Composite consumption index:
    - C_t = [ (1−ω) C_{H;t}^{(ε−1)/ε} + ω C_{M;t}^{(ε−1)/ε} ]^{ε/(ε−1)}
    - ε>0 is elasticity of substitution between domestic and imported goods
    - 0<ω<1 is the weight of imported goods in domestic consumption
  - Domestic and imported consumption composites:
    - C_{H;t} = [ ∫_0^1 C_{H;t}(j)^{1−η} dj ]^{1/(1−η)}
    - C_{M;t} = [ ∫_0^1 C_{M;t}(j)^{1−η} dj ]^{1/(1−η)}
    - η>1 is elasticity of substitution among varieties.
- Income and financial positions:
  - Households receive profits Π_t and wages W_t, and make new borrowing net of interest payments.
  - Two types of one-period non-contingent debt:
    - Domestic-currency debt B_t at nominal interest rate i_t.
    - Foreign-currency debt D^H_t at nominal interest rate i^*_t facing premium ζ^D_t:
      - ζ^D_t = ζ^D_2 [ exp( S_t D^H_{t+1} / P_t GDP_t − S^D_H P GDP ) − 1 ]^2
      - (premium introduced to maintain stationarity in net foreign assets; in calibration elasticity is very close to zero: ζ^D_t = 0.0075)
  - Household budget constraint (period t):
    - P_t C_t + (1+i_{t−1}) B_t + (1+i^*_{t−1}) ζ^D_{t−1} S_t D^H_t = W_t H_t + B_{t+1} + S_t D^H_{t+1} + Π_t
  - Household chooses sequences {C_t, H_t, B_{t+1}, D^H_{t+1}}_{t=0}^∞ to maximize utility subject to the budget constraint.

### 2.2 Firms
- Firm types and price setting:
  - Three firm types: production firms, importing firms, and unfinished capital producing firms.
  - Production and importing firms have market power and face quadratic menu (price adjustment) costs in units of consumption:
    - (λ_i / 2) (P_{i;t}(j)/P_{i;t−1}(j) − 1)^2 for i = H, X and analogous λ^M for importing firms.
  - Local currency pricing; price stickiness causes incomplete exchange rate pass-through in the short run.
- Real exchange rate and price indexes:
  - Aggregate export price index: P_{X;t} = [ ∫_0^1 P_{X;t}(j)^{1−η} dj ]^{1/(1−η)}
  - Real exchange rate: REX_t = S_t P^*_t / P_t
    - S_t: nominal exchange rate (domestic currency price of foreign currency)
    - P^*_t: foreign aggregate price index

#### 2.2.1 Production firms
- Technology (variety j):
  - Y_t(j) = A_t N_t(j)^{1−ξ} K_t(j)^{ξ}
  - A_t: labor productivity (common across production firms)
  - Composite labor input:
    - N_t(j) = [ H_t(j)^{1−κ} H^E_t(j)^{κ} ]
  - K_t(j): capital provided by entrepreneurs
- Demand for variety j in market i (i = H, X):
  - Y_{i;t}(j) = [ P_{i;t}(j) / P_{i;t} ]^{−η} Y_{i;t}

#### 2.2.2 Importing firms
- Monopolistically competitive, owned by domestic households.
- Import goods at prices S_t P^*_t and sell domestically.
- Face price adjustment cost parameter λ^M ≥ 0 — causes delay in import price adjustments after exchange rate changes.

#### 2.2.3 Unfinished capital producing firms
- Aggregate investment:
  - I_t = [ ω I_{H;t}^{(ε−1)/ε} + (1−ω) I_{M;t}^{(ε−1)/ε} ]^{ε/(ε−1)}
  - I_{H;t} = ω (P_{H;t}/P_t)^{−1} I_t
  - I_{M;t} = (1−ω) (P_{M;t}/P_t)^{−1} I_t
- Adjustment costs and capital accumulation:
  - Adjustment cost: (λ_I / 2) (I_t / K_t − ϵ)^2
  - Capital law of motion:
    - K_{t+1} = [ I_t / K_t − (λ_I / 2) (I_t / K_t − ϵ)^2 ] K_t + (1−ϵ) K_t
    - ϵ is the depreciation rate
  - Optimality with respect to I_t yields nominal price of a unit of capital Q_t.

### 2.3 Entrepreneurs
- Role and productivity:
  - Entrepreneurs transform unfinished capital goods K_{t+1}(k) into finished capital with idiosyncratic productivity !_{t+1}(k); output is !_{t+1}(k) K_{t+1}(k).
  - !_t(k) is i.i.d. across time and firms, drawn from distribution F(:) with p.d.f. f(:) and E(:) = 1.
  - Productivity observed by entrepreneurs but not by lenders; lenders form perceptions !̃_{t+1}(k) = !_{t+1}(k) %_t where %_t ∈ [0,1] follows ln(%_t) = ρ% ln(%_{t−1}) + " %.
  - The origin of the financial shock is a change in lenders' perception (" %).
- Financing and contracting:
  - Entrepreneurs borrow externally through perfectly competitive financial intermediaries.
  - Contracting involves costly state verification (CVS) with monitoring cost fraction ϕ of the return.
  - Linearity and symmetry imply all entrepreneurs face the same financial contract at the aggregate level.
- Key first-order condition for investment financing:
  - E_t[RK_{t+1}] = E_t[(1 + ˜i_t)(1 + β_{t+1})]
    - (1 + β_{t+1}) is the external risk premium.
- Leverage and risk:
  - Greater external financing increases incentives for riskier projects, raising default probability and external finance premium.
  - A fall in entrepreneurs' net worth increases leverage and raises the external finance premium.
  - Survival rate # ≈ 99:33 per cent (a proportion of entrepreneurs die each period).

- Borrowing scenarios analyzed:
  - (i) only foreign borrowing (benchmark),
  - (ii) only domestic borrowing,
  - (iii) both foreign and domestic borrowing.
- Only Foreign Borrowing (benchmark):
  - Entrepreneurs borrow only from foreign lenders in foreign currency.
  - Budget constraint: P_t NW_t(k) = Q_t K_{t+1}(k) − S_t D^F_{t+1}(k)
  - Resulting FOC (aggregate): E_t[RK_{t+1}] = E_t[(1 + ˜i_t)(1 + β_{t+1})]
- Only Domestic Borrowing:
  - Entrepreneurs borrow only from domestic lenders in domestic currency.
  - Budget constraint: P_t NW_t = Q_t K_{t+1} − D^D_{t+1}
  - FOC: E_t[RK_{t+1}] = E_t[(1 + i_t)(1 + β^D_{t+1})]
- Both Foreign and Domestic Borrowing:
  - Hybrid case with two entrepreneur types (F and D) and aggregate capital K_t = K^F_t + K^D_t.
  - FOCs:
    - E_t[RK_{t+1}] = E_t[(1 + ˜i_t)(1 + β^F_{t+1})]
    - E_t[RK_{t+1}] = E_t[(1 + i_t)(1 + β^D_{t+1})]

### 2.4 Financial Intermediaries and Macroprudential Policy
- Financial intermediaries:
  - Continuum of perfectly competitive financial intermediaries channel funds; zero-profit implies lending rates equal expected cost absent macroprudential measures.
- Macroprudential regulation:
  - Modeled as generating a "regulation premium" RPt that raises costs for financial intermediaries and is passed onto borrowers.
  - Lending cost with regulation:
    - E_t[RK_{t+1}] = E_t[(1 + ˜i_t)(1 + β_{t+1})(1 + RPt)]
  - Baseline specification links RPt positively to nominal credit growth:
    - RPt = (S_t DF_t / S_{t−1} DF_{t−1} − 1)
  - Rationale: macroprudential measures can be targeted and directly affect cost of externally sourced credit, while the policy rate is a broader instrument and may be less effective with open financial accounts.
  - Macroprudential policy is countercyclical: it raises costs in booms and lowers them in busts.

### 2.5 Monetary Policy
- Monetary policy represented by a Taylor-type rule with smoothing:
  - 1 + i_t = [ (1 + i) (π_t)^{φ_π} (Y_t/Y)^{φ_Y} (credit growth)^{φ_D} ]^{g} [1 + i_{t−1}]^{1−g}
  - Parameter domains:
    - {φ_π} ∈ (1;1], {φ_Y} ∈ (0;1], {φ_D} ∈ (−1;1], g ∈ [0;1].
  - $ (interest rate smoothing) in text corresponds to g in the rule above.
- Alternative policy designs considered:
  - Monetary policy reacting to inflation and output gap.
  - Monetary policy reacting also to nominal credit growth ("lean against the wind").
  - Delegation of lean actions to macroprudential policy (macroprudential instrument responds to credit growth).
- Interaction between monetary policy and macroprudential policy is central to experiments.

### Model purpose, scope, and key mechanisms
- An open-economy New Keynesian DSGE with a financial accelerator (Bernanke et al. (1999) tradition) and elements from Gali and Monacelli (2002), De Paoli (2009), Gertler et al. (2007), Kannan et al. (2012), Ozkan and Unsal (2012), Unsal (2013).
- Main questions:
  - Should monetary policy react to financial market developments (credit growth) or delegate responses to macroprudential instruments?
  - How does the borrowing source (domestic vs foreign) affect desirability and effectiveness of monetary vs macroprudential policy?
  - How robust are policy mixes to real-time shock uncertainty?
- Key modeling features:
  - Price stickiness with menu costs for domestic, export, and import prices (λ_i, λ^M).
  - Incomplete exchange rate pass-through and segmented local currency pricing.
  - Financial frictions: borrowing premia for household foreign borrowing and regulation premium for intermediaries.
  - Entrepreneurs’ financing structure (domestic and/or foreign) affects transmission of policies.

### Model parametrization (selected values)
- Discount factor, β = 0:99 (implying riskless annual return ≈ 4 per cent; time in quarters).
- Inverse of IES, ψ = 1.
- Inverse of elasticity of labour supply, φ = 2.
- Degree of openness (1 − ω) = 0:35.
- Share of capital in production, ξ = 0:35.
- Elasticity of substitution between differentiated goods of same origin, η = 11 (implying mark-up 1:1).
- Price adjustment cost = 120 for all sectors.
- Quarterly depreciation rate, ϵ = 0:025.
- Share of entrepreneurs' labour, κ = 0:01 (1 per cent of total wage bill goes to entrepreneurs).
- Monetary policy baseline: φ_π = 1:5, φ_Y = 0:5.
- Interest rate smoothing parameter, g = 0:5.
- Persistence of perception shock, ρ% = 0:5 (shock dies away in 9 quarters).
- Steady state leverage ratio = 0:3.
- Quarterly external risk premium = 200 basis points.
- Monitoring cost parameter, ϕ = 0:2.
- Resulting survival rate # ≈ 99:33 per cent.

### Model dynamics: shocks and qualitative transmission
- Unanticipated financial (perception) shock:
  - A one per cent rise in perceived risk (perception shock of 1 per cent) leads to a reversal of capital of about 2.5 percent of output under the baseline scenario.
  - Mechanism: higher perceived risk → higher external finance premium → higher lending cost → fewer entrepreneurial projects → lower leverage → partial decline in risk premium but future capital supply falls → investment falls → lower demand for domestic currency → depreciation → foreign-currency debt burden rises (balance sheet effect).
- Negative productivity shock:
  - A 1 percent fall in productivity leads to falls in consumption, investment and output; rise in inflation; fall in credit growth, asset prices and capital flows.
  - Tension: inflation and credit growth move in opposite directions, creating a trade-off between macroeconomic and financial stability.

### Policy experiments and main findings
- Policy regimes compared:
  - (i) standard Taylor rule (TR);
  - (ii) TR combined with a macroprudential instrument (MP);
  - (iii) TR that responds to nominal credit growth (TR with CG).
- Financial shock (perception shock of 1 per cent) — qualitative results:
  - Under standard TR, policy rates lowered in response to negative output gap and lower inflation; lower policy rate partially offsets higher risk premium.
  - Macroprudential policy (countercyclical RPt) damps responses because RPt falls following the financial shock, reducing lending rates and the financial accelerator.
  - TR responding to credit growth lowers policy rate more relative to standard TR, further mitigating lending rate impacts and reducing declines in consumption, investment, output, asset prices and credit growth; exchange rate depreciates further, leading to a smaller fall in inflation relative to standard TR.
  - Conclusion: leaning against the wind through either policy rate or macroprudential instrument helps improve macroeconomic and financial stability in response to the financial shock.
- Productivity shock (1 per cent negative) — qualitative results:
  - Macroprudential policy reduces falls in investment, output, credit growth and asset prices but is expansionary and raises inflation by undoing some tightening from higher policy rate.
  - TR responding to credit growth mitigates output and credit declines compared with standard TR, but inflation rises by about 50 percent more compared to baseline.
  - Conclusion: responding to financial market developments under a productivity shock improves financial stability but may worsen macroeconomic stability (higher inflation).

### Optimal policy rules and welfare evaluation
- Welfare objective:
  - Maximize household welfare V_t from recursive expected utility: V_t = U(C_t, H_t) + β E_t V_{t+1}
  - Second-order approximation around deterministic steady state used to compute welfare.
- Welfare metric:
  - Consumption equivalent a (fraction of consumption required to equate welfare under any given policy V_t to welfare under optimal Taylor rule V^{opt}_t).
- Welfare results for a 1% financial shock (expressed in units of steady state consumption):
  - Taylor rule (TR): 0.2106
  - TR with credit growth (CG): 0.1593
  - TR + macroprudential policy (MP): 0.1140
  - Optimized Taylor rule with CG (OTR with CG): -0.0324
  - OTR + optimized MP (OMP): -0.1098
  - OTR with CG + OMP: -0.1178
- Optimized coefficients for a 1% financial shock:
  - Opt. Taylor rule (OTR): Inflation = 1.1; Output gap = -; Credit gr. = -
  - OTR with CG: Inflation = 1.1; Output gap = -; Credit gr. = 0.6
  - OTR + OMP: Inflation = 2.4; Output gap = -; Macropru. Credit gr. = 1.1
  - OTR with CG + OMP: Inflation = 1.7; Output gap = -; Credit gr. (monetary) = 0.1; Credit gr. (macropru.) = 0.9
- Key interpretations:
  - The optimized coefficient for credit growth in the macroprudential instrument is not zero (1.1) when MP is present.
  - The optimized coefficient for credit growth in the Taylor rule is 0.6, but welfare gains relative to the optimal Taylor rule are smaller.
  - When MP is in place, including nominal credit growth in the monetary policy rule has negligible welfare effects and the optimized monetary coefficient is close to zero.
- Welfare results for a 1% productivity shock:
  - Taylor rule (TR): 0.2163
  - TR with credit growth (CG): 0.3302
  - TR + macroprudential policy (MP): 0.2411
- Optimized coefficients for a 1% productivity shock:
  - OTR: Inflation = 1.1; Output gap = -; Credit gr. = -
  - OTR with CG: Inflation = 1.1; Output gap = -; Credit gr. = 0
  - OTR + OMP: Inflation = 1.1; Output gap = -; Macropru. Credit gr. = 0
  - OTR with CG + OMP: Inflation = 1.1; Output gap = -; Credit gr. (monetary) = 0; Credit gr. (macropru.) = 0
- Robustness and shock-origin uncertainty:
  - Delegating "lean against the wind" to macroprudential policy is welfare-improving under a financial shock and less costly under a productivity shock, making the policy combination more robust to uncertainty.
  - Interest rate inertia used in reported results: g = 0:5. Results slightly change with varying g, but main conclusions remain.

### The role of the borrowing source
- Two channels make borrowing source crucial:
  - With foreign currency borrowing, exchange rate depreciation reduces entrepreneurial net worth and amplifies the financial accelerator, worsening the financial-sector impact and making monetary-policy-based financial stabilization more destabilizing.
  - When credit is solely external, borrowing cost depends on foreign interest rate, external finance premium, and regulation premium, so the domestic policy rate does not directly influence cost of credit—reducing monetary policy effectiveness for financial stabilization relative to macroprudential tools.
- Welfare and optimized coefficients under a 1% financial shock by borrowing source:
  - Foreign borrowing:
    - Welfare loss: Opt. Taylor Rule = -0.0321; Opt. MP Rule = -0.1098
    - Optimized coefficient of credit growth: Taylor Rule = 0.63; MP Rule = 1.14
  - Domestic borrowing:
    - Welfare loss: Opt. Taylor Rule = -0.0205; Opt. MP Rule = -0.0310
    - Optimized coefficient of credit growth: Taylor Rule = 0.47; MP Rule = 0.65
  - Domestic and Foreign borrowing:
    - Welfare loss: Opt. Taylor Rule = -0.0262; Opt. MP Rule = -0.0447
    - Optimized coefficient of credit growth: Taylor Rule = 0.51; MP Rule = 0.82
- Key interpretations:
  - Under foreign borrowing, using monetary policy to respond to financial market developments is much inferior (about 7 percent of steady state consumption difference) to using macroprudential policy.
  - The optimized macroprudential credit growth coefficient (1.14) exceeds the optimized monetary credit growth coefficient (0.63) under foreign borrowing.
  - When borrowing is only domestic, responding via policy rate or macroprudential instrument is nearly indifferentiable in welfare terms.

### Conclusions and policy implications
- Main conclusions:
  - Following a financial shock, leaning against the wind via either policy rate or macroprudential measures helps macroeconomic and financial stability; macroprudential policy performs quantitatively better.
  - When macroprudential measures are present, welfare gains from adding credit growth to the traditional monetary policy rule are negligible.
  - Under a productivity shock, responding to financial market developments via monetary policy is more costly than using macroprudential policies.
  - Using monetary and macroprudential policies to pursue separate objectives—monetary stability and financial stability—yields a policy mix more robust to shock-origin uncertainty.
  - In economies with sizable foreign borrowing, a separate macroprudential instrument is more desirable because monetary policy cannot directly influence foreign borrowing costs and would otherwise require large policy rate changes that raise volatility.
- Model caveat and future research:
  - The analysis assumes a fully flexible exchange rate and excludes exchange rate interventions; examining exchange rate interventions alongside monetary and macroprudential policies is an important extension.

*Italic source: _wp14112 - 2.   The*

### 2.   The

### 2.   The Model

### 2.1 Households
- Representative infinitely lived household maximizes:
  - E
    0
    1
    Σ
    t=0
    β
    t
    1
    1−ψ
    (C
    t
    −
    H
    t
    1+φ
    1+φ
    )
    1−ψ
  - Parameters and preferences:
    - 0<β<1
    - ψ>0 is the inverse of the intertemporal elasticity of substitution
    - φ>0 is the inverse elasticity of labour supply
    - Utility specification allows for Greenwood, Hercowitz and Huffman (GHH, 1988) preferences over hours (eliminates wealth effects from labor supply).
- Composite consumption index:
  - C
    t
    =
    [ (1−ω)
    C
    H;t
    (ε−1)/ε
    + ω
    C
    M;t
    (ε−1)/ε
    ]^{ε/(ε−1)}
  - Parameters:
    - ε>0 is elasticity of substitution between domestic and imported goods
    - 0<ω<1 is the weight of imported goods in domestic consumption
  - Domestic and foreign consumption composites:
    - C
      H;t
      =
      [ ∫_0^1 C
      H;t
      (j)^{1−η} dj ]^{1/(1−η)}
    - C
      M;t
      =
      [ ∫_0^1 C
      M;t
      (j)^{1−η} dj ]^{1/(1−η)}
    - η>1 is elasticity of substitution among varieties.
- Income and financial positions:
  - Households receive profits Π_t, wages W_t, and make new borrowing net of interest payments.
  - Two types of one-period non-contingent debt:
    - Domestic-currency debt B_t at nominal interest rate i_t.
    - Foreign-currency debt D^H_t at nominal interest rate i^*_t and facing premium ζ^D_t given by:
      - ζ^D_t = ζ^D_2 [ exp( S_t D^H_{t+1} / P_t GDP_t − S^D_H P GDP ) − 1 ]^2
      - (premium introduced to maintain stationarity in net foreign assets; in calibration elasticity is very close to zero: ζ^D_t = 0.0075 — note: calibration comment appears in text)
  - Household budget constraint (period t):
    - P_t C_t + (1+i_{t−1}) B_t + (1+i^*_{t−1}) ζ^D_{t−1} S_t D^H_t = W_t H_t + B_{t+1} + S_t D^H_{t+1} + Π_t
  - Household chooses sequences {C_t, H_t, B_{t+1}, D^H_{t+1}}_{t=0}^∞ to maximize utility subject to the budget constraint.

### 2.2 Firms
- Three firm types: production firms, importing firms, and unfinished capital producing firms.
- Price setting and stickiness:
  - Production and importing firms have market power and face quadratic menu (price adjustment) costs expressed in units of consumption:
    - (λ_i / 2) (P_{i;t}(j)/P_{i;t−1}(j) − 1)^2 for i = H, X (production markets) and analogous λ^M for importing firms.
  - Local currency pricing; price stickiness causes incomplete exchange rate pass-through in short run.

#### 2.2.1 Production firms
- Technology (variety j):
  - Y_t(j) = A_t N_t(j)^{1−ξ} K_t(j)^{ξ}
  - A_t: labor productivity (common across production firms)
  - N_t(j): composite labor input combining household and entrepreneurial labor:
    - N_t(j) = [ H_t(j)^{1−κ} H^E_t(j)^{κ} ]
  - K_t(j): capital provided by entrepreneurs
- Firms minimize costs given input prices and maximize expected discounted profits using household intertemporal rate of substitution β_t U_{c;t}.
- Demand for variety j in market i (i = H, X):
  - Y_{i;t}(j) = [ P_{i;t}(j) / P_{i;t} ]^{-η} Y_{i;t}

- Aggregate export price index:
  - P_{X;t} = [ ∫_0^1 P_{X;t}(j)^{1−η} dj ]^{1/(1−η)}

- Real exchange rate:
  - REX_t = S_t P^*_t / P_t
  - S_t: nominal exchange rate (domestic currency price of foreign currency)
  - P^*_t: foreign aggregate price index

#### 2.2.2 Importing firms
- Monopolistically competitive, owned by domestic households.
- Import goods at prices S_t P^*_t and sell domestically.
- Face price adjustment cost parameter λ^M ≥ 0 (analogous to production firms) — causes delay in import price adjustments after exchange rate changes.

#### 2.2.3 Unfinished capital producing firms
- Aggregate investment:
  - I_t = [ ω I_{H;t}^{(ε−1)/ε} + (1−ω) I_{M;t}^{(ε−1)/ε} ]^{ε/(ε−1)}
  - Domestic and imported investment goods prices are P_{H;t} and P_{M;t}, respectively.
  - I_{H;t} = ω (P_{H;t}/P_t)^{−1} I_t
  - I_{M;t} = (1−ω) (P_{M;t}/P_t)^{−1} I_t
- Unfinished capital producers combine investment I_t and rented capital K_t to produce new capital subject to quadratic adjustment costs:
  - Adjustment cost: (λ_I / 2) (I_t / K_t − ϵ)^2
  - Capital law of motion:
    - K_{t+1} = [ I_t / K_t − (λ_I / 2) (I_t / K_t − ϵ)^2 ] K_t + (1−ϵ) K_t
    - ϵ is the depreciation rate
- Optimality with respect to I_t yields nominal price of a unit of capital Q_t.

### 2.3 Entrepreneurs
- Entrepreneurs borrow to finance capital provided to production firms (details introduced later in model; subsections listed: Only Foreign Borrowing; Only Domestic Borrowing; Both Foreign and Domestic Borrowing).
- When entrepreneurs borrow from domestic sources, funds are provided by households and channeled through financial intermediaries — modifying household budget constraint to include domestic lending to entrepreneurs D^D_{t+1} and its role in incomes and outstanding debt (text indicates budget constraint is modified accordingly).

### 2.4 Financial Intermediaries and Macroprudential Policy
- Macroprudential regulation is modeled as generating a "regulation premium" that raises costs for financial intermediaries, passed onto borrowers as higher lending rates.
- Regulation premium is specified as a rule responding to nominal credit growth.
- Rationale: macroprudential measures can be targeted at specific markets and directly affect cost of credit including when borrowing is external, whereas the policy rate is a broader instrument and may be less effective with open financial accounts.

### 2.5 Monetary Policy
- Monetary policy is represented by a Taylor-type rule.
- Alternative policy designs considered include:
  - Monetary policy reacting to inflation and output gap.
  - Monetary policy also reacting to nominal credit growth ("lean against the wind").
  - Delegation of lean actions to macroprudential policy (macroprudential instrument responds to credit growth, generating a regulation premium).
- Interaction between monetary policy and macroprudential policy is central to model experiments.

### Model purpose, scope, and key mechanisms
- Open economy New Keynesian DSGE with financial accelerator (Bernanke et al. (1999) tradition) and elements from Gali and Monacelli (2002), De Paoli (2009), Gertler et al. (2007), Kannan et al. (2012), Ozkan and Unsal (2012), Unsal (2013).
- Main questions addressed:
  - Whether monetary policy should react to financial market developments (credit growth) versus delegating such responses to macroprudential instruments.
  - The role of borrowing source (domestic vs foreign) for the desirability and effectiveness of monetary vs macroprudential policy.
  - Robustness of policy mixes to real-time shock uncertainty (policy must perform well when policymakers do not observe shock origins).
- Key modeling features:
  - Price stickiness with menu costs for domestic and export prices, and for import prices (λ_i, λ^M).
  - Incomplete exchange rate pass-through and segmented local currency pricing.
  - Financial frictions: borrowing premia for household foreign borrowing and regulation premium for intermediaries.
  - Entrepreneurs’ financing structure (domestic and/or foreign) affects transmission of policies.

### Main findings (as stated)
- Responding to credit growth through the monetary instrument improves macroeconomic stability and welfare following a negative financial shock.
- In the presence of macroprudential measures, there are no significant welfare gains from monetary policy also reacting to credit growth beyond its response to output gap and inflation.
- Welfare costs of responding to credit growth after a productivity shock are much higher if the response is through the policy rate than through the macroprudential instrument.
  - Implication: delegating "lean against the wind" to macroprudential policy is more robust to shock uncertainty.
- Source of borrowing matters:
  - Greater size of foreign borrowing increases the benefits from macroprudential measures, because macroprudential instruments can directly influence the cost of externally sourced credit while the policy rate cannot as effectively.

*Italic source: _wp14112 - 2.   The*

### 2.3  Entrepreneurs

### 2.3  Entrepreneurs

### Role of entrepreneurs and production technology
- Entrepreneurs transform unfinished capital goods Kt+1(k) into finished capital goods with idiosyncratic productivity !t+1(k) so that output is !t+1(k)Kt+1(k).
- Idiosyncratic productivity !t(k) is i:i:d: across time and firms, drawn from distribution F(:) with p.d.f f(:) and E(:) = 1.
- Productivity is observed by the entrepreneur but not by lenders; lenders form perceptions !̃t+1(k) = !t+1(k)%t where %t ∈ [0,1] follows ln(%t) = % ln(%t−1) + "%. The origin of the financial shock is a change in lenders' perception ("%).6,7,8

### Financing and contracting
- Entrepreneurs finance investment by external borrowing through perfectly competitive financial intermediaries.
- Contracting involves costly state verification (CVS) with monitoring cost fraction  of the return. The contracting problem identifies capital demand Kt+1(k) and a cut-off productivity !t+1(k) such that participation constraints of the lender are satisfied.
- Linearity and symmetry of the contracting problem (constant returns to scale) imply all entrepreneurs face the same financial contract at the aggregate level.

### Key first-order condition for investment financing
- Expected lending cost equated to expected return on capital:
  - Et[RKt+1] = Et[(1 + ĩt)(1 + t+1)]
  - (1 + t+1) is the external risk premium.9

### Leverage and risk
- Greater use of external financing increases incentive for riskier projects, raising default probability and external finance premium.
- A fall in entrepreneurs' net worth increases leverage and raises the external finance premium.
- A proportion of entrepreneurs die each period (survival rate # ≈ 99:33 per cent), ensuring borrowing constraints remain binding and self-financing never occurs.

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### Borrowing scenarios analyzed
- The paper considers three alternative assumptions about the source of borrowing:
  - (i) only foreign borrowing (benchmark),
  - (ii) only domestic borrowing,
  - (iii) both foreign and domestic borrowing.
- The source and currency denomination of borrowing affect exchange rate exposure and balance sheet effects.

H3 Only Foreign Borrowing (benchmark)
- Entrepreneurs borrow only from foreign lenders in foreign currency; relevant for emerging markets.7
- Entrepreneur budget constraint:
  - Pt NWt(k) = Qt Kt+1(k) − St DFt+1(k)
  - DFt+1 denotes foreign currency denominated debt; entrepreneurs are exposed to exchange rate risk through St.
- Lenders misperceive productivity as !̃t+1(k) = !t+1(k)%t and observe productivity only at monitoring cost .
- Resulting FOC (aggregate):
  - Et[RKt+1] = Et[(1 + ĩt)(1 + t+1)].

H3 Only Domestic Borrowing
- Entrepreneurs borrow only from domestic lenders (households) in domestic currency; financial autarky case.
- Budget constraint and FOC:
  - Pt NWt = Qt Kt+1 − DDt+1
  - Et[RKt+1] = Et[(1 + it)(1 + Dt+1)]
  - DDt+1 denotes domestic currency denominated debt; (1 + Dt+1) denotes default premia on domestic borrowing.

H3 Both Foreign and Domestic Borrowing
- Hybrid case: entrepreneurs may borrow from both foreign (F) and domestic (D) sources depending on relative costs.
- Aggregate conceptualization uses two types of entrepreneurs (F and D) with budget constraints:
  - Pt NWFt(k) = Qt KFt+1(k) − St DFt+1(k)
  - Pt NWDt(k) = Qt KDt+1(k) − DDt+1(k)
- Lenders share the same misperception dynamics: !̃v t+1(k) = !v t+1(k)%t for v = F, D.
- First-order conditions:
  - Et[RKt+1] = Et[(1 + ĩt)(1 + F t+1)]
  - Et[RKt+1] = Et[(1 + it)(1 + D t+1)]
- Total capital Kt = KFt + KDt.

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### Financial intermediaries and macroprudential policy
- Continuum of perfectly competitive financial intermediaries channel funds; zero-profit implies lending rates equal Et[(1 + ĩt)(1 + F t+1)] absent macroprudential measures (baseline: only foreign borrowing).
- Macroprudential policy modeled as measures that raise the cost of financial intermediation; this increased cost is passed onto borrowers as a regulation premium RPt.
- Lending cost with macroprudential regulation:
  - Et[RKt+1] = Et[(1 + ĩt)(1 + t+1)(1 + RPt)]
- Baseline specification links RPt positively to nominal credit growth:
  - RPt = (St DFt / St−1 DFt−1 − 1)
- Macroprudential policy is countercyclical: it counteracts perceived risk declines in good times and risk rises in bad times by raising costs in booms and lowering them in busts.11,12

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### Monetary policy rule
- Simple implementable monetary policy rule with smoothing:
  - 1 + it = [(1 + i) (πt)^{π} (Yt/Y)^{Y} (credit growth)^{D} D]^{ $ } [1 + it−1]^{1−$}
- Parameter domains:
  - {π} ∈ (1;1], {Y} ∈ (0;1], {D} ∈ (−1;1], $ ∈ [0;1].
- Variables and interpretation:
  - $ is interest rate smoothing parameter; i and Y denote steady-state nominal interest rate and output; πt is CPI inflation; (credit growth) denotes nominal credit growth in domestic currency.
- Initial values for π, Y, D, and $ used in calibration; optimal values of π, Y, D and g (coe¢ cient of nominal credit growth in the macroprudential tool) are derived by maximizing household welfare.

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### Model parametrization (selected values)
- Discount factor,  = 0:99 (implying riskless annual return ≈ 4 per cent; time in quarters).
- Inverse of IES,  = 1.
- Inverse of elasticity of labour supply, ' = 2.
- Degree of openness (1 − ) = 0:35.
- Share of capital in production,  = 0:35.
- Elasticity of substitution between differentiated goods of same origin,  = 11 (implying mark-up 1:1).
- Price adjustment cost = 120 for all sectors.
- Quarterly depreciation rate,  = 0:025.
- Share of entrepreneurs' labour, ; = 0:01 (1 per cent of total wage bill goes to entrepreneurs).
- Monetary policy baseline: π = 1:5, Y = 0:5.
- Interest rate smoothing parameter, $ = 0:5.
- Persistence of perception shock, % = 0:5 (shock dies away in 9 quarters).
- Steady state leverage ratio = 0:3.
- Quarterly external risk premium = 200 basis points.
- Monitoring cost parameter,  = 0:2.
- Resulting survival rate # ≈ 99:33 per cent.

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### Model dynamics: shocks and qualitative transmission
- Unanticipated financial shock: one per cent rise in perceived risk (perception shock of 1 per cent) leads to a reversal of capital of about 2.5 percent of output under the baseline scenario.
  - Mechanism: higher perceived risk → higher external finance premium → higher lending cost → entrepreneurs undertake fewer projects → lower leverage → risk premium partially declines → but future capital supply falls → investment falls → lower demand for domestic currency → depreciation → foreign-currency-denominated debt burden rises (balance sheet effect).
- Negative productivity shock: 1 percent fall in productivity leads to
  - fall in consumption, investment and output;
  - rise in inflation;
  - fall in credit growth, asset prices and capital flows.
  - Tension arises because inflation and credit growth move in opposite directions, creating a trade-off between macroeconomic and financial stability.

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### Policy experiments and main findings
- Three policy regimes compared in impulse response analysis:
  - (i) standard Taylor rule;
  - (ii) Taylor rule combined with a macroprudential instrument;
  - (iii) Taylor rule that responds to nominal credit growth.
- Financial shock (perception shock of 1 per cent):
  - Under standard Taylor rule, policy rates lowered in response to negative output gap and lower inflation; lower policy rate partially offsets higher risk premium.
  - Macroprudential policy (countercyclical RPt) damps responses of real and financial variables because RPt falls following the financial shock, reducing lending rates and the financial accelerator.
  - Taylor rule responding to credit growth lowers policy rate more relative to standard Taylor rule, further mitigating lending rate impacts and reducing declines in consumption, investment, output, asset prices and credit growth; exchange rate depreciates further, leading to smaller fall in inflation relative to standard Taylor rule.
  - Conclusion: leaning against the wind through either policy rate or macroprudential instrument helps improve macroeconomic and financial stability in response to the financial shock.
- Productivity shock (1 per cent negative):
  - Macroprudential policy reduces falls in investment, output, credit growth and asset prices but is expansionary and raises inflation by undoing some tightening from higher policy rate.
  - Taylor rule responding to credit growth mitigates output and credit declines compared with standard Taylor rule, but inflation rises by about 50 percent more compared to baseline.
  - Conclusion: responding to financial market developments under a productivity shock improves financial stability but may worsen macroeconomic stability (higher inflation).

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### Optimal policy rules and welfare evaluation
- Objective: maximize household welfare Vt built from recursive expected utility:
  - Vt = U(Ct, Ht) +  Et Vt+1
  - Second-order approximation around deterministic steady state used to compute welfare under alternative policies.
- Welfare comparison metric: consumption equivalent  (fraction of consumption required to equate welfare under any given policy Vt to welfare under optimal Taylor rule Vopt t).
  - Expression given (under  = 2) as:
    -  = ( (Vopt t − Vt)(1 − )(C̄^{1+'} H̄^{1+'}) / (2 C (1 − (Vopt t − Vt)(1 − )(C̄^{1+'} H̄^{1+'})) ) )
  - Higher  implies higher welfare loss (policy less desirable).
- Numerical search over grid of parameters {π, Y, D, g} finds optimal simple monetary and macroprudential policy parameters that maximize Vt in response to financial and productivity shocks; Tables (referenced in text) summarize optimized parameters and welfare comparisons.

*Italic source: Excerpt from _wp14112 - 2.3  Entrepreneurs (IMF working paper PDF)_*

### 5.1  Optimal monetary versus macroprudential policy rules

### _wp14112 - 5.1  Optimal monetary versus macroprudential policy rules

### Optimal policy responses to shocks
- Under both financial and productivity shocks, the optimal response to inflation is "close to unity" and the response to output gap is zero, consistent with Schmitt-Grohe and Uribe (2007) and Faia and Monacelli (2007). Hence the analysis sets the output gap coefficient to zero and focuses on the parameters on inflation and nominal credit growth in the monetary policy rule, and nominal credit growth in the macroprudential policy rule.
- When optimizing policy coefficients, the presence of a macroprudential instrument calls for a more aggressive monetary policy response to inflation (e.g., 2.4 versus 1.1 in the optimized configurations for a financial shock), because a strong expansionary macroprudential response can increase demand and inflation.

### Welfare impacts and optimized coefficients: financial shock
- Welfare losses (expressed in units of steady state consumption) in response to a 1% financial shock (Table 3):
  - Taylor rule (TR): 0.2106
  - TR with credit growth (CG): 0.1593
  - TR + macroprudential policy (MP): 0.1140
  - Optimized Taylor rule with CG (OTR with CG): -0.0324
  - OTR + optimized MP (OMP): -0.1098
  - OTR with CG + OMP: -0.1178
- Improvement from responding to credit market developments:
  - Welfare loss decreases by about 0.05 and 0.1 percent of steady state consumption under TR with credit growth and MP rule, respectively (text summary consistent with Table 3).
- Optimized coefficients in response to a 1% financial shock (Table 4):
  - Opt. Taylor rule (OTR): Inflation = 1.1; Output gap = -; Credit gr. = -
  - OTR with CG: Inflation = 1.1; Output gap = -; Credit gr. = 0.6
  - OTR + OMP: Inflation = 2.4; Output gap = -; Macropru. Credit gr. = 1.1
  - OTR with CG + OMP: Inflation = 1.7; Output gap = -; Credit gr. (monetary) = 0.1; Credit gr. (macropru.) = 0.9
- Key interpretations:
  - The optimized coefficient for credit growth in the macroprudential instrument is not zero (1.1) when macroprudential policy is present.
  - The optimized coefficient for credit growth in the Taylor rule is not zero either (0.6), but welfare gains relative to the optimal Taylor rule are smaller (0.03 in steady state consumption units).
  - When macroprudential instrument is in place, including nominal credit growth in the monetary policy rule has negligible welfare effects and the optimized monetary coefficient is close to zero.

### Welfare impacts and optimized coefficients: productivity shock
- Welfare losses in response to a 1% productivity shock (Table 5):
  - Taylor rule (TR): 0.2163
  - TR with credit growth (CG): 0.3302
  - TR + macroprudential policy (MP): 0.2411
- Optimized coefficients in response to a 1% productivity shock (Table 6):
  - Opt. Taylor rule (OTR): Inflation = 1.1; Output gap = -; Credit gr. = -
  - OTR with CG: Inflation = 1.1; Output gap = -; Credit gr. = 0
  - OTR + OMP: Inflation = 1.1; Output gap = -; Macropru. Credit gr. = 0
  - OTR with CG + OMP: Inflation = 1.1; Output gap = -; Credit gr. (monetary) = 0; Credit gr. (macropru.) = 0
- Key interpretations:
  - Under a productivity shock, responding to financial market developments through the policy rate increases welfare loss (TR with CG: 0.3302 versus TR: 0.2163). The coefficient on nominal credit growth in the Taylor rule optimizes to zero.
  - Macroprudential measures also increase welfare under the productivity shock, but welfare costs are 1/5 of the costs when the Taylor rule responds to credit growth (text summary).

### Robustness and policy design under shock uncertainty
- Policymakers face uncertainty about shock origin in real time. Systematic responses to financial market developments via monetary or macroprudential tools should be "robust"—minimizing costs of policy mistakes.
- In the model, delegating "lean against the wind" to macroprudential policy is either welfare-improving (under a financial shock) or less costly (under a productivity shock), yielding a policy combination more robust to shock uncertainty.
- Interest rate inertia coefficient used in reported results: $= 0:5 (footnote). Optimized coefficients and welfare evaluations slightly change with varying $, but main results remain valid.

### The role of the borrowing source
- Two channels make the source of borrowing (foreign versus domestic) crucial for policy desirability:
  - With foreign borrowing (foreign currency denomination), exchange rate depreciation reduces entrepreneurial net worth and amplifies the financial accelerator, worsening financial-sector impact and making monetary-policy-based financial stabilization require more aggressive and destabilizing responses.
  - When credit is solely external, borrowing cost is a function of the foreign interest rate, external finance premium, and regulation premium, so the domestic policy rate does not directly influence cost of credit—reducing effectiveness of monetary policy for financial stabilization relative to macroprudential tools.
- Welfare and optimized coefficients under a 1% financial shock by borrowing source (Table 7):
  - Foreign borrowing:
    - Welfare loss: Opt. Taylor Rule = -0.0321; Opt. MP Rule = -0.1098
    - Optimized coefficient of credit growth: Taylor Rule = 0.63; MP Rule = 1.14
  - Domestic borrowing:
    - Welfare loss: Opt. Taylor Rule = -0.0205; Opt. MP Rule = -0.0310
    - Optimized coefficient of credit growth: Taylor Rule = 0.47; MP Rule = 0.65
  - Domestic and Foreign borrowing:
    - Welfare loss: Opt. Taylor Rule = -0.0262; Opt. MP Rule = -0.0447
    - Optimized coefficient of credit growth: Taylor Rule = 0.51; MP Rule = 0.82
- Key interpretations:
  - Under foreign borrowing, using monetary policy to respond to financial market developments is much inferior (about 7 percent of steady state consumption difference) to using macroprudential policy.
  - The optimized macroprudential credit growth coefficient (1.14) exceeds the optimized monetary credit growth coefficient (0.63) under foreign borrowing.
  - When borrowing is only domestic, responding via policy rate or macroprudential instrument is nearly indifferentiable in welfare terms; optimized credit-growth coefficients in both instruments are very close.
  - Welfare gains from both policies are smaller under domestic borrowing because the shock’s impact on the financial sector and overall economy is smaller.

### Conclusions and policy implications
- Main conclusions:
  - Following a financial shock, leaning against the wind via either policy rate or macroprudential measures helps macroeconomic and financial stability; macroprudential policy performs quantitatively better.
  - When macroprudential measures are present, welfare gains from adding credit growth to the traditional monetary policy rule are negligible.
  - Under a productivity shock, responding to financial market developments via monetary policy is more costly than using macroprudential policies.
  - Using monetary and macroprudential policies to pursue separate objectives—monetary stability and financial stability—yields a policy mix more robust to shock origin uncertainty.
  - In economies with sizable foreign borrowing, a separate macroprudential instrument is even more desirable because monetary policy cannot directly influence foreign borrowing costs and would otherwise require large policy rate changes that raise macroeconomic and financial volatility.
- Model caveat and future research:
  - The analysis assumes a fully flexible exchange rate and excludes exchange rate interventions from the policy toolkit. The authors note that examining exchange rate interventions alongside monetary and macroprudential policies is an important extension for future work.

*Source: _wp14112 - 5.1  Optimal monetary versus macroprudential policy rules*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2014/_wp14112.pdf_