## wp17123 - Part VII concludes.

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### II. EXPENDITURES IN THE CLOSED ECONOMY
- Model components (closed economy):
  - Consumption: tC described by a Keynesian consumption function with marginal propensity to consume CYa, 01CYa. (Equation (1a))
  - Taxes: ttYT with tax revenue tt TP0 (tax rate  plus lump-sum tax policy tTP). (Equations (2), (1b))
  - Investment: 0tI Ir a a r with 0Ir a . (Equation (3))
  - Government spending: 0tG a tGP (government policy shock tGP). (Equation (4))
- National income identity (closed): Closedt t t tY C I G   . (Equation (4))

A. Consumption: deeper interpretation and rescaling
- Permanent / transitory decomposition:
  - Introduce potential output PY and add/subtract PY to separate permanent and cyclical tax components; cyclical tax term: ( )P t tY Y . (Equation (5))
- Deeper parameters:
  - Long-run pre-tax savings rate: ; short-run (cyclical) pre-tax savings rate: cyc.
  - Long-run average propensity to consume (pre-tax): (1 ) .
  - Short-run marginal propensity to consume (pre-tax): (1 )cyc .
- Reinterpretation of consumption coefficients:
  - CYa = (1 )cyc .
  - 0Ca has deeper form *[(1 ) (1 )](1 )P C cyc      (see Equations (6a), (6b) and surrounding text).
  - Under strict PIH: cyc = 1.
  - Under liquidity-constrained/hand-to-mouth behavior: 01cyc .
  - Continuum of Ricardian Equivalence views accommodated: for one-off tax change tTP, strict REH  (1 )cyc = 0.

B. Rescaling investment and government spending
- Neutral/steady-state real interest rate: r (marginal product of capital at steady state minus depreciation / subjective time preference).
- Investment: 0tI Ir a a r and reinterpret 0Ia in terms of potential output: 0I a = * (1 )PP YY    (steady-state investment ratio  corresponds to depreciation on steady-state capital stock). (Equations (7) and surrounding text)
- Government constant: 0P G aY .

C. Deriving the IS curve — rescaled approach
- Define output gap: /1 Ptt gap Y Y .
- Scale interest response: / P Ir Ir aY   . Fiscal shocks measured as percent of potential: / P tt tp TP Y and / P tt gp GP Y .
- IS curve in gap form (rescaled): Closed IS expressed as combination of:
  - long-run ratios summing to unity: [(1 )(1 ) + (1 ) +  = 1],
  - short-run components: (1 ){[(1 )( )] }cyc t t tp    , ()Ir t rr  , and t gp.
- Closed-economy IS curve solved for gap: (1 )cyc cyc       (so 1/ cyc is the Keynesian multiplier) and /0 Ir cyc    ensures IS negative slope. (Equations (8), (9))

### III. EQUILIBRIUM IN A CLOSED ECONOMY: CORE AND EXPENDITURE COMPONENTS
- Core New Keynesian system (closed):
  - IS curve (gap, interest rate).
  - Monetary policy (Taylor-type) reaction function: *()e DISC t Closed t gap t t i r gap r             (Equation (10))
  - Phillips curve: 1()e ttt gap ss       (Equation (11)), with 0 and supply shock tss (percent of potential).
- Expectation treatment: e exogenous for algebraic solution.
- RR schedule (equilibrium real rate consistent with Taylor rule + Phillips curve):
  - RR form: ,* ()e DISC t RR Closed RR RRgap t RRss t t r r b b gap b ss r         (Equation (13)) with RRb   and defined RRgap b , RRss b .
- Equilibrium output gap obtained by intersecting IS and RR: closed-economy eq gap expression given in (14). (Equation (14))

Example scenarios (Figures 1–2) — shocks and computed outcomes
- Scenario shocks (top of Figure 1):
  - base: Gov't Spending 0.0% ; Tax Measures (one-off) 0.0% ; Supply shock (% of YP) 0.0% ; Inflation expectations (gap w.r.t. target) 0.0% ; Deviation from Taylor Rule (shift) 0.0%.
  - alt(i): Gov't Spending 1.0% ; Tax Measures 0.0% ; Supply shock 0.0% ; Inflation expectations 0.0% ; Deviation from Taylor Rule 0.0%.
  - alt(ii): Gov't Spending 1.0% ; Tax Measures 0.0% ; Supply shock 0.0% ; Inflation expectations 0.0% ; Deviation from Taylor Rule -1.0%.
- Computed component contributions to equilibrium output gap (Figure 1):
  - base: (a) Inflation expectations component 0.0% ; (b) Supply shock component 0.0% ; (c) Fiscal component 0.0% ; (d) Discretionary monetary component 0.0% ; Output gap 0.0%.
  - alt(i): (a) 0.0% ; (b) 0.0% ; (c) 0.7% ; (d) 0.0% ; Output gap 0.7%.
  - alt(ii): (a) 0.0% ; (b) 0.0% ; (c) 0.7% ; (d) 0.4% ; Output gap 1.1%.
- Interpretation:
  - under alt(i) government spending multiplier (accounting for endogenous monetary response) = 0.7;
  - under alt(ii) monetary accommodation (DISCt r = -1.0 percent) adds 0.4 percent via movement along IS, total output gap 1.1 percent.

Closed-economy currency-unit results and demand decomposition (Figure 2 table)
- Levels:
  - Gross Domestic Product16.79 16.90 16.97
  - Consumption 11.21 11.24 11.26
  - Investment 3.06 2.97 3.03
  - Government Spending 2.52 2.69 2.69
- Demand side decomposition of output gap (percent of potential):
  - Output gap 0.0% 0.7% 1.1%
  - Consumption 0.0% 0.2% 0.3%
  - Investment 0.0% -0.5% -0.2%
  - Government Spending 0.0% 1.0% 1.0%
- Equilibrium core-variable results (Figure 2):
  - Output gap (a)-(b)+(c)+(d) 0.0% 0.7% 1.1%
  - Equilibrium inflation rate 3.0% 4.0% 4.6%
  - Equilibrium real interest rate 2.0% 2.8% 2.3%

Graphical interpretation
- alt(i): fiscal expansion shifts IS right; joint increase of output and real interest rate; inflation rises.
- alt(ii): same fiscal shock but monetary accommodation shifts RR; output higher than alt(i) and interest rate lower; inflation higher still.

### IV. THE SMALL OPEN ECONOMY: EXPORTS, IMPORTS, AND EXTERNAL FINANCIAL PRESSURES
- Open-economy output identity: Opent t t t t tY C I G X IM     . (Equation (15))

Exports
- Structure: *[ ]P t x t X Y x rpx    (Equation (16))
  - x determined by long-run external prices/productivity; 0x   ; rpx = percent deviation of relative price of exports RPXt from long-run norm.
  - Relative price of exports: * X tt t t SP RPX P    . (Equation (16) definition)
  - Baseline RPX normalized to unity; ln() tt rpx RPX  .

Imports
- Structure: *[ ]P t cyc t im t IM Y im im gap rpim       (Equation (17))
  - im determined by long-run external prices/productivity; cycim > 0 ; 0im   ; rpim = percent deviation of RPIM from long-run norm.
  - Relative price of imports: * IM tt t t SP RPIM P    . (Equation (17) definition)
  - Baseline RPIM normalized to unity; ln() tt rpim RPIM  .

External price level and real exchange rate
- External price level EXTt P defined as weighted average of export and import prices (weights  and 1-). (Equations (20), (21))
- Real exchange rate: * = EXT tt t t SP Q P    . (Equation (19))

Decomposition and external pressures
- Relative prices of exports and imports are functions of real exchange rate q and scaled terms-of-trade TT ( X IM t t tTT P P ). (Equations (22), (23))
- Natural rate: EXT r plus baseline risk premium rp: r = EXTr + rp.
- External financial pressures: [ ] t EXT EXT t t efp r rp r rp     .
- Real interest parity determining short-run q deviation: EXT t t t t q r rp r q     , 0 q  .
  - Domestic monetary tightening appreciates real exchange rate; external financial pressures depreciate real exchange rate.
- Exact decompositions (22ꞌ) and (23ꞌ): domestic monetary policy affects relative prices through q; external financial pressures and terms-of-trade affect them externally.

B. Open economy IS curve
- Substituting domestic and external functions into output identity yields open-economy IS (gap) with additional terms:
  - Compressed fiscal component: (1 ) t t cyc t fp gp tp     .
  - Compound parameters: nx x im      ; (1 ) nx x im         .
  - Terms-of-trade tTT appears as IS shift term; improvement in tTT shifts IS right. (Equation (24))

C. Monetary policy and inflation in the open economy
- Monetary policy reaction in open economy adds external financial pressures tefp:
  - *()e DISC t Open t gap t t t i r b b gap efp r            . (Equation (25))
  - tefp in reaction function implies central bank tracks world financial markets; in extreme cases raises interest rate to defend exchange rate.
- Open-economy Phillips curve includes pass-through of external financial pressures:
  - 1()e t Open t t gap ss efp         . (Equation (26))
  - Parameter  captures exchange rate pass-through of external financial pressures.
- Combining (25) and (26) yields open-economy RR (reduced-form real rate) with external financial pressures coefficient RRefp = [1 ]1 bb     .

D. Equilibrium in the open economy — core variables and trade balance
- Open-economy IS flipped to express real interest rate; combining with RR gives equilibrium gap (Equation (29)) with key term ()Ir nx    determining net effect of external financial tightening:
  - Ir  < 0 captures expenditure-reducing effect of external tightening.
  - nx  > 0 captures expenditure-switching (depreciation improves net exports).
  - Assumption: ()Ir nx    < 0 so net external financial tightening reduces output.
- Sign and economic interpretation:
  - Inflation expectations gap e* > 0 reduces output.
  - Favorable supply shock tss increases output.
  - Increases in domestic and foreign demand (tfp and ln() nx t TT  ) raise output.
  - External financial pressures have two opposing channels: central bank reaction reduces output; depreciation improves net exports — but central bank channel dominates.
- Equilibrium nominal rate: eqttr eqttri   .
- Equilibrium real exchange rate from parity: EXTeq eq t t t q r rp r q     .
- Equilibrium trade balance (percent of potential) as function of eq gap and eq q (conditional on tTT): (Equation (30))
  - ( ) [ *(1 ) ] ln( ) * eq eq eq t x im t x im t cyc t nx x im q TT im gap            

Open-economy scenario examples (Figures 4–6)
- Scenario shocks:
  - base: no shocks.
  - alt(i): export prices fall by 4 percent (terms-of-trade shock).
  - alt(ii): export prices fall by 4 percent and tefp = 4 percent (400 basis point increase in risk premium).
- Computed impacts on output gap (Figure 6 summary):
  - Terms-of-trade shock reduces output by 0.55 percent (alt(i)).
  - Adding adverse external financial pressures (alt(ii)) further reduces output by 0.98 percent.
- Inflation results (Figure 5 / text):
  - alt(i): equilibrium inflation falls from 3 percent target to 2.2 percent.
  - alt(ii): equilibrium inflation falls further; final quoted value in text: 1.2 percent.
- Graphical channel summaries:
  - Terms-of-trade shock shifts IS left; central bank reduces interest rate (movement along RR) softening impact; net exports deteriorate but real exchange rate depreciates.
  - External financial pressures depreciate currency (higher import prices) and shift Phillips curve up (exchange-rate pass-through), producing lower output and different inflation outcome depending on policy response.

### Net exports and capital outflow scenario (alt(ii) vs alt(i))
- Under alt(ii) higher real interest rates at home further squeeze demand so equilibrium output is even lower under alt(ii) than alt(i).
- Import compression under alt(ii) shifts the tan NX line to the right (from the dotted to the dashed line).
- The real exchange rate depreciates more under alt(ii) than alt(i). (Without the central bank’s defensive interest rate hike under alt(ii), the depreciation would have been even more severe.)
- Income and price effects together produce an improvement in the net export balance under alt(ii) relative to alt(i), but:
  - The net export improvement under alt(ii) should be interpreted as a forced adjustment — a capital outflow scenario accompanied by an even sharper reduction of output under alt(ii) than under alt(i).
- Demand-side burden of adjustment under a capital outflow scenario:
  - Investment: minus 1.4 percent of potential output
  - Consumption: minus 0.4 percent of potential output
  - These impacts are consistent with prior analyses: current account improves while domestic expenditures fall.

Key shock parameter values (Figure 4, shocks table)
- External financial pressures (alt(ii)):
  - Total external financial pressures: 4.0%
  - Risk premium -- dev. from baseline: 4.0%
- External Terms of Trade (alt(i) and alt(ii)):
  - TT log deviation from baseline: -4.0% (alt(i)), -4.0% (alt(ii))
  - Export price log dev: -4.0% (alt(i)), -4.0% (alt(ii))
  - Import price log dev: 0.0% (all scenarios)
- Calculation of equilibrium output gap — component by component:
  - External financial pressure component (e): 0.00% (base), 0.00% (alt(i)), -0.98% (alt(ii))
  - External terms of trade component (f): 0.00% (base), -0.55% (alt(i)), -0.55% (alt(ii))

Solutions for core variables, external sector, and expenditure components (Figure 6)
- Output gap (a)-(b)+(c)+(d)+(e)+(f): 0.0% (base), -0.5% (alt(i)), -1.5% (alt(ii))
- Equilibrium inflation rate: 3.0% (base), 2.2% (alt(i)), 1.2% (alt(ii))
- Equilibrium real interest rate: 2.0% (base), 1.3% (alt(i)), 4.3% (alt(ii))
- Real price of exports (deviation from norm): 0.0% (base), -3.2% (alt(i)), -2.2% (alt(ii))
- Real price of imports (deviation from norm): 0.0% (base), 0.8% (alt(i)), 1.8% (alt(ii))
- Real exchange rate (deviation from norm): 0.0% (base), 0.7% (alt(i)), 1.7% (alt(ii))
- Real exchange rate index (Base = 100): 100.0 (base), 100.7 (alt(i)), 101.7 (alt(ii))

Currency-unit results (levels)
- Gross Domestic Product: 18.33 (base), 18.23 (alt(i)), 18.05 (alt(ii))
- Consumption: 11.92 (base), 11.89 (alt(i)), 11.85 (alt(ii))
- Investment: 3.34 (base), 3.41 (alt(i)), 3.08 (alt(ii))
- Government Spending: 2.75 (all scenarios)
- Net Exports: 0.33 (base), 0.18 (alt(i)), 0.38 (alt(ii))
  - Exports: 1.45 (base), 1.21 (alt(i)), 1.29 (alt(ii))
  - Imports: 1.12 (base), 1.04 (alt(i)), 0.91 (alt(ii))

Ratios and gaps
- Net Exports / YP: 1.8% (base), 1.0% (alt(i)), 2.1% (alt(ii))
- Baseline Net Exports / YP: 1.8% (base), 1.8% (alt(i)), 1.8% (alt(ii))
- NX gap: 0.0% (base), 0.8% (alt(i)), -0.3% (alt(ii))

Demand-side decomposition of output gap (percent of potential)
- Output gap: 0.0% (base), -0.5% (alt(i)), -1.5% (alt(ii))
  - Consumption: 0.0% (base), -0.1% (alt(i)), -0.4% (alt(ii))
  - Investment: 0.0% (base), 0.4% (alt(i)), -1.4% (alt(ii))
  - Government Spending: 0.0% (all)
  - Net Exports: 0.0% (base), -0.8% (alt(i)), 0.3% (alt(ii))
    - Exports: 0.0% (base), -1.3% (alt(i)), -0.9% (alt(ii))
    - Imports: 0.0% (base), -0.5% (alt(i)), -1.2% (alt(ii))

### Monetary policy, the Expanded Marshall-Lerner (EML) condition, and net exports
- A discretionary monetary loosening (DISC_t r < 0) induces a depreciation of the real exchange rate (q rises).
- Narrow Marshall-Lerner intuition: (η_x - η_im) > 0 implies depreciation, ignoring other effects, causes the trade balance to improve.
- Expanded Marshall-Lerner (EML) condition extends the standard condition to include output-gap effects on imports:
  - A monetary loosening will cause the trade balance to improve if the price (real exchange rate) effect dominates the output-gap-induced import effect.
  - Graphical implications:
    - If EML holds: depreciation (upward movement along tan lines) dominates leftward shift of tan line from output-gap reduction → net exports increase (alt(i) left panel).
    - If EML fails: output-gap effect dominates → net exports decrease (alt(i) right panel).

### Long-run expenditure shares and microeconomic links
- Closed economy steady-state results (selected identities and implications):
  - Steady-state first-order condition equates gross after-tax marginal product of capital net of depreciation to subjective rate of time preference.
  - Steady-state capital, output, investment share, and consumption ratio are derived algebraically linking production parameters and preferences.
- Small open economy steady-state results:
  - Natural real interest rate is exogenous: EXT r = r + rp.
  - Steady-state capital stock and steady-state output expressed in terms of external real rate, productivities, prices, and tax/depreciation parameters.
  - Wage equalization across non-tradables and exports pins the allocation of labor:
    - Labor share to non-tradables (ω) determined by relative productivities and sector prices.
  - Steady-state shares of exports, government, private consumption derived from these primitives.
- Assumption in steady state: country receives constant external transfer SS Z which is minus one times net exports.

### Extensions: logarithms, growth rates, and elasticities
- Behavioral relationships can be written in growth-rate form with elasticity parameters.
- Consumption growth and investment growth approximations:
  - ln() approximations used to map level equations into growth rate/elasticity forms.
  - Short-run marginal propensity parameters reinterpreted as elasticities/semi-elasticities (examples shown for consumption and investment).

### Advantages of simpler static macroeconomic models (comparative notes)
- Traditional graphical exposition (IS, RR/LM, Phillips Curve) provides intuition via shifts.
- Impact multipliers and illustrative calculations available as “back-of-the-envelope” cross-checks for complex models (qualitative/illustrative).
- Expenditure-side equations connect to deeper macro issues (e.g., Solow, permanent income, Ricardian equivalence).
- Transparent depiction of open-economy relationships: domestic monetary policy, external financial tightening, and terms-of-trade effects are explicitly decomposed (e.g., equations (22′) and (23′)).
- Facilitates cross-checks of parameter values for mutual consistency (e.g., coherence between IS and Phillips Curve ensures consistent discretionary monetary policy effects).

### Key model implications and comparative-static results
- External financial outflow (a ‘sudden stop’ to external capital) will:
  - Result in a fall of domestic expenditures and output.
  - Result in a rise in net exports.
  - This outcome is reflected in equation (29).
  - Consistent with evidence in Calvo (1998) and Blanchard, Ostry, Ghosh, and Chamon (BOGC,2015).
- Domestic monetary tightening can both:
  - Appreciate the exchange rate.
  - Worsen the trade balance, under parameter combinations given by the expanded Marshall Lerner condition (see Part IV.E for details).

### Theoretical foundations for steady-state expenditure shares
- Long-run shares are linked to technology and tastes in a manner consistent with some real business cycle or ‘fresh water’ models (see Section V).
- Treatment of external prices (relative prices of exports and imports, real exchange rate, and terms of trade) in equations (22’) and (23’) is described as an improvement over most extant models.

### Model extensions and ongoing work
- Extensions to include forward-looking inflation and exchange rate expectations are discussed in Tanner (2017, forthcoming).
- Author is developing extensions including exchange rate management and sterilized intervention, following Benes, Berg, Portillo, and Vavra (2015).
- Overall assessment: ‘simple’ models can supplement and cross-check more sophisticated counterparts; attention to algebra linking different metrics can add considerable insight.

### Appendix: The ‘Macronia’ Model — Financial programming exercise
- The IMF ICD online course FPP2x includes a hypothetical case study “Macronia” similar to the paper’s open economy model.
- Real sector uses traditional ‘elasticities’ (Section VI); parameters calibrated to match section VI equations to assess vulnerabilities and design adjustment programs.
- Additional features added:
  - Output as a determinant of investment — an accelerator function. Investment equation rewritten (see (A1)–(A6) grouping).
  - Interest rate smoothing added to central bank’s interest rate rule in nominal terms.
    - Continuous smoothing parameter shown as 01   ( 0   implies no smoothing).
- Equilibrium real interest rate (Phillips curve substituted into Taylor rule) yields composite expressions (compact forms shown as (A1)–(A6)).
- Compound coefficients and error term definitions (verbatim strings preserved):
  - (1 RR RR bb   , (1) RRgapRRgap bb     , (1) RRssRRss bb     , (1 RRefp RRefp bb       are compound coefficients and
  - 1 () DISC DISC e t t t r r i r       is a compound error term that includes both the contemporaneous discretionary element and the smoothing component 1 () e t ir    .
- Adding the accelerator and interest-rate-smoothing elements yields an equilibrium output gap expression summarized in equation (A6).
- Examples and videos of the Macronia solution are available in the ICD FPP2x course (model explanation videos referenced).

*Source: Author’s calculations (wp17123 - Part VII concludes).*

### Part VII concludes.

### wp17123 - Part VII concludes.

### II. EXPENDITURES IN THE CLOSED ECONOMY
- Model components (closed economy):
  - Consumption: tC described by a Keynesian consumption function with marginal propensity to consume CYa, 01CYa. (Equation (1a))
  - Taxes: ttYT with tax revenue tt TP0 (tax rate  plus lump-sum tax policy tTP). (Equations (2), (1b))
  - Investment: 0tI Ir a a r with 0Ir a . (Equation (3))
  - Government spending: 0tG a tGP (government policy shock tGP). (Equation (4))
- National income identity (closed): Closedt t t tY C I G   . (Equation (4))

### A. Consumption: deeper interpretation and rescaling
- Permanent / transitory decomposition:
  - Introduce potential output PY and add/subtract PY to separate permanent and cyclical tax components; cyclical tax term: ( )P t tY Y . (Equation (5))
- Deeper parameters:
  - Long-run pre-tax savings rate: ; short-run (cyclical) pre-tax savings rate: cyc.
  - Long-run average propensity to consume (pre-tax): (1 ) .
  - Short-run marginal propensity to consume (pre-tax): (1 )cyc .
- Reinterpretation of consumption coefficients:
  - CYa = (1 )cyc .
  - 0Ca has deeper form *[(1 ) (1 )](1 )P C cyc      (see Equations (6a), (6b) and surrounding text).
  - Under strict PIH: cyc = 1. Under liquidity-constrained/hand-to-mouth behavior: 01cyc .  
  - Continuum of Ricardian Equivalence views accommodated: for one-off tax change tTP, strict REH  (1 )cyc = 0.

### B. Rescaling investment and government spending
- Neutral/steady-state real interest rate: r (marginal product of capital at steady state minus depreciation / subjective time preference).
- Rewriting investment: 0tI Ir a a r and reinterpret 0Ia in terms of potential output: 0I a = * (1 )PP YY    (steady-state investment ratio  corresponds to depreciation on steady-state capital stock). (Equations (7) and surrounding text)
- Government constant: 0P G aY .

### C. Deriving the IS curve — rescaled approach
- Define output gap: /1 Ptt gap Y Y .
- Scale interest response: / P Ir Ir aY   . Fiscal shocks measured as percent of potential: / P tt tp TP Y and / P tt gp GP Y .
- IS curve in gap form (rescaled): Closed IS expressed as combination of:
  - long-run ratios summing to unity: [(1 )(1 ) + (1 ) +  = 1],
  - short-run components: (1 ){[(1 )( )] }cyc t t tp    , ()Ir t rr  , and t gp.
- Closed-economy IS curve solved for gap: (1 )cyc cyc       (so 1/ cyc is the Keynesian multiplier) and /0 Ir cyc    ensures IS negative slope. (Equations (8), (9))

### III. EQUILIBRIUM IN A CLOSED ECONOMY: CORE AND EXPENDITURE COMPONENTS
- Core New Keynesian system (closed):
  - IS curve (gap, interest rate).
  - Monetary policy (Taylor-type) reaction function: *()e DISC t Closed t gap t t i r gap r             (Equation (10))
  - Phillips curve: 1()e ttt gap ss       (Equation (11)), with 0 and supply shock tss (percent of potential).
- Expectation treatment: e exogenous for algebraic solution.
- RR schedule (equilibrium real rate consistent with Taylor rule + Phillips curve):
  - RR form: ,* ()e DISC t RR Closed RR RRgap t RRss t t r r b b gap b ss r         (Equation (13)) with RRb   and defined RRgap b , RRss b .
- Equilibrium output gap obtained by intersecting IS and RR: closed-economy eq gap expression given in (14). (Equation (14))
- Example scenarios (Figures 1–2) — shocks and computed outcomes:
  - Scenario shocks (top of Figure 1):
    - base: Gov't Spending 0.0% ; Tax Measures (one-off) 0.0% ; Supply shock (% of YP) 0.0% ; Inflation expectations (gap w.r.t. target) 0.0% ; Deviation from Taylor Rule (shift) 0.0%.
    - alt(i): Gov't Spending 1.0% ; Tax Measures 0.0% ; Supply shock 0.0% ; Inflation expectations 0.0% ; Deviation from Taylor Rule 0.0%.
    - alt(ii): Gov't Spending 1.0% ; Tax Measures 0.0% ; Supply shock 0.0% ; Inflation expectations 0.0% ; Deviation from Taylor Rule -1.0%.
  - Computed component contributions to equilibrium output gap (Figure 1):
    - base: (a) Inflation expectations component 0.0% ; (b) Supply shock component 0.0% ; (c) Fiscal component 0.0% ; (d) Discretionary monetary component 0.0% ; Output gap 0.0%.
    - alt(i): (a) 0.0% ; (b) 0.0% ; (c) 0.7% ; (d) 0.0% ; Output gap 0.7%.
    - alt(ii): (a) 0.0% ; (b) 0.0% ; (c) 0.7% ; (d) 0.4% ; Output gap 1.1%.
  - Interpretation: under alt(i) government spending multiplier (accounting for endogenous monetary response) = 0.7; under alt(ii) monetary accommodation (DISCt r = -1.0 percent) adds 0.4 percent via movement along IS, total output gap 1.1 percent.

- Closed-economy currency-unit results and demand decomposition (Figure 2 table):
  - Gross Domestic Product16.79 16.90 16.97
  - Consumption 11.21 11.24 11.26
  - Investment 3.06 2.97 3.03
  - Government Spending 2.52 2.69 2.69
  - Demand side decomposition of output gap (percent of potential):
    - Output gap 0.0% 0.7% 1.1%
    - Consumption 0.0% 0.2% 0.3%
    - Investment 0.0% -0.5% -0.2%
    - Government Spending 0.0% 1.0% 1.0%
  - Equilibrium core-variable results (Figure 2):
    - Output gap (a)-(b)+(c)+(d) 0.0% 0.7% 1.1%
    - Equilibrium inflation rate 3.0% 4.0% 4.6%
    - Equilibrium real interest rate 2.0% 2.8% 2.3%
- Graphical interpretation:
  - alt(i): fiscal expansion shifts IS right; joint increase of output and real interest rate; inflation rises.
  - alt(ii): same fiscal shock but monetary accommodation shifts RR; output higher than alt(i) and interest rate lower; inflation higher still.

### IV. THE SMALL OPEN ECONOMY: EXPORTS, IMPORTS, AND EXTERNAL FINANCIAL PRESSURES
- Open-economy output identity: Opent t t t t tY C I G X IM     . (Equation (15))
- Exports:
  - Structure: *[ ]P t x t X Y x rpx    (Equation (16))
  - x determined by long-run external prices/productivity; 0x   ; rpx = percent deviation of relative price of exports RPXt from long-run norm.
  - Relative price of exports: * X tt t t SP RPX P    . (Equation (16) definition)
  - Baseline RPX normalized to unity; ln() tt rpx RPX  .
- Imports:
  - Structure: *[ ]P t cyc t im t IM Y im im gap rpim       (Equation (17))
  - im determined by long-run external prices/productivity; cycim > 0 ; 0im   ; rpim = percent deviation of RPIM from long-run norm.
  - Relative price of imports: * IM tt t t SP RPIM P    . (Equation (17) definition)
  - Baseline RPIM normalized to unity; ln() tt rpim RPIM  .
- External price level and real exchange rate:
  - External price level EXTt P defined as weighted average of export and import prices (weights  and 1-). (Equations (20), (21))
  - Real exchange rate: * = EXT tt t t SP Q P    . (Equation (19))
- Decomposition: relative prices of exports and imports are functions of real exchange rate q and scaled terms-of-trade TT ( X IM t t tTT P P ). (Equations (22), (23))
- Baseline and external pressures:
  - Natural rate: EXT r plus baseline risk premium rp: r = EXTr + rp. (Text)
  - External financial pressures: [ ] t EXT EXT t t efp r rp r rp     . (Text)
- Real interest parity determining short-run q deviation: EXT t t t t q r rp r q     , 0 q  . (Text)
  - Domestic monetary tightening appreciates real exchange rate; external financial pressures depreciate real exchange rate.
- Exact decompositions (endogenous/exogenous drivers) of rpx and rpim shown in (22ꞌ) and (23ꞌ): domestic monetary policy affects relative prices through q; external financial pressures and external terms-of-trade affect them externally.

### B. Open economy IS curve
- Substituting domestic and external functions into output identity yields open-economy IS (gap) with additional terms:
  - Compressed fiscal component: (1 ) t t cyc t fp gp tp     .
  - Compound parameters: nx x im      ; (1 ) nx x im         .
  - Terms-of-trade tTT appears as IS shift term; improvement in tTT shifts IS right. (Equation (24))

### C. Monetary policy and inflation in the open economy
- Monetary policy reaction in open economy adds external financial pressures tefp:
  - *()e DISC t Open t gap t t t i r b b gap efp r            . (Equation (25))
  - tefp in reaction function implies central bank tracks world financial markets; in extreme cases raises interest rate to defend exchange rate.
- Open-economy Phillips curve includes pass-through of external financial pressures:
  - 1()e t Open t t gap ss efp         . (Equation (26))
  - Parameter  captures exchange rate pass-through of external financial pressures.
- Combining (25) and (26) yields open-economy RR (reduced-form real rate) with external financial pressures coefficient RRefp = [1 ]1 bb     .

### D. Equilibrium in the open economy — core variables and trade balance
- Open-economy IS flipped to express real interest rate; combining with RR gives equilibrium gap (Equation (29)) with key term ()Ir nx    determining net effect of external financial tightening:
  - Ir  < 0 captures expenditure-reducing effect of external tightening.
  - nx  > 0 captures expenditure-switching (depreciation improves net exports).
  - Assumption: ()Ir nx    < 0 so net external financial tightening reduces output.
- Sign and economic interpretation:
  - Inflation expectations gap e* > 0 reduces output.
  - Favorable supply shock tss increases output.
  - Increases in domestic and foreign demand (tfp and ln() nx t TT  ) raise output.
  - External financial pressures have two opposing channels: central bank reaction reduces output; depreciation improves net exports — but central bank channel dominates.
- Equilibrium nominal rate: eqttr eqttri   .
- Equilibrium real exchange rate from parity: EXTeq eq t t t q r rp r q     . (Text)
- Equilibrium trade balance (percent of potential) as function of eq gap and eq q (conditional on tTT): (Equation (30))
  - ( ) [ *(1 ) ] ln( ) * eq eq eq t x im t x im t cyc t nx x im q TT im gap              (Equation (30))

- Open-economy scenario examples (Figures 4–6):
  - Scenario shocks:
    - base: no shocks.
    - alt(i): export prices fall by 4 percent (terms-of-trade shock).
    - alt(ii): export prices fall by 4 percent and tefp = 4 percent (400 basis point increase in risk premium).
  - Computed impacts on output gap (Figure 6 summary):
    - Terms-of-trade shock reduces output by 0.55 percent (alt(i)).
    - Adding adverse external financial pressures (alt(ii)) further reduces output by 0.98 percent.
  - Inflation results (Figure 5 / text):
    - alt(i): equilibrium inflation falls from 3 percent target to 2.2 percent.
    - alt(ii): equilibrium inflation falls further; final quoted value in text: 1.2 percent (compared to... [text cut off]).
  - Graphical channel summaries:
    - Terms-of-trade shock shifts IS left; central bank reduces interest rate (movement along RR) softening impact; net exports deteriorate but real exchange rate depreciates.
    - External financial pressures depreciate currency (higher import prices) and shift Phillips curve up (exchange-rate pass-through), producing lower output and different inflation outcome depending on policy response.

*Source: Author’s calculations (wp17123 - Part VII concludes).*

### 2.2 percent under alt(i)).

### wp17123 - 2.2 percent under alt(i)).

### Net exports and capital outflow scenario (alt(ii) vs alt(i))
- Under alternative (ii) (alt(ii)) higher real interest rates at home further squeeze demand so equilibrium output is even lower under alt(ii) than alt(i).
- Import compression under alt(ii) shifts the tan NX line to the right (from the dotted to the dashed line).
- The real exchange rate depreciates more under alt(ii) than alt(i). (Without the central bank’s defensive interest rate hike under alt(ii), the depreciation would have been even more severe.)
- Income and price effects together produce an improvement in the net export balance under alt(ii) relative to alt(i), but:
  - The net export improvement under alt(ii) should be interpreted as a forced adjustment — a capital outflow scenario accompanied by an even sharper reduction of output under alt(ii) than under alt(i).
- Demand-side burden of adjustment under a capital outflow scenario:
  - Investment: minus 1.4 percent of potential output
  - Consumption: minus 0.4 percent of potential output
  - These impacts are consistent with prior analyses: current account improves while domestic expenditures fall.

### Key shock parameter values (Figure 4, shocks table)
- External financial pressures (alt(ii)):
  - Total external financial pressures: 4.0%
  - Risk premium -- dev. from baseline: 4.0%
- External Terms of Trade (alt(i) and alt(ii)):
  - TT log deviation from baseline: -4.0% (alt(i)), -4.0% (alt(ii))
  - Export price log dev: -4.0% (alt(i)), -4.0% (alt(ii))
  - Import price log dev: 0.0% (all scenarios)
- Calculation of equilibrium output gap — component by component:
  - External financial pressure component (e): 0.00% (base), 0.00% (alt(i)), -0.98% (alt(ii))
  - External terms of trade component (f): 0.00% (base), -0.55% (alt(i)), -0.55% (alt(ii))

### Solutions for core variables, external sector, and expenditure components (Figure 6)
- Output gap (a)-(b)+(c)+(d)+(e)+(f): 0.0% (base), -0.5% (alt(i)), -1.5% (alt(ii))
- Equilibrium inflation rate: 3.0% (base), 2.2% (alt(i)), 1.2% (alt(ii))
- Equilibrium real interest rate: 2.0% (base), 1.3% (alt(i)), 4.3% (alt(ii))
- Real price of exports (deviation from norm): 0.0% (base), -3.2% (alt(i)), -2.2% (alt(ii))
- Real price of imports (deviation from norm): 0.0% (base), 0.8% (alt(i)), 1.8% (alt(ii))
- Real exchange rate (deviation from norm): 0.0% (base), 0.7% (alt(i)), 1.7% (alt(ii))
- Real exchange rate index (Base = 100): 100.0 (base), 100.7 (alt(i)), 101.7 (alt(ii))

Currency-unit results (levels)
- Gross Domestic Product: 18.33 (base), 18.23 (alt(i)), 18.05 (alt(ii))
- Consumption: 11.92 (base), 11.89 (alt(i)), 11.85 (alt(ii))
- Investment: 3.34 (base), 3.41 (alt(i)), 3.08 (alt(ii))
- Government Spending: 2.75 (all scenarios)
- Net Exports: 0.33 (base), 0.18 (alt(i)), 0.38 (alt(ii))
  - Exports: 1.45 (base), 1.21 (alt(i)), 1.29 (alt(ii))
  - Imports: 1.12 (base), 1.04 (alt(i)), 0.91 (alt(ii))

Ratios and gaps
- Net Exports / YP: 1.8% (base), 1.0% (alt(i)), 2.1% (alt(ii))
- Baseline Net Exports / YP: 1.8% (base), 1.8% (alt(i)), 1.8% (alt(ii))
- NX gap: 0.0% (base), 0.8% (alt(i)), -0.3% (alt(ii))

Demand-side decomposition of output gap (percent of potential)
- Output gap: 0.0% (base), -0.5% (alt(i)), -1.5% (alt(ii))
  - Consumption: 0.0% (base), -0.1% (alt(i)), -0.4% (alt(ii))
  - Investment: 0.0% (base), 0.4% (alt(i)), -1.4% (alt(ii))
  - Government Spending: 0.0% (all)
  - Net Exports: 0.0% (base), -0.8% (alt(i)), 0.3% (alt(ii))
    - Exports: 0.0% (base), -1.3% (alt(i)), -0.9% (alt(ii))
    - Imports: 0.0% (base), -0.5% (alt(i)), -1.2% (alt(ii))

### Monetary policy, the Expanded Marshall-Lerner (EML) condition, and net exports
- A discretionary monetary loosening (DISC_t r < 0) induces a depreciation of the real exchange rate (q rises).
- Narrow Marshall-Lerner intuition: (η_x - η_im) > 0 implies depreciation, ignoring other effects, causes the trade balance to improve.
- Expanded Marshall-Lerner (EML) condition extends the standard condition to include output-gap effects on imports:
  - A monetary loosening will cause the trade balance to improve if the price (real exchange rate) effect dominates the output-gap-induced import effect.
  - Graphically:
    - If EML holds: depreciation (upward movement along tan lines) dominates leftward shift of tan line from output-gap reduction → net exports increase (alt(i) left panel).
    - If EML fails: output-gap effect dominates → net exports decrease (alt(i) right panel).

### Long-run expenditure shares and microeconomic links
- Closed economy steady-state results (selected identities and implications):
  - Steady-state first-order condition equates gross after-tax marginal product of capital net of depreciation to subjective rate of time preference.
  - Steady-state capital, output, investment share, and consumption ratio are derived algebraically linking production parameters and preferences.
- Small open economy steady-state results:
  - Natural real interest rate is exogenous: EXT r = r + rp.
  - Steady-state capital stock and steady-state output expressed in terms of external real rate, productivities, prices, and tax/depreciation parameters.
  - Wage equalization across non-tradables and exports pins the allocation of labor:
    - Labor share to non-tradables (ω) determined by relative productivities and sector prices.
  - Steady-state shares of exports, government, private consumption derived from these primitives.
- Assumption in steady state: country receives constant external transfer SS Z which is minus one times net exports.

### Extensions: logarithms, growth rates, and elasticities
- Behavioral relationships can be written in growth-rate form with elasticity parameters.
- Consumption growth and investment growth approximations:
  - ln() approximations used to map level equations into growth rate/elasticity forms.
  - Short-run marginal propensity parameters reinterpreted as elasticities/semi-elasticities (examples shown for consumption and investment).

### Advantages of simpler static macroeconomic models (comparative notes)
- Traditional graphical exposition (IS, RR/LM, Phillips Curve) provides intuition via shifts.
- Impact multipliers and illustrative calculations available as “back-of-the-envelope” cross-checks for complex models (qualitative/illustrative).
- Expenditure-side equations connect to deeper macro issues (e.g., Solow, permanent income, Ricardian equivalence).
- Transparent depiction of open-economy relationships: domestic monetary policy, external financial tightening, and terms-of-trade effects are explicitly decomposed (e.g., equations (22′) and (23′)).
- Facilitates cross-checks of parameter values for mutual consistency (e.g., coherence between IS and Phillips Curve ensures consistent discretionary monetary policy effects).

*Source: Author’s calculations.*

### part III for details). Second, the model shows the conditions required to ensure that an

### wp17123 - part III for details). Second, the model shows the conditions required to ensure that an

### Key model implications and comparative-static results
- External financial outflow (a ‘sudden stop’ to external capital) will:
  - Result in a fall of domestic expenditures and output.
  - Result in a rise in net exports.
  - This outcome is reflected in equation (29).
  - Consistent with evidence in Calvo (1998) and Blanchard, Ostry, Ghosh, and Chamon (BOGC,2015).
- Domestic monetary tightening can both:
  - Appreciate the exchange rate.
  - Worsen the trade balance, under parameter combinations given by the expanded Marshall Lerner condition (see Part IV.E for details).

### Theoretical foundations for steady-state expenditure shares
- Long-run shares are linked to technology and tastes in a manner consistent with some real business cycle or ‘fresh water’ models (see Section V).
- Treatment of external prices (relative prices of exports and imports, real exchange rate, and terms of trade) in equations (22’) and (23’) is described as an improvement over most extant models.

### Model extensions and ongoing work
- Extensions to include forward-looking inflation and exchange rate expectations are discussed in Tanner (2017, forthcoming).
- Author is developing extensions including exchange rate management and sterilized intervention, following Benes, Berg, Portillo, and Vavra (2015).
- Overall assessment: ‘simple’ models can supplement and cross-check more sophisticated counterparts; attention to algebra linking different metrics can add considerable insight.

### Appendix: The ‘Macronia’ Model — Financial programming exercise
- The IMF ICD online course FPP2x includes a hypothetical case study “Macronia” similar to the paper’s open economy model.
- Real sector uses traditional ‘elasticities’ (Section VI); parameters calibrated to match section VI equations to assess vulnerabilities and design adjustment programs.
- Additional features added:
  - Output as a determinant of investment — an accelerator function. Investment equation rewritten (see (A1)–(A6) grouping).
  - Interest rate smoothing added to central bank’s interest rate rule in nominal terms.
    - Continuous smoothing parameter shown as 01   ( 0   implies no smoothing).
- Equilibrium real interest rate (Phillips curve substituted into Taylor rule) yields composite expressions (compact forms shown as (A1)–(A6)).
- Compound coefficients and error term definitions (verbatim strings preserved):
  - (1 RR RR bb   , (1) RRgapRRgap bb     , (1) RRssRRss bb     , (1 RRefp RRefp bb       are compound coefficients and
  - 1 () DISC DISC e t t t r r i r       is a compound error term that includes both the contemporaneous discretionary element and the smoothing component 1 () e t ir    .
- Adding the accelerator and interest-rate-smoothing elements yields an equilibrium output gap expression summarized in equation (A6).
- Examples and videos of the Macronia solution are available in the ICD FPP2x course (model explanation videos referenced).

*Italic: Source — wp17123 (pdf): content excerpt including Part III discussion, references, and Appendix on the ‘Macronia’ model.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17123.pdf_