## _wp08204 - 7. Sensitivity to Borrowing Premium: Productive Transfer to Nontraded Sector

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---

### Introduction and objective
- Foreign aid context:
  - Foreign aid increased to nearly $60 billion (official development assistance from members of the OECD and OPEC) by the end of the 20th century.
  - G-8 finance ministers pledged $50 billion in additional aid to low income countries by 2010.
  - A 1994 World Bank study estimated infrastructure requirements to be $200 billion a year.
- Objective:
  - Analyze how foreign aid allocations (untied/pure transfers vs tied/productive transfers) affect relative prices (real exchange rate), sectoral allocation, capital accumulation, debt, and welfare in a dynamic two-sector dependent-economy model that includes an endogenous borrowing premium.
  - Key focus areas:
    - Real exchange rate adjustments (Dutch disease vs Balassa-Samuelson effects).
    - Interaction with constrained access to international capital markets (borrowing premium as function of debt relative to asset value).
    - Welfare tradeoffs across allocations.

### Model structure and calibration
- Economic structure and notation:
  - Two sectors: traded (T) and nontraded (N); real exchange rate proxied by p (price of nontraded in terms of traded; increase in p = real appreciation).
  - Private factors: capital K and labor L mobile across sectors; capital produced in nontraded sector and depreciates at rate δ.
  - Government revenue: lump-sum taxes T and foreign transfers TR (denominated in traded output).
  - Government spending on productivity: T G and N G; allocation rules parameterized by λ (share of transfer devoted to tax reduction vs spending) and φ (share of spending allocated to nontraded sector).
  - International borrowing rate is endogenous and increases with the country’s ratio of debt N to the value of physical assets pK (borrowing premium specification shown in the source).
- Functional forms (as presented in the source):
  - UCC form (22a) and Cobb-Douglas sector production functions (22b), (22c).
  - Borrowing premium specification (equation label (22d)): "*(/) = aNpK rr   eξ+" (as shown in the source).
- Calibration highlights:
  - Two benchmark scenarios:
    - Case I: traded sector more capital intensive (αβ>).
    - Case II: nontraded sector more capital intensive (βα>).
  - Base values of government expenditures: T G = 0.05 and N G = 0.17.
  - Optimal (welfare-maximizing) government spending (starting from zero transfers):
    - Base Case I (0.35,0.25 αβ==): ˆT G = 0.079, ˆN G = 0.196.
    - Base Case II (0.25,0.35 αβ==): ˆT G = 0.118, ˆN G = 0.300.
  - Benchmark steady-state statistics:
    - Case I (traded capital-output ratio 3.5, nontraded 2.5): overall capital-output ratio 2.89; traded sector produces 39% of total output, employs 36% of labor; long-run relative price p = 1.365.
    - Case II (traded 2.5, nontraded 3.5): overall capital-output ratio 3.1; long-run relative price p = 0.922.
  - Borrowing-premium parameter values considered for sensitivity:
    - a = 0.01 (easy access), a = 0.1 (medium access), a = 10 (highly restricted access).
    - The source notes: "The borrowing premium =0.1a and the weight on the borrowing premium ξ are chosen..." and that increases in a beyond 10 have negligible effects except on debt.

### Key mechanisms and theoretical results
- Long-run invariance to pure (untied) transfers:
  - Untied transfers (λ = 0 → pure tax reduction) are pure demand shocks and have no long-run effect on the relative price p or sectoral capital intensities under perfect sectoral factor mobility.
  - Long-run decline in traded output under pure transfers is a "current account balance effect", not Dutch disease.
- Tied transfers and sectoral productivity:
  - Aid tied to traded-sector productivity (T G ↑) → Balassa-Samuelson effect → long-run appreciation (p ↑).
  - Aid tied to nontraded-sector productivity (N G ↑) → long-run depreciation (p ↓).
  - Mixed allocations can explain mixed empirical evidence on aid and real exchange rates.
- Borrowing premium and collateral channel:
  - International lenders impose a premium that increases with the country’s debt relative to the value of physical assets (NpK). This affects external borrowing cost and interacts with aid allocation and resulting asset values (pK).
- Dynamics:
  - The full model is a fourth-order dynamic system (state variables: K, N, p, μ).
  - Numerical linearization around steady state yields saddlepath dynamics with instantaneous jumps in μ and p.
  - The relative price p generally responds very quickly to shocks; speed of adjustment can be slower with more restricted access to world capital markets (larger a) or when sectoral capital intensities differ substantially.
  - Equation (23) (linear approximation) illustrates fast adjustment of p for the chosen parameters; production elasticities α, β limit differences in sectoral capital intensities, yielding rapid p adjustment in simulations.

### Numerical results: permanent aid transfer of 0.15 units of traded output (≈ about 5% of baseline GDP)
- Transfer size used in simulations: 0.15 units of traded output ≈ about 5% of baseline GDP.
- General dynamic response:
  - Real exchange rate responds virtually instantaneously to the aid shock in all cases.
  - Adjustments are faster when the traded sector is capital intensive and slower when access to world capital markets is restricted.
- Pure transfer (untied; pure tax reduction)
  - Traded sector capital intensive (αβ>):
    - Immediate rise in consumption of both goods; capital and labor shift to nontraded sector; capital declines gradually.
    - Slight initial appreciation of p detectable but real exchange rate virtually unchanged in long run.
    - Debt initially declines then increases after about four periods but remains below pre-aid level.
    - Wealth and welfare initially increase then slightly decline over time.
  - Nontraded sector capital intensive (βα>):
    - Initial rise in consumption and debt increases initially.
    - Capital stock increases over time to a higher steady-state level; transitional dynamics differ from αβ> case.
- Tied to traded-sector productivity (increase in T G)
  - Long-run real exchange rate appreciates by about 11.5%-14.5% (depending on sectoral capital intensities) for Cobb-Douglas calibrations.
  - Steady-state debt rises regardless of sectoral capital intensities, because p rises and thus the collateral value pK rises.
  - Traded consumption rises significantly in steady state; nontraded consumption changes little.
  - Case-specific dynamics:
    - If traded sector is capital intensive (αβ>): capital stock declines more than under pure transfer; immediate reduction in borrowing of 0.2 percentage points encouraging debt accumulation; consumption and welfare eventually decline faster than for pure transfer.
    - If nontraded sector is capital intensive (βα>): economy accumulates capital to support nontraded production; debt rises with capital accumulation; small overshooting of p and other variables occurs but is quickly eliminated.
- Tied to nontraded-sector productivity (increase in N G)
  - Generates substantial real exchange rate depreciation (p ↓); nontraded consumption expands strongly because of both higher productivity and lower relative price.
  - Capital stock increases in the new steady state even when traded sector is capital intensive; capital-labor ratios rise.
  - Largest decline in domestic traded production among allocations considered (labor shifts to nontraded, traded productivity unchanged).
  - Transitional dynamics:
    - Substantial current account deficits and large overshooting of debt (debt vastly overshoots its long-run level).
    - Borrowing premium initially soars because pK falls.
    - Real exchange rate deviations are long-lived:
      - Average half-life of deviation ≈ 20 periods when traded sector is capital intensive.
      - Average half-life ≈ 30 periods when nontraded sector is capital intensive.
      - By contrast, half-life ≈ 2-3 periods when aid directed to traded sector.
    - Ultimately, growing capital stock raises wealth so consumption and welfare continue to rise.

### Welfare comparisons and optimal allocation
- All allocations yield welfare gains relative to pre-aid equilibrium because foreign aid expands consumption possibilities.
- Ranking of polar allocations (both sectoral capital intensity cases):
  - Allocating aid to the traded sector (T G ↑) is inferior to either pure transfer or allocation to the nontraded sector.
  - If traded sector is more capital intensive (Case I), a pure transfer dominates allocation to the nontraded sector.
  - If nontraded sector is more capital intensive (Case II), allocating to the nontraded sector dominates a pure transfer.
- Optimal mixed allocation (Case I example reported in the source):
  - Pure transfer yields welfare gain of 7.53%.
  - Welfare can be improved to 7.98% by setting λ = 0.49, φ = 0.54 (i.e., 51% of aid allocated to tax reduction and 49% to productivity enhancement; of the productivity share, 54% allotted to nontraded sector and 46% to traded sector).
  - This optimal mix is associated with: 2% real appreciation of the exchange rate, 1.34% increase in the capital stock, and 5.14% reduction in traded output.
- General implication:
  - Optimal policy typically spreads aid partially across tax cuts and productive spending and across sectors (reflecting diminishing returns to aid).
  - The precise optimal mix depends on initial distance of T G and N G from their welfare-maximizing levels and on sectoral capital intensities.

### Policy-relevant findings and implications
- Untied (pure) transfers:
  - Do not affect long-run relative prices under perfect sectoral factor mobility; long-run decline in traded output under untied transfers is a current account effect rather than Dutch disease.
  - Produce small, short-lived Dutch disease–like effects (short-run appreciation) that are generally small but increase with more restricted access to international capital markets.
- Tied transfers:
  - Sectoral allocation matters crucially: T G increases cause long-run appreciation (Balassa-Samuelson); N G increases cause long-run depreciation.
  - Tying aid to nontraded productivity can generate larger welfare gains when initial public infrastructure is suboptimally low, and can stimulate capital accumulation and sustained welfare improvements—despite short-run debt overshooting and borrowing-premium spikes.
  - Aid tied to traded-sector productivity raises collateral values and steady-state debt; appreciation can boost GNP in traded-goods units but may reduce competitiveness.
- Borrowing-premium sensitivity:
  - The economy’s access to world capital markets (parameter a) alters transitional dynamics and magnifies short-run relative-price responses; higher borrowing costs (larger a) make short-run Dutch-disease effects more pronounced and slow adjustment.
- Optimal policy recommendation (model-based):
  - Partial allocation of aid across tax reduction and productive spending, and partial allocation of productive spending across traded and nontraded sectors, is typically optimal due to diminishing returns.
  - The precise optimal mix depends on sectoral capital intensities and the initial gap between current and welfare-maximizing levels of government spending.

### Growth–welfare tradeoff and fiscal coordination
- Example scenario:
  - Government increases its taxes by 0.053 units.
  - That scenario yields:
    - Welfare increase of 10.74%
    - Increase in capital of 19.9%
    - 4% deprecation of the real exchange rate
    - 2.4% reduction in the traded sector
- Implication:
  - Recipient economy must co-ordinate fiscal policy with foreign aid programs to manage growth–welfare tradeoffs.

### Real exchange rate movements, Dutch disease, and capital intensity
- No monotonic relationship between changes in the real exchange rate and welfare.
- Real exchange rate appreciation associated with expenditure in the traded sector is an equilibrium effect, not necessarily a 'disease'.
- Contrary to standard Dutch disease narrative:
  - The traded sector contracts most when the real exchange rate depreciates sharply (associated with spending on NG).
  - The traded sector contracts least (and may expand) when the real exchange rate appreciates (associated with spending on TG).
- Capital accumulation patterns:
  - Capital stock rises when the nontraded sector is capital intensive because the wealth effect of aid expands the nontraded sector and requires larger capital input.
  - Capital mostly falls when the traded sector is capital intensive; labor and capital move to a labor-intensive sector allowing shedding of excess capital.
  - If government uses aid to increase NG, productivity gains in the sector producing capital can offset capital shedding, resulting in overall capital rise.

### Effect of cost of debt (parameter a)
- Parameter a summarizes accessibility to world financial markets.
- Benchmark: 0.10a= yields equilibrium debt-output ratio around 0.60.
- Cases examined: 0.01a= (easy access), 0.1a= (medium access, benchmark), 10a= (highly restricted access).
- Long-run:
  - T k% and N k% determined by production conditions alone; varying a does not affect their long-run values or the steady-state real exchange rate p%.
  - Main long-run effect: higher borrowing premium discourages holding debt.
  - For cost function (22d) a 10-fold increase in a is associated with a 10-fold decline in long-run debt, N%.
  - With long-run borrowing rate fixed by time preference, long-run capital stock is independent of a.
  - Changes in steady-state values of remaining variables are quite small.
- Transitional dynamics:
  - Varying a leads to sharply contrasting transitional dynamics in real exchange rate and borrowing rate.
  - Less access to international financial markets (higher a) produces larger responses in real exchange rate and initial borrowing rate.
- Specific examples:
  - Pure transfer with TN kk> (Fig. 5.1(A)): real exchange rate initially depreciates with high access (low a) and appreciates with restricted access (high a).
  - Aid to traded sector and traded sector capital intensive (Fig. 6): adjustment is faster the higher a; when nontraded sector is capital intensive, interest rate overshoots steady state.
  - Aid to nontraded sector only (Fig. 7): with easy access (0.01a=), after about 5 periods sectoral capital intensities, real exchange rate and interest rate remain almost unchanged through the transition; convergence happens quicker the lower the cost of external borrowing.

### Benchmark economy and selected steady-state values
- Preference parameters: γ = 1.5, θ = 0.5, ρ = 0.05
- Production parameters:
  - Case I: α = 0.35, β = 0.25
  - Case II: α = 0.25, β = 0.35
- Productivity parameters: A = 2, B = 1.7
- Depreciation rate: 0.05 = δK
- World interest rate: * = 0.03 r
- Premium on borrowing: = 0.1 a
- Weight on premium: 1 = ξ
- Government Expenditure: TG = 0.05, NG = 0.17
- Elasticities of government expenditures: ν1 = 0.1, ν2 = 0.15
- Transfers: TR = 0.0
- Selected steady-state ratios (Table 2 highlights):
  - A. Traded sector more capital intensive (α=0.35, β=0.25): TT K/L = 7.802, NN K/L = 4.830, pK/X_T = 3.5, K/Y_N = 2.5, pK/(X+PY_T) = 2.888, T_L/X = 0.355, pX/(pY+X_T) = 1.365, G_T/pX = 0.388, G_N/(pY+X_T) = 0.227.
  - B. Nontraded sector more capital intensive (α=0.25, β=0.35): TT K/L = 6.393, NN K/L = 10.33, pK/X_T = 2.5, K/Y_N = 3.5, pK/(X+PY_T) = 3.102, T_L/X = 0.433, pX/(pY+X_T) = 0.922, G_T/pX = 0.398, G_N/(pY+X_T) = 0.227.

### Steady-state responses and welfare (selected entries from Tables 3–4)
- I. Traded sector more capital intensive (α=0.35, β=0.25):
  - Pure transfer (0λ=): p%Δ = 0; %KΔ = -1.29; %XΔ = -7.24; Long-run Welfare Gain = 7.53%
  - Spent on TG only (1;0λφ==): p%Δ = 0.149; %KΔ = -2.33; %XΔ = -2.97; Long-run Welfare Gain = 6.15%
  - Spent on NG only (1;1λφ==): p%Δ = 0.05; %KΔ = 8.62; %XΔ = -9.23; Long-run Welfare Gain = 6.85%
  - Opt. alloc. (0.49;0.54λφ==): p%Δ = 0.074; %KΔ = 1.34; %XΔ = -5.14; Long-run Welfare Gain = 7.98%
- II. Nontraded sector more capital intensive (α=0.25, β=0.35):
  - Pure transfer (0λ=): p%Δ = 0.05; %KΔ = 1.38; %XΔ = -7.03; Long-run Welfare Gain = 7.94%
  - Spent on TG only (1;0λφ==): p%Δ = 0.192; %KΔ = 2.42; %XΔ = 0.37; Long-run Welfare Gain = 7.55%
  - Spent on NG only (1;1λφ==): p%Δ = 0.05; %KΔ = 21.29; %XΔ = -8.17; Long-run Welfare Gain = 9.51%
  - Opt. alloc. (1.31;0.74λφ==): p%Δ = 0.108; %KΔ = 19.91; %XΔ = -2.42; Long-run Welfare Gain = 10.74%

*Source: IMF Working Paper chapter 7, “Sensitivity to Borrowing Premium: Productive Transfer to Nontraded Sector” (content unit _wp08204 - 7, supplied PDF).*

### Chapter 1 of Tekin’s Ph.D. thesis written at the University of Washington under Turnovsky’s supervision. Substantial fin

### Chapter 1 of Tekin’s Ph.D. thesis written at the University of Washington under Turnovsky’s supervision

### Authors, acknowledgements, and contribution
- Authors listed: Valerie Cerra, IMF; Serpil Tekin, University of Washington; Stephen J. Turnovsky, University of Washington.
- Substantial financial support provided by the Castor Endowment at the University of Washington.
- Document is Chapter 1 of Serpil Tekin’s Ph.D. thesis under Turnovsky’s supervision.

### Structure and major themes (table of contents)
- I. Introduction (Page 4)
- II. Two Sector Model of Foreign Aid (Page 7)
  - A. The Economic Structure (Page 8)
  - B. Macroeconomic Equilibrium (Page 12)
- III. Steady State Equilibrium (Page 14)
  - A. Long-Run Effects of Transfers on the Relative Price (Page 15)
  - B. Transfers, Economic Activity, and the Dutch Disease (Page 16)
- IV. Numerical Analysis (Page 17)
  - A. Calibration (Page 18)
  - B. Optimal Government Spending (Page 19)
  - C. Initial Benchmark Equilibria (Page 19)
- V. Foreign Aid Flows: General Characteristics of Real Exchange Rates (Page 20)
- VI. Pure Transfer (Page 21)
  - A. Traded Sector is Capital Intensive: (αβ>) (Page 21)
  - B. Nontraded sector is capital intensive: (βα>) (Page 22)
- VII. Productive Government Spending in the Traded Sector (Page 22)
  - A. Traded sector is capital intensive (αβ>) (Page 23)
  - B. Nontraded sector is capital intensive (βα>) (Page 23)
- VIII. Productive Government Spending in the Nontraded Sector (Page 24)
- IX. Welfare Analysis (Page 25)
- X. Effect of Cost of Debt (Page 27)
- XI. Conclusions (Page 28)
- Appendix (Page 41)
- References (Page 43)

### Key empirical and analytical components highlighted in the chapter
- A two-sector theoretical model of foreign aid, with explicit treatment of economic structure and macroeconomic equilibrium.
- Steady-state equilibrium analysis, including:
  - Long-run effects of transfers on the relative price.
  - Analysis of transfers, economic activity, and the Dutch Disease.
- Extensive numerical analysis components:
  - Calibration procedures (section IV.A).
  - Consideration of optimal government spending (section IV.B).
  - Specification of initial benchmark equilibria (section IV.C).
- Comparative analysis of transfer types and government spending:
  - Pure transfer cases with sectoral capital-intensity distinctions (VI.A and VI.B).
  - Productive government spending allocated to traded and nontraded sectors (VII and VIII).
- Welfare analysis and sensitivity to financing costs:
  - Formal welfare analysis (Section IX).
  - Analysis of the effect of the cost of debt (Section X).

### Empirical materials and outputs listed
- Tables:
  - Table 1. The Benchmark Economy (Page 29)
  - Table 2. Key Steady-State Equilibrium Ratios (Page 29)
  - Table 3. Steady-State Responses to Permanent Changes (Page 30)
  - Table 4. Welfare Analysis (Page 31)
- Figures:
  - Figure 1. Capital and Debt (Page 32)
  - Figure 2. Financial Variables (Page 33)
  - Figure 3. Sectoral Activity and Output (Page 34)
  - Figure 4. Consumption and Welfare (Page 36)
  - Figure 5. Sensitivity to Borrowing Premium:  Untied Transfer (Page 38)
  - Figure 6. Sensitivity to Borrowing Premium:  Productive Transfer to Traded Sector (Page 39)

### Analytical focus and intended contributions (as indicated by chapter organization)
- The chapter develops theory and numerical examples to assess how different forms of foreign aid and different allocations of government spending affect sectoral outcomes, prices, capital accumulation, welfare, and the real exchange rate.
- Particular attention is given to:
  - The role of sectoral capital intensity (notation: αβ> and βα> used to designate which sector is capital intensive).
  - Distinguishing pure transfers from productive transfers targeted to traded or nontraded sectors.
  - The welfare implications of transfers and productive spending under varying debt costs and borrowing premia.

*Source: Chapter 1 of Tekin’s Ph.D. thesis (IMF PDF)._

### 7.  Sensitivity to Borrowing Premium:  Productive Transfer to Nontraded Sector .................40

### _wp08204 - 7.  Sensitivity to Borrowing Premium:  Productive Transfer to Nontraded Sector

### Introduction and objective
- Foreign aid increased to nearly $60 billion (official development assistance from members of the OECD and OPEC) by the end of the 20th century; G-8 finance ministers pledged $50 billion in additional aid to low income countries by 2010.
- A 1994 World Bank study estimated infrastructure requirements to be $200 billion a year.
- Objective: analyze how foreign aid allocations (untied/pure transfers vs tied/productive transfers) affect relative prices (real exchange rate), sectoral allocation, capital accumulation, debt, and welfare in a dynamic two-sector dependent-economy model that includes an endogenous borrowing premium.
- Key focus: (i) real exchange rate adjustments (Dutch disease vs Balassa-Samuelson effects), (ii) interaction with constrained access to international capital markets (borrowing premium as function of debt relative to asset value), and (iii) welfare tradeoffs across allocations.

### Model structure and calibration
- Economic structure:
  - Two sectors: traded (T) and nontraded (N); real exchange rate proxied by p (price of nontraded in terms of traded; increase in p = real appreciation).
  - Private factors (capital K and labor L) mobile across sectors; capital produced in nontraded sector and depreciates at rate δ.
  - Government revenue: lump-sum taxes T and foreign transfers TR (denominated in traded output). Government spending on productivity: T G and N G; allocation rules parameterized by λ (share of transfer devoted to tax reduction vs spending) and φ (share of spending allocated to nontraded sector).
  - International borrowing rate is endogenous and increases with the country’s ratio of debt N to the value of physical assets pK (borrowing premium specification shown in the source).
- Functional forms used (as presented in the source):
  - UCC form (22a) and Cobb-Douglas sector production functions (22b), (22c).
  - Borrowing premium specification as shown in the text: "*(/) = aNpK rr   eξ+" (equation label (22d) in the source).
- Calibration highlights:
  - Two benchmark scenarios:
    - Case I: traded sector more capital intensive (αβ>).
    - Case II: nontraded sector more capital intensive (βα>).
  - Base values of government expenditures: T G = 0.05 and N G = 0.17.
  - Optimal (welfare-maximizing) government spending (starting from zero transfers):
    - Base Case I (0.35,0.25 αβ==): ˆT G = 0.079, ˆN G = 0.196.
    - Base Case II (0.25,0.35 αβ==): ˆT G = 0.118, ˆN G = 0.300.
  - Benchmark steady-state statistics:
    - Case I (traded capital-output ratio 3.5, nontraded 2.5): overall capital-output ratio 2.89; traded sector produces 39% of total output, employs 36% of labor; long-run relative price p = 1.365.
    - Case II (traded 2.5, nontraded 3.5): overall capital-output ratio 3.1; long-run relative price p = 0.922.
  - Borrowing-premium parameter values considered for sensitivity: a = 0.01 (easy access), a = 0.1 (medium access), a = 10 (highly restricted access). The source also notes calibration choices: "The borrowing premium =0.1a and the weight on the borrowing premium ξ are chosen..." and that increases in a beyond 10 have negligible effects except on debt.

### Key mechanisms and theoretical results
- Long-run invariance to pure (untied) transfers:
  - Untied transfers (λ = 0 → pure tax reduction) are pure demand shocks and have no long-run effect on the relative price p or sectoral capital intensities under perfect sectoral factor mobility; long-run decline in traded output under pure transfers is a "current account balance effect", not Dutch disease.
- Tied transfers and sectoral productivity:
  - Aid tied to traded-sector productivity (T G ↑) raises traded productivity → Balassa-Samuelson effect → long-run appreciation of real exchange rate (p ↑).
  - Aid tied to nontraded-sector productivity (N G ↑) raises nontraded productivity → long-run depreciation of real exchange rate (p ↓).
  - Mixed allocations can explain mixed empirical evidence on aid and real exchange rates.
- Borrowing premium and collateral channel:
  - International lenders impose a premium that increases with the country’s debt relative to the value of physical assets (NpK). This affects the country’s external borrowing cost and interacts with aid allocation and resulting asset values (pK).
- Dynamics:
  - The full model is a fourth-order dynamic system (state variables: K, N, p, μ). Numerical linearization around steady state yields saddlepath dynamics with instantaneous jumps in μ and p.
  - The relative price p generally responds very quickly to shocks; speed of adjustment can be slower with more restricted access to world capital markets (larger a) or when sectoral capital intensities differ substantially.
  - Equation (23) (linear approximation) illustrates fast adjustment of p for the chosen parameters; production elasticities α, β limit differences in sectoral capital intensities, yielding rapid p adjustment in simulations.

### Numerical results: permanent aid transfer of 0.15 units of traded output (equals about 5% of baseline GDP)
- General:
  - Transfer size used in simulations: 0.15 units of traded output ≈ about 5% of baseline GDP.
  - Real exchange rate responds virtually instantaneously to the aid shock in all cases; adjustments are faster when the traded sector is capital intensive and slower when access to world capital markets is restricted.
- Pure transfer (untied; λ = 1? context: pure transfer = tax reduction; treated as pure demand shock)
  - Traded sector capital intensive (αβ>): immediate rise in consumption of both goods; capital and labor shift to nontraded sector; capital declines gradually; slight initial appreciation of p detectable but real exchange rate virtually unchanged in long run; debt initially declines then increases after about four periods but remains below pre-aid level; wealth and welfare initially increase then slightly decline over time.
  - Nontraded sector capital intensive (βα>): initial rise in consumption and debt increases initially; capital stock increases over time to a higher steady-state level; transitional dynamics differ (capital accumulates rather than is discarded).
- Tied to traded-sector productivity (increase in T G)
  - Long-run real exchange rate appreciates by about 11.5%-14.5% (depending on sectoral capital intensities) for Cobb-Douglas calibrations.
  - Steady-state debt rises regardless of sectoral capital intensities, because p rises and thus the collateral value pK rises.
  - Traded consumption rises significantly in steady state; nontraded consumption changes little.
  - Case-specific dynamics:
    - If traded sector is capital intensive (αβ>): capital stock declines more than under pure transfer; immediate reduction in borrowing of 0.2 percentage points encouraging debt accumulation; consumption and welfare eventually decline faster than for pure transfer.
    - If nontraded sector is capital intensive (βα>): economy accumulates capital to support nontraded production; debt rises with capital accumulation; small overshooting of p and other variables occurs but is quickly eliminated.
- Tied to nontraded-sector productivity (increase in N G)
  - Generates substantial real exchange rate depreciation (p ↓); nontraded consumption expands strongly because of both higher productivity and lower relative price.
  - Capital stock increases in the new steady state even when traded sector is capital intensive; capital-labor ratios rise.
  - Largest decline in domestic traded production among allocations considered (labor shifts to nontraded, traded productivity unchanged).
  - Transitional dynamics: substantial current account deficits and large overshooting of debt (debt vastly overshoots its long-run level), borrowing premium initially soars because pK falls; real exchange rate deviations are long-lived:
    - Average half-life of deviation ≈ 20 periods when traded sector is capital intensive.
    - Average half-life ≈ 30 periods when nontraded sector is capital intensive.
    - By contrast, half-life ≈ 2-3 periods when aid directed to traded sector.
  - Ultimately, growing capital stock raises wealth so consumption and welfare continue to rise.

### Welfare comparisons and optimal allocation
- All allocations yield welfare gains relative to pre-aid equilibrium because foreign aid expands consumption possibilities.
- Ranking of polar allocations (both sectoral capital intensity cases):
  - Allocating aid to the traded sector (T G ↑) is inferior to either pure transfer or allocation to the nontraded sector.
  - If traded sector is more capital intensive (Case I), a pure transfer dominates allocation to the nontraded sector.
  - If nontraded sector is more capital intensive (Case II), allocating to the nontraded sector dominates a pure transfer.
- Optimal mixed allocation (Case I example reported in the source):
  - Pure transfer yields welfare gain of 7.53%.
  - Welfare can be improved to 7.98% by setting λ = 0.49, φ = 0.54 (i.e., 51% of aid allocated to tax reduction and 49% to productivity enhancement; of the productivity share, 54% allotted to nontraded sector and 46% to traded sector).
  - This optimal mix is associated with: 2% real appreciation of the exchange rate, 1.34% increase in the capital stock, and 5.14% reduction in traded output.
- General implication: optimal policy typically spreads aid partially across tax cuts and productive spending and across sectors (reflecting diminishing returns to aid); the optimal mix depends on initial distance of T G and N G from their welfare-maximizing levels and on sectoral capital intensities.

### Policy-relevant findings and implications (as emphasized in the source)
- Untied (pure) transfers:
  - Do not affect long-run relative prices under perfect sectoral factor mobility; long-run decline in traded output under untied transfers is a current account effect rather than Dutch disease.
  - Produce small, short-lived Dutch disease–like effects (short-run appreciation) that are generally small but increase with more restricted access to international capital markets.
- Tied transfers:
  - Sectoral allocation matters crucially: T G increases cause long-run appreciation (Balassa-Samuelson); N G increases cause long-run depreciation.
  - Tying aid to nontraded productivity can generate larger welfare gains when initial public infrastructure is suboptimally low (as in many developing economies), and can stimulate capital accumulation and sustained welfare improvements—despite short-run debt overshooting and borrowing-premium spikes.
  - Aid tied to traded-sector productivity raises collateral values and steady-state debt; appreciation can boost GNP in traded-goods units but may reduce competitiveness.
- Borrowing-premium sensitivity:
  - The economy’s access to world capital markets (parameter a) alters transitional dynamics and magnifies short-run relative-price responses; higher borrowing costs (larger a) make short-run Dutch-disease effects more pronounced and slow adjustment.
- Optimal policy recommendation (model-based):
  - Partial allocation of aid across tax reduction and productive spending, and partial allocation of productive spending across traded and nontraded sectors, is typically optimal due to diminishing returns.
  - The precise optimal mix depends on sectoral capital intensities and the initial gap between current and welfare-maximizing levels of government spending.

*Source: IMF Working Paper chapter 7, “Sensitivity to Borrowing Premium: Productive Transfer to Nontraded Sector” (content unit _wp08204 - 7), as provided in the supplied PDF content.*

### 0.05 to 0.108) and (

### _wp08204 - 0.05 to 0.108) and (

### Growth–welfare tradeoff and fiscal coordination
- Aid received may exceed the amount of fiscal adjustment required; example: government increases its taxes by 0.053 units.
- That scenario yields:
  - Welfare increase of 10.74%
  - Increase in capital of 19.9%
  - 4% deprecation of the real exchange rate
  - 2.4% reduction in the traded sector
- Implication: recipient economy must co-ordinate fiscal policy with foreign aid programs to manage growth–welfare tradeoffs.

### Real exchange rate movements and Dutch disease
- No monotonic relationship between changes in the real exchange rate and welfare.
- Real exchange rate appreciation associated with expenditure in the traded sector is an equilibrium effect, not necessarily a 'disease'.
- Contrary to the standard Dutch disease narrative:
  - The traded sector contracts most when the real exchange rate depreciates sharply (associated with spending on NG).
  - The traded sector contracts least (and may expand) when the real exchange rate appreciates (associated with spending on TG).
- Mechanism: intersectoral mobility of capital and labor pins long-run real exchange rate to supply-side conditions; appreciation or depreciation reflect productivity gains expanding supply in traded or nontraded sectors.
- Fall in the relative price of nontraded goods (depreciation) shifts consumption to nontraded goods, causing a relatively larger contraction of the traded sector than when the real exchange rate appreciates.

### Capital accumulation and sectoral capital intensity
- Capital stock rises when the nontraded sector is capital intensive because the wealth effect of aid expands the nontraded sector and requires larger capital input.
- Capital mostly falls when the traded sector is capital intensive; labor and capital move to a labor-intensive sector allowing shedding of excess capital.
- If government uses aid to increase NG, extensive productivity gains in the sector producing capital can offset capital shedding, resulting in overall capital rise.

### Allocation of aid, optimal policy, and the transfer problem
- Baseline assumes government spending below optimal levels; tied aid inflows can correct non-optimal allocation while adding productive capacity.
- Question: If pre-aid government policy is already optimal, will aid worsen welfare (transfer problem)?
  - Finding: there is no transfer problem; in all cases aid still leads to welfare gains.
  - With pre-aid government expenditures at their respective optimum:
    - The pure transfer is very close to the optimal post-aid policy.
    - The pure transfer provides larger welfare gains than either form of government spending.
    - Gains from aid are smaller than when the government starts from a non-optimal initial equilibrium.
- Result runs counter to the Burnside–Dollar proposition that benefits of aid increase with the quality of government policy.

### Effect of cost of debt (parameter a)
- Key parameter a summarizes accessibility to world financial markets.
- Benchmark: 0.10a= yields equilibrium debt-output ratio around 0.60.
- Cases examined: 0.01a= (easy access), 0.1a= (medium access, benchmark), 10a= (highly restricted access).
- Long-run:
  - T k% and N k% determined by production conditions alone; varying a does not affect their long-run values or the steady-state real exchange rate p%.
  - Main long-run effect: higher borrowing premium discourages holding debt.
  - For cost function (22d) a 10-fold increase in a is associated with a 10-fold decline in long-run debt, N%.
  - With long-run borrowing rate fixed by time preference, long-run capital stock is independent of a.
  - Changes in steady-state values of remaining variables are quite small.
- Transitional dynamics:
  - Varying a leads to sharply contrasting transitional dynamics in real exchange rate and borrowing rate.
  - Less access to international financial markets (higher a) produces larger responses in real exchange rate and initial borrowing rate.
- Specific cases:
  - Pure transfer with TN kk> (Fig. 5.1(A)): real exchange rate initially depreciates with high access (low a) and appreciates with restricted access (high a). Reason: long-run decline in capital causes initial appreciation; long-run decline in debt causes opposite effect; dominance depends on access.
  - Aid allocated to the traded sector and traded sector capital intensive (Fig. 6): adjustment of sectoral capital intensities, real exchange rate, and interest rate is faster the higher a. When nontraded sector is capital intensive, interest rate overshoots steady state. Countries with very large costs of external borrowing that invest aid entirely into traded sector will tend to experience high economic volatility.
  - Aid allocated to the nontraded sector only (Fig. 7): with easy access (0.01a=), after about 5 periods sectoral capital intensities, real exchange rate and interest rate remain almost unchanged through the transition. Convergence happens quicker the lower the cost of external borrowing.

### Conclusions (main findings)
- Concerns that untied aid causes Dutch disease with adverse effects are essentially unfounded when capital is freely mobile between sectors:
  - Pure transfers have no long-run effects on the real exchange rate.
  - Traded sector decline reflects aid denominated in traded output substituting for exports in financing imports, not Dutch disease.
  - Untied aid may cause short-run real appreciation, but effects are very temporary and almost negligible.
- Tied transfers generate permanent relative price effects via productivity changes:
  - Aid to traded-sector productivity tends to appreciate the real exchange rate (Balassa–Samuelson effect).
  - Aid to nontraded-sector productivity tends to depreciate the real exchange rate.
- Tradeoffs emphasized for policymakers:
  - (i) real exchange movements,
  - (ii) long-run capital accumulation,
  - (iii) economic welfare measured by intertemporal utility.
- Policy implications:
  - Untied pure wealth-enhancing aid raises welfare but may be associated with long-run decline in capital stock if traded sector is more capital intensive.
  - Aid tied to traded-sector productivity may cause undesired appreciation and possible capital stock decline, but productivity enhancement often dominates leading to net welfare increase.
  - Aid directed to productivity enhancement in nontraded sector (e.g., infrastructure) likely yields greater increases in productive capital and welfare.
  - Optimal allocation is to share aid across uses discussed.
  - Diversity of effects across allocations may explain inclusive empirical results linking aid to growth and real exchange rate movements.

### Benchmark economy and key steady-state values (as reported)
- Preference parameters:
  - γ = 1.5, θ = 0.5, ρ = 0.05
- Production parameters:
  - Case I: α = 0.35, β = 0.25
  - Case II: α = 0.25, β = 0.35
- Productivity parameters: A = 2, B = 1.7
- Depreciation rate: 0.05 = δK
- World interest rate: * = 0.03 r
- Premium on borrowing: = 0.1 a
- Weight on premium: 1 = ξ
- Government Expenditure: TG = 0.05, NG = 0.17
- Elasticities of government expenditures: ν1 = 0.1, ν2 = 0.15
- Transfers: TR = 0.0
- Selected steady-state ratios (Table 2):
  - A. Traded sector more capital intensive (α=0.35, β=0.25): TT K/L = 7.802, NN K/L = 4.830, pK/X_T = 3.5, K/Y_N = 2.5, pK/(X+PY_T) = 2.888, T_L/X = 0.355, pX/(pY+X_T) = 1.365, G_T/pX = 0.388, G_N/(pY+X_T) = 0.227, etc.
  - B. Nontraded sector more capital intensive (α=0.25, β=0.35): TT K/L = 6.393, NN K/L = 10.33, pK/X_T = 2.5, K/Y_N = 3.5, pK/(X+PY_T) = 3.102, T_L/X = 0.433, pX/(pY+X_T) = 0.922, G_T/pX = 0.398, G_N/(pY+X_T) = 0.227, etc.

### Steady-state responses and welfare (selected entries)
- Table 3 and Table 4 summarize steady-state responses and long-run welfare changes for transfers of 0.15 starting from initial allocation: 0.05;0.17;0.22;0.0 (TN GG TTR).
- Selected long-run changes and welfare gains (Table 4):
  - I. Traded sector more capital intensive (α=0.35, β=0.25):
    - Pure transfer (0λ=): p%Δ = 0; %KΔ = -1.29; %XΔ = -7.24; Long-run Welfare Gain = 7.53%
    - Spent on TG only (1;0λφ==): p%Δ = 0.149; %KΔ = -2.33; %XΔ = -2.97; Long-run Welfare Gain = 6.15%
    - Spent on NG only (1;1λφ==): p%Δ = 0.05; %KΔ = 8.62; %XΔ = -9.23; Long-run Welfare Gain = 6.85%
    - Opt. alloc. (0.49;0.54λφ==): p%Δ = 0.074; %KΔ = 1.34; %XΔ = -5.14; Long-run Welfare Gain = 7.98%
  - II. Nontraded sector more capital intensive (α=0.25, β=0.35):
    - Pure transfer (0λ=): p%Δ = 0.05; %KΔ = 1.38; %XΔ = -7.03; Long-run Welfare Gain = 7.94%
    - Spent on TG only (1;0λφ==): p%Δ = 0.192; %KΔ = 2.42; %XΔ = 0.37; Long-run Welfare Gain = 7.55%
    - Spent on NG only (1;1λφ==): p%Δ = 0.05; %KΔ = 21.29; %XΔ = -8.17; Long-run Welfare Gain = 9.51%
    - Opt. alloc. (1.31;0.74λφ==): p%Δ = 0.108; %KΔ = 19.91; %XΔ = -2.42; Long-run Welfare Gain = 10.74%

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08204.pdf*

### References

### References

### Theoretical foundations and growth models
- Balassa, B., 1964, “The purchasing-power parity doctrine: A reappraisal,” Journal of Political Economy, Vol. 72, pp. 584–596.
- Bardhan, P.K., 1967, “Optimal foreign borrowing,” in K. Shell (ed.), Essays on the Theory of Optimal Economic Growth (Cambridge, Massachusetts: MIT Press.)
- Barro, R.J., 1990, “Government spending in a simple model of endogenous growth,” Journal of Political Economy, Vol. 98, pp. S103–S125.
- Kiyotaki, N. and J. Moore, 1997, “Credit cycles,” Journal of Political Economy, Vol. 105, pp. 211–48.
- Sachs, J., 1984, “Theoretical issues in international borrowing,” Princeton Studies in International Finance, No. 54.
- Samuelson, P.A., 1964, “Theoretical notes on trade problems,” Review of Economics and Statistics, Vol. 46, pp. 145–54.
- Turnovsky, S.J., 1997, International Macroeconomic Dynamics (Cambridge, Massachusetts: MIT Press.)
- Turnovsky, S.J. and P. Sen, 1995, “Investment in a two-sector dependent economy,” Journal of the Japanese and International Economies, Vol. 9, pp. 29–55.

### Aid, growth, and policy effectiveness (empirical and theoretical)
- Adam, C.S. and D.L. Bevan, 2006, “Aid and the supply side: Public investment, export performance, and Dutch disease in low-income countries,” World Bank Economic Review, Vol. 20, pp. 261–90.
- Burnside, C. and D. Dollar, 2000, “Aid, policies, and growth,” American Economic Review, Vol. 90, pp. 847–68.
- Collier, P. and D. Dollar, 2002, “Aid allocation and policy reduction,” European Economic Review, Vol. 46, pp. 1475–1500.
- Dalgaard, C-J., 2008, “Donor policy rules and aid effectiveness,” Journal of Economic Dynamics and Control, Vol. 32, pp. 1895–1920.
- Dalgaard, C-J., H. Hansen, and F. Tarp, 2004, “On the empirics of foreign aid and growth,” Economic Journal, Vol. 114, pp. F217–F243.
- Devarajan, S., D.S. Go, J. Page, S. Robinson, and K. Thierfelder, 2008, “Aid, growth, and real exchange rate dynamics,” World Bank Policy Research Paper 4480.
- Easterly, W., 2001, The Elusive Quest for Growth: Economists' Adventures and Misadventures in the Tropics (Cambridge, Massachusetts: MIT Press)
- Easterly, W., 2003, “Can foreign aid buy growth?” Journal of Economic Perspectives, Vol. 17, pp. 23–48.
- Easterly, W., R. Levine, and D. Roodman, 2004, “Aid, policies, and growth: Comment,” American Economic Review, Vol. 94, pp. 774–80.
- Hansen, H., and F. Tarp, 2000, “Aid effectiveness disputed,” Journal of International Development, Vol. 12, pp. 375–98.
- Hansen, H., and F. Tarp, 2001, “Aid and growth regressions,” Journal of Development Economics, Vol. 64, pp. 547–70.
- Nkusu, M., 2004, “Aid and the Dutch disease for low-income countries: Informed diagnoses for prudent prognoses,” IMF Working Paper 04/49.
- Rajan, R. and A. Subramanian, 2005, “Aid and growth: What does the cross-country evidence really show?” NBER Working Paper 11,513.
- Devarajan et al., 2008, “Aid, growth, and real exchange rate dynamics,” World Bank Policy Research Paper 4480. (Note: entry appears in the list as provided.)

### Dutch disease, sectoral dynamics, and nontraded goods
- Corden, W.M., 1984, “Booming sector and Dutch disease economics: Survey and consolidation,” Oxford Economic Papers, Vol. 36, pp. 359–80.
- Corden, W.M. and P.J. Neary, 1982, “Booming sector and de-industrialization in a small open economy,” Economic Journal, Vol. 92, pp. 825–48.
- Brock, P.L., 1988, “Investment, the current account, and the relative price of nontraded goods in a small open economy,” Journal of International Economics, Vol. 24, pp. 235–53.
- Brock, P.L. and S J. Turnovsky, 1994, “The dependent economy model with traded and nontraded capital goods,” Review of International Economics, Vol. 2, pp. 306–25.
- Morshed, M. and S.J. Turnovsky, 2004, “Intersectoral adjustment costs and real exchange rate dynamics in a two-sector dependent economy model,” Journal of International Economics, Vol. 62, pp. 147–77.
- Yano, M. and J. Nugent, 1999, “Aid, nontraded goods, and the transfer paradox in small countries,” American Economic Review, Vol. 89, pp. 431–49.
- Kang, J.S., A. Prati, and A. Rebucci, 2007, “Aid, exports, and growth: A time series perspective on the Dutch disease hypothesis,” International Monetary Fund.
- Chatterjee, S., Sakoulis, G., and S.J. Turnovsky, 2003, “Unilateral capital transfers, public investment, and economic growth,” European Economic Review, Vol. 47, pp. 1077–1103.
- Chatterjee, S. and S.J. Turnovsky, 2007, “Foreign aid and economic growth: The role of flexible labor supply,” Journal of Development Economics, Vol. 87, 2007, pp. 507–33.
- Brock, P.L., 1988, “Investment, the current account, and the relative price of nontraded goods in a small open economy,” Journal of International Economics, Vol. 24, pp. 235–53. (Note: entry appears in the list as provided.)

### Macroeconomic management, infrastructure, and datasets
- Isard, P., L. Lipschitz, A. Mourmouras, and B. Yontcheva (eds.), 2006, The Macroeconomic Management of Foreign Aid, Opportunities and Pitfalls (Washington, D.C.: International Monetary Fund)
- World Bank, 1994, World Development Report 1994: Infrastructure for Development. (New York: Oxford University Press)
- World Bank, 2004, World Development Indicators, CD-ROM, Washington, D.C.

*Source: _wp08204 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2008/_wp08204.pdf_