## _wp12129

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### Introduction — key findings and mechanisms
- Developing-country features distinguishing fiscal transmission from developed-economy models:
  - Capital account openness often limited → restricted international risk sharing and greater crowding out when government borrowing is domestic.
  - Specialization in traded-good production with small profit margins → traded output sensitive to real exchange rate movements.
- External financing of government debt has two opposing effects on the fiscal multiplier:
  - Reduces crowding out of consumption and investment → increases expansionary effect of government spending.
  - Induces capital inflows that appreciate the real exchange rate → reduces traded output and offsets expansionary effects.
- For plausible calibrations, the real exchange rate channel dominates: more external financing results in a smaller fiscal multiplier for government spending.
- A debt-elastic country premium implies larger debt service and larger fiscal adjustments in the future → lower fiscal multiplier in the longer run.
- The model offers a theoretical explanation for the twin-deficit hypothesis in developing countries: fiscal deficits financed externally reduce crowding out but cause real exchange rate appreciation and larger current account deficits.

### Model framework and key mechanisms
- Two-sector New Keynesian small-open-economy model with:
  - Non-traded and traded goods sectors.
  - Sectoral labor and capital rigidities; production disincentive ι capturing lower governance quality.
  - Financial frictions: large share of hand-to-mouth households, debt-elastic country risk premium, and portfolio adjustment cost v governing private capital account openness.
  - Explicit central bank balance sheet to analyze fiscal–monetary–reserve interactions and exchange rate regimes.
- Household heterogeneity:
  - Continuum of households; fraction f savers, 1−f hand-to-mouth.
  - Savers own aggregate capital and choose portfolio including foreign liabilities subject to adjustment cost (v).
  - Hand-to-mouth households consume all disposable income each period.
- Government and fiscal rules:
  - Flow budget constraint (22) with debt split B^c_t (domestic), B^{cb}_t (central bank), s_t B^{f∗}_t (foreign).
  - Foreign borrowing rate r^∗_t = r_{rf} + p (s^b_t / s^b)^{ξ}, ξ ≥ 0 (equation (23)).
  - Government spending aggregator G_t CES between traded and non-traded goods (24) with time-varying home bias φ^G_t (26).
  - Fiscal stabilization rules: log (G_t / G) (27), log (Z_t / Z) (28), log (τ_t / τ) (29) with γ_Z and γ_τ controlling adjustments when s^b rises.

### Calibration highlights and steady-state statistics
- Calibration based on Mexican data 1999–2008; key values:
  - Public external debt share = 0.6.
  - Share hand-to-mouth households 1−f = 0.6 (f = 0.4).
  - φ = 0.5; ̄φ^G = 0.7; φ^G = 0.8 (alternative φ^G = 0.4 examined).
  - χ = 0.44; θ = 12; ̃θ = 12.
  - σ = 2; ψ = 2.
  - v = 0.01 (baseline); scenario ξ = 3 examined.
  - ρ_l = 0.9; ρ_k = 0.2.
  - ς_p = 65; ς_w = 145 (sticky for one year).
  - δ = 0.025; investment-output ratio = 0.21.
  - ι = 0.007 (disincentive parameter).
- Selected steady-state statistics (Table 1):
  - consumption/output 0.69
  - investment/output 0.21
  - government consumption/output 0.11
  - foreign reserve/annual output 0.08
  - money/annual output 0.11
  - public debt/annual output 0.24
  - external public debt/total government debt 0.6
  - annualized inflation rate 8.33%
  - tax revenues/output 0.15
  - remittance/output 0.02
  - annual nominal interest rate 10%

### Experiment: 10-percent shock in government consumption (~1 percent of GDP)
- Multiplier computation: cumulative present-value multipliers following Mountford and Uhlig (2009), horizons k = 4, 20 (equation (43)).
- Presentation conventions: baseline responses without external borrowing shown as solid lines; partial external financing (60-percent external debt) as dotted-dashed lines.

A. Without External Financing — key dynamics and magnitudes
- Dominant channel: real interest rate increases from higher domestic government borrowing → crowds out investment; forward-looking savers reduce consumption.
- Hand-to-mouth households drive initial aggregate consumption increase (consume labor income immediately).
- Short-run unusual feature: initial real interest rate decline due to nominal appreciation from traded output expansion; sensitivity to traded price stickiness noted.
- Real appreciation occurs but magnitude small → small effects on traded output.
- Multipliers (cumulative, present-value):
  - End of fifth year: traded production multiplier = −0.29; overall fiscal multiplier = 0.39.
  - Investment multiplier = −0.16 at end of first year and −0.50 at end of fifth year.
- Interpretation: real interest rate and real exchange rate channels both create leakage; fiscal multiplier positive but less than 1.

B. With External Financing (60-percent external public debt) — key dynamics and magnitudes
- External funds relieve competition for domestic saving → crowding-out mitigated.
- External financing amplifies real appreciation → reduces traded output and the fiscal multiplier in the short run.
- Quantitative responses:
  - Traded goods multiplier at end of first (fifth) year = −0.56 (−0.71).
  - Current account deficits on impact:
    - Without external financing: rise by 1.26 percent of GDP.
    - With 60-percent external financing: rise by 1.67 percent of GDP.
  - Crowding-out (consumption + investment multipliers) at end of fifth year:
    - Without external financing: −0.59.
    - With 60-percent external financing: −0.17.
- Dynamics and longer-run outcome:
  - With external financing, real interest rate rises less → smaller investment decline → aggregate consumption more positive.
  - Although the short-run fiscal multiplier can be larger without external financing, GDP becomes more negative after three years without external financing; in the longer run GDP is less negative under external financing because investment and capital fall less.

### Country premium on external debt and fiscal multipliers
- Baseline ξ = 0; scenario ξ = 3 examined.
- Debt-elastic premium (ξ = 3) requires stronger fiscal consolidation to sustain solvency:
  - Fiscal adjustments change from γ_Z = −0.005, γ_τ = 0.005 to γ_Z = −0.03, γ_τ = 0.03.
  - Larger transfer cuts and tax increases reduce consumption (including hand-to-mouth) and discourage work and investment.
- Quantitative comparisons (Table 3 excerpts):
  - End of first year:
    - With ξ = 3: GDP multiplier = 0.60.
    - Baseline with external financing (ξ = 0): GDP multiplier = 0.58.
  - End of fifth year:
    - With ξ = 3: GDP multiplier = 0.29.
    - Without premium: GDP multiplier = 0.32.
  - End of tenth year:
    - With ξ = 3: cumulative multiplier = 0.02.
    - Without: cumulative multiplier = 0.22.
- Policy implication: rising country premia increase borrowing costs and required fiscal adjustments → reduce effectiveness of deficit-financed stimulus.

### Twin-deficit interactions (fiscal deficits and current account deficits)
- With limited capital mobility (v = 0.01 baseline), external financing amplifies current account deterioration:
  - No external borrowing: one-dollar increase in fiscal deficits → 20-cent increase in current account deficits at end of first year.
  - 40-percent external financing: → 48-cent increase.
  - 80-percent external financing: → 77-cent increase.
- Under near perfect capital mobility (v = 0.0001), fraction of external borrowing has little influence; across scenarios a one-percentage-point rise in fiscal deficits causes a current account deterioration ≈ 0.5 percentage point of GDP.

### Other country characteristics affecting fiscal multipliers (selected quantitative outcomes)
- Baseline (row (1), Table 3):
  - 1yr: GDP 0.71, Non-traded 0.94, Traded −0.23, Consumption 0.07, Investment −0.16
  - 5yr: GDP 0.39, Non-traded 0.68, Traded −0.29, Consumption −0.09, Investment −0.50
- With external financing (60-percent) (row (2)):
  - 1yr: GDP 0.58, Non-traded 1.14, Traded −0.56, Consumption 0.18, Investment −0.06
  - 5yr: GDP 0.32, Non-traded 1.03, Traded −0.71, Consumption 0.00, Investment −0.17
- Debt-elastic premium ξ = 3 (row (3)):
  - 1yr: GDP 0.60, Non-traded 1.10, Traded −0.50, Consumption 0.16, Investment −0.08
  - 5yr: GDP 0.29, Non-traded 0.80, Traded −0.51, Consumption −0.15, Investment −0.32
- Less home bias φ^G = 0.4 (row (4)):
  - 1yr: GDP 0.48, Non-traded 0.30, Traded 0.18, Consumption −0.06, Investment −0.16
  - 5yr: GDP 0.28
- More sectoral rigidities (row (5)):
  - 1yr: GDP 0.91, Non-traded 1.13, Traded −0.21, Consumption 0.18, Investment −0.17
  - 5yr: GDP 0.45
- More hand-to-mouth (f = 0.2) (row (6)):
  - 1yr: GDP 0.79, Non-traded 1.01, Traded −0.23, Consumption 0.27, Investment −0.23
  - 5yr: GDP 0.36
- Fixed exchange rate (ω = 100,000) (row (7)):
  - 1yr: GDP 0.91, Non-traded 0.69, Traded 0.22, Consumption −0.07, Investment −0.27
  - 5yr: GDP 0.38
- Fixed exchange rate without sterilization (row (8)):
  - 1yr: GDP 0.96, Non-traded 0.94, Traded 0.01, Consumption 0.18, Investment −0.15
  - 5yr: GDP 0.48
- More open capital account v = 0.0001 (row (9)):
  - 1yr: GDP 0.63, Non-traded 0.30, Traded −0.43, Consumption 0.14, Investment −0.10
  - 5yr: GDP 0.36
- Near closed capital account v = 100 (row (10)):
  - 1yr: GDP 0.82, Non-traded 0.83, Traded −0.01, Consumption −0.00, Investment −0.19
  - 5yr: GDP 0.40

### Interaction insights and robustness
- Features that increase the fiscal multiplier: greater home bias in government purchases, higher sectoral rigidities, larger share of hand-to-mouth households, fixed exchange rate, more closed capital account.
- Home bias sensitivity: when home bias increases from 0 to 1:
  - No external financing: 1yr fiscal multiplier rises from 0.26 to 0.83.
  - Full external financing: 1yr fiscal multiplier rises from 0.01 to 0.62.
- Capital account openness effect depends on prior government external borrowing share:
  - If government finances most spending domestically, more open capital account reduces multiplier (private foreign borrowing rises, appreciating the real exchange rate).
  - If government already borrows externally, a more open capital account can raise the multiplier (private foreign borrowing falls in response to appreciation).

### Conclusions and policy implications
- Financing source matters:
  - International funds reduce domestic crowding out but cause real appreciation that typically dominates → smaller short-run fiscal multipliers with external financing in the calibrated developing-country environment.
  - Debt-elastic risk premia further reduce multipliers in the longer run via higher debt service and required fiscal consolidation.
- Composition and country features:
  - Greater reliance on traded goods in government purchases reduces the multiplier (leakage).
  - Sectoral rigidities and higher share of hand-to-mouth households increase the multiplier.
  - Fixed exchange rate reduces real appreciation and raises short-run multipliers; sterilization of reserve interventions matters.
- Overall: across most scenarios the fiscal multiplier is below 1. Productive public investment (public capital) is not modeled here; such spending can raise multipliers above 1 but is outside the paper’s baseline assumption that government spending is non-productive.
- Policy takeaway: in developing countries, the expansionary impact of deficit-financed government consumption is limited by real exchange rate appreciation and financing constraints; external financing and country-risk dynamics can materially alter both short- and long-run effectiveness.

*Source: _wp12129 - References (extracted content from the supplied IMF PDF).*

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

### _wp12129 - References .............................................................................................................

### Introduction — key findings and mechanisms
- The paper analyzes government spending effects in developing countries, highlighting differences from developed-economy models, notably:
  - Capital account openness is often limited in developing countries, implying restricted international risk sharing and greater crowding out of investment and consumption when government borrowing is domestic.
  - Developing countries tend to specialize in traded-good production with small profit margins, making traded output sensitive to real exchange rate movements.
- External financing of government debt has two opposing effects on the fiscal multiplier:
  - Reduces crowding out of consumption and investment, increasing the expansionary effect of government spending.
  - Induces capital inflows that appreciate the real exchange rate, reducing traded output and offsetting expansionary effects.
- For plausible calibrations, the real exchange rate channel dominates: more external financing results in a smaller fiscal multiplier for government spending.
- A debt-elastic country premium implies that larger debt services—and larger fiscal adjustments in the future—lower the fiscal multiplier in the longer run.
- Provides a theoretical explanation for the twin-deficit hypothesis in developing countries: fiscal deficits financed externally reduce crowding out but cause real exchange rate appreciation and larger current account deficits, generating co-movement between fiscal and current account deficits.
- Other factors affecting government spending effects:
  - Composition of government purchases (traded vs. non-traded): more government spending on traded goods introduces leakage (foreign production meets part of demand), producing a smaller fiscal multiplier.
  - Sectoral rigidities and a larger fraction of hand-to-mouth households increase the fiscal multiplier:
    - Less mobile labor and capital across sectors elevate factor prices, raising income and consumption.
    - Hand-to-mouth households consume all disposable income, so their consumption responds positively to government spending increases.
  - Exchange rate regime: fiscal multiplier is larger under a fixed exchange rate; conditioning on more home bias in government spending, a fixed exchange rate implies smaller real exchange rate appreciation and less negative effect on traded output.
  - Capital account openness: effect on the fiscal multiplier depends on extent of external government borrowing:
    - If government does not borrow much externally, households increase foreign borrowing to smooth consumption; more open capital account appreciates the real exchange rate more, suppressing the multiplier.
    - If government has already borrowed a lot externally, households reduce foreign borrowing in response to real appreciation; then a more open capital account can raise the multiplier.
- Model framework: a two-sector New Keynesian small-open-economy model that includes:
  - Sectoral labor and capital rigidities, and a disincentive parameter on production to capture lower governance quality.
  - Financial frictions: a large share of hand-to-mouth households, a debt-elastic country risk premium, and an adjustment cost on foreign liabilities (a la Schmitt-Grohe and Uribe (2003)) to control capital account openness.
  - A central bank balance sheet to study interactions among fiscal, monetary, and reserve policy and the influence of exchange rate regimes.

### Model setup — agents, preferences, and markets
- Aggregate structure:
  - Two sectors: non-traded and traded goods.
  - Numeraire: domestic composite consumption consisting of non-traded and traded goods.
  - Large share of hand-to-mouth households due to less developed financial infrastructure.
- Households:
  - Continuum of households on [0,1]; fraction f are savers and 1−f are hand-to-mouth.
  - Notation: superscript a for savers, h for hand-to-mouth.
- Savers:
  - Choose c^a_t(j), m^a_t(j), l^a_t(j), i^a_t(j), k^a_t(j), W_t(j), b^c a_t(j), and b^* a_t(j) to maximize
    E_t Σ_{t=0}^∞ β^t [u^a(c^a_t(j), m^a_t(j)) − κ^a (1+ψ)^{-1} (l^a_t(j))^{1+ψ} ].
  - Budget constraint (in units of domestic composite consumption):
    c^a_t(j) + m^a_t(j) + i^a_t(j) + b^c a_t(j) − s_t b^* a_t(j)
    + (v/2) s_t [b^* a_t(j) − b^* a(j)]^2
    + (ς_w/2) [W_t(j)/W_{t−1}(j) − π]^2 W_t l^a_t P_t
    =
    (1−τ_t)[W_t(j)/P_t l^a_t(j) + r^k_t k^a_{t−1}(j)]
    + m^a_{t−1}(j)/π_t + R_{t−1} b^c a_{t−1}(j)/π_t − s_t R^* b^* a_{t−1}/π^*
    + s_t r^m_*(j) + z_t(j) + Ω^N_t(j) + Ω^T_t(j).
  - Utility function:
    u^a(c^a_t, m^a_t) = (1/(1−σ)){ [ θ_a (c^a_t)^{(η−1)/η} + (1−θ_a) (m^a_t)^{(η−1)/η} ]^{η/(η−1)} }^{1−σ}.
  - Consumption and investment are CES baskets of non-traded and traded goods with intratemporal elasticity χ and home bias φ:
    c^a_t = [ φ^{1/χ} (c^{aN}_t)^{(χ−1)/χ} + (1−φ)^{1/χ} (c^{aT}_t)^{(χ−1)/χ} ]^{χ/(χ−1)}.
    i^a_t analogous.
  - Law of one price for traded goods: P^T_t = S_t P^*_t.
  - CPI: P_t = [ φ (P^N_t)^{1−χ} + (1−φ)(P^T_t)^{1−χ} ]^{1/(1−χ)}; relative prices p^N_t ≡ P^N_t/P_t and s_t ≡ S_t P^*_t/P_t.
  - Capital accumulation:
    k^a_t = (1−δ) k^a_{t−1} + [ 1 − κ_k/2 (i^a_t / i^a_{t−1} − 1)^2 ] i^a_t.
  - Foreign borrowing subject to portfolio adjustment cost v/2 s_t (b^* a_t − b^* a)^2; v governs private capital account openness (large v ≈ limited access).
  - Nominal rigidities via Rotemberg-type quadratic adjustment costs: (ς_w/2)[W_t(j)/W_{t−1}(j) − π]^2.
  - Savers are sole owners of aggregate capital and receive dividends Ω^N_t and Ω^T_t from firms.
- Hand-to-mouth households:
  - Same utility form as savers but consume all disposable income each period.
  - Budget constraint:
    c^h_t(j) + m^h_t(j) = (1−τ_t) W_t/P_t l^h_t(j) + m^h_{t−1}(j)/π_t + s_t r^m_*(j) + z_t(j).
  - Set wage equal to average wage chosen by savers W_t; supply same hours as savers l^h_t = l^a_t.
- Firms and production:
  - Non-traded goods: monopolistic competition with intermediate goods producers indexed i∈[0,1].
    - Technology: y^N_t(i) = z^N (k^N_{t−1}(i))^{1−α_N} (l^N_t(i))^{α_N}.
    - Aggregation: Y^N_t = [ ∫_0^1 y^N_t(i)^{(θ−1)/θ} di ]^{θ/(θ−1)}.
    - Demand: y^N_t(i) = (p^N_t(i)/p^N_t)^{−θ} Y^N_t.
    - Firm profit/dividend term Ω^N_t(j) includes real price-adjustment cost (ς_p) and a production disincentive ι > 0 to capture low governance-quality costs.
  - Traded goods: perfectly competitive producers; law of one price holds.

### Analytical and policy implications emphasized
- External financing considerations:
  - Empirical evidence: Panizza (2008) reports external public debt averages 60 percent of total government debt for Latin American countries in 2005 (dropping from about 75 percent in 1994).
  - External financing reduces domestic crowding out but induces real exchange rate appreciation that can dominate and reduce the fiscal multiplier.
  - Debt-elastic country premium amplifies long-run negative effects on the fiscal multiplier via higher future debt servicing and required fiscal adjustments.
- Exchange rate regime and home bias:
  - Fixed exchange rate regime yields a larger fiscal multiplier relative to flexible exchange rates, particularly when government purchases have home bias.
- Composition and leakage:
  - Higher share of government spending on traded goods increases leakage through foreign production and reduces fiscal multiplier.
- Financial frictions and household heterogeneity:
  - A larger fraction of hand-to-mouth households increases the multiplier because these households consume all disposable income.
- Capital account openness:
  - Ambiguous effect; depends on whether government or private sector is the main source of external borrowing prior to the shock.
- The model is designed to capture interactions among fiscal, monetary, and reserve policies via an explicit central bank balance sheet.

### Model notation and key parameters (as presented)
- Households and preferences: β, ψ, κ^a, σ, η, θ_a, χ, φ.
- Household composition: fraction f (savers) and 1−f (hand-to-mouth).
- Prices and exchange rates: P_t, P^N_t, P^T_t, π_t, π^*_t, S_t, s_t.
- Capital and investment: k^a_t, i^a_t, δ, κ_k.
- Financial frictions and openness: v (portfolio adjustment cost), b^* a (steady-state foreign liability), R^*, R_t.
- Nominal and real rigidities: ς_w (wage adjustment cost), ς_p (price adjustment cost).
- Sectoral parameters: θ (elasticity of substitution across non-traded varieties), ρ_k, ρ_l (elasticities of substitution for capital and labor across sectors), δ_k, δ_l (steady-state factor shares), α_N.
- Production disincentive capturing governance: ι > 0.

*Source: _wp12129 - References .............................................................................................................*

### 2.  Traded Good Sector

### 2.  Traded Good Sector

### Production and firm objective
- Representative traded-sector production technology:
  - y^T_t = z^T_t (k^T_{t−1})^{1−α_T} (l^T_t)^{α_T}. (20)
- Firm chooses labor and capital to maximize weighted present-value profits:
  - E_t ∑_{t=0}^∞ β^t λ^a_t [ (1−ι) s_t y^T_t − w^T_t l^T_t − r^T_t k^T_{t−1} + ι s_t Y^T_t ] ≡ Ω^T_{t,t}. (21)
- Y^T_t denotes total traded output.

### C. The Government — structure, financing, and fiscal rules
- Flow budget constraint (in units of domestic composite consumption):
  - τ_t (w_t L_t + r^k_t K_{t−1}) + B^c_t + B^{cb}_t + s_t B^{f∗}_t = p^g_t G_t + Z_t + R_{t−1} B^c_{t−1}/π_t + B^{cb}_{t−1}/π_t + s_t R^∗_{t−1} B^{f∗}_{t−1}/π^∗. (22)
- Government debt composition:
  - B^c_t : held by domestic households (or c for consumers).
  - B^{cb}_t : held by the central bank.
  - B^{f∗}_t : held by foreigners.
- Foreign borrowing rate specification (debt-elastic premium):
  - r^∗_t = r_{rf} + p (s^b_t / s^b)^{ξ}, ξ ≥ 0, where s^b_t = B_t / Y_t and r^∗_t = R^∗_t − 1. (23)
  - r_{rf} is the risk free rate; p and s^b are steady-state premium and debt-to-GDP ratio.
- Government spending aggregator (CES between traded and non-traded):
  - G_t = [ (φ^G_t)^{1/χ} (G^N_t)^{(χ−1)/χ} + (1−φ^G_t)^{1/χ} (G^T_t)^{(χ−1)/χ} ]^{χ/(χ−1)}. (24)
  - Relative price of government spending to CPI:
    - p^G_t = [ φ^G_t (p^N_t)^{(1−χ)} + (1−φ^G_t) (s_t)^{1−χ} ]^{1/(1−χ)}. (25)
- Time-varying home bias in government spending for additional spending:
  - φ^G_t = ̄φ^G + (p^g_t G_t − p^g G) / (p^g G) (φ^G − ̄φ^G). (26)
- Fiscal rules (stochastic and stabilization responses):
  - log (G_t / G) = ρ_G log (G_{t−1} / G) + φ log (Y_t / Y) + ε^G_t. (27)
  - log (Z_t / Z) = ρ_Z log (Z_{t−1} / Z) + γ_Z log (s^b_{t−1} / s^b). (28)
  - log (τ_t / τ) = ρ_τ log (τ_{t−1} / τ) + γ_τ log (s^b_{t−1} / s^b). (29)
- Stabilization mechanism when debt-to-output rises:
  - Government adjusts transfers (Z_t) or income tax rate (τ_t) via γ_Z and γ_τ.
- Calibration notes on fiscal rules and parameters:
  - φ = 0.5 in baseline (procyclical response in government consumption).
  - γ_Z = −0.005, γ_τ = 0.005 (small fiscal adjustment coefficients).
  - All autocorrelation coefficients in fiscal rules (27)-(29) set to 0.9.
  - Steady-state home bias in consumption φ = 0.5; ̄φ^G = 0.7; φ^G = 0.8 (alternative φ^G = 0.4 examined).
  - Elasticity of substitution between traded and non-traded goods χ = 0.44.
  - Elasticity of substitution between varieties of non-traded goods θ = 12;  ̃θ = 12.
  - Intertemporal substitution parameters set σ = 2 and ψ = 2.
  - Public debt share sB^{f∗}_B_i = 0.6 (steady-state external share).
  - Share of hand-to-mouth households 1−f = 0.6.
  - Procyclicality reference: Ilzetzki and Vegh (2008) estimates range from 0.39 to 0.61.

### D. Reserve and Monetary Policy
- Central bank balance sheet identity:
  - M_t − M_{t−1}/π_t = B^{cb}_t − B^{cb}_{t−1}/π_t + s_t (FR^{∗}_t − FR^{∗}_{t−1}/π^∗). (30)
- Reserve policy process:
  - FR^{∗}_t = (1 − ρ_{FR}) FR^{∗} + ρ_{FR} FR^{∗}_{t−1} − ω (π^S_t − 1), where π^S = S_t / S_{t−1}. (31)
  - ω = 0 indicates a flexible exchange regime; very large ω approximates fixed exchange rate.
- Monetary policy rule targeting CPI inflation via money aggregate:
  - M_t = M_{t−1}/π_t [ (1 + μ) (π_t / π)^{−φ_π} ]. (32)
  - 1 + μ is the steady-state growth rate of nominal money.
- Derived process for central bank holdings of government debt:
  - B^{cb}_t − B^{cb}_{t−1}/π_t = M_{t−1}/π_t [ (1 + μ) (π_t / π)^{−φ_π} − 1 ] − s_t (FR^{∗}_t − FR^{∗}_{t−1}/π^∗). (33)

### E. Aggregation and key identities
- Aggregation across households/types:
  - X_t = ∫_0^1 x_t(j) dj = f x^a_t + (1−f) x^h_t, x ∈ {c, c^N, c^T, m, l}. (34)
  - Lump-sum transfers and remittances identical across households: X_t = x_t, x ∈ {z, rm^∗}. (35)
  - Only savers access asset and capital markets; aggregate i, k, b^c, b^∗ satisfy:
    - X_t = ∫_0^1 x_t(j) dj = f x^a_t, x ∈ {i, k, b^c, b^∗}. (36)
- Total government borrowing:
  - B_t = B^c_t + B^{cb}_t + s_t B^{f∗}_t. (37)
- Total demand for non-traded goods:
  - D^N_t = φ [ C_t + I_t + ς_w / 2 ( (W_t / W_{t−1} − π)^2 / (W_t l^a_t P_t) ) + ς_p / 2 ( (π^N_t / π^N_{t−1} − 1)^2 / (p^N_t Y^N_t) ) ] + ν (p^G_t)^{χ} G_t. (38)
- Non-traded goods market clearing:
  - Y^N_t = (p^N_t)^{−χ} D^N_t. (39)
- Current account deficits (CA^d_t):
  - CA^d_t = C_t + I_t + p^G_t G_t + v/2 (B^∗_t − B^∗)^2 + ς_w / 2 ( (W_t / W_{t−1} − π)^2 / (W_t l^a_t P_t) ) + ς_p / 2 ( (π^N_t / π^N_{t−1} − 1)^2 / (p^N_t Y^N_t) ) − p^N_t Y^N_t − s_t Y^T_t + s_t (R^∗_{t−1} − 1) B^∗_{t−1}/π^∗ + s_t (R^∗_{t−1} − 1) B^{f∗}_{t−1}/π^∗ − s_t R^M^∗. (40)
- Balance of payments condition:
  - CA^d_t = s_t [ (B^∗_t − B^∗_{t−1}/π^∗) + (B^{f∗}_t − B^{f∗}_{t−1}/π^∗) − (FR^{∗}_t − FR^{∗}_{t−1}/π^∗) ]. (41)
- GDP in domestic composite consumption units:
  - Y_t = p^N_t Y^N_t + s_t Y^T_t. (42)

### II. Equilibrium, solution, and calibration — key calibration choices
- Model linearized and solved by Sims (2001) algorithm.
- Calibration based on Mexican data 1999–2008 (Country Tables of International Financial Statistics).
- Parameter and calibration highlights:
  - Public external debt share = 0.6.
  - Share hand-to-mouth households = 1−f = 0.6.
  - φ = 0.5 (procyclicality of government consumption in baseline).
  - γ_Z = −0.005, γ_τ = 0.005; autocorrelations = 0.9.
  - ̄φ^G = 0.7, φ^G = 0.8 (alternative φ^G = 0.4 examined).
  - χ = 0.44, θ = 12,  ̃θ = 12.
  - σ = 2, ψ = 2.
  - Adjustment cost parameter v = 0.01 (baseline; literature uses < 1e^{−4} for stationarity).
  - Country risk premia elasticity baseline ξ = 0; scenario with ξ = 3 examined.
    - With annual risk free rate = 4 percent and debt-to-annual GDP ratio = 0.24, ξ = 3 implies a 1-percentage-point increase in debt-to-GDP leads to a 12.5 percent increase in premia.
  - Labor mobility parameter ρ_l = 0.9; capital mobility ρ_k = 0.2.
  - Price and wage stickiness: ς_p = 65 and ς_w = 145 (sticky for one year).
  - Investment-output ratio = 0.21; depreciation rate δ = 0.025.
  - Disincentive parameter in production ι = 0.007 (sensitive to investment-output ratio; if ratio = 0.19 then ι = 0.1).

### IV. Government spending effects and external financing — experiment and main findings
- Shock studied: a 10-percent shock in government consumption, roughly 1 percent of GDP.
- Presentation:
  - Baseline responses without external borrowing: solid lines in Figure 1.
  - Responses with partial external financing (60-percent external debt): dotted-dashed lines in Figure 1.
  - Y-axis in figures: percent deviations from steady state; x-axis: years after shock.
  - Cumulative present-value multipliers computed following Mountford and Uhlig (2009):
    - Multiplier definition for X ∈ {GDP, Y^N, Y^T, C, I}: cumulative, present-value at k quarters is
      ∑_{i=1}^k (∏_{j=1}^i (R_{t+j−1})^{−1}) 4 X_{t+i−1} / ∑_{i=1}^k (∏_{j=1}^i (R_{t+j−1})^{−1}) 4 G_{t+i−1}, k = 4, 20. (43)

A. Without External Financing — key dynamics and magnitudes
- Dominant channel remains the real interest rate:
  - Higher government borrowing → higher interest rate → crowds out investment; forward-looking households reduce consumption to increase saving.
  - Fiscal multiplier positive but less than 1 due to leakages via consumption and investment.
- Initial dynamics:
  - Production in both sectors increases initially due to more labor input.
  - Non-traded prices and CPI rise → monetary tightening → nominal and real interest rates increase → investment crowded out.
  - Presence of a large share of hand-to-mouth households: aggregate consumption increases initially because hand-to-mouth households consume more from higher labor income.
- Unusual short-run decline in real interest rate:
  - Traded goods price falls initially due to nominal appreciation from traded output expansion → CPI decline → brief monetary expansion → nominal and real rate fall initially.
  - This feature may diminish if traded good prices are sticky.
- Real exchange rate response:
  - Model predicts real appreciation driven by demand for non-traded goods inducing substitution toward traded goods; real exchange rate must appreciate to clear goods market.
  - The magnitude of real appreciation is small; effects on traded output are small.
- Multipliers (cumulative, present-value):
  - At end of fifth year: traded production multiplier = −0.29; overall fiscal multiplier = 0.39 (row (1) in Table 3).
  - Investment multiplier = −0.16 at end of first year and −0.50 at end of fifth year.
- Interpretation:
  - Real interest rate and real exchange rate channels both introduce leakage reducing fiscal multipliers.
  - When government spending financed with domestic borrowing, real exchange rate channel is operating but less important.

B. With External Financing — key dynamics and magnitudes
- Scenario: 60 percent of government debt financed externally (steady-state level).
- Intuition:
  - External funds relieve competition for domestic saving → crowding-out mitigated.
  - But external financing amplifies real appreciation → reduces traded output and the fiscal multiplier.
- Quantitative responses:
  - At end of first (fifth) year, cumulative multiplier of traded goods = −0.56 (−0.71).
  - Current account deficits on impact:
    - Without external financing: rise by 1.26 percent of GDP.
    - With 60-percent external financing: rise by 1.67 percent of GDP.
  - Crowding-out (sum of consumption and investment multipliers) at end of fifth year:
    - Without external financing: −0.59.
    - With 60-percent external financing: −0.17.
- Dynamics and longer-run outcome:
  - With external financing, real interest rate rises less → smaller investment decline → aggregate consumption more positive (smaller fall in savers' consumption).
  - Although fiscal multiplier is larger without external financing at end of fifth year, GDP becomes more negative after three years without external financing.
  - In the longer run, because investment and capital fall less with external financing and real exchange rate differences narrow, GDP is less negative under external financing.

*Italic source: _wp12129 - 2.  Traded Good Sector (extracted from the supplied IMF PDF content).*

### 1.  Country Premium on External Debt

### 1. Country Premium on External Debt

### Country-premium effects on fiscal multipliers
- Baseline calibration assumes no debt-elastic country premium when borrowing externally (ξ = 0).
- Introducing a debt-elastic premium (ξ = 3) lowers the fiscal multiplier in the longer run because it requires larger fiscal adjustments to maintain budget sustainability.
- With a debt-elastic premium:
  - Fiscal adjustments change from baseline (γZ = −0.005, γτ = 0.005) to (γZ = −0.03, γτ = 0.03) to sustain solvency.
  - Transfers are cut more and the income tax rate is raised higher, reducing consumption of hand-to-mouth households and discouraging work and investment.
- Quantitative comparisons (from Table 3):
  - End of the first year:
    - Fiscal multiplier with debt-elastic premium (ξ = 3): 0.60 (row (3), 1yr)
    - Fiscal multiplier without debt-elastic premium (baseline with external financing): 0.58 (row (2), 1yr)
  - End of the fifth year:
    - With debt-elastic premium: 0.29 (row (3), 5yr)
    - Without such a premium: 0.32 (row (2), 5yr)
  - End of the tenth year (cumulative, discussed in text):
    - With debt-elastic premium: 0.02
    - Without: 0.22
- Interpretation:
  - A rising country premium increases borrowing costs and debt service, eroding expansionary effects of deficit-financed stimulus and potentially producing small or negative multipliers.

### Policy implication
- When external borrowing raises country risk premia, debt-sustainability considerations necessitate stronger fiscal consolidation (larger cuts to transfers and higher taxes), which reduces the effectiveness of government spending as stimulus.

---

### Twin Deficit Hypothesis (interaction of fiscal and current account deficits)
- Financing sources matter for the co-movement between fiscal deficits and current account deficits, especially under limited capital mobility.
- Definitions:
  - Fiscal deficits = government spending on consumption, transfers, and interest payments less tax receipts.
- Scenarios (Figure 3 summaries, v = 0.01 unless specified):
  - No external borrowing (government finances deficits domestically):
    - End of first year: a one-dollar increase in fiscal deficits → 20-cent increase in current account deficits.
  - 40 percent external financing:
    - End of first year: one-dollar increase in fiscal deficits → 48-cent increase in current account deficits.
  - 80 percent external financing:
    - End of first year: one-dollar increase in fiscal deficits → 77-cent increase in current account deficits.
- Under near perfect capital mobility (v = 0.0001):
  - Fraction of external borrowing has little influence on current account deficits.
  - Across scenarios: a one-percentage-point rise in fiscal deficits causes a current account deterioration equal to about 0.5 percentage point of GDP.

### Interpretation
- With limited capital mobility, greater external financing of fiscal deficits leads to larger current account deteriorations.
- With near-perfect capital mobility, total external borrowing is roughly constant and the link weakens; non-Ricardian behavior and traded output sensitivity to the real exchange rate still produce a moderate co-movement.

---

### Other country characteristics affecting fiscal multipliers (V. OTHER COUNTRY CHARACTERISTICS)
- General note: Exercises assume no external financing unless otherwise stated. The section studies influence of:
  1) composition of government purchases (traded vs. non-traded),
  2) sectoral rigidities of production factors,
  3) share of hand-to-mouth households,
  4) exchange rate regime,
  5) capital account openness,
  and interactions with external financing.

#### A. Composition of Government Purchases
- Baseline home bias φG = 0.8; alternative φG = 0.4.
- When government demands more traded goods (φG = 0.4):
  - Less of increased demand is met by domestic production → smaller fiscal multiplier.
  - Table 3 (row (4)):
    - End of first year: fiscal multiplier = 0.48; non-traded production multiplier = 0.30 (compared to baseline 0.94).
    - End of fifth year: fiscal multiplier = 0.28.
  - Consumption is much more negative due to wage decline from labor shifts and real depreciation.

#### B. Sectoral Rigidities of Production Factors
- Increased rigidities amplify demand pressure and enlarge multipliers by raising wages and rental rates in the non-traded sector.
- Table 3 (row (5)):
  - End of first year: fiscal multiplier = 0.91 (vs. baseline 0.71).
  - End of fifth year: fiscal multiplier = 0.45.
- Consumption multiplier particularly large; investment falls slightly more but wealth effect dominates.

#### C. Fraction of Hand-to-Mouth Households
- Higher fraction breaks Ricardian offsets and increases multipliers via immediate consumption response to labor income.
- Also increases crowding out in investment when combined with limited capital mobility.
- Table 3 (row (6), f = 0.2):
  - End of first year: GDP multiplier = 0.79 (from 0.71); consumption multiplier = 0.27 (from 0.07); investment multiplier = −0.23 (from −0.16).
  - End of fifth year: GDP multiplier = 0.36.

#### D. Exchange Rate Regime
- Fixed exchange rate regimes yield larger short-run multipliers than flexible regimes.
- Table 3 (row (7), ω = 100,000):
  - End of first year: fiscal multiplier = 0.91 (vs. baseline 0.71).
  - End of fifth year: fiscal multiplier = 0.38.
- Mechanisms:
  - Fixed regime prevents price of traded goods from falling → less real appreciation → less negative effect on traded output.
  - Sterilized reserve interventions (monetary specification) induce crowding out via higher real interest rates.
  - If reserve interventions are not sterilized, multiplier further increases (row (8)):
    - End of first year without sterilization: fiscal multiplier = 0.96.
    - End of fifth year without sterilization: fiscal multiplier = 0.48.

#### E. Capital Account Openness
- Baseline v = 0.01 (limited mobility). Consider v = 0.0001 (very open) and v = 100 (almost closed).
- Figure 5 and Table 3:
  - v = 0.0001 (almost perfect mobility), row (9):
    - End of first year: fiscal multiplier = 0.63.
    - End of fifth year: fiscal multiplier = 0.36.
  - v = 100 (near closed), row (10):
    - End of first year: fiscal multiplier = 0.82.
    - End of fifth year: fiscal multiplier = 0.40.
- Without external financing, more open capital account → less crowding out but more contraction in traded output → overall less expansionary in the short run; GDP bounces back more quickly in the longer run.

#### F. Interactions with External Financing
- Figure 6 summarizes cumulative fiscal multiplier at end of first year across external financing shares and country parameters.
- Key observations:
  - Fiscal multiplier generally below 1 across scenarios.
  - Features that increase the multiplier: more home bias in government purchases, higher sectoral rigidities, larger share of hand-to-mouth households, fixed exchange rate, more closed capital account.
  - Multiple characteristics need to be present to obtain multiplier above 1. Example: no external financing + φG = 1 + fixed exchange rate → fiscal multiplier = 1.12 at end of first year.
  - Home bias has the largest influence: when home bias increases from 0 to 1:
    - Under no external financing: fiscal multiplier at end of first year rises from 0.26 to 0.83.
    - Under full external financing: rises from 0.01 to 0.62.
  - Capital account openness effect depends on government external borrowing share:
    - If government finances most spending domestically, a more open capital account (small v) reduces the multiplier because private sector increases foreign borrowing to smooth consumption.
    - If government already borrows a lot externally, a more open capital account can raise the multiplier because private foreign borrowing falls, reducing real appreciation.

---

### Conclusions
- Financing source affects fiscal multipliers in developing countries:
  - Access to international funds reduces crowding out in consumption and investment, raising the multiplier.
  - External inflows cause real appreciation which strongly reduces traded output; the real exchange rate channel typically dominates, yielding a smaller short-run multiplier with external financing.
  - When debt-elastic risk premia are present, external financing further reduces multipliers in the longer run due to higher debt service and needed fiscal adjustments.
- Other factors:
  - Greater reliance on traded goods for government purchases reduces the multiplier.
  - More sectoral rigidities and higher share of hand-to-mouth households increase the multiplier.
  - Fixed exchange rate reduces real appreciation and lessens negative traded-output effects, raising short-run multipliers.
  - The effect of capital account openness on the multiplier depends on the magnitude of government external borrowing.
- Overall: For most scenarios studied, the fiscal multiplier is below one, suggesting government spending in developing countries is often less expansionary than policymakers might hope.
- Caveat: Model assumes government spending is non-productive; productive public investment (e.g., public capital) can raise multipliers above one. External financing of spending (including aid) tends to have smaller expansionary effects in lower-income countries.

---

### Key calibration and steady-state statistics (selected)
- Steady-state shares and rates (Table 1):
  - consumption/output 0.69 (Mexico, average 1999-2008)
  - investment/output 0.21 (Mexico, average 1999-2008)
  - government consumption/output 0.11 (Mexico, average 1999-2008)
  - trade balance/output 0.01 (model implication)
  - foreign reserve/annual output 0.08 (Mexico, average 1999-2008)
  - money/annual output 0.11 (M1, Mexico, average 1999-2008)
  - public debt/annual output 0.24 (Mexico, gross debt, average 1999-2008)
  - private foreign debt/annual output 0.09 (model implication)
  - external public debt/total government debt 0.6 (average of Latin America in 2005)
  - annualized inflation rate 8.33% (CPI, Mexico, average 1997-2008)
  - tax revenues/output 0.15 (cash receipts, Mexico, average 1999-2008)
  - transfers/output 0.03 (model implication)
  - remittance/output 0.02 (net foreign transfers to Mexico, average 1999-2008)
  - annual nominal interest rate 10% (principal rate, Mexico, average 1997-2008)

- Baseline parameter highlights (Table 2):
  - φ0.5 degree of consumption home bias
  - χ0.44 elasticity of substitution between traded and non-traded
  - β0.996 the discount factor
  - f0.4 fraction of savers
  - ̄φG0.7 steady state home bias of government purchases
  - γz −0.005 transfer adjustment parameter (stabilize debt growth)
  - γτ 0.005 income tax rate adjustment parameter (stabilize debt growth)
  - v0.01 implying limited international capital mobility
  - ω0 flexible exchange rate regime
  - ξ0.0 country risk premium (baseline)

- Selected entries from Table 3 (Fiscal Multipliers for Government Spending):
  - (1) baseline, 1yr: GDP 0.71, Non-traded 0.94, Traded −0.23, Consumption 0.07, Investment −0.16
  - (1) baseline, 5yr: GDP 0.39, Non-traded 0.68, Traded −0.29, Consumption −0.09, Investment −0.50
  - (2) with external financing, 1yr: GDP 0.58, Non-traded 1.14, Traded −0.56, Consumption 0.18, Investment −0.06
  - (2) with external financing, 5yr: GDP 0.32, Non-traded 1.03, Traded −0.71, Consumption 0.00, Investment −0.17
  - (3) debt-elastic country premium (ξ = 3), 1yr: GDP 0.60, Non-traded 1.10, Traded −0.50, Consumption 0.16, Investment −0.08
  - (3) debt-elastic country premium (ξ = 3), 5yr: GDP 0.29, Non-traded 0.80, Traded −0.51, Consumption −0.15, Investment −0.32
  - (4) less home bias (φG = 0.4), 1yr: GDP 0.48, Non-traded 0.30, Traded 0.18, Consumption −0.06, Investment −0.16
  - (5) more sectoral rigidities (ρl = 0.2, ρk = 0.1), 1yr: GDP 0.91, Non-traded 1.13, Traded −0.21, Consumption 0.18, Investment −0.17
  - (6) more hand-to-mouth households (f = 0.2), 1yr: GDP 0.79, Non-traded 1.01, Traded −0.23, Consumption 0.27, Investment −0.23
  - (7) fixed exchange rate (ω = 100,000), 1yr: GDP 0.91, Non-traded 0.69, Traded 0.22, Consumption −0.07, Investment −0.27
  - (8) fixed exchange rate no sterilization, 1yr: GDP 0.96, Non-traded 0.94, Traded 0.01, Consumption 0.18, Investment −0.15
  - (9) more open capital account (v = 0.0001), 1yr: GDP 0.63, Non-traded 0.30, Traded −0.43, Consumption 0.14, Investment −0.10
  - (10) near closed capital account (v = 100), 1yr: GDP 0.82, Non-traded 0.83, Traded −0.01, Consumption −0.00, Investment −0.19

*Source: _wp12129 - 1.  Country Premium on External Debt (IMF working paper content provided).*

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*Source: _wp12129 - REFERENCES*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12129.pdf_