## _wp1065

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---

### The transfer problem and paper framing
- Traditional transfer-problem view: aid induces higher expenditure on traded and non-traded goods, raising absorption (an increase in the current account deficit net of the transfer) and requiring a real appreciation to restore internal and external balance.
- Paper emphasizes distinction between spending of aid (determined by fiscal response) and absorption of aid (influenced by central bank reserve policy when international capital market access is limited).
- Key innovation: a tractable two-sector dynamic general equilibrium model with nominal rigidities (new‑Keynesian paradigm) tailored to low-income country features:
  - Little market power in export markets.
  - Limited international capital mobility.
  - Consumers' limited participation in domestic financial markets (non‑asset holders).
  - Extended central bank policy set: Taylor-type monetary rule plus a separate rule determining rate of reserve accumulation.

### Empirical motivation: Uganda and African aid surge stylized facts
- Net aid increased by about 3 percentage points of GDP (on average) during 2000–2004; in present value terms the surge represented 11 percent of Uganda’s GDP in 2000–2001.
- Overall aid to sub‑Saharan Africa rose 42 percent in real terms from 1999 to 2004.
- Surge concentrated in budget support.
- Fiscal and reserve responses in Uganda during the surge:
  - Government spending (net of interest payments) increased by an average of 2.3 percentage points of GDP.
  - Central bank reserves increased by 2.3 percent (of GDP); current account deficit (before aid) financed 0.6 percent; base money growth rose only 0.3 percent of GDP—i.e., almost all reserves accumulation was sterilized.
  - Treasury‑bill rates: nominal and (ex‑post) real rates increased by about 200 basis points during the aid‑surge period; 6‑month and 1 year rates increased by about 500 and 600 basis points, respectively.

### Model structure and parameters (baseline calibration highlights)
- Small open‑economy DSGE with two goods: traded (T) and non‑traded (N).
- Agents: households (asset holders and non‑asset holders), firms (monopolistic non‑traded, competitive traded), central bank, fiscal authority.
- Aid process: A* t = A* + ρA(A* t−1 − A*) + εt.
- Fiscal allocation parameter γ measures fraction of aid initially spent.
- Reserve policy parameter ω measures fraction of aid not accumulated as central bank reserves (ω is direct measure of short‑term aid absorption when capital account is closed).
- Portfolio adjustment costs Q(b a* t ) = υ/2 (b a* t − b a* )^2; benchmark υb = +∞ (closed capital account).
- Nominal rigidities: Rotemberg price adjustment cost parameter ζ; sticky‑price benchmark ζ = 10 (firms change prices every 3.5 quarters).
- Selected calibrated parameters (Benchmark):
  - β = 0.99
  - κ_A = 0.078
  - ψ = 2
  - κ_g = 0.182
  - φ_g = 0.8
  - κ_c = 0.896
  - ζ = 10
  - ρ_A = 0.87
  - χ = 0.85
  - ρ_R = 0.9
  - α = 0.7
  - υ_b = 10000000
  - φ = 0.634
  - p = 0.42
  - δ = 0.75
  - φ_π = 1.5
- Shock simulated: 50 percent increase in A* t (about 3 percentage points of GDP), matching the Uganda surge magnitude.

### Main simulated scenarios and outcomes (closed capital account benchmark)
- Complete spending and absorption (γ = 1, ω = 1):
  - Real exchange rate appreciates.
  - Impact on real GDP close to zero: expansion of non‑traded sector nearly offset by contraction in traded sector.
  - Small increase in non‑traded inflation; headline inflation falls; nominal and real interest rates unchanged.
  - Sticky‑price responses similar to flexible‑price results.
- Complete spending, zero absorption (γ = 1, ω = 0; Uganda‑like: government spends but central bank accumulates reserves):
  - Real exchange rate shows a depreciation (contrasting with flexible‑price equilibrium).
  - Large decline in non‑traded markups and considerable increase in inflation.
  - Monetary policy reaction results in a large increase in real interest rates.
  - Output expands (driven by larger labor supply—crowding out of consumption—and demand pressures).
  - Sticky‑price dynamics differ markedly from flexible‑price: higher output and inflation, lower markups, higher real wages, more depreciated real exchange rate.
- No spending and reserve accumulation:
  - Little initial impact on real exchange rate, consumption, or wages.

### Mechanisms: why spending without absorption can depreciate the real exchange rate
- Not absorbing aid (reserve accumulation) raises the natural real interest rate r^n t, generating a positive output gap when monetary policy is not optimal.
- Nominal rigidities amplify demand effects via reductions in non‑traded sector markups (μN t decreases):
  - Reduced internal‑balance pressure for appreciation.
  - Increased labor demand and real wages.
  - Larger markup declines can produce a relative real depreciation even when the flexible‑price equilibrium predicts appreciation.
- Decomposition under closed capital account: s^t = s^n t − d_μ μ^N t (equation (46)); depreciation requires markup decline term to dominate natural appreciation.

### Sensitivity analysis and robustness (selected findings)
- φg ↑ (more government spending on non‑traded goods): produces more appreciation; depreciation under zero absorption is smaller.
- Removing non‑asset holders (p ↑ to 1): reduces demand pressures when aid is not absorbed; real exchange rate appreciates instead.
- Imperfect labor substitutability across sectors: increases flexible‑price s^n t appreciation, making depreciation less likely.
- Lower aid persistence (ρA from 0.87 to 0.6, shock size increased so first‑year impact matches benchmark):
  - Under full absorption: smaller real appreciation; slightly higher inflation and output.
  - Under zero absorption: larger real depreciation and significantly higher output and inflation.
- Alternative preferences (Greenwood–Hercowitz–Huffman utility; p = 1):
  - Flexible prices: similar results; output response to spending‑without‑absorption ≈ 0.
  - Sticky prices: spending‑but‑not‑absorbing yields larger demand pressures and even larger real depreciation—core results robust.
- Opening the capital account (υb = 0.0125):
  - Reserve accumulation has smaller impact on real variables.
  - Sterilized accumulation during an aid‑financed fiscal expansion cannot generate short‑term real depreciation; unsterilized accumulation leads to depreciation regardless of capital mobility.

### Monetary policy variants and implications
- Benchmark Taylor‑rule (φπ = 1.5) produces real depreciation with higher inflation under spending without absorption.
- Headline inflation targeting:
  - When authorities target headline inflation, outcomes similar to benchmark because headline and non‑traded inflation move similarly when aid is not absorbed.
  - Under spending‑and‑absorb, targeting headline inflation loosens policy (higher non‑traded inflation, smaller appreciation, output expansion).
- Incomplete sterilization (money in utility; money demand m^t = c^t − y i^t):
  - Central bank can finance reserve accumulation by increasing money supply instead of bonds; incomplete sterilization f < 1 loosens policy.
  - Incomplete sterilization (benchmark f = 0.9) yields large depreciation, large output increases, and spike in inflation.
- Money‑targeting (operational monetary aggregate with lagged i t−1 coefficient one):
  - Under no absorption, money targeting produces similar real exchange rate and output effects but much smaller inflation response (lagged interest rate anchors inflation).

### Quantitative table excerpts (selected exact figures)
- Table 1. Selected Macroeconomic Variables, Uganda, 1998–2004 (averages and differences):
  - Net Aid: 1998–2000 = 7.9; 2000–2004 = 10.6; Difference = 2.7 (percent of GDP).
  - Expenditure (excluding external interest): 18.2; 20.5; Difference = 2.3.
  - Net Aid (Balance of Payments, percent of GDP): 7.7; 10.8; Difference = 3.1.
  - Current account deficit net of aid: 11.5; 12.1; Difference = 0.6.
  - Reserve accumulation: −0.3; 2.3; Difference = 2.5.
  - Base money growth: 0.4; 0.7; Difference = 0.3.
  - Real effective exchange rate (depreciation): 9.1; 6.3.
  - Terms of trade (worsening): 14.4; 5.9.
  - 91‑day real Treasury‑bill rate: 5.6; 8.4; Difference = 2.8.
  - Inflation: 3.1; 3.3; Difference = 0.2.
  - 91‑day Treasury‑bill rate: 8.2; 11.6; Difference = 3.4.
- Table 3 / Table 4 selected percent deviations (preserve reported figures):
  - No Reserve Accumulation, Benchmark:
    - ˆs = −2.7
    - ˆy = 0.0
    - ˆπ = −0.5
    - ˆr_t − E_t[ˆπ_{t+1}] = −0.3
  - Full Reserve Accumulation, Benchmark:
    - ˆs = 0.9
    - ˆy = 1.2
    - ˆπ = 7.0
    - ˆr_t − E_t[ˆπ_{t+1}] = 5.5
  - Role of monetary policy (Table 4 selected):
    - Benchmark No Res. Accumul.:
      - ˆs_t = −2.7; ˆy_t = 0.0; ˆπ_t = −0.5; ˆr_t − E_t[ˆπ_{t+1}] = −0.3.
    - Headline IT No Res. Accumul.:
      - ˆs_t = −1.5; ˆy_t = 0.4; ˆπ_t = 0.8; ˆr_t − E_t[ˆπ_{t+1}] = 0.9.
    - Inc. Sterilization Full Res. Accumul.:
      - ˆs_t = 6.6; ˆy_t = 3.4; ˆπ_t = 18.7; ˆr_t − E_t[ˆπ_{t+1}] = 14.7.

### Policy‑relevant conclusions and recommendations
- Short‑run macroeconomic impact of aid surges depends critically on the joint fiscal–reserve policy response (γ, ω) and the composition of government spending (φg).
- Two broad policy messages:
  - Spend‑and‑absorb (γ high, ω high): tends to generate real appreciation, limited crowding out, modest inflationary pressure.
  - Spend‑but‑accumulate‑reserves (γ high, ω low): can generate demand pressures, higher real interest rates, larger inflation under sticky prices, and relative real depreciation—outcomes similar to Uganda's experience.
- Monetary policy stance matters for inflation outcomes:
  - Incomplete sterilization (money‑financed reserve accumulation) risks large inflation and depreciation.
  - Money‑targeting with lagged interest rates can limit inflation while producing similar real dynamics.
- Opening the capital account reduces the real effects of reserve accumulation; sterilized accumulation is less likely to cause depreciation when capital is mobile.

### Caveats and suggested extensions
- Analysis focuses on short‑run effects; persistent real depreciation beyond initial quarters requires additional real rigidities not modeled here.
- Companion work planned to add investment, real rigidities, uncertainty, and terms‑of‑trade shocks for quantitative assessment relative to Uganda.
- Welfare implications of fiscal–reserve policy interactions and applications to resource booms or sterilized interventions are reserved for further papers.

### Appendix B — Introducing money in the utility function (selected model implications)
- Asset‑holders' utility: u(c_a_t, M_a_t/P_t, l_a_t) = log{[ z_a (c_a_t)^{η−1/η} + (1−z_a) (M_a_t/P_t)^{η−1/η} ]^{η/(1−η)}} − κ 1+ψ (l_a_t)^{1+ψ}.
- Aggregate log‑linear money demand: ˆm_t = ˆc_t − y ˆı_t (equation (58)).
- Euler equation revised (equation (59)) includes an inflation‑tax term and implies demand for non‑traded goods depends positively on ˆπ_t; IB_a equation includes extra term −ε_π ˆπ_t where ε_π = κ_m Γ (equation (60)).
- Monetary policy linkage: Taylor rule and open market operations imply full sterilization is required for a standard interest‑rate rule; introduce f (0≤f≤1) to model incomplete sterilization (equation (62)): f measures departure from full sterilization.
- Numerical sensitivity: incomplete sterilization and money in utility can materially increase depreciation, output, and inflation responses (see Table 4 selected figures above).

*Source: _wp1065 (IMF working paper content).*

### References..............................................................................................44

### I. INTRODUCTION

### The transfer problem and standard expectation
- The traditional literature on the "transfer problem" predicts that aid leads the representative agent to increase expenditure on both traded and non-traded goods, raising absorption (an increase in the current account deficit net of the transfer).
- An appreciation of the real exchange rate is required to shift demand toward traded goods and supply toward non-traded goods, ensuring internal balance (equilibrium in the market for non-traded goods) and external balance (balance of payments).
- The analysis is similar when the government directly receives the aid: higher absorption corresponds to higher government spending.
- Little attention is paid to how the reserve policy of the central bank may affect the impact of aid.

### Empirical motivation: the Uganda and African experience
- In Uganda during the first half of the decade, aid inflows and aid-financed government spending increased considerably, yet the current account deficit net of aid did not increase. Instead, the additional aid ended up accumulated as reserves.
- Concurrent outcomes observed in Uganda and other African countries with large aid surges (Berg, and others (2007)):
  - A fiscal expansion.
  - Large accumulation of reserves.
  - A real depreciation.
  - A considerable increase in real interest rates — a variable often ignored in transfer analyses.

### Distinction emphasized: spending versus absorption
- The paper highlights the crucial distinction between the spending of aid (determined by fiscal policy response) and the absorption of aid (influenced by central bank reserve policy when international capital market access is limited).
- Empirical observation for Uganda: aid was spent but not absorbed.
- Typical institutional mechanics: in a canonical aid transaction, FX from aid accrues to the government, which sells it to the central bank for a local currency deposit; the central bank then independently decides whether to accumulate the FX as reserves and whether to sterilize that accumulation.
- Multiple policy-mix combinations can result in different combinations of spending and absorption.

### Contribution: framework centered on fiscal/reserve policy interaction
- The paper provides a tractable two-sector dynamic general equilibrium model with nominal rigidities, conforming to the new-Keynesian paradigm but tailored to low-income country features:
  - Little market power in export markets.
  - Limited international capital mobility.
  - Consumers' limited participation in domestic financial markets.
  - As an extension: potentially limited flexibility in labor reallocation across sectors.
- The central bank's policy set is extended to include:
  - The standard monetary policy rule (Taylor-type).
  - A separate rule determining the rate of reserve accumulation.
- The model’s tractability allows a graphic representation of external balance, internal balance, and the labor market.

### Key theoretical intuition
- A policy combination that results in spending but not absorbing aid is akin to a domestically-financed fiscal expansion:
  - Public spending increases while the foreign exchange from aid is not used to increase external financing.
  - The increase in spending crowds out the private sector — aid is effectively "used" twice: once to increase government spending, once to increase reserves.
- This mechanism motivates the use of a new-Keynesian framework with non-Ricardian features (limited participation in domestic financial markets) to study short-run aid macroeconomics.

### Main model results (explicit bullets as stated)
- A policy mix that results in spending and absorbing the aid:
  - Leads to an appreciation of the natural real exchange rate and little movement in the natural rate of interest.
  - ("Natural" denotes flexible-price equilibrium values.)
- A policy that results in spending without absorption:
  - Moderates the appreciation of the natural real exchange rate and increases the natural rate of interest.
  - The moderated appreciation is because there is no increase in external financing.
  - The rise in the natural rate of interest reflects crowding out of the private sector.
- Introducing nominal rigidities in the non-traded sector:
  - The increase in the natural rate of interest implies spending but not absorbing the aid generates demand pressures (temporary increases in inflation and the aggregate output gap).
  - This is analogous to the standard closed-economy new-Keynesian model when monetary policy is not optimal.
- Demand pressures are associated with a more depreciated real exchange rate relative to the flexible-price case:
  - Demand pressures increase aggregate labor demand and real wages.
  - A more depreciated real exchange rate—relative to its "natural" value—is required to guarantee external balance.
- For the real exchange rate to depreciate in absolute terms, demand-related pressures must dominate the "natural" real appreciation.

### Factors affecting likelihood and magnitude of real depreciation
- Limited participation in domestic financial markets increases the likelihood of a real depreciation because it amplifies demand pressures.
- Incomplete sterilization of reserves (a looser monetary policy) increases the chance of depreciation.
- A more aggressive monetary policy (a higher coefficient on inflation in the Taylor rule) works in the opposite direction (reducing depreciation likelihood).
- The natural appreciation becomes smaller if the share of government spending on traded goods increases.
- Labor market frictions increase the magnitude of the natural appreciation required to reallocate labor across sectors.

### Calibration and robustness: Uganda simulation
- When calibrated to Uganda and simulating a temporary aid increase, assuming aid is spent but not absorbed:
  - The model generates a temporary real depreciation and an increase in the real interest rate.
  - The real depreciation result is robust to variations considered, including changes in preferences and plausible variations in monetary policy.
- Caveat: once the capital account is open, the mapping between reserve accumulation and absorption is considerably weakened:
  - Aid generally leads to a real appreciation unless reserve accumulation is not fully sterilized.
  - The assumption of limited capital mobility is broadly consistent with Uganda's post-aid-surge capital account behavior.

### Scope, positioning, and related literature
- The model is not intended to match the quantitative dynamic behavior of macro variables in Uganda; rather, it clarifies different short-run transmission mechanisms of aid.
- Novelty claim: one of the first papers applying DSGE-type models to low-income country macroeconomics.
- Related works and contrasts noted:
  - Buffie, and others (2008), Adam, and others (2009): discuss reserve policy role but often feature currency substitution and fiscal dominance.
  - Prati, and Tressel (2005): analyze optimal reserve policy in a two-period real model with a traded-sector externality.
  - Arellano, and others (2009), Cerra, and others (2008), Chatterjee and Turnovsky (2007): real models focused on medium-to-long run.
  - Old literature on "counterpart funds" identified related mechanisms but lacked coherent modeling.
  - Recent fiscal analysis in new-Keynesian closed-economy models (Gali, Lopez-Salido, and Valles (2007), Monacelli and Perotti (2008)) emphasize limited participation/non-standard preferences; these features are also important here.
  - Corsetti, Meier, and Muller (2009) find real depreciation following a debt-financed fiscal expansion via a different mechanism involving uncovered interest parity.

### Paper organization
- Section 2: briefly discusses the experience of Uganda.
- Section 3: presents the model.
- Section 4: focuses on the short-run equilibrium when prices are flexible.

*Source: _wp1065 - References..............................................................................................44*

### Section 5 adds nominal rigidities, and discusses the calibration and simulated results. Finally, section

### _wp1065 - Section 5 adds nominal rigidities, and discusses the calibration and simulated results. Finally, section

### Uganda aid-surge: stylized facts and motivating observations
- Net aid increased by about 3 percentage points of GDP (on average) during 2000–2004, with a subsequent fall below pre-surge levels after 2005.
- In present value terms the surge represented 11 percent of Uganda’s GDP in 2000–2001.
- Overall aid to sub-Saharan Africa rose 42 percent in real terms from 1999 to 2004.
- The surge in Uganda was concentrated in budget support rather than project aid.
- Fiscal and reserve responses observed:
  - Government spending (net of interest payments) increased by an average of 2.3 percentage points of GDP during the surge.
  - Central bank reserves increased by 2.3 percent (of GDP); current account deficit (before aid) financed 0.6 percent; base money growth rose only 0.3 percent of GDP—i.e., almost all reserves accumulation was sterilized.
  - Treasury-bill rates: nominal and (ex-post) real rates increased by about 200 basis points during the aid-surge period; 6-month and 1 year rates increased by about 500 and 600 basis points, respectively.

### Model structure and key mechanisms
- Small open-economy DSGE with two goods: traded (T) and non-traded (N).
- Agents: households (asset holders and non-asset holders), firms (monopolistic non-traded, competitive traded), central bank, fiscal authority.
- Aid process: A* t = A* + ρA(A* t−1 − A*) + εt (Aid shock is only source of uncertainty).
- Fiscal allocation parameter γ measures fraction of aid initially spent (short-term aid spending).
- Reserve policy parameter ω measures fraction of aid not accumulated as central bank reserves (ω is direct measure of short-term aid absorption when capital account is closed).
- Portfolio adjustment costs Q(b a* t ) = υ/2 (b a* t − b a* )^2 control capital mobility; benchmark uses υb = +∞ (closed capital account).
- Nominal rigidities introduced via Rotemberg price adjustment costs with parameter ζ; sticky-price simulations set ζ > 0 (benchmark ζ = 10, firms change prices every 3.5 quarters).

### Calibration highlights (Uganda baseline)
- β set so equilibrium annual real interest rate is 4 percent.
- φg = 0.8 (share of government spending on non-traded goods).
- υb = +∞ (closed capital account in baseline).
- ψ = 2 (inverse of labor supply elasticity); ζ = 10.
- Share of asset holders p = 40 percent (based on financial access survey).
- ρA chosen so aid increase has half-life ~ 1.5 years; ρR chosen to make reserve accumulation persistent.
- Taylor-rule parameter φπ = 1.5 (benchmark monetary policy).

### Simulated scenarios and main results
- Shock simulated: 50 percent increase in A* t (about 3 percentage points of GDP) — similar magnitude to Uganda’s surge.
- Flexible-price vs sticky-price comparisons are central to the interpretation.

- Complete spending and absorption (γ = 1, ω = 1; FX sold and fiscal spending increases):
  - Real exchange rate appreciates.
  - Impact on real GDP close to zero: expansion of non-traded sector nearly offset by contraction in traded sector.
  - Small increase in non-traded inflation; headline inflation falls; nominal and real interest rates unchanged.
  - Sticky-price responses similar to flexible-price results in this case.

- Complete spending, zero absorption (γ = 1, ω = 0; government spends but central bank accumulates reserves — Uganda-like):
  - Real exchange rate shows a depreciation (contrasting with flexible-price equilibrium).
  - Large decline in non-traded markups and considerable increase in inflation.
  - Monetary policy reaction results in a large increase in real interest rates.
  - Output expands (driven by larger labor supply—crowding out of consumption—and demand pressures).
  - Sticky-price dynamics differ markedly from flexible-price: higher output and inflation, lower markups, higher real wages, more depreciated real exchange rate.

- Other fiscal/reserve combinations (qualitative):
  - Spending and full FX sale: appreciation and slight consumption increase.
  - Spending with reserve accumulation: smaller appreciation or potential depreciation depending on φg, and private consumption can be crowded out.
  - No spending and reserve accumulation: little initial impact on real exchange rate, consumption, or wages.

### Mechanisms generating demand pressures and temporary depreciation
- Not absorbing aid (reserve accumulation) raises the natural real interest rate r^n t (equation (45) structure), which—given a non-optimal monetary response—creates a positive output gap and demand pressures.
- Nominal rigidities amplify the demand effect via reductions in non-traded sector markups (μN t decreases), which:
  - Reduce internal-balance pressures for appreciation,
  - Increase labor demand and real wages,
  - Can lead to a relative real depreciation even when the flexible-price equilibrium predicts appreciation.
- Decomposition under closed capital account:
  - s^t = s^n t − d_μ μ^N t (equation (46)): real exchange rate combines flexible-price component and a term proportional to markup decline; larger markup declines (d_μ μ^N t) make depreciation more likely.

### Sensitivity analysis (selected findings)
- φg ↑ (more government spending on non-traded goods): produces more appreciation; depreciation under zero absorption is smaller.
- Removing non-asset holders (p ↑ to 1): reduces demand pressures when aid is not absorbed; real exchange rate appreciates instead.
- Imperfect labor substitutability across sectors: leads to more appreciation regardless of reserve behavior (flexible-price s^n t more appreciated).
- Lower aid persistence (ρA from 0.87 to 0.6, shock size increased so first-year impact matches benchmark):
  - Under full absorption: smaller real appreciation; slightly higher inflation and output.
  - Under zero absorption: larger real depreciation and significantly higher output and inflation.
- Alternative preferences (Greenwood–Hercowitz–Huffman utility; p = 1):
  - Under flexible prices: similar results; output response to spending-without-absorption ≈ 0.
  - Under sticky prices: spending-but-not-absorbing yields larger demand pressures and even larger real depreciation — core results robust.

- Opening the capital account (υb = 0.0125):
  - Reserve accumulation has smaller impact on real variables.
  - Sterilized accumulation during aid-financed fiscal expansion cannot generate short-term real depreciation; unsterilized accumulation will lead to depreciation regardless of capital mobility.

### Monetary policy variants and implications for inflation
- Benchmark Taylor-rule (interest-rate targeting, φπ = 1.5) produces a real depreciation with higher inflation under spending without absorption.
- Headline inflation targeting:
  - If authorities target headline inflation, outcomes similar to benchmark because headline and non-traded inflation move similarly when aid is not absorbed.
  - Under spending-and-absorb, targeting headline inflation looses policy (higher non-traded inflation, smaller appreciation, output expansion).
- Incomplete sterilization (introduce money in utility, money demand: m^t = c^t − y i^t):
  - Central bank can finance reserve accumulation by increasing money supply instead of bonds; incomplete sterilization f < 1 loosens policy.
  - Incomplete sterilization (benchmark f = 0.9) yields large depreciation, large output increases, and spike in inflation.
- Money-targeting (operational monetary aggregate target):
  - Interest rule includes lagged i t−1 with coefficient one; inflation coefficient adjusted so comparability with φπ.
  - Under no absorption, money targeting results in similar exchange rate and output effects but much smaller inflation response (lagged interest rate anchors inflation).

### Policy-relevant conclusions and recommendations (from model results)
- Short-run macroeconomic impact of aid surges depends critically on the joint fiscal-reserve policy response (γ, ω) and spending composition (φg).
- Two broad policy messages:
  - Spend-and-absorb (γ high, ω high): tends to generate real appreciation, limited crowding out, modest inflationary pressure.
  - Spend-but-accumulate-reserves (γ high, ω low): can generate demand pressures, higher real interest rates, larger inflation under sticky prices, and relative real depreciation — outcomes similar to what was observed in Uganda.
- Monetary policy stance matters for inflation outcomes:
  - Incomplete sterilization (money-financed reserve accumulation) risks large inflation and depreciation.
  - Money-targeting with lagged interest rates can limit inflation while producing similar real dynamics.
- Opening the capital account reduces the real effects of reserve accumulation; sterilized accumulation is less likely to cause depreciation when capital is mobile.

### Research caveats and extensions noted in the content
- Analysis focuses on short-run effects; persistent real depreciation beyond initial quarters requires additional real rigidities not modeled here.
- Companion work planned to add investment, real rigidities, uncertainty, and terms-of-trade shocks to assess quantitative match to Uganda.
- Welfare implications of fiscal-reserve policy interactions and applications to resource booms or sterilized interventions are reserved for further papers.

*Source: _wp1065 - Section 5 adds nominal rigidities, and discusses the calibration and simulated results. Finally, section*

### Appendix B : Introducing money in the utility function

### Appendix B : Introducing money in the utility function

### Model specification with money in utility
- Utility function for asset holders (equation (53)):
  u(c_a_t, M_a_t/P_t, l_a_t) = log{[ z_a (c_a_t)^{η−1/η} + (1−z_a) (M_a_t/P_t)^{η−1/η} ]^{η/(1−η)}} − κ 1+ψ (l_a_t)^{1+ψ}
- Non-asset holders’ utility is the same as in (53) except that z_a ≠ z_h.
- Real money balances defined as m_i_t = M_i_t/P_t enter the budget constraints (equations (54) and (55)):
  - Asset‑holders’ budget constraint (54) includes m_a_t − m_a_{t−1}/π_t.
  - Non‑asset holders’ resource identity (55): c_h_t = w_t l_h_t − τ_h − $a + m_h_t − m_h_{t−1}/π_t.

### Money demand and aggregation
- First‑order conditions with respect to m_i_t yield money demand equations:
  - m_a_t = ( (1−z_a)/z_a )^{η} c_a_t ( i_{t−1}/i_t )^{−η}  (equation (56))
  - m_h_t = ( (1−z_h)/z_h )^{η} c_h_t  (equation (57))
- Prices p_a and p_h chosen so m_a c_a = m_h c_h = m_c = κ_m κ_c.
- Aggregate log-linear money demand (adding log-linear versions of (56) and (57)):
  - ˆm_t = ˆc_t − y ˆı_t,  where y = p^{η} β^{1−β}  (equation (58)).
  - This corresponds to eq. (47) in the text.

### Euler equation, inflation tax, and demand for non‑traded goods
- Euler equation (revised to account for inflation impact on non‑asset holders’ income) (equation (59)):
  ˆc_t = E_t(ˆc_{t+1}) − σ(ˆi_t − ˆπ_{t+1}) + λ[ˆy_t − E_t(ˆy_{t+1})] − θ_m[ˆτ_t − E_t(ˆτ_{t+1})],
  where ˆτ_t = ˆm_t − ˆm_{t−1} + π_t and θ_m = (1−p) κ_m α ψ Ξ^{−1}.
- With steady state positive real money balances, central bank liabilities are backed by government debt b_cb and an inflation tax accrues to the government.
- Demand for non‑traded goods depends positively on ˆπ_t, implying the IB_a equation includes an extra term −ε_π ˆπ_t where:
  - ε_π = κ_m Γ  (equation (60)).

### Monetary policy, open market operations, and incomplete sterilization
- Using eqs. (48) and (58) to link open market operations to a simple Taylor rule yields (equation (61)):
  ˆb_c_t − (1−ς) ˆb_c_{t−1} = −κ_m(ˆc_t − y φ_π ˆπ^N_t − ˆm_{t−1} + ˆπ_t) + (ˆR^*_t − ˆR^*_{t−1}).
- To allow incomplete sterilization, modify (61) introducing f (degree of sterilization) with 0≤f≤1 (equation (62)):
  ˆb_c_t − (1−ς) ˆb_c_{t−1} = −κ_m(ˆc_t − y φ_π ˆπ^N_t − ˆm_{t−1} + ˆπ_t) + f(ˆR^*_t − ˆR^*_{t−1}).
- Using (48) and (62) to solve for the nominal interest rate yields the policy rule in equation (49).
- Interpretation: Following a Taylor rule requires full sterilization of reserve accumulation; f measures departure from full sterilization.

### Numerical results and calibrated parameters (selected)
- Table 1. Selected Macroeconomic Variables, Uganda, 1998-2004 (averages and differences):
  - Net Aid: 1998-2000 = 7.9; 2000-2004 = 10.6; Difference = 2.7 (Fiscal, percent of GDP).
  - Expenditure (excluding external interest): 18.2; 20.5; Difference = 2.3.
  - Net Aid (Balance of Payments, percent of GDP): 7.7; 10.8; Difference = 3.1.
  - Current account deficit net of aid: 11.5; 12.1; Difference = 0.6.
  - Reserve accumulation: −0.3; 2.3; Difference = 2.5.
  - Base money growth: 0.4; 0.7; Difference = 0.3.
  - Real effective exchange rate (depreciation): 9.1; 6.3.
  - Terms of trade (worsening): 14.4; 5.9.
  - 91‑day real Treasury‑bill rate: 5.6; 8.4; Difference = 2.8.
  - Inflation: 3.1; 3.3; Difference = 0.2.
  - 91‑day Treasury‑bill rate: 8.2; 11.6; Difference = 3.4.
  - Source: IMF Staff Reports, IFS, Bank of Uganda.
- Table 2. Benchmark: Calibrated parameters (selected):
  - β = 0.99
  - κ_A = 0.078
  - ψ = 2
  - κ_g = 0.182
  - φ_g = 0.8
  - κ_c = 0.896
  - ζ = 10
  - ρ_A = 0.87
  - χ = 0.85
  - ρ_R = 0.9
  - α = 0.7
  - υ_b = 10000000
  - φ = 0.634
  - p = 0.42
  - δ = 0.75
  - φ_π = 1.5

### Sensitivity analysis (high‑level highlights)
- Table 3 and Table 4 report percent deviations from steady state under alternative specifications (examples below preserve exact reported figures):
  - No Reserve Accumulation, Benchmark:
    - ˆs = −2.7
    - ˆy = 0.0
    - ˆπ = −0.5
    - ˆr_t − E_t[ˆπ_{t+1}] = −0.3
  - Full Reserve Accumulation, Benchmark:
    - ˆs = 0.9
    - ˆy = 1.2
    - ˆπ = 7.0
    - ˆr_t − E_t[ˆπ_{t+1}] = 5.5
  - Sensitivity variants include: Flex Prices, Low ρ_A, No h, Implicit Labor substitution, GHH preferences, Open K, ζ = 0, φ_g = 1, p = 1, ρ_A = 0.6, υ_b = 0.0125, No Reserve Accumulation scenarios and Full Reserve Accumulation scenarios. Selected outcomes vary substantially across these variants (see reported percent deviations in Tables 3–4).
- Role of monetary policy (Table 4 selected figures):
  - Benchmark No Res. Accumul.:
    - ˆs_t = −2.7; ˆy_t = 0.0; ˆπ_t = −0.5; ˆr_t − E_t[ˆπ_{t+1}] = −0.3.
  - Headline IT No Res. Accumul.:
    - ˆs_t = −1.5; ˆy_t = 0.4; ˆπ_t = 0.8; ˆr_t − E_t[ˆπ_{t+1}] = 0.9.
  - Inc. Sterilization Full Res. Accumul.:
    - ˆs_t = 6.6; ˆy_t = 3.4; ˆπ_t = 18.7; ˆr_t − E_t[ˆπ_{t+1}] = 14.7.

*Source: Appendix B, "_wp1065 - Appendix B : Introducing money in the utility function" (IMF working paper content).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp1065.pdf_