## 3. Foreign Aid and Trade Balance Volatility

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### Introduction and motivation
- G-8 announcement: a $50 billion increase in official development assistance aimed at achieving the Millennium Development Goals (MDGs).
- Central questions:
  - How should monetary and fiscal policies respond to foreign aid inflows?
  - Can policy mitigate Dutch disease effects and reduce transmission of aid volatility to trade balance, consumption, and growth?
- Empirical puzzles and literature context:
  - Rajan and Subramanian (2005b): decline in labor-intensive and tradable manufacturing with higher aid (Dutch disease mechanism).
  - Bulir and Hamann (2002): aid volatility documented; Arellano et al. (2005): volatile aid flows cause substantial welfare losses.
  - Pallage and Robe (2003): median welfare cost of business cycles in developing countries between 10 and 30 times that of the United States.
- Key empirical observation: in 44 percent of sample years aid arrives during negative shocks; in such years aid can support exports.

### Model setup and key assumptions
- Economy: two-period, two-sector small open economy with exportable, importable, and non-tradable goods.
- Preferences and production:
  - Agents value real money balances (money-in-utility-function) and have Cobb-Douglas preferences over tradable and non-tradable goods; discount rate set to 1 in baseline.
  - Exportable (y_X) and non-tradable (y_N) sectors with decreasing returns to scale (0<α<1); aggregate labor fixed.
  - Learning-by-doing (LBD) externalities located in export sector: size of export sector in period one raises period-two productivity (equations (5) and (6)).
  - Public good P_x produced in period one using aid raises period-two productivity; production exhibits h′>0, h′′<0.
- Public finance and aid timing:
  - Donors set exogenously total dollar net present value A of aid and its allocation across periods.
  - A fraction λ of A (0<λ<1) finances period-one public good P_x; remainder transfers to consumers.
  - Public good uses tradable and nontradable inputs in proportions implied by consumer preferences.
- Financial/monetary structure:
  - Closed capital account; government bonds only interest-bearing instrument.
  - Fixed exchange rate assumed (EEE==21 in text figures); central bank balance sheet at end of period one summarized by equations (10) and (10’).
  - Net domestic assets BB−0 reflect monetary and fiscal decisions: BATRBB−−=−110.
  - Central bank can control net domestic assets and affect nominal interest rate r.
- Resource constraints:
  - Current accounts defined in foreign currency with trade balance TBt (equations (12-1) and (12-2)); intertemporal constraint implies 0=+CACA21.
  - Consolidated public sector budgets show intertemporal transfer via accumulation of international reserves by the central bank (equations (13-1) and (13-2)).
- Fiscal-monetary equivalence:
  - With flexible wages and non-traded prices and lump-sum taxes/transfers, fiscal and monetary policy are perfect substitutes for achieving any level of net domestic assets.

### Partial and general equilibrium theoretical findings
- Front-loading vs back-loading aid (keeping PV A constant):
  - Front-loading consumption aid increases period-one money supply, lowers interest rates, raises period-one consumption (tradable and non-tradable), and deteriorates the trade balance; the current account (including aid) improves and international reserves rise.
  - Front-loading productivity-enhancing aid tends to produce a greater deterioration of the trade balance and smaller accumulation of international reserves; more productive public investment → larger trade balance deterioration.
  - LBD externalities: larger LBD externalities reduce the deterioration in the trade balance from front-loading aid and increase accumulation of international reserves.
- Monetary policy and sterilization:
  - Reducing net domestic assets (sterilization) can fully offset the trade-balance deterioration from front-loading consumption aid by absorbing extra bond supply, raising interest rates, depressing private consumption, lowering nontradable prices, and improving the trade balance.
  - Proposition I (summary):
    - For constant PV A, increasing period-one consumption aid deteriorates the trade balance but raises international reserves; larger LBD externalities → smaller trade-balance deterioration and larger reserves accumulation.
    - Increasing period-one productivity-enhancing aid leads to greater trade-balance deterioration and smaller reserves accumulation; larger LBD externalities → smaller deterioration.
  - Proposition II (monetary policy):
    - Deterioration from front-loading consumption aid can be fully offset by a reduction in net domestic assets of the same size as the aid increase, regardless of LBD externalities.
    - Deterioration from front-loading productivity-enhancing aid can be offset by a greater reduction in net domestic assets than the size of the aid increase.
    - With LBD externalities, sterilization raises productivity and future consumption by reducing current private consumption.
- Comparison with other models:
  - Contrary to Krugman (1987) with sticky wages, here monetary tightening can improve the trade balance and raise exports because nontradable prices are flexible and LBD implies permanent productivity effects.

### Empirical evidence — panel results and stylized facts
- Data: unbalanced panel of 58 aid-receiving countries, median aid-to-GDP > 2 percent, population > 1 million, period 1960–2003.
- Sample summary statistics:
  - Mean aid-to-GDP ratio: 8.5 percent.
  - Median aid-to-GDP ratio: 7.3 percent.
  - “Negative-shock” years: about 44 percent of the sample.
  - Post-conflict years: 21 percent of the sample.
  - “Normal” years: about one third of the sample.
- Estimation methods: OLS and System GMM (SGMM) to address dynamic panel bias and endogeneity; instruments include lags t-2 and t-3 for aid, and additional lags for controls.
- Trade balance effects of aid:
  - Pooled estimates:
    - OLS: a one-percent-of-GDP increase in aid worsens the trade balance by 0.16–0.17 percent of GDP.
    - SGMM: a one-percent-of-GDP increase in aid worsens the trade balance by 0.24–0.29 percent of GDP.
  - “Normal” years (excluding negative shocks): a one-percent-of-GDP increase in aid can worsen the trade balance by as much as 0.54 percent of GDP (estimated).
  - In years of negative shocks, SGMM shows aid has either no effect or a positive effect on the trade balance.
- Exports effects of aid:
  - SGMM: in “normal” years aid significantly depresses exports; a one-percent-of-GDP increase in aid can reduce exports by 0.57 percent of GDP in normal years.
  - In years of negative shocks, foreign aid has no effect or tends to improve exports.
  - Evidence that aid has a significant negative effect on exports only before trade liberalization in one specification.
- Net domestic assets (NDA_dif) and policy offset:
  - NDA_dif captures annual change in central bank net domestic assets-to-GDP; negative NDA_dif implies sterilization (reductions in net domestic assets).
  - Estimated NDA_dif effects: coefficients strongly significant and negative in both trade balance and export regressions (OLS and SGMM), implying sterilization improves the trade balance and supports exports.
  - Reported ranges and examples:
    - Negative change in net domestic assets (t) coefficients range from -0.225 to -0.267 (statistically significant at 1% or 5% in reported specifications).
    - Other reported NDA_dif examples: -0.126, -0.149, -0.155, -0.006, -0.188, -0.171, -0.213, -0.143 (mixed significance).
  - Interaction with reserves: Reserves * change in net domestic assets (t) reported as -1.742 and -0.868 in selected specifications (statistical significance reported).
- Additional numerical evidence fragments in supplied content:
  - “0.18 percent of GDP at impact, with exports rising―according to SGMM estimates―by” (partial line).
  - “0.13 percent of GDP.” (presented as a key empirical finding in the excerpt).
- Identification and robustness:
  - Controls: export prices, export demand, negative natural shocks, post-conflict dummies; interactions with AID.
  - SGMM instruments: aid instrumented with lags t-2 and t-3; included 3-year lags of commodity price index and negative shock dummy.
  - J-test accepts exclusion restrictions used in specifications; first-stage F statistics reported for some instruments (examples: Std_AID F-statistics 5.34, 14.77, 14.84; Std_AID_Cn F-statistics 19.33, 31.01, 27.51).
- Cross-sectional evidence on volatility and sterilization:
  - Higher volatility of aid flows (Std_AID) significantly associated with higher volatility of the trade-balance-to-GDP ratio: selected Std_AID coefficients include 0.399, 0.571, 1.062, 0.612, 0.508 (significance reported).
  - Sterilization mitigates link between aid volatility and trade-balance volatility: Std_AID_Cn (Std_AID × sterilization dummy) coefficients include -0.272, -0.300, -0.226, -0.222, -0.301, -0.297, -0.257, -0.243 (several statistically significant).

### Policy implications and normative conclusions
- Macroeconomic policy prescriptions:
  - Sterilization (reductions in net domestic assets) can limit adverse Dutch disease effects by preventing real appreciation and protecting tradable sectors.
  - Sterilization reduces transmission of aid volatility to the trade balance and exports.
  - Expansionary policy can be optimal when immediate consumption and productivity returns to aid are large and donors’ disbursements are back-loaded—but this requires sufficient international reserves.
- When sterilization is welfare-improving:
  - Economy better off saving part of its aid for later (e.g., when expected future aid supporting consumption will drop).
  - Net current productivity effect of aid is low or negative because of Dutch disease.
- Important caveat:
  - In negative-shock years (44 percent of observations), aid can support exports; tightening policy in response to aid surges during such years may be inappropriate.
- Trade-offs and limits:
  - Sterilization costs (interest differentials and potential distortionary taxation to finance sterilization) can be large; introducing distortionary taxes would make sterilization costly.
  - Alternative: saving aid via government deposits at the central bank, though postponing aid-financed public investment may be costly.

### The optimal timing of aid and role of monetary policy (planner vs decentralized equilibrium)
- Two-step approach:
  1. Social planner chooses optimal distribution of consumption aid over time given PV A and aid for public investment A ~.
  2. Given an arbitrary distribution of aid, decentralized equilibrium may not achieve planner’s allocation; monetary policy can sometimes implement the planner’s allocation.
- Social planner’s maximization (selection highlights):
  - Maximize W(C1, C2, M P) = log C1 + β log C2 + χ log PM subject to AAAA ~ 21 ++ = and intertemporal smoothing condition * 2 2 1 1 11 C r P C P β + ==.
- Appendix I construction:
  - Introduce fictitious aid flows F1 and F2 with AFF=+21 such that current account balanced every period (T B1− = F1, T B2− = F2).
  - Optimal reserves accumulation: opt opt FA R 1`1 ~ − += with optimal trade balance AAR TB opt opt ~ 11 − − =.
- Proposition III — main cases:
  - Without LBD externalities:
    - If 0 1 TB < opt 1 TB (external financing constraint binding), monetary policy can implement planner allocation by setting nominal interest rate *11 r = ropt so unconstrained decentralized allocation equals opt.
    - If 0 1 TB > opt 1 TB, monetary policy cannot improve welfare; only front-loading aid can implement the optimum.
  - With LBD externalities:
    - Unconstrained decentralized allocation always implies overconsumption (*11 TB < opt 11 TB).
    - If 0 1 TB < opt 1 TB, monetary policy (raising interest rate above *r) can implement the optimum; alternatively donors can back-load aid to induce a binding external constraint.
    - If 0 1 TB > opt 1 TB, only front-loading aid can implement the optimal allocation (external balance constraint must remain binding).
- Intuition:
  - If aid is too front-loaded at interest rate *r, agents wish to save; central bank can raise bond supply (reduce net domestic assets) to prevent interest rates from falling and enable consumption smoothing.
  - If aid is too back-loaded, agents borrow against future aid; central bank must buy bonds (increase net domestic assets) to allow dissaving, but reserves may limit permissibility of expansionary policy.
  - With LBD, unconstrained decentralized outcome overconsumes because individuals do not internalize productivity gains from a larger export sector; monetary tightening can correct overconsumption by raising interest rates.

### Appendices — key mechanisms, existence, and robustness
- Appendix I:
  - Static equilibrium core relations: labor-market equalization, non-traded goods market equilibrium, money demand (A-3), aggregate resource constraints (A-4a, A-4b), intertemporal smoothing (A-5).
  - Unknowns: 15 real and nominal variables; 14 equations — implication that monetary policy (face value of bonds or nominal interest rate r) can target the current account via reserves R.
  - Existence and unicity: uniqueness of equilibrium for given R; existence requires certain bounds on R (defined via function G(R) and minimum current account surplus Rˆ).
  - Sufficient condition related to net domestic assets and growth: example numerical implication: if g = 5 percent and net domestic assets of central bank are worth 20 percent of GDP, this implies that 001.0 ≥ χ.
- Appendix I — proofs of Propositions I & II:
  - Decomposition of money supply (s M) and money demand (d M) loci as functions of trade balance and period-one aid (equations 13 & 14).
  - Impact of increased first-period consumption aid: money supply shifts up; downward pressure on interest rates; private consumption rises; trade balance deteriorates but by less than increase in A1.
  - Impact of increased aid for public investment: money demand shifts down (agents anticipate higher future income), trade balance deteriorates more than with consumption aid.
  - Sterilization: opposite shift in money supply improves current account and raises interest rate.
  - LBD externalities steepen money demand; given LBD, a given aid front-load produces smaller trade-balance deterioration and larger increases in equilibrium money balances than without LBD.
- Appendix II-a / II-b:
  - Results generalize to a managed float: central bank can replicate fixed-exchange-rate allocations by targeting price levels and reserves and choosing net domestic assets appropriately.
  - Figures 3a–3c show differences between consumption-frontloading without LBD, with LBD, and productivity-enhancing aid.
- Appendix III:
  - Pseudo first-stage system GMM diagnostics: instrument sets, F-tests, and over-identification J-statistics reported; many first-stage F tests > 10 (above 20 in 8 out of 10 regressions); Level regressions for NDA show low persistence consistent with weak F in those equations.

*Italic: Source: IMF Working Paper — 3. Foreign Aid and Trade Balance Volatility (content unit _wp06145).*

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

### _wp06145 - References................................................................................................................................59

### Figures
- 1.    Partial Equilibrium Effects of Aid Inflows and Macroeconomic Policy ..........................14
- 2.    General Equilibrium..........................................................................................................15
- 3a.   Front-Loading Consumption Aid without LBD Externalities .........................................16
- 3b.   Front-Loading Consumption Aid with LBD Externalities ..............................................55
- 3c.   Front-Loading Productivity-Enhancing Aid ....................................................................56
- 4.     Sterilization without LBD Externalities...........................................................................18

### Tables
- 1a.  The Impact of Aid and Macroeconomic Policies on the Trade Balance...........................33
- 1b.  The Impact of Aid and Macroeconomic Policies on the Trade Balance ..........................34
- 2a.  The Impact of Aid and Macroeconomic Policies on Exports ...........................................35
- 2b.  The Impact of Aid and Macroeconomic Policies on Exports ...........................................36

*Source: _wp06145 - References..............................................................................................................*

### 3.    Foreign Aid and Trade Balance Volatility........................................................................37

### 3.    Foreign Aid and Trade Balance Volatility

### Introduction and motivation
- At the Group of Eight (G-8) meeting in Scotland in July 2005, world leaders announced a $50 billion increase in official development assistance to poor countries aimed at achieving the Millennium Development Goals (MDGs).
- The paper studies how macroeconomic policies should respond to foreign aid inflows, developing a model where monetary and fiscal policies can help achieve an optimal spending path and have persistent effects on real variables in the presence of externalities.
- Context from prior literature:
  - Rajan and Subramanian (2005b) document a decline in the share of labor intensive and tradable industries in manufacturing as foreign aid increases, consistent with a Dutch disease mechanism.
  - Bulir and Hamann (2002) document aid volatility; Arellano et al. (2005) find volatile aid flows result in substantial welfare losses.
  - Pallage and Robe (2003) estimate a median welfare cost of business cycles in developing countries between 10 and 30 times that of the United States.
- Key empirical puzzles motivating the analysis:
  - Does macroeconomic policy mitigate Dutch disease effects?
  - Can policy reduce transmission of aid volatility to trade balance, consumption, and growth?

### Model setup and key assumptions
- Economy: two-sector small open economy with exportable, importable, and non-tradable goods; lasts two periods.
- Agents value real money balances (money-in-utility-function) and have Cobb-Douglas preferences over tradable and non-tradable goods; discount rate set to 1.
- Production: exportable (y_X) and non-tradable (y_N) sectors with decreasing returns to scale (0<α<1); aggregate labor fixed.
- Learning-by-doing (LBD) externalities located in export sector; the size of the export sector in period one, 1,X L, raises period-two productivity in both sectors (equations (5) and (6)).
- Public good P_x produced in period one using aid raises period-two productivity; production has decreasing marginal returns captured by h(·) with h′>0, h′′<0.
- Public sector:
  - Donors set exogenously the total dollar net present value A of aid over the two periods and its allocation across periods.
  - A fraction λ of A (0<λ<1) finances the period-one public good P_x; remainder transfers to consumers (equations (7-1) and (7-2)).
  - Public good production uses tradable and nontradable inputs in proportion implied by consumer preferences (equation (8)); public good financed only with foreign aid (equation (9)).
- Financial/monetary structure:
  - Capital account closed; government bonds only interest-bearing instrument.
  - Fixed exchange rate assumed (EEE==21), reflecting that the majority of aid-receiving countries have adopted either a fixed exchange rate regime or a managed float.
  - Central bank balance sheet at end of period one: REBBM⋅+−=)(01 (equation (10)), where:
    - 1 M is stock of money between period one and two;
    - BB−0 is net domestic assets (domestic bonds held by central bank);
    - R is net foreign assets (international reserves).
  - Net domestic assets BB−0 reflect both monetary and fiscal decisions: BATRBB−−=−110 (equation (10’)).
  - Central bank controls net domestic assets to target aggregate demand, real exchange rate, and net foreign assets; it can affect nominal interest rate r since capital account closed.
- Resource constraints and intertemporal budget:
  - Current accounts defined in foreign currency with trade balance TBt (equations (12-1) and (12-2)); intertemporal constraint implies 0=+CACA21.
  - Consolidated public sector budget constraints show intertemporal transfer of resources achieved through accumulation of international reserves by central bank (equations (13-1) and (13-2)).
- Equivalence of monetary and fiscal policy:
  - With flexible wages and non-traded prices, lump-sum taxes/transfers, fiscal and monetary policy are perfect substitutes; any level of net domestic assets can be achieved via monetary operations or fiscal adjustments.

### Partial and general equilibrium effects (theoretical findings)
- Front-loading foreign aid (changing timing while keeping net present value constant) has partial and general equilibrium effects on spending, trade balance, and productivity through:
  - Real exchange rate changes and resource reallocation away from tradable sectors (Dutch disease channel).
  - LBD externalities imply temporary real appreciation or policy-induced changes can have permanent effects on growth and competitiveness.
- Policy instruments:
  - Reducing net domestic assets (sterilization) can undo money supply expansion from aid inflows, prevent real appreciation, preserve tradable sector competitiveness, raise international reserves, and increase national savings—this is equivalent to postponing aid spending.
  - Expansionary macroeconomic policies can sometimes improve welfare if immediate consumption and productivity benefits of aid are large while donor disbursements are back-loaded; expansionary policy can front-load consumption provided international reserves are sufficiently large.
- Distinction from other models:
  - Krugman (1987) with sticky wages predicts monetary tightening reduces exports; this paper (with flexible nontradable prices and LBD) predicts monetary tightening can improve the trade balance and raise exports.
  - Sterilization literature (e.g., Calvo et al. 1995) finds monetary policy nonneutral in short run due to tradable price stickiness; here temporary sterilization effects translate into permanent growth effects via LBD.

### Empirical evidence and results
- Panel evidence on aid-receiving countries:
  - Foreign aid disbursements tend to deteriorate the trade balance (consistent with Dutch disease or higher import financing as aid rises).
  - Foreign aid inflows tend to depress exports in “normal” years (years not post-conflict and not affected by natural disasters or large negative commodity export price shocks).
  - Tighter macroeconomic policies improve the trade balance and raise exports; expansionary policies deteriorate the trade balance and lower exports (provided enough international reserves to finance larger trade gap).
  - Caveat: in years of negative shocks, which account for 44 percent of observations in the sample, foreign aid may have a positive effect on exports—suggesting aid can buffer exports from negative shocks and that tightening policy in response to aid surges in such years could be inappropriate.
- Cross-sectional evidence:
  - Controlling for openness to trade, countries where central bank net domestic assets fall in response to a surge in aid flows (“sterilization”) experience significantly smaller volatility of their trade balance.
  - This result holds when controlling for (i) country-specific commodity export price shocks, and (ii) potential endogeneity from donors’ responses to volatile exports and imports.

### Policy implications and normative conclusions
- Macroeconomic policies—monetary and fiscal—can be used to:
  - Limit adverse Dutch disease effects by preventing real appreciation and protecting tradable sectors.
  - Reduce transmission of aid volatility to trade balance and exports by sterilizing aid-related money supply expansion.
- Sterilization (reducing net domestic assets in response to aid inflows) is welfare-improving when:
  - The economy is better off saving part of its aid for later (e.g., when expected future aid supporting consumption will drop).
  - The net current productivity effect of aid is low or negative due to Dutch disease.
- Expansionary policy may be optimal when immediate consumption and productivity returns to aid are large and donors’ disbursements are back-loaded—but requires sufficient reserves.
- Important caveat for policy: when aid arrives during negative shocks (44 percent of sample years), aid can support exports; in such situations tightening macroeconomic policy in response to aid would be unnecessary and inappropriate.

### Model scope, limitations, and relation to literature
- Model abstracts from access to international capital markets (closed capital account) and assumes lump-sum fiscal instruments and flexible nontraded prices.
- Sterilization bears no direct welfare cost in this framework because taxes are lump-sum; introducing distortionary taxation would make sterilization costly but would not change main qualitative results.
- Findings align with empirical characteristics of aid recipients: small open economies, closed capital accounts, and evidence of LBD in export sectors (cited micro studies: Van Biesebroeck (2005), Blalock and Gertler (2004), Fernandes and Isgut (2005)).
- Contribution: shows how macro policy can replicate or substitute for an optimal spending/current account path in presence of aid and LBD externalities; complements literature on optimal management of exogenous transfers and sterilization.

*Source: IMF Working Paper — 3. Foreign Aid and Trade Balance Volatility (chapter/section content).*

### Appendix II-b. In Appendix II-a, we discuss how these results can be generalized to a

### Appendix II-b. In Appendix II-a, we discuss how these results can be generalized to a managed float.

### A. Partial Equilibrium Effects of Aid and Macroeconomic Policy
- Figure 1 illustrates the partial equilibrium effects of aid inflows and monetary policy on the real exchange rate in period one.
- The upward sloping locus (A-1) reflects labor market equilibrium:
  - Perfect labor mobility requires the marginal product of labor in the non-tradable and export sectors to be equalized.
  - To maintain this equality, the price of non-tradable goods (and, thus, the real exchange rate) needs to increase as employment in the non-tradable sector increases and its marginal productivity declines.
- The downward sloping locus (A-2) reflects goods market equilibrium:
  - Higher prices of non-tradable goods imply a lower demand for non-tradable goods and, therefore, lower employment in the non-tradable sector.
- Effects of aid and monetary policy in partial equilibrium:
  - As part of foreign aid is spent on nontradable goods, demand for nontradable goods rises, shifting locus (A-2) up and resulting in real exchange rate appreciation.
  - Monetary policy can undo such appreciation by reducing aggregate demand and shifting locus (A-2) back.
  - These are partial equilibrium effects: by reducing aggregate demand, monetary policy reduces imports, improving the current account balance and accumulating international reserves; that accumulation will increase back money supply and have an upward feedback effect on non-tradable prices.
- Note: Section A of Appendix I derives the equations underlying the loci (A-1) and (A-2).

### B. General Equilibrium Effects of Aid and Macroeconomic Policy
- Figure 2: general equilibrium level of money balances (vertical axis) as a function of the trade balance in period one (horizontal axis).
  - The upward-sloping line (13) captures the positive relationship (derived from the central bank’s balance sheet (10) and the current account balances (12)) between money supply and its three counterparts:
    - i) the domestic currency value of the trade balance, 1 TBE⋅
    - ii) the first-period aid inflows expressed in domestic currency, )~ (1 AAE+⋅
    - iii) the net domestic assets of the central bank BB− 0.
  - Equation (13) as presented: () )~ (101 AAEBBTBEM s +⋅+−+⋅=
  - For notational simplicity, the nominal exchange rate E is assumed to be equal to 1 in the figures.
  - The downward-sloping curve (14) shows how money demand declines as the trade balance improves:
    - Intuition: for a given income, a higher trade balance in period one is associated with higher savings, smaller consumption, and, therefore, lower money demand.
  - Equation (14) as presented: ATBI ATBI M d ++ − − − ⋅ = 12 11 1 ~ 1 1 χ
  - Appendix I derives equations (13)-(14), establishes existence and unicity of an equilibrium, and derives the two boundaries of the money demand function.
  - The curve (14) is defined when the trade balance is: i) above the threshold AAR ~ ˆ 1 −− that ensures nominal interest rates above the zero lower bound and ii) below the threshold AAR ~ 1max −− that ensures positive consumption in period one.

- Effects of front-loading foreign aid (Figure 3a; no LBD externalities):
  - Front-loading consumption aid (increasing 1 A while keeping A constant) shifts period one money supply up.
  - Initially higher money supply puts downward pressure on interest rates and induces agents to increase period one consumption and reduce period two consumption.
  - Higher period one consumption of tradables deteriorates the trade balance and causes a partial reduction of the initial increase in money supply.
  - Offset is partial and leaves interest rates below the initial level because part of the higher consumption is spent on nontradables.
  - Given that the trade balance deteriorates less than the initial increase in period one aid, the current account (which includes aid flows) improves.
  - The new equilibrium: lower trade balance and higher money balances.
  - Impact with externalities follows same logic; productivity-enhancing aid is discussed in Appendix II-b.

- Proposition I: For a constant net present value of total aid:
  - Increasing period one consumption aid deteriorates the trade balance but improves the current account and, therefore, raises the stock of international reserves. The larger LBD externalities are, the smaller is the deterioration in the trade balance and the larger is the accumulation of international reserves.
  - Increasing period one productivity-enhancing aid leads to a greater deterioration of the trade balance and a smaller accumulation of international reserves. The more productive public investment is, the greater is the deterioration of the trade balance and the smaller is the accumulation of international reserves. The larger LBD externalities are, the smaller is the deterioration in the trade balance.
- Proof: see Appendix I.

### C. General Equilibrium Effects of Macroeconomic Policy
- Figure 4: sterilization can offset effects of front-loading consumption aid.
  - As interest rates increase to absorb the additional supply of bonds, private agents postpone consumption, nontradable prices fall relative to tradable prices, and the trade balance improves.
  - In the limit, monetary policy can fully undo the effects of an increase of consumption aid on the trade balance.
  - Similar temporary effects of monetary policy are noted in Edwards (1988) and Calvo, and others (1995), where a temporary depreciation of the real exchange rate is associated with higher real domestic interest rates.
- With LBD externalities:
  - Money demand is steeper, so the same reduction in net domestic assets leads to a smaller improvement of the trade balance, but the trade balance would have deteriorated less initially.
  - Monetary policy permanently affects the productive structure: monetary tightening temporarily depreciates the real exchange rate, leads to an expansion of the export sector, which leads to greater LBD and higher productivity in the future.
  - Krugman (1987) also argues monetary policy has permanent effects with externalities, but with opposite effects under his assumptions of balanced trade and sticky domestic wages.
- Sterilizing money supply effects of front-loading productivity-enhancing aid:
  - Will reduce period one private sector consumption, improve the trade balance, and raise international reserves and national savings, while allowing higher aid-financed public expenditure.
  - Full sterilization would shift back the money supply line to its original position while money demand remains shifted down, so the current account and international reserves would remain below their initial level (Figure 5 reference).
  - In the presence of LBD externalities, sterilization raises productivity and future consumption by reducing current private consumption, partially offsetting Dutch disease effects of an increase in first period aid (1 A∆ or A∆ %).
  - Associating sterilization with an increase in aid-financed productivity-enhancing public expenditure A ∆ % would maximize productivity benefits of aid, to be traded off against costs in terms of postponed consumption, which could be large under a negative output shock.

- Proposition II summarizes general equilibrium effects of monetary policy:
  - The deterioration in the trade balance associated with front-loading consumption aid can be fully offset by a reduction in net domestic assets (“sterilization”) of the same size of the aid increase no matter whether there are or not LBD externalities.
  - The deterioration in the trade balance associated with front-loading productivity-enhancing aid can be offset by a greater reduction in net domestic assets (“sterilization”) than the size of the aid increase.
  - In the presence of LBD externalities, sterilization raises productivity and future consumption by reducing current private consumption.
- Proof: see Appendix I.

### IV. THE OPTIMAL TIMING OF AID AND MACROECONOMIC POLICY
- Two-step approach:
  1. Define the welfare maximization program of a social planner who chooses an optimal distribution of consumption aid over time given the net present value of aid inflows A.
  2. Show that, given an arbitrary distribution of aid over time, agents may not achieve the welfare-maximizing allocation in the decentralized equilibrium and discuss how monetary policy can improve welfare.

#### A. Social Planner’s Problem and Optimal Timing of Aid
- Assumptions:
  - Net present value of aid A and the aid for public investment A ~ are exogenously fixed.
  - Social planner chooses optimally 1 A and 2 A, given a real interest rate equal to the subjective discount rate of the representative agent.
- Social planner’s formal maximization program:
  - Maximize W(C1, C2, M P) = log C1 + β log C2 + χ log PM subject to:
    1. AAAA ~ 21 ++ =, where A ~ and A are exogenous;
    2. * 2 2 1 1 11 C r P C P β + ==, where 1 ≤ β is the subjective discount factor of the representative agent and * r is the nominal interest rate that, in equilibrium, determines a real interest rate equal to 1 1 β −.
  - Note: This real interest rate is also the real interest rate that would prevail under perfect capital mobility if the rest of the world had the same discount factor β.

*Italic: Source: _wp06145 - Appendix II-b. In Appendix II-a, we discuss how these results can be generalized to a managed float.*

### Appendix I derives a sufficient condition for a solution to this problem to exist. Our approach

### _wp06145 - Appendix I derives a sufficient condition for a solution to this problem to exist. Our approach

### Appendix I: planner construction and fictitious aid
- Social planner solves by choosing fictitious aid flows F1 and F2 with AFF=+21 such that the current account is balanced in every period (i.e., T B1− = F1 and T B2− = F2).
- Optimal consumption/trade-balance path characterized by opt T B1− = opt F1 and opt T B2− = opt F2, along which donors distribute aid so private agents implement the consumption plan associated with subjective discount factor β without aggregate saving/dissaving.
- If aid is not distributed optimally (opt FA1~ ≠+ and opt FA2 ≠), equivalent welfare can be achieved through accumulation/decumulation of international reserves and corresponding current account deficits/surpluses.
- Welfare-maximizing accumulation of reserves needs to be opt opt FA R 1`1 ~ − += with associated optimal trade balance AAR TB opt opt ~ 11 − − =, providing an optimal path for the real exchange rate opt opt e e 2 1 , .

### Decentralized equilibrium and the role of monetary policy
- Monetary policy affects the real interest rate and therefore agents’ decisions; characterize monetary stance by nominal interest rate ropt chosen to target the optimal trade-balance path (or equivalently the real exchange rate path opt opt TB TB 2 1 , , / opt opt e e 2 1 , ,).
- Define:
  - *1 TB: trade balance associated with the unconstrained decentralized allocation if agents could borrow/lend at interest rate *r (associated with β) without limit.
  - 0 1 TB: lowest possible period-one trade balance financeable given stock of international reserves and period-one consumption aid A1.
- When the external financing constraint is binding (0 1 TB < opt 1 TB), front-loading aid (raising A1) can reduce 0 1 TB until the optimal allocation becomes implementable in a decentralized equilibrium.

### Proposition III — main cases and policy implications
- In the absence of LBD externalities:
  - When 0 1 TB < opt 1 TB, monetary policy can make private agents achieve the optimal allocation through an unconstrained decentralized equilibrium (i.e., *11 TB = opt 11 TB) by maintaining a nominal interest rate *11 r r opt = such that, in equilibrium, the real exchange rate is opt opt e e 2 1 , .
  - When 0 1 TB > opt 1 TB, monetary policy cannot improve welfare; only front-loading aid can make agents achieve the optimal allocation.
- In the presence of LBD externalities:
  - The unconstrained decentralized allocation always leads to overconsumption (i.e., *11 TB < opt 11 TB and opt e e 1 * 1 >).
  - When 0 1 TB < opt 1 TB, monetary policy can make private agents achieve the optimal allocation through a decentralized equilibrium by targeting an interest rate *opt r r >. (Alternatively, donors can back-load aid to induce a binding external constraint so that *0 11 1 opt TB TB TB <=.)
  - When 0 1 TB > opt 1 TB, monetary policy cannot improve welfare and only front-loading aid can implement the optimal allocation. (However, the external balance constraint must remain binding in equilibrium so that *0 11 1 opt TB TB TB <=.)

### Intuition — timing of aid and macro policy without LBD externalities
- If at interest rate *r first-period aid is too front-loaded:
  - Agents wish to save part of first-period aid; they increase demand for government bonds, bidding down interest rates.
  - Monetary authority prevents rates from falling by raising supply of bonds (reducing net domestic assets), enabling greater private saving and consumption smoothing.
  - As private consumption falls, trade balance improves, real exchange rate depreciates, and international reserves increase.
  - With no limit to reduction in net domestic assets (net domestic assets can become negative) and to accumulation of reserves, private agents can always achieve the optimal allocation via decentralized equilibrium if the central bank targets *r.
- If at *r first-period aid is too back-loaded:
  - Agents wish to borrow against future aid, sell government bonds, bidding up interest rates.
  - Monetary authorities must buy bonds (increase net domestic assets) to allow dissaving; as consumption rises, trade balance deteriorates and reserves fall.
  - When reserves reach zero the external balance constraint becomes binding and monetary policy cannot further offset an excessively back-loaded distribution.

### Intuition — timing with LBD externalities
- With LBD externalities, unconstrained decentralized outcome always implies overconsumption.
- Monetary policy can raise the interest rate above *r to reduce current consumption and real exchange rate appreciation, aligning the real exchange rate with opt opt e e 2 1 , .
- If the external constraint is binding at *r because of overconsumption only (i.e., *0 11 1 opt TB TB TB <<), raising the interest rate to *opt r r > can implement the optimal allocation.
- If the optimal allocation is infeasible because the external constraint would remain binding even after correcting overconsumption (i.e., *0 11 1 opt TB TB TB <<), only front-loading aid can achieve the optimal allocation; the external constraint must remain binding (i.e., *0 11 1 opt TB TB TB <=).

### Empirical evidence — panel estimates (stylized facts consistent with model)
- Data: unbalanced panel of 58 aid-receiving countries, median aid-to-GDP > 2 percent, population > 1 million, period 1960–2003.
- Sample summary statistics:
  - Mean aid-to-GDP ratio: 8.5 percent.
  - Median aid-to-GDP ratio: 7.3 percent.
  - “Negative-shock” years represent about 44 percent of the sample.
  - Post-conflict years represent 21 percent of the sample.
  - “Normal” years account for about one third of the sample.
- Estimation methods: OLS and System Generalized Method of Moments (SGMM); SGMM used to address dynamic panel bias and potential endogeneity of foreign aid and macro policies.
- Baseline dynamic panel specification includes trade-balance-to-GDP or exports-to-GDP as dependent variable, country fixed effects, foreign aid-to-GDP, annual change in central bank net domestic assets-to-GDP (difNDA_), and controls (index of real commodity export prices, log of import demand by trading partners). Additional dummies: negative shock, post-conflict, trade liberalization; some interactions with AID.

### Empirical findings — trade balance and exports responses to aid
- Trade balance:
  - When not distinguishing subsamples, a one-percent-of-GDP increase in aid worsens the trade balance by:
    - 0.16–0.17 percent of GDP in OLS regressions.
    - 0.24–0.29 percent of GDP in SGMM regressions.
  - In “normal” years (excluding negative shocks), a one-percent-of-GDP increase in aid can worsen the trade balance by as much as 0.54 percent of GDP (estimated).
  - In years of negative shocks, SGMM estimates show aid has either no effect or a positive effect on the trade balance.
  - Estimating separate coefficients for post-conflict years does not materially change these conclusions.
- Exports:
  - SGMM regressions show that in “normal” years aid significantly depresses exports.
  - The impact on exports can be as large as a one-percent-of-GDP increase in aid reducing exports by 0.57 percent of GDP in normal years.
  - In years of negative shocks, foreign aid has no effect or tends to improve exports.
  - Column (10) evidence: aid has a significant negative effect on exports only before trade liberalization in one specification.
- Identification and robustness:
  - Controls include export prices, export demand, negative natural shocks, and post-conflict dummies to limit omitted-variable bias.
  - SGMM treats aid as endogenous: aid at time t instrumented with lags t-2 and t-3; also include 3-year lags of commodity price index and negative shock dummy in instrument set. J-test accepts exclusion restrictions used.

### Empirical findings — net domestic assets (NDA_dif) and policy offset
- NDA_dif (annual change in central bank’s net domestic assets-to-GDP) captures macroeconomic policy response to aid inflows; can reflect monetary policy and fiscal policy actions.
- Sterilization interpretation:
  - If countries sterilize aid: NDA_dif takes negative values (reductions in net domestic assets offset aid-driven rise in net foreign assets).
  - Expansionary macroeconomic policies associated with positive NDA_dif.
- Estimated effects:
  - In both trade balance and export regressions (OLS and SGMM), NDA_dif coefficient is strongly significant and negative (columns referenced in text).
  - These estimates suggest sterilization policy improves the trade balance and maintains export levels in the face of aid inflows.
- Note: the manuscript text is truncated before completing a numerical statement on the magnitude of the NDA_dif effect; no additional numeric value is provided in the supplied content.

*Source: _wp06145 - Appendix I and accompanying sections (excerpt provided).*

### 0.18 percent of GDP at impact, with exports rising―according to SGMM estimates―by

### _wp06145 - 0.18 percent of GDP at impact, with exports rising―according to SGMM estimates―by

### Key finding
- 0.18 percent of GDP at impact, with exports rising―according to SGMM estimates―by

*Source: _wp06145 - 0.18 percent of GDP at impact, with exports rising―according to SGMM estimates―by*

### 0.13 percent of GDP.

### _wp06145 - 0.13 percent of GDP.

### Key empirical findings
- Monetary tightening (reductions in net domestic assets, NDA_dif) improves the trade balance and raises exports.  
  - Negative change in net domestic assets (t) coefficients (Table 1b / Table 2b system GMM specifications) range from -0.225 to -0.267 (statistically significant at 1% or 5% in reported specifications).
  - Positive change in net domestic assets (t) coefficients are smaller in magnitude and less consistently significant, examples include -0.126, -0.149, -0.155, -0.006, -0.188, -0.171, -0.213, -0.143 (mixed significance; some at 10% or 5%).
- Interaction with international reserves matters: the interaction term Reserves * change in net domestic assets (t) is reported as -1.742 and -0.868 in selected specifications, with statistical significance reported (e.g., [2.20]**, [0.97]).
- The government balance has the expected positive sign on exports and trade balance but is statistically significant only in some export regressions (examples: Government balance (t) reported coefficients 0.024 and -0.018 in Table 1a; 0.027 and 0.106 in Table 2b with significance in export regressions).
- Panel system GMM specification treats NDA_dif and the government balance as predetermined to address possible central bank observability of contemporaneous shocks; identifying assumption: lags of NDA_dif dated t-1 or earlier are orthogonal to first-differences of the export/trade balance error term.
- Sargan tests support instrumentation validity; pseudo first-stage suggests weak instruments are unlikely to distort system GMM results (Appendix III referenced).

### Cross-section evidence on volatility and sterilization
- Higher volatility of aid flows (Std_AID) is significantly associated with higher volatility of the trade-balance-to-GDP ratio.
  - Selected Std_AID coefficients (Table 3, median ODA/GDP > 4% sample) include 0.399, 0.571, 1.062, 0.612, 0.508 (with reported significance e.g., (2.70)**, (3.41)***, (3.40)***, (4.63)***, (2.96)***).
- Sterilization mitigates the link between aid volatility and trade balance volatility:
  - Std_AID_Cn (Std_AID multiplied by sterilization dummy) coefficients include -0.272, -0.300, -0.226, -0.222, -0.301, -0.297, -0.257, -0.243 (several statistically significant, e.g., (2.31)**, (1.79)*, (2.22)**, (1.89)*).
- Mean_MX (trade openness scaling variable) and Std_COMM (commodity price volatility) enter positively:
  - Example Mean_MX entries: 0.127, 0.124, 0.118, 0.124, 0.142, 0.127, 0.124, 0.116, 0.124, 0.147 (all reported with high significance, e.g., (8.77)***, (10.31)***).
  - Example Std_COMM entries: 0.00039, 0.00044, 0.00035, 0.00042, 0.00053, 0.00039, 0.00047, 0.00031, 0.00044, 0.00056 (significance reported in many specifications).

### First-stage and robustness checks
- First-stage regressions for system GMM show lags of Aid / GDP and NDA / GDP with multiple coefficients; examples:
  - In Table 4a (difference equation) Change in NDA/GDP (t-1) reported 0.047 with [1.58]; in level equation Change in NDA/GDP (t-1) reported -0.992 with [18.38]***.
  - Several lagged Aid / GDP coefficients and lagged trade-balance/export variables are reported with statistical significance (e.g., Aid / GDP (t-2) coefficients -0.152, -0.044, -0.102 with [2.87]***, [1.23], [1.42]; Aid / GDP (t-2) levels 0.234, -0.032, -0.007 with [5.10]***, [0.91], [0.08]).
- Standard tests of instrument strength and over-identification:
  - IV first-stage F statistics reported in Table 3 (examples): Std_AID F-statistics 5.34, 14.77, 14.84; Std_AID_Cn F-statistics 19.33, 31.01, 27.51; Mean_MX sometimes weak (Frankel and Romer instrument confirmed to be weak in literature).
  - J-Statistics (p-values) reported in Table 3 examples: 0.43, 0.20, 0.32, 0.15 for over-identifying restrictions; Stock and Yogo critical values referenced (7.56 and 16.87 thresholds for tests with two endogenous variables and four instruments).

### Theoretical mechanism and interpretation
- Theoretical model distinguishing flexible-price environment (learning-by-doing externalities and large informal sectors) from sticky-price models (Krugman, 1987):
  - In the paper’s model, domestic prices are flexible; a monetary contraction depreciates the real exchange rate and makes exports more competitive.
  - In sticky-wage/price models, monetary contraction reduces domestic demand and imports but does not spur exports; in the long run exports fall as real exchange rate appreciates.
- Role of international reserves:
  - With closed capital accounts, expansionary macro policies cannot deteriorate the trade balance unless international reserves finance it; initial reserves moderate the effect of positive NDA_dif on trade balance and exports.
  - Without reserves, nominal depreciation would offset domestic price increases and leave the real exchange rate and exports unchanged.
- Sterilization costs and limits:
  - Sterilization costs (difference between interest rates on sterilization bonds and international reserves) can be large and distortionary; taxes to finance sterilization can reduce welfare if they are distortionary or depress interest-sensitive private investment.
  - Saving aid via government deposits at the central bank is an alternative but may be costly if fiscal surpluses are achieved by postponing aid-financed public investment.

### Policy implications and prescriptions
- Macroeconomic policy can be used to limit Dutch disease effects of aid and smooth trade balance and export volatility caused by aid volatility.
- Policy effectiveness depends on timing/distribution of aid and reserve levels:
  - When aid is front-loaded, accumulating international reserves (higher national savings) can improve welfare.
  - When aid is back-loaded, expansionary monetary or fiscal policy can improve welfare only if the stock of international reserves is large enough.
- Coordination and trade-offs:
  - Coordination between fiscal and monetary authorities is crucial; lack of coordination complicates implementation.
  - Policymakers should weigh sterilization costs and potential adverse effects on private investment against benefits of reducing Dutch disease effects.
- Context-specificity:
  - The empirical results suggest the impact of aid on exports depends on country circumstances; in reconstruction or large negative-shock periods, aid can have positive effects on exports.
- Donor-community reference:
  - The declared objective to raise ODA to 0.7 percent of industrial countries’ GDP from a level currently about one third of that target is welcomed in the paper’s view (numerical target and qualitative statement reported as in source).

*Italic line: Source: _wp06145 - 0.13 percent of GDP.*

### APPENDIX I

### APPENDIX I: Solution Strategy

### Static equilibrium and core relations
- Perfect mobility of labor implies equal marginal productivity of labor in tradable and non-tradable goods markets:
  - ()
tNNtNtNtNXtXtXt
LFapLLFapw
,,,,,,
′
⋅⋅=−
′
⋅⋅= , t=1,2.
- Hence:
  - ′
′
⋅=
N
X
tN
tX
tt
F
F
a
a
qe
,
,
, t=1,2. (A-1)
- Non-traded goods market equilibrium yields the two period-specific equilibrium relations (combining labor-market and aggregate budget constraints):
  - Period 1: ()[]()()()()⎥⎥⎦⎤⎢⎢⎣⎡−+−⋅⋅−=−⋅⋅*1`11111111T NXXN N NN p RA LLFaqxLFae γγ (A-2a)
  - Period 2: ()()()()()⎥⎥⎦⎤⎢⎢⎣⎡+ +−⋅⋅−=⋅⋅*2,`2 2,2,12,2, 2 1 T NXXNNN p RA LLFaqLFae γγ (A-2b)
- Demand for real money balances:
  - ⎟⎠⎞⎜⎝⎛+= r CP M 1 11 1 χ (A-3)
- Economy-wide resource constraints (aggregate private-sector constraint substituted):
  - 1111 AIRCP+=+ (A-4a)
  - RAICP++= 2222 (A-4b)
- Intertemporal consumption smoothing condition linking interest rates and CPI:
  - 1 2 12 / 1 C C PP r = + (A-5)

### Unknowns and equations; role of monetary policy
- The model has 15 unknown variables:
  - real exchange rates 1 e and 2 e,
  - equilibrium allocations of labor 1,N L and 2,N L,
  - CPI levels 1 P and 2 P,
  - aggregate consumption indices 1 C and 2 C,
  - nominal interest rate r,
  - nominal value of domestic currency 1 M and foreign currency * 1 M,
  - face value of bonds B held by private agents,
  - reserves R accumulated during period 1,
  - allocation of aid for productive purposes A ~ between non-tradable Nx and tradable goods Tx.
- There are 14 equations:
  - equilibrium on non-traded good market,
  - demand for labor in traded and non-traded sectors,
  - definition of the consumer price index,
  - aggregate resource constraints,
  - demand for domestic bonds,
  - demand for real money balances,
  - money supply identity,
  - balanced budget equation,
  - production technology of the public good.
- Implication:
  - The government can use monetary policy (face value of bonds B sold to private agents, or nominal interest rate r) to affect macroeconomic outcomes by targeting the current account via accumulation of reserves R.
- Real consumption indexes (as given):
  - ()
⎪⎪⎩⎪⎪⎨⎧⎥⎥⎦⎤⎢⎢⎣⎡⋅+ +⋅+⋅=
⎥⎥⎦⎤⎢⎢⎣⎡⋅ −+⋅+⋅=
*2,2 2 2,2 2 2 2,22 *1,1 1 1,1 1 1 1,11 T XN T XN pe RA y e q yeC pe RA y e q yeC γ γ

### Interpretation of national savings and monetary policy channel
- With a closed capital account and no accumulated factor of production, national savings are reflected in accumulation of foreign currency by the central bank and individuals.
- Monetary policy affects inter-temporal allocation of resources insofar as it has a (temporary) effect on the current account balance by reducing (or increasing) aggregate demand through effects on nominal and real interest rates and private savings decisions.

---

### A. Proofs of Propositions — Existence and Unicity of Equilibrium

### Strategy and main claims
- Assume for simplicity 0 ~ =A (result extends to 0 ~ ≠A).
- Two-step approach:
  - Show that if an equilibrium exists, it is unique.
  - Establish existence of an equilibrium.

### Unicity of equilibrium
- Aggregate intertemporal decisions characterized by current account balance in period 1 (equivalently reserves R).
- For each current account balance R there exists a unique real-economy equilibrium characterized by:
  - real exchange rates ( )Re 1 and ( )Re 2,
  - price levels ( )1 RP and ( )2 RP,
  - consumptions ( )RC 1 and ( )RC 2,
  - labor allocations ( )RL N1, and ( )RL N2.
- The real side is a standard Dutch disease model with learning-by-doing externality (references listed in source).
- Accumulation of reserves R is pinned down by money market equilibrium: s M and d M loci are well-behaved; at most one R guarantees money market equilibrium.

### Existence of equilibrium — necessary conditions
- Money demand locus derived by combining (A-3) and intertemporal smoothing:
  - 2211 11 1 CPCP M d − ⋅ = χ
- Necessary condition for existence:
  - 2211 CPCP < , which translates into a constraint on admissible current accounts (reserves R).
- Under assumption of constant international price of import good ( ** 2, * 1, TTT ppp == ), and using Appendix I.A equations, the condition becomes:
  - ()22,22,211,11,1 2AyeyqAyeyqR NXNX +⋅+⋅−+⋅+⋅>
- Define G(R) via:
  - ()⎟⎠⎞⎜⎝⎛+−+= 2 2 1 1 A E I A E I RG.
- Monotonicity and sign properties show existence of a minimum current account surplus Rˆ (ˆR) above which an equilibrium always exists:
  - ˆR in [ max , 0 ] with Rˆ defined by implicit function:
    - ()() RA E RI RA E RI ˆ ˆ ˆ ˆ 2 2 1 1 ++ = − + if ()00>G,
    - and 0 ˆ = R if ()00≤G,
    - max R defined by implicit function: ()0 max 11 = R CP, or: ()0 1 max1 max > += A E RI R.
- G is increasing in degree of frontloading of foreign aid (21 A A −), hence Rˆ increases with 21 A A − but by less than 21 A A −.

### Additional sufficiency condition
- Beyond the two constraints on R, require:
  - () () 00 = ≥ = R M R M sd
- Equivalent inequality (translated into condition on net domestic assets and growth rate):
  - g AI BB AI AI AI BB ⋅ + − = ⎥⎦⎤⎢⎣⎡ − + + ⋅ + − ≥ 22 0 21 22 22 0 1 χ
  - where g is growth rate of income including aid between period 1 and 2.
- Numerical example:
  - If g = 5 percent and net domestic assets of central bank are worth 20 percent of GDP, this implies that 001.0 ≥ χ.

---

### B. Proof of Propositions I & II — Real and Monetary Effects of Aid Inflows and Monetary Policy

### Decomposition of current account and money-market loci
- Current account R expressed as sum of trade balance in period 1 and first period aid:
  - A A T B R ~ 11 ++ = , and 22 A T B R − − = .
- Present value result:
  - The present value of the trade deficit equals the present value of aid inflows.
- Money demand and money supply loci as functions of trade balance and aid inflow in period 1:
  - () () ⎪⎪⎩⎪⎪⎨⎧ ++ − − − − ⋅ = ATBI ATBI M AATBBBM d s 12 11 110 1 ~ 1 1 χ  (equations 13 & 14)
- d M locus is an equilibrium relation between income, external balance, and money demand; it is a decreasing function of the first-period trade balance.

### Impact of increased first-period aid (holding total PV of aid A and bond supply constant)
- Increase in first-period consumption aid A1 realized by lowering second-period aid:
  - Money supply initially shifts up by amount of the aid inflow, for a given trade balance.
  - At initial trade balance, money supply exceeds money demand → downward pressure on interest rates.
  - Agents reduce savings, increase money demand and consumption → deterioration of trade balance in period 1.
  - Movement is left along d M locus; new equilibrium at 1 1 E.
  - Deterioration of trade balance is smaller in absolute terms than increase in first-period aid because part is spent on non-tradable goods. Equilibrium current account (including aid) improves by less than increase in A1.

### Impact of increased aid for public investment ( A ~)
- Money demand curve shifts down because larger share of trade balance generated by public investment reduces private money demand.
- For given trade balance, private sector must save more → depresses money demand.
- As A ~ increases productivity in period 2, 2 I increases → money demand shifts further down (agents anticipate higher second-period income and save more).
- For small χ, money supply effect dominates demand effect, and money will increase in equilibrium.
- Summary conclusion:
  - Same increase in aid has different implications depending on whether spent on public investment versus private consumption.
  - Deterioration of trade balance is greater if aid is spent on public investment and is larger the more productive the foreign aid is.

### Impact of sterilization (reduction in net domestic assets of central bank)
- Opposite shift in money supply curve without shift in money demand curve → new equilibrium with improved current account and higher interest rate.

### Impact of Dutch disease (learning-by-doing) externalities
- With LBD, money demand schedule is steeper.
- Reasoning:
  - LBD externality implies an improvement in the equilibrium current account net of aid → lower aggregate consumption in period 1 → lower consumption of non-traded good in period 1 → larger traded sector → higher productivity gain in period 2.
  - For a given aggregate consumption, agents anticipate productivity effect and reduce first-period consumption → lower money demand.
  - Since agents do not internalize effect of own consumption on productivity, savings remain too low from welfare perspective.
  - Given A A R T B ~ 11 − − = , money demand in money–trade balance space is steeper.
- Formal slope result:
  - For any trade balance 1 TB, slope of money demand schedule:
    - 0 1 2 2 22 1 22 221 11 111 1 1 < ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡ ∂ ∂ ⋅ ∂ ∂ + ∂ ∂ ⋅ ∂ ∂ + ∂ ∂ ⋅ ∂ ∂ = +++−−+ = 321321321321321321 TB I I CP TB CP CP M TB CP CP M dTB dM dd TBTB d
  - 0 1 2 = ∂ ∂ TB I if 0 = z and 0 1 2 > ⎟⎟⎠⎞⎜⎜⎝⎛ ∂ ∂ TB I dz d . Hence 0 1 < ⎟⎟⎠⎞⎜⎜⎝⎛ dTB dM dz d d.
- Implications:
  - An increase in first-period aid leads to a smaller deterioration of the trade balance the larger the LBD externality.
  - Symmetrically, a given reduction in net domestic assets of the central bank leads to a smaller improvement in the trade balance the larger the LBD externality.

---

### Proposition III: The Optimal Allocation of Aid

### Planner’s problem and setup
- Assume A ~ exogenous; focus on time allocation of consumption aid for given PV of aid A.
- Social planner chooses time allocation of aid to maximize representative agent intertemporal utility subject to:
  - (1) total net present value of consumption aid and aid for public investment set exogenously;
  - (2) interest rate equal to rate of time preference of agents:
    - 1 11 22 * − == CP CP rr, where 1 1 * − = β r (1 < β) is subjective discount rate (previously assumed 1 = β).
- Donor objective (for given PV of aid A) choosing trade balance TB (with A A R TB ~ 11 − − = ):
  - ⎭⎬⎫⎩⎨⎧ ⎟⎟⎠⎞⎜⎜⎝⎛+ + += 1 2 * 1 loglog 1 1 log 1 P M C r C W Max TB χ
  - where ⎟⎠⎞⎜⎝⎛+⋅= * 1 1 1 1 r C P M χ is demand for money, and 1 C and 2 C are consumption indexes; productivity parameters depend on equilibrium trade balance:
    - ) ~ ( 1 222 A A R a a a XN − − ==

### Transformation and solution approach
- Problem is equivalent to deriving optimal saving plan for economy where subjective discount rate is:
  - ()() χ β + ⋅ + = 11 1 *
r
- By transforming to fictitious aid flows F1 and F2 in balanced current-account economy:
  - R A A F − += ~ 11 1 and R A F += 2 2 ; total PV preserved: A F F = + 21
- Optimal accumulation of reserves and trade balance in first period:
  - opt opt F A A R 1 ` 1 ~ − + = and A A R T B opt opt ~ 11 − − =

### Comparative statics and welfare conditions (sketch)
- Derivative of welfare with respect to F1 and F2 decomposed into labor, price, consumption and productivity effects (detailed decomposition in source).
- Notable identities and envelope conditions used:
  - (1) 0 , , = ∂ ∂ ⋅ ∂ ∂ = ∂ ∂ tN t tN I W L I L W , t=1,2 (from firms' profit maximization)
  - (2) 0 = ∂ ∂ t t e C, t=1,2
  - (3) 0 2 2 22 = ∂ ∂ ⋅ ∂ ∂ = ∂ ∂ e C C W e W
  - (4) 0 1 1 11 = ∂ ∂ ⋅ ∂ ∂ = ∂ ∂ e C C W e W
  - (5) tt t t tt FI F C C W F W + = ∂ ∂ ⋅ ∂ ∂ = ∂ ∂ * 1 , t=1,2, with: t t t E I I = *
- These conditions allow comparison between decentralized equilibrium allocation of aid flows and the social planner’s optimum, and identify when reallocation of aid or monetary policy can improve welfare.

*Source: _wp06145 - APPENDIX I*

### APPENDIX I

### _wp06145 - APPENDIX I

### Marginal benefit/cost, labor allocation, and sufficient conditions
- Marginal benefit (MB) and marginal cost (MC) of increasing 1F are given respectively by:
  - 1*1 1 1 )( FI FMB +=
  - () 1 1 1 1, 2 2 *2 *2 2 2 *2 1 1 F e e L h a z FI I FI FMC N ∂ ∂ ∂ ∂ ⋅⋅ + + + =
    - where 12 FAF−=
- Sufficient condition for the MC curve to be downward sloping: 2 a z h small, equivalent to: 1, 1 1 X zL a z + <<. A sufficient condition therefore: 1 1 << a z.
- Identity for MC derivatives:
  - ()1 2 21 1 1 ' F I I MC F MC FMC ∂ ∂ ⋅ ∂ ∂ + ∂ ∂ =
- Combined derivative expression (expanded in source) showing contributions of F, L, h, a, z, FI, I, N terms (preserved as presented in the source).
- Labor allocated to non-traded sector in period 1 solves (assuming ttXtN aaa == ,, t=1,2):
  - 1,11, 1, 1 1, *1 1 N p F N N N N LaL LL q LL L q T γγ γ αα + ⎟⎟⎠⎞ ⎜⎜⎝⎛ − ⋅⋅ ⎟⎟⎠⎞ ⎜⎜⎝⎛ − = ⎟⎟⎠⎞ ⎜⎜⎝⎛ − −
    - which gives an implicit function: () 0, 11, =FLH N
- One can show:
  - () ⎟⎟⎟⎠⎞ ⎜⎜⎜⎝⎛ ∂ ∂ ∂ ∂ ∂ ∂ − = ∂ ∂ N N L H F H F F L 1 1 2 1 12 .
  - () () 0 1 2 1 2 * 2 1 12 > ⋅ = ∂ ∂ N N T N L La p F L α γ α
- With LDB externality: 0 1 2 < ∂ ∂ F I . A sufficient condition for 2 I MC ∂ ∂ to be positive: 2 a z h is small and 1 1, F L N ∂ ∂ not too large (holds if non-traded sector is large enough).
  - Indeed: () N NN T N LZ La p F L ⋅ = ∂ ∂ α γ * 1 1, 1 .

### Constraints on the trade balance and role of reserves
- Time path of aid does not always matter in decentralized equilibrium if the central bank holds enough reserves initially; agents can reduce holdings of public bonds (reducing savings) and increase consumption.
- No ceiling on issuance of public bonds 0 B and redistribution of bond income imply no ceiling on net domestic assets of the central bank even if private agents' bonds B never negative.
- Monetary policy can be arbitrarily expansionary as long as the external balance constraint is met; expansionary monetary policy increases private consumption. Equilibrium aggregate international reserves act as storage technology for consumption smoothing.
- Economy-wide budget constraints (as presented):
  - ⎪⎩⎪⎨⎧ ++ = − ++ = ++ RAICP RAAIxpxpCP NNTT 2222 111,1,1,1,11 ~ with 12 ~ AAAA − − = and Axpxp NNTT ~ 1,1,1,1, = +
- If central bank has limited reserves 0 R, and first period revenues low relative to second period, constraint 0 RR ≤ − will bind and distribution of aid matters.
  - Consider 0 0 = R. The trade balance for which external balance constraint binds:
    - AATB ~ 11 − − =
    - indeed AATBR ~ 0 11 − − = ⇔ = .
  - This trade balance is a decreasing function of first period aid.
- Additional condition: constraint RR ˆ > must be met. Using Rˆ and trade balance gives:
  - ()()() ⎟⎠⎞ ⎜⎝⎛ − − − − ⋅ − − > 2 1 211111 ~ max ATB I A ATB I A ATB .
  - RHS of this inequality is decreasing in first period aid.
- Interior decentralized equilibrium constraint: 0 11 TBTB > where 0 1 TB is defined implicitly:
  - ()()() ⎟⎠⎞ ⎜⎝⎛ − − − − ⋅ − − = 2 0 121 0 111 0 1 ~ 2 1 , ~ max ATB I A ATB I A ATB
- In an economy where * rr ≈, lower bound for equilibrium trade balance for well-defined money demand is 2211 CPCP = , or AARBT ~ ˆˆ 11 − − =.
  - Using Rˆ one can show:
    - ()()() 111 ~ 2 ˆ 1 0 11 − + ⋅ + ≤ + ⇔ ≤ agaaTBBT
      - where g is the growth rate of nominal GDP between period 1 and period 2,
      - and 1 1 1 I A a = , 1 ~ ~ I A a = , and 2 I A a = .

### Decentralized outcome versus optimal outcome: redistributing aid and scenarios
- Define * 1 TB the equilibrium trade balance when the central bank has unlimited initial reserves.
- A corner equilibrium (0 1 * 1 TB TB <) is more likely when:
  - (1) total aid flows are large relative to GDP,
  - (2) GDP expected to grow at a high rate,
  - (3) aid flows are backloaded.
- Allocation of aid affects consumption patterns and welfare.

Case analyses (preserving source structure):
- No LDB and h=0:
  - opt 1 TB * 1 TB = .
  - Increasing 1 A will increase first period consumption and improve welfare as long as 0 1 * 1 TB TB <.
  - If opt 1 TB * 1 TB ≥, further increase in 1 A won't affect consumption and welfare (i.e., when 2 A becomes small).
  - Negative first period income shock (holding future growth constant) makes front-loading aid more likely to improve welfare.
- With LDB and h=0:
  - opt 1 TB * 1 TB < (agents do not internalize impact of first period consumption on LDB).
  - Three subcases:
    1. 0 11 * 1 TB TB opt << : Optimal to increase first period aid, but by less than without LDB, until 0 11 TB TB opt = (external balance still binding: 0 1 * 1 TB TB <).
    2. opt 1 TB TB 1 0 1 * 1 << : Optimal to decrease first period aid until opt 1 TB 1 0 1 = (make the external balance more constrained).
    3. opt 1 TB TB 1 * 1 0 1 << : Economy not constrained, but optimal to make it constrained by reducing first period aid until opt 1 TB TB 1 0 1 * 1 = < .
  - Alternative in cases (2) and (3): central bank can raise interest rate above * r to induce higher private saving.
- With LDB and 0 ≠ h:
  - Desired decentralized equilibrium trade balance * 1 TB may be above or below the h=0 case depending on relative effects, but agents always overconsume in period 1, hence:
    - opt 1 TB * 1 TB < .

### Appendix II-a: Managed float regimes (monetary policy and intervention)
- Results generalize to managed float: equilibrium real exchange rate adjusts via nominal exchange rate instead of price level.
- CPI levels 1 P and 2 P are nominal anchors (price level targets). Central bank targets foreign exchange reserves 0 R.
- Nominal exchange rates derived from current account constraints:
  - In first period equilibrium nominal exchange rate 1 E equates supply (export revenues + aid inflows) and demand (imports, reserves bought by central bank 0 R, foreign currency held by private agents).
  - In second period supply = reserves held by central bank + foreign currency held by agents + export revenues + foreign aid; demand = imports.
  - Source presents system of equations (preserved as presented):
    - () ()() ()() ⎪⎩⎪⎨⎧ = +++ ++ ⋅ = ⋅ + ⋅ ++ 2, * 2,22, * 2, * 10 11, * 1,1, * 1,1, * 1, * 10 ~ TTXX XXTTTT cpAypMR AAypxpcpMR
- Central bank chooses net domestic assets BB − 0 to generate aggregate demand consistent with targeted price levels and international reserves.
- Any allocation under fixed exchange rates can be replicated under managed float by setting price targets * 1 P and * 2 P, target reserves * 0 R = , and net domestic assets BB − 0 so private sector holds * B. This replicates the same real exchange rates * 1 e and * 2 e via:
  - ⎟⎟⎠⎞ ⎜⎜⎝⎛ ⋅ − = * 1, * 1 * 1 1 1 * 1 T e pE P γ
    and
  - ⎟⎟⎠⎞ ⎜⎜⎝⎛ ⋅ − = * 2, * 2 * 2 1 1 * 2 T e pE P γ

### Appendix II-b: General equilibrium effects of front-loading aid with LBD and productivity-enhancing aid
- With LBD externalities:
  - Money demand schedule is steeper; front-loading consumption aid has smaller effect on trade balance (Figure 3b).
  - Mechanism: real appreciation from increased period-one aid shrinks traded sector, reducing period-two productivity (equations (5) and (6)) and period-two income 2 I (equation (14)). Agents anticipate lower future consumption and save more in period one at the initial interest rate → higher saving demand puts downward pressure on interest rates → given savings supply, a lower interest rate achieves same trade balance at higher money demand.
  - Therefore, a given 1 A ∆ increases equilibrium money balances more with LBD than without LBD; 1 A ∆ has smaller impact on trade balance with LBD as individuals increase first-period consumption by a smaller amount (anticipating lower second-period income).
  - Atomistic individuals do not internalize their own consumption impact on productivity growth → savings too low from welfare viewpoint.
- Without LBD, front-loading productivity-enhancing aid for public investment (increasing A ~ by reducing 2 A while keeping A constant):
  - Shifts money supply up and money demand down (Figure 3c).
  - Two components of downward shift in money demand:
    1. Higher productivity raises 2 I (equation (14)) → agents expect higher future consumption → save less at initial interest rate → for given bond supply, upward pressure on interest rates → money demand down.
    2. Higher A ~ reduces consumption aid, further reducing money demand at each trade balance.
  - With productivity-enhancing aid, trade balance deteriorates more than with consumption aid, while money balances increase if χ small enough (i.e., drop in money demand not too large). More productive public investment → higher expected future consumption → greater trade balance deterioration.
- With LBD and productivity-enhancing aid:
  - Period-two productivity benefit somewhat smaller; A ∆ % raises nontradable prices and reduces competitiveness, causing at least as much real appreciation as consumption aid and a greater deterioration of trade balance.
  - Footnote: difference arises because composition of tradable vs non-tradable spending may alter responses (source notes assumption that spending for investment or consumption have same composition).

### Appendix III: Pseudo first stage of system GMM panel regressions
- Pseudo first stage reported for:
  - Trade balance regression (1) of Table 1a.
  - Export regression (1) of Table 2a.
- Instrument set:
  - For endogenous variables (Aid/GDP, Exports/GDP, Trade Balance/GDP): lags t-2 and t-3 (levels or changes depending on specification).
  - For pre-determined variable (Change in Net Domestic Assets/GDP): lags t-1 to t-3 (levels or changes).
  - Difference equations: changes instrumented on lags levels of the three variables.
  - Level equations: levels instrumented on lags of the changes of the three variables.
  - Two strictly exogenous variables in first stage and second stage: contemporaneous Exports Commodity Price Index, contemporaneous Real Import Demand from Trading Partners.
  - Two additional strictly exogenous instruments in first stage: Dummy for Drought and Exports Commodity Price Index, both dated t-3.
- Weak instruments check:
  - Report F tests of joint significance of lags of each instrumented variable.
  - Excluding levels equations for change in net domestic assets, F tests typically above 10 (above 20 in 8 out of 10 regressions), suggesting point estimates, standard errors and specification tests unlikely biased by weak instruments.
  - Low F test in level regressions for net domestic asset confirms typically no persistence in changes in net domestic assets.

*Source: APPENDIX I–III of _wp06145 - APPENDIX I*

### REFERENCES

### _wp06145 - REFERENCES

### Aid, Growth, and Policy Effectiveness
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- Arellano, C., A. Bulir, T.D. Lane, and L.J. Lipschitz, 2005, “The Dynamic Implications of Foreign Aid and Its Variability,” IMF Working Paper 05/119 (Washington: International Monetary Fund).
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- Clemens, M., S. Radelet, and R. Bhavnani, 2004, “Counting Chickens When They Hatch: The Short-Term Effect of Aid on Growth” (unpublished; Washington: Center for Global Development).
- Cordella, T., and G. Dell’Ariccia, 2003, “Budget Support Versus Project Aid,” IMF Working Paper 03/88 (Washington: International Monetary Fund).
- Dalgaard, Carl-Johan, Henrik Hansen, and Finn Tarp, 2004, “On the Empirics of Foreign Aid and Growth,” Economic Journal, Vol. 114, No. 127, pp. 191–216.
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- Svensson J., 2000 “Foreign Aid and Rent Seeking,” Journal of International Economics, Vol. 51, No. 2, pp. 437–61.
- Prati, A., R. Sahay, and T. Tressel, 2003, “Is There a Case for Sterilizing Foreign Aid Inflows?” International Monetary Fund, mimeo.
- Prati, A., and T. Tressel, 2006, “What Is the Most Effective Monetary Policy for Aid-Receiving Countries?” UNDESA Working Paper No.12 (New York: United Nations).

### Exchange Rate, Dutch Disease, and Terms of Trade
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- Calvo, G., C. Reinhart, and C. Végh, 1995, “Targeting the Real Exchange Rate: Theory and Evidence,” Journal of Development Economics, Vol. 47 (June), pp. 97–133.
- De Gregorio, J., and H. Wolf, 1994, “Terms of Trade Productivity and the Real Exchange Rate,” NBER Working Paper No. 4807 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Devarajan, S., 1987, “Real Exchange Rate Misalignment in the CFA Zone,” Journal of African Economies, Vol. 6, No.1, pp. 35–53.
- Krugman, P., 1987, “The Narrow Moving Band, the Dutch Disease, and the Competitive Consequences of Mrs. Thatcher: Notes on Trade in the Presence of Dynamic Scale Economies,” Journal of Development Economics, Vol. 27, pp. 41–55.
- Matsen, Egil, and Ragnar Torvik, 2005, “Optimal Dutch Disease,” Journal of Development Economics, Vol. 78, No.2, pp. 494–515.
- Matsuyama, K. “Agricultural Productivity, Comparative Advantage and Economic Growth,” Journal of Economic Theory, Vol. 58, pp. 317–34.
- Torvik, R., 2000, “Natural Resources, Rent Seeking and Welfare,” Journal of Development Economics, Vol. 67, pp. 455–70.
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- Van Wijnbergen, S., 1984, “The ‘Dutch Disease’: A Disease After All?” Economic Journal, Vol. 94, No. 373, pp. 41–55.

### Volatility, Shocks, and Growth
- Acemoglu, D., S. Johnson, J. Robinson, and Y. Thaicharoen, 2002, “Institutional Causes, Macroeconomic Symptoms: Volatility, Crises and Growth,” NBER Working Paper No. 9124 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Aghion, P., G. Angeletos, A. Banerjee, and K. Manova, 2005, “Volatility and Growth: Credit Constraints and Productivity-Enhancing Investment,” NBER Working Paper No. W11349 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Ramey, G. and V. A. Ramey, 1995, “Cross-Country Evidence on the Link Between Volatility and Growth,” American Economic Review, Vol. 85, No. 5, pp. 1138–51.
- Pallage, S. and M. A. Robe, 2003, “On the Welfare Costs of Economic Fluctuations in Developing Countries,” International Economic Review, Vol. 44, No. 2, pp. 677–98.
- Pallage, S. and M. A. Robe, 2001, “Foreign Aid and the Business Cycle,” Review of International Economics, Vol. 9, No. 4, pp. 641–72.
- Tornell, A., and P. Lane, 1999, “The Voracity Effect,” American Economic Review, Vol. 89, No. 1, pp. 22–46.
- Tornell, A., and P. Lane, 1998, “Are Windfalls a Curse? A Non-Representative Agent Model of the Current Account,” Journal of International Economics, Vol. 44, pp. 83–112.
- Ramcharan, R., 2005, “Cataclysms and Currencies: Does the Exchange Rate Regime Matter for Real Shocks?,” IMF Working Paper 05/85 (Washington: International Monetary Fund).

### Trade, Productivity, and Exporting
- Blalock, G., and P.J. Gertler, 2004, “Learning from Exporting Revisited in a Less Developed Setting,” Journal of Development Economics, Vol. 75, pp. 397–416.
- Frankel, J., and D. Romer, “Does Trade Cause Growth?” American Economic Review, Vol. 89, No. 3, pp. 379–99.
- Sekkat, K., and A. Varoudakis, 2000, “Exchange Rate Management and Manufactured Exports in Sub-Saharan Africa,” Journal of Development Economics, Vol. 61 pp. 237–53.
- Van Biesebroeck, J., 2005, “Exporting Raises Productivity in Sub-Saharian African Manufacturing Firms,” Journal of International Economics, Vol. 67, No. 2, pp. 373–91.
- Wacziarg, R., and K. H. Welch, 2003, “Trade Liberalization and Growth: New Evidence,” NBER Working Paper No. 10152 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Cashin, P., L. Cespedes, and R. Sahay, 2004, “Commodity Currencies and the Real Exchange Rate,” Journal of Development Economics, Vol. 75, pp. 239–68.

### Institutions, Corruption, and Rent Seeking
- Alesina, A., and B. Weder, 2002, “Do Corrupt Governments Receive Less Foreign Aid,” American Economic Review, Vol. 92, No. 4, pp. 1126–37.
- Alesina A., and D. Dollar, 2000, “Who Gives Foreign Aid to Whom and Why?” Journal of Economic Growth, Vol. 5 (March), pp. 33–63.
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- Torvik, R., 2000, “Natural Resources, Rent Seeking and Welfare,” Journal of Development Economics, Vol. 67, pp. 455–70.
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- Van Wijnbergen, S., 1984, “The ‘Dutch Disease’: A Disease After All?” Economic Journal, Vol. 94, No. 373, pp. 41–55.

### Methods, Instruments, and Monetary Policy
- Stock, J. H., and M. Yogo, 2005, “Testing for Weak Instruments in IV Regressions,” in Identification and Inference for Econometric Models: A Festschrift in Honor of Thomas Rothenberg ed. by D.W.K. Andrews and J.H. Stock (New York: Cambridge University Press).
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- Prati, A., R. Sahay, and T. Tressel, 2003, “Is There a Case for Sterilizing Foreign Aid Inflows?” International Monetary Fund, mimeo.
- Prati, A., and T. Tressel, 2006, “What Is the Most Effective Monetary Policy for Aid-Receiving Countries?” UNDESA Working Paper No.12 (New York: United Nations).
- International Monetary Fund, 2005b, “Monetary Policy Implementation at Different Stages of Market Development,” IMF Occasional Paper No. 244 (Washington: International Monetary Fund).

*References list as provided in the content unit _wp06145 - REFERENCES.*

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