## _wp16138 - References

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### Introduction: purpose, model features, and main results
- Purpose:
  - Study the effects of fiscal policy in an environment with financial frictions both within country and across borders, using a small-open-economy extension of the Del Negro, Eggertsson, Ferrero and Kiyotaki (2011) model (DEFK).
- Key model features:
  - Two types of financial assets: government bonds (liquid) and private equity (partially liquid due to a resaleability constraint).
  - Representative household split into entrepreneurs (invest in physical capital) and workers (earn labour income).
  - Entrepreneurs face two liquidity constraints: a borrowing constraint and a resaleability constraint on equity holdings.
  - Government spending introduced to DEFK framework; small-open-economy extension (SOE-DEFK) incorporates features from Leeper, Traum and Walker (2011) and small-open-economy assumptions from Gali and Monacelli (2005).
  - International asset markets incomplete; home savers have access to foreign government bonds denominated in foreign currency.
  - Trading of foreign bonds incurs a debt-elastic risk premium, denoted by the parameter η (theta in source), a function of the home country's net foreign asset position b_F_t.
- Main quantitative findings:
  - In the SOE-DEFK model, the long-term fiscal multiplier in the small open economy is as large as 1.6 if international capital mobility is imperfect (where the debt-elastic risk premium is high).
  - If capital can flow freely across borders, the fiscal multiplier is smaller than unity in the SOE-DEFK model.
  - In a standard open-economy DSGE model without liquidity frictions, the fiscal multiplier is small regardless of the degree of capital mobility.
- Mechanism behind large multipliers:
  - Government bonds are more liquid than private equity; fiscal expansion financed by issuing government bonds increases liquidity in private-sector wealth.
  - Increased liquidity allows entrepreneurs to increase investment in physical capital, crowding-in private investment and consumption and producing a large fiscal multiplier in the presence of liquidity constraints.
  - Under perfect international capital mobility, higher domestic real interest rates after fiscal expansion induce savers to borrow abroad to buy domestic government bonds, leading to a buildup of foreign debt in private-sector wealth and reducing liquidity available to entrepreneurs, thereby lowering the multiplier.
  - With imperfect international capital mobility (high η), private sector accumulates fewer foreign debts after fiscal expansion, leaving more domestic liquidity and producing multipliers similar to a closed economy.
- Additional behavioral results:
  - In the SOE-DEFK model, consumption increases and the real exchange rate depreciates over the long run in response to a fiscal expansion—responses more consistent with empirical SVAR evidence.
- Crisis-time result:
  - In a liquidity crisis, the nominal interest rate is bound at zero for longer when the small open economy has imperfect access to foreign capital markets.
  - Fiscal policy is more effective at the zero lower bound, so the fiscal multiplier is even larger in crisis times than in normal times in the SOE-DEFK model.
- Robustness:
  - Results are robust to changes in (i) the degree of trade openness in the goods market, (ii) the trade elasticity of substitution, and (iii) the pricing assumption for exporting firms.

### II. Model overview (SOE-DEFK) and international friction
- Structure and assumptions:
  - SOE-DEFK is a small-open-economy version of DEFK where government bonds are liquid and private equity is illiquid.
  - Each period, a random portion of households become entrepreneurs with profitable investment opportunities subject to borrowing and resaleability constraints.
  - A tightening of the resaleability constraint on private equity can cause the nominal interest rate to fall to its zero lower bound, modeling a liquidity crisis.
  - Open-economy features include differentiated intermediate goods trade, home bias in preferences, final-goods bundling of home and imported intermediates, government consumes only domestically produced goods, nominal rigidities from staggered price- and wage-setting, and exporting firms adopting local currency pricing.
  - Government spending is exogenous (AR(1)); nominal interest rate follows a Taylor (1993) rule; home economy is small relative to the world.
- International asset market friction:
  - Trading foreign government bonds incurs a debt-elastic risk premium proportional to b_F_t, with parameter η > 0 measuring elasticity.
  - If b_F_t >0 (net creditor), households receive a rate lower than the international risk-free rate; if b_F_t <0 (net debtor), households pay a premium.
  - A larger η implies higher premium for a given b_F_t, interpreted as less access to foreign capital markets.
  - Domestic and foreign government bonds are assumed default risk-free; the premium reflects intermediary costs and taxes associated with trading foreign bonds, not default risk.

### II.B Simulation of shocks: definitions and shock processes
- Government spending shock:
  - Measured as a percentage of GDP.
  - Process: b_G_t = rho_G b_G_{t-1} + e_G_t, where b_G_t ≡ ln(G_t/Ḡ).
  - Normal times: fiscal policy shocks are the only source of disturbance; liquidity frictions remain present.
- Liquidity crisis shock:
  - Modeled as a large drop in the equity resaleability parameter ε_t.
  - Evolution: b_epsilon_t = e_epsilon_t < 0 where b_epsilon_t ≡ ln(ε_t/ε̄).
  - Deterministic-exit assumption: b_epsilon_t stays constant and below steady state for a deterministic number of periods; agents have perfect foresight about duration and expect no subsequent shocks.
  - Deterministic exit provides a lower-bound estimate of the fiscal multiplier for a given expected duration of the liquidity crisis.

### Methodology and multiplier definitions (Appendix)
- Cumulative fiscal multiplier definition:
  - Et 1 Σt=0 dYt / Et 1 Σt=0 dGt.
- Shock exercise:
  - Introduce a government spending shock of 1% of GDP at steady state.
- Models compared:
  - SOE-DEFK model (with liquidity constraints).
  - "Standard model" (small-open-economy DSGE model without liquidity-constraint features); φ adjusted to 0.9915 in the standard model to match steady-state interest rates.
- Scenarios analyzed:
  - (i) Small open economy under perfect international capital mobility (η = 0).
  - (ii) Small open economy with imperfect access to international capital markets (η = 0.1).
  - (iii) Closed economy (no access to international capital markets).

### Key quantitative results — cumulative fiscal multipliers (normal times)
- Standard model:
  - Closed economy: 0.7
  - Small open economy: around 0.6
- SOE-DEFK model:
  - Closed economy: 1.7
  - Small open economy, η = 0: 0.9
  - Small open economy, η = 0.25: 1.6
- UK-specific illustrative calculation:
  - If the UK’s risk premium parameter η is at the lower end of Adolfson et al. (2007)'s estimate (range between 0.131 and 0.145), the SOE-DEFK model predicts the UK's government spending multiplier to be as large as 1.5.

### Role of the risk premium parameter (η) and mechanism
- Higher η implies less access to international capital markets.
- In the standard model, multiplier values are largely insensitive to η.
- In the SOE-DEFK model:
  - η = 0 → multiplier = 0.9.
  - η = 0.25 → multiplier ≈ 1.6, close to the closed-economy value of 1.7.
- Mechanism summary:
  - Fiscal expansion financed mainly by public debt; higher interest rates and expected future taxes induce households to increase government bond holdings.
  - Government bonds are more liquid than private equity; liquid wealth enables entrepreneurs to finance investment by selling bonds.
  - Result: crowding-in of investment and consumption over the long run and a hump-shaped persistent investment response, producing larger cumulative multipliers.

### Comparative dynamics: consumption, investment, and real exchange rate
- SOE-DEFK with perfect international capital mobility (η = 0):
  - Government spending multiplier = 0.9.
  - Initial consumption fall upon impact = 0.2%.
  - Closed-economy initial consumption fall upon impact = 0.4%.
  - Mechanism: households borrow abroad to acquire domestic government bonds, creating large foreign debts that reduce future liquidity.
- SOE-DEFK with η = 0.1:
  - Initial consumption fall upon impact = 0.33%.
  - Investment remains above steady state even after 25 periods.
  - Cumulative government spending multiplier = 1.5 (vs. 0.9 under frictionless international capital markets).
- Real exchange rate behavior:
  - Upon a positive government spending shock, real interest rate rises and real exchange rate initially appreciates (s_t falls), causing imports to rise and exports to fall.
  - Over the long run, the real exchange rate depreciates (s_t rises); depreciation is larger with frictions (η>0) and persistent even when η = 0 due to domestic financial frictions.
  - Long-run real depreciation reduces relative wealth of the small open economy, dampening crowding-in effects relative to the closed-economy case; nonetheless, at η = 0.1 the cumulative fiscal multiplier on private consumption is still positive and the multiplier on overall output remains almost as large as in the closed-economy case.

### Sensitivity analysis of open-economy parameters (Table 1 results)
- Exercise: vary degree of trade openness (ψ) and elasticity of substitution (κ), and consider law of one price for exporters; report cumulative multipliers for η = 0 and η = 0.1.
- Table 1 — Government spending multiplier in the SOE-DEFK model in normal times: sensitivity analysis
  - ψ = 0.2: η = 0 → 1.04 ; η = 0.1 → 1.53
  - ψ = 0.34 (baseline): η = 0 → 0.90 ; η = 0.1 → 1.50
  - ψ = 0.5: η = 0 → 0.79 ; η = 0.1 → 1.48
  - κ = 0.7: η = 0 → 0.99 ; η = 0.1 → 1.52
  - κ = 1 (baseline): η = 0 → 0.90 ; η = 0.1 → 1.50
  - κ = 2: η = 0 → 0.74 ; η = 0 → 1.48
  - Law of one price: η = 0 → 0.78 ; η = 0.1 → 1.42
- Interpretation:
  - Greater trade openness (higher ψ) slightly reduces the multiplier when η = 0 because initial real exchange rate appreciation worsens trade balance and net foreign assets.
  - When η = 0.1 the effect of changing ψ is smaller because changing net foreign asset positions is more costly.
  - Changes in κ have modest effects; law of one price reduces the multiplier somewhat because export prices (in foreign currency) are more flexible and export demand is depressed more quickly.

### Fiscal multipliers in crisis times (liquidity crisis / ZLB)
- Crisis setup:
  - Simulate a liquidity crisis expected to last for 5 years by imposing a negative shock to the resaleability constraint parameter ε_t and a government spending shock of 1% of GDP at t = 1.
  - Cumulative crisis-times multiplier defined as Et 1 Σ_t=0 (dY_t − dȲ_t) / Et 1 Σ_t=0 dG_t, where dY_t = change in output due to combined liquidity and government spending shocks, and dȲ_t = change due to liquidity shock alone.
- Crisis-time multipliers (summary):
  - Normal-times multiplier under η = 0: 0.9.
  - In a five-year crisis:
    - η = 0 → multiplier in crisis = 0.9 (same as normal times).
    - η = 0.2 → multiplier increases from 1.58 (normal times) to 1.91 (five-year liquidity crisis), approaching closed-economy crisis multiplier of 1.93.
- ZLB and duration:
  - Liquidity shock causes ZLB to bind only if η > 0.
  - Fiscal policy is more effective at the ZLB; crisis-time multipliers increase only when η > 0.
- IRF mechanisms across regimes:
  - Closed economy in crisis:
    - Investment falls by almost 10% upon impact.
    - Large falls in labor hours, output, consumption; severe deflation.
    - Central bank cuts nominal interest rate to zero; deflation raises real interest rate, discouraging consumption.
    - Fiscal expansion creates inflationary pressure at ZLB, reducing real interest rate and promoting consumption — larger fiscal multiplier in crisis.
  - SOE with perfect capital mobility (η = 0) in crisis:
    - Investment falls substantially, but savers switch to foreign government bonds; large capital outflow leads to real exchange rate depreciation, stimulating exports and alleviating recession.
    - Post-shock fall in output ≈ −3% (about one third of closed-economy fall of −10%).
    - Inflation does not go too negative; real interest rate remains below steady state; ZLB does not bind.
    - Fiscal multiplier in crisis = same as in normal times = 0.9.
  - SOE with imperfect capital mobility (η = 0.1) in crisis:
    - Savers less willing to switch to foreign bonds; no large capital outflow; real exchange rate does not depreciate.
    - Output fall comparable to closed economy; deflation and ZLB bind.
    - ZLB binds longer than in closed economy.
    - Fiscal multiplier increases from 1.5 in normal times to 1.8 in crisis times.
- Policy implication:
  - Fiscal policy can be highly effective in a liquidity crisis if the small open economy has imperfect access to foreign capital markets (higher η), because limited capital mobility prolongs the ZLB and increases the potency of fiscal stimulus.
  - Empirical context: global liquidity crises can reduce capital mobility (e.g., international capital flows fell sharply during the 2008 financial crisis), making fiscal stimulus more effective in crisis periods.

### Summary and paper-level conclusions
- Extension: liquidity-constrained DEFK model extended to a small-open-economy framework with financial frictions at both domestic and international levels.
- Normal times:
  - With perfect international capital mobility (η = 0), SOE fiscal multiplier < 1 even with domestic liquidity frictions.
  - With imperfect international capital mobility, multiplier increases markedly and can be almost as large as closed-economy value (1.7 reported).
  - Key insight: when foreign funds are not fully accessible, liquidity created by domestic fiscal expansion is more valuable, strengthening fiscal policy effectiveness.
- Crisis times:
  - Liquidity shock plus fiscal expansion: if access to foreign capital markets is imperfect (higher η), the nominal interest rate is more likely to be bound at zero for longer, and fiscal multipliers become larger than in normal times.
- Overall conclusion:
  - The fiscal multiplier is larger when financial frictions exist at both domestic and international levels; this result is strengthened during financial crises.

*Source: _wp16138 - References (text extract from the linked PDF).*

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

### _wp16138 - References

### Figures and Table Inventory
- Figures listed:
  - 1. Government Spending Multiplier in Normal Times Under Different Values of the Risk Premium Parameter: SOE-DEFK Model vs. The Standard Model
  - 2. IRFs to A Government Spending Shock in Normal Times: SOE-DEFK Model
  - 3. IRFs to A Government Spending Shock in Normal Times: SOE-DEFK Model
  - 4. IRFs to A Government Spending Shock in Normal Times: Standard Model
  - 5. IRFs to A Government Spending Shock in Normal Times: Standard Model
  - 6. Government Spending Multiplier and The Duration of ZLB in a 5-Year Liquidity Crisis in the SOE-DEFK Model
  - 7. IRFs to a Government Spending Shock in a 5-Year Liquidity Crisis: SOE-DEFK Model
  - 8. IRFs to a Government Spending Shock in a 5-Year Liquidity Crisis: SOE-DEFK Model
- Table listed:
  - 1. Government Spending Multiplier in the SOE-DEFK Model in Normal Times: Sensitivity Analysis

### Introduction: purpose, model features, and main results
- Purpose:
  - Study the effects of fiscal policy in an environment with financial frictions both within country and across borders, using a small-open-economy extension of the Del Negro, Eggertsson, Ferrero and Kiyotaki (2011) model (DEFK).
- Key model features:
  - Two types of financial assets: government bonds (liquid) and private equity (partially liquid due to a resaleability constraint).
  - Representative household split into entrepreneurs (invest in physical capital) and workers (earn labour income).
  - Entrepreneurs face two liquidity constraints: a borrowing constraint and a resaleability constraint on equity holdings.
  - Government spending introduced to DEFK framework; small-open-economy extension (SOE-DEFK) incorporates features from Leeper, Traum and Walker (2011) and small-open-economy assumptions from Gali and Monacelli (2005).
  - International asset markets incomplete; home savers have access to foreign government bonds denominated in foreign currency.
  - Trading of foreign bonds incurs a debt-elastic risk premium, denoted by the parameter theta ( in source), a function of the home country's net foreign asset position b_F_t.
- Main quantitative findings:
  - In the SOE-DEFK model, the long-term fiscal multiplier in the small open economy is as large as 1.6 if international capital mobility is imperfect (where the debt-elastic risk premium is high).
  - If capital can flow freely across borders, the fiscal multiplier is smaller than unity in the SOE-DEFK model.
  - In a standard open-economy DSGE model without liquidity frictions, the fiscal multiplier is small regardless of the degree of capital mobility.
- Mechanism behind large multipliers:
  - Government bonds are more liquid than private equity; fiscal expansion financed by issuing government bonds increases liquidity in private-sector wealth.
  - Increased liquidity allows entrepreneurs to increase investment in physical capital, crowding-in private investment and consumption and producing a large fiscal multiplier in the presence of liquidity constraints.
  - Under perfect international capital mobility, higher domestic real interest rates after fiscal expansion induce savers to borrow abroad to buy domestic government bonds, leading to a buildup of foreign debt in private-sector wealth and reducing liquidity available to entrepreneurs, thereby lowering the multiplier.
  - With imperfect international capital mobility (high theta), private sector accumulates fewer foreign debts after fiscal expansion, leaving more domestic liquidity and producing multipliers similar to a closed economy.
- Additional behavioral results:
  - In the SOE-DEFK model, consumption increases and the real exchange rate depreciates over the long run in response to a fiscal expansion—responses more consistent with empirical SVAR evidence (cited examples: Monacelli and Perotti (2006); Ravn, Schmitt-Grohe and Uribe (2012)).
- Crisis-time result:
  - In a liquidity crisis, the nominal interest rate is bound at zero for longer when the small open economy has imperfect access to foreign capital markets.
  - Fiscal policy is more effective at the zero lower bound, so the fiscal multiplier is even larger in crisis times than in normal times in the SOE-DEFK model.
- Robustness:
  - Results are robust to changes in (i) the degree of trade openness in the goods market, (ii) the trade elasticity of substitution, and (iii) the pricing assumption for exporting firms.

### II. Model Overview (SOE-DEFK)
- Structure and assumptions:
  - SOE-DEFK is a small-open-economy version of DEFK where government bonds are liquid and private equity is illiquid.
  - Each period, a random portion of households become entrepreneurs with profitable investment opportunities subject to borrowing and resaleability constraints.
  - A tightening of the resaleability constraint on private equity can cause the nominal interest rate to fall to its zero lower bound, modeling a liquidity crisis.
  - Open-economy features:
    - Home economy trades differentiated intermediate goods with the rest of the world; home bias in consumer preferences.
    - Final-goods firms bundle home-produced and imported intermediate goods for consumption and investment.
    - Government consumes only domestically produced goods.
    - Nominal rigidities arise from staggered price- and wage-setting by intermediate-goods firms and labour unions.
    - Exporting firms adopt local currency pricing.
  - Policy rules:
    - Government spending is exogenous and follows an AR(1) process.
    - Nominal interest rate follows a Taylor (1993) rule.
  - World representation:
    - Home economy is small relative to the world and does not influence foreign variables; the rest of the world is modeled as one large economy.
- International asset market friction:
  - Trading foreign government bonds incurs a debt-elastic risk premium bF_t -> premium  bF_t, with parameter  >0 measuring elasticity (theta in source).
  - If b_F_t >0 (net creditor), households receive a rate lower than the international risk-free rate; if b_F_t <0 (net debtor), households pay a premium.
  - A larger  implies higher premium for a given b_F_t, interpreted as less access to foreign capital markets.
  - Domestic and foreign government bonds are assumed default risk-free; the premium reflects intermediary costs and taxes associated with trading foreign bonds, not default risk.

### II.B Simulation of Shocks: definitions and shock processes
- Government spending shock:
  - Measured as a percentage of GDP.
  - Follows an AR(1) process: b_G_t = rho_G b_G_{t-1} + e_G_t, where b_G_t ≡ ln(G_t/Ḡ) and rho_G is the persistence parameter.
  - Normal times: fiscal policy shocks are the only source of disturbance; liquidity frictions (borrowing and resaleability constraints) remain present.
- Liquidity crisis shock:
  - Modeled as a large drop in the equity resaleability parameter epsilon_t.
  - Evolution: b_epsilon_t = e_epsilon_t < 0 where b_epsilon_t ≡ ln(epsilon_t/epsilon̄).
  - Unlike DEFK's two-state Markov process, the author assumes b_epsilon_t stays constant and below steady state for a deterministic number of periods (deterministic exit).
  - Agents have perfect foresight about the deterministic duration of the liquidity crisis and expect no subsequent shocks.
  - Deterministic-exit assumption provides a lower-bound estimate of the fiscal multiplier for a given expected duration of the liquidity crisis.
- Literature note:
  - Carlstrom, Fuerst and Paustian (2014) find the fiscal multiplier can be unboundedly large with a stochastic exit from a liquidity-trap crisis; deterministic-exit avoids that stochastic inflation of the multiplier.

### III. The Fiscal Multiplier in a Small Open Economy (beginning)
- Calibration:
  - The SOE-DEFK model is calibrated to the UK economy as described in the Online Appendix.

*Source: _wp16138 - References (text extract from the linked PDF).*

### Appendix and use it to study the scal multiplier in a liquidity constrained envi-

### _wp16138 - Appendix and use it to study the scal multiplier in a liquidity constrained environment

### Methodology and definitions
- Focus: the cumulative fiscal multiplier, defined as Et 1 Σt=0 dYt / Et 1 Σt=0 dGt.
- Shock: introduce a government spending shock of 1% of GDP to the system at steady state.
- Models used:
  - SOE-DEFK model (small-open-economy model with liquidity constraints).
  - "Standard model" (small-open-economy DSGE model without liquidity-constraint features).
- Calibration note: in the standard model, parameter  (phi) is adjusted to 0.9915 to keep steady-state interest rates in line with those in the SOE-DEFK model.

### Scenarios analyzed
- (i) Small open economy under perfect international capital mobility (η = 0).
- (ii) Small open economy with imperfect access to international capital markets (η = 0.1).
- (iii) Closed economy (no access to international capital markets).

### Key quantitative results — cumulative fiscal multipliers (normal times)
- Standard model:
  - Closed economy: 0.7
  - Small open economy: around 0.6 (does not change much with η)
- SOE-DEFK model:
  - Closed economy: 1.7
  - Small open economy, η = 0: 0.9
  - Small open economy, η = 0.25: 1.6
- UK-specific illustrative calculation:
  - If the UK’s risk premium parameter η is at the lower end of Adolfson et al. (2007)'s estimate (range between 0.131 and 0.145), the SOE-DEFK model predicts the UK's government spending multiplier to be as large as 1.5.

### Role of the risk premium parameter (η)
- Higher η implies less access by the small open economy to international capital markets.
- In the standard model, multiplier values are largely insensitive to η.
- In the SOE-DEFK model, the multiplier increases quickly as η becomes larger:
  - Perfect capital mobility (η = 0) → multiplier = 0.9.
  - Larger η (e.g., η = 0.25) → multiplier ≈ 1.6, close to the closed-economy value of 1.7.
- Interpretation: fiscal policy is more effective in boosting output when access to international capital markets is limited and cross-border capital flows are costly.

### Mechanism driving the larger multipliers in SOE-DEFK
- In SOE-DEFK, a government spending expansion is financed mainly by public debt because tax adjustments are slow.
- Higher interest rates and expected future taxes cause households to delay consumption and increase government bond holdings.
- Government bonds are more liquid than private equity, improving households' liquidity.
- When attractive investment opportunities arise, entrepreneurs sell liquid assets (government bonds) to finance new capital.
- Result: crowding-in effects on both investment and private consumption over the long run, producing hump-shaped and persistent increases in investment and a larger cumulative fiscal multiplier (e.g., 1.7 in a closed economy).

### Contrast with the standard model (no liquidity frictions)
- Government spending raises output and inflation, increasing real interest rates.
- Higher real interest rates crowd out private consumption and investment, producing a small multiplier.
- In an open-economy setting, higher domestic interest rates lead to real exchange rate appreciation (drop in s_t), reducing net exports and further lowering the multiplier relative to a closed economy.
- Degree of access to international capital markets (η) has little effect on impulse responses in the standard model.

### Implications
- A standard New Keynesian DSGE model without liquidity frictions suggests fiscal stimulus is ineffective in a small open economy regardless of access to foreign capital.
- Introducing liquidity frictions (SOE-DEFK) reverses this: fiscal expansion creates liquidity that can be used to finance investment, making fiscal policy substantially more effective when international capital mobility is limited (higher η).

*Source: _wp16138 - Appendix and use it to study the fiscal multiplier in a liquidity constrained environment*

### 2. The increase in investment has a knock-on eect on private consumption, which

### _wp16138 - 2. The increase in investment has a knock-on effect on private consumption, which

### Main comparative findings: closed economy vs small open economy (SOE)
- Closed-economy DEFK model: increase in investment produces a knock-on rise in private consumption a few quarters after the investment rise; overall increase in output is larger and much more persistent compared to the standard model.
- SOE-DEFK with perfect international capital mobility (= 0):
  - Government spending multiplier = 0.9.
  - Initial consumption fall upon impact = 0.2%.
  - Mechanism: households can borrow and lend at the international risk-free rate without premium, borrow from abroad to acquire domestic government bonds (negative net foreign asset position, b̄F_t), so the consumption fall is smaller than in the closed-economy case (closed-economy consumption fall upon impact = 0.4%), but borrowing creates large foreign debts that reduce future liquidity for investment, weakening investment persistence and the crowding-in effect on consumption.
- SOE-DEFK with a risk premium for trading foreign assets (= 0.1):
  - Initial consumption fall upon impact = 0.33%.
  - Real exchange rate appreciates by less upon impact (imports increase by less), households accumulate fewer foreign debts (less negative net foreign asset position), leaving entrepreneurs with more liquidity to invest.
  - Investment remains above steady state even after 25 periods from the shock (much more persistent).
  - Cumulative government spending multiplier = 1.5 (vs. 0.9 under frictionless international capital markets).
  - Key implication: fiscal policy is more powerful in promoting output growth when the economy faces difficulty borrowing from abroad.

### Real exchange rate behavior and empirical relevance
- SOE-DEFK model:
  - Upon a positive government spending shock, real interest rate rises and real exchange rate initially appreciates (s_t falls), causing imports to rise and exports to fall.
  - Over the long run, as government spending and interest rates return to steady state, the real exchange rate depreciates (s_t rises).
  - Magnitude of long-run depreciation depends on degree of international capital mobility; depreciation is larger with frictions (>0).
  - Even when = 0, real exchange rate still depreciates in the long run due to domestic financial frictions (depreciation is milder but very persistent).
- Consistency with empirical evidence:
  - The real depreciation predicted by the SOE-DEFK model aligns with SVAR evidence cited (Monacelli and Perotti (2006); Ravn, Schmitt-Grohe and Uribe (2012)) that real exchange rate depreciates in response to government spending rises.
- Wealth effect:
  - Long-run real depreciation reduces relative wealth of the small open economy, dampening crowding-in effects on private consumption and investment relative to closed-economy case.
  - Nonetheless, at = 0.1 the cumulative fiscal multiplier on private consumption is still positive, and the multiplier on overall output remains almost as large as in the closed-economy case.

### Sensitivity analysis of open-economy parameters (Table 1 results)
- Exercise overview:
  - Vary degree of trade openness () from baseline 0.34 to 0.2 and 0.5.
  - Vary elasticity of substitution between home-produced and foreign goods () from baseline 1 to 0.7 and 2.
  - Consider law of one price alternative for exporters.
  - Reported multipliers are cumulative government spending multipliers under two cases: (i) = 0; (ii) = 0.1.
- Table 1 — Government spending multiplier in the SOE-DEFK model in normal times: sensitivity analysis
  -  = 0.2: = 0 → 1.04 ; = 0.1 → 1.53
  -  = 0.34 (baseline): = 0 → 0.90 ; = 0.1 → 1.50
  -  = 0.5: = 0 → 0.79 ; = 0.1 → 1.48
  -  = 0.7: = 0 → 0.99 ; = 0.1 → 1.52
  -  = 1 (baseline): = 0 → 0.90 ; = 0.1 → 1.50
  -  = 2: = 0 → 0.74 ; = 0.1 → 1.48
  - Law of one price: = 0 → 0.78 ; = 0.1 → 1.42
- Interpretation:
  - As  increases (less home bias / more trade openness), the multiplier decreases slightly because a larger initial real exchange rate appreciation worsens the trade balance and net foreign assets, reducing domestic liquidity and crowding-in less consumption and investment.
  - The impact of changing  is smaller when = 0.1 because it is more expensive to change the net foreign asset position.
  - Lower trade elasticity (= 0.7) raises the multiplier slightly when = 0 due to less severe drop in net exports when the real exchange rate appreciates; when = 0.1 the opposing effects of larger long-run depreciation and reduced relative wealth roughly offset, leaving the multiplier fairly constant.
  - Under the law of one price, the multiplier decreases somewhat for both = 0 and = 0.1 because export prices (denominated in foreign currency) are more flexible and export demand is depressed more quickly following domestic fiscal expansion.
- Conclusion from sensitivity analysis: fiscal multiplier in SOE-DEFK with frictional international capital markets remains much larger than under frictionless capital markets.

### Fiscal multipliers in times of crisis (liquidity crisis / ZLB)
- Crisis setup:
  - Simulate a liquidity crisis expected to last for 5 years by imposing a negative shock to the resaleability constraint parameter (_t) and a government spending shock of 1% of GDP (fiscal stimulus assumed at t = 1, same quarter as liquidity shock).
  - Cumulative crisis-times multiplier defined as Et 1 Σ_t=0 (dY_t − dȲ_t) / Et 1 Σ_t=0 dG_t, where dY_t = change in output due to combined liquidity and government spending shocks, and dȲ_t = change due to liquidity shock alone.
- Crisis-time multipliers (summary):
  - Normal-times multiplier under = 0: 0.9.
  - In a five-year crisis:
    - When = 0, multiplier in crisis = 0.9 (same as normal times).
    - As  increases (more frictions), multiplier in crisis becomes much larger than in normal times.
    - Example: = 0.2 → multiplier increases from 1.58 (normal times) to 1.91 (five-year liquidity crisis), approaching closed-economy crisis multiplier of 1.93.
- Duration of zero nominal interest rate (ZLB) and its role:
  - Liquidity shock causes ZLB to bind only if > 0 (frictions in international capital markets).
  - Fiscal policy is more effective in boosting output at the ZLB; hence crisis-time multipliers increase only when > 0.
- IRF mechanisms across regimes:
  - Closed economy in crisis:
    - Investment falls by almost 10% upon impact.
    - Large falls in labor hours, output, consumption; severe deflation.
    - Central bank cuts nominal interest rate to zero; deflation raises real interest rate, further discouraging consumption.
    - Fiscal expansion creates inflationary pressure at ZLB, reducing real interest rate and promoting consumption — larger fiscal multiplier in crisis.
  - SOE with perfect capital mobility (= 0) in crisis:
    - Investment falls substantially, but savers switch to foreign government bonds when domestic returns fall.
    - Large capital outflow leads to real exchange rate depreciation, stimulating exports and alleviating recession.
    - Post-shock fall in output ≈ −3% (about one third of closed-economy fall of −10%).
    - Inflation does not go too negative; real interest rate remains below steady state; ZLB does not bind.
    - Fiscal multiplier in crisis = same as in normal times = 0.9.
  - SOE with imperfect capital mobility (= 0.1) in crisis:
    - Savers less willing to switch to foreign bonds; no large capital outflow; real exchange rate does not depreciate.
    - Output fall comparable to closed economy; deflation and ZLB bind.
    - ZLB binds longer than in closed economy.
    - Fiscal multiplier increases from 1.5 in normal times to 1.8 in crisis times.
- Policy implication:
  - Fiscal policy can be highly effective in a liquidity crisis if the small open economy has imperfect access to foreign capital markets (higher ), because limited capital mobility prolongs the ZLB and increases the potency of fiscal stimulus.
  - Empirical context: global liquidity crises can reduce capital mobility (e.g., international capital flows fell sharply during the 2008 financial crisis), making fiscal stimulus more effective in crisis periods.

### Summary and conclusions (paper-level)
- Extension: liquidity-constrained DEFK (Del Negro et al. (2011)) model extended to a small-open-economy framework with financial frictions at both country and international levels.
- Normal times:
  - With perfect international capital mobility (= 0), SOE fiscal multiplier < 1 even with domestic liquidity frictions.
  - With imperfect international capital mobility, multiplier increases markedly and can be almost as large as closed-economy value (1.7 reported in text).
  - Key insight: when foreign funds are not fully accessible, liquidity created by domestic fiscal expansion is more valuable, strengthening fiscal policy effectiveness.
- Crisis times:
  - Liquidity shock plus fiscal expansion: if access to foreign capital markets is imperfect (higher ), the nominal interest rate is more likely to be bound at zero for longer, and fiscal multipliers become larger than in normal times.
  - Overall conclusion: the fiscal multiplier is larger when financial frictions exist at both domestic and international levels; this result is strengthened during financial crises.

*Source: _wp16138 - 2. The increase in investment has a knock-on effect on private consumption, which (IMF PDF).*

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*From: _wp16138 - References*

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