## _wp08237

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---

### Introduction and scope
- Objective: study the extent to which PRGF-supported programs allow aid to be used over time, focusing on:
  - extent to which an increase in aid is allowed to be spent through an increase in the fiscal deficit (net of aid);
  - extent to which an increase in aid is absorbed through an increase in the current account deficit (net of aid);
  - how macroeconomic stability considerations influence programmed spending and absorption;
  - short- and long-run perspectives on immediate use versus smoothing of aid.
- Context:
  - PRGF arrangements approved since inception in 1999 through 2007; dataset tracks Fund’s projections and programming for PRGF episodes.
  - Observational unit: country-document; dataset comprises observations from "369 documents, pertaining to 51 countries."
  - Data span: years "spanning 1996–2010" from each document.

### Data, definitions, and empirical approach
- Aid definition (cash basis): "the net transfer of financial resources from donors to recipient countries," including:
  - "all official net transfers and loans," net official borrowing added to official transfers/grants, with interest payments to official creditors deducted;
  - the flow component of exceptional financing (the part of debt relief not used for clearing arrears).
- Key constructed variables (all expressed as shares of GDP):
  - Current account deficit net of aid = current account deficit minus current account components of aid (official transfers net of interest payments).
  - Fiscal deficit net of aid = fiscal deficit minus grants net of interest payments on external debt.
- Volatility measure: "On average, a PRGF-eligible country can expect that aid will vary about 5 percentage points of GDP with respect the average aid that it received in the previous 5 year, and the average deviation is higher than 10 percentage points of GDP for about one in four countries."
- Estimation approach:
  - Reduced-form pooled regressions with contemporaneous and lagged changes in aid to capture smoothing; pooled OLS preferred due to heterogeneity and data structure.
  - Controls include inflation, reserves coverage (months of imports), lagged deficits, PPP-GDP per capita, SSA dummy, real GDP growth, lagged terms of trade, and others.
  - Robust variances used for pooled regressions; fixed effects also reported.

### Conceptual framework: spending and absorption
- Definitions:
  - Absorption ratio: degree to which an aid increase finances a widening of the current account deficit (excluding aid) vs. increasing net foreign assets.
  - Spending ratio: degree to which an aid increase channeled through the government budget finances a widening of the fiscal deficit (excluding aid) vs. substitution for domestic financing.
- Distinct possible outcomes:
  - If fiscal deficit moves with the current account deficit, "the spending and absorption are the same."
  - If central bank sells more aid-based foreign exchange than needed for government spending, "absorption is greater than spending."
  - If fiscal deficit increases while aid is kept as reserves, "spending is greater than absorption."

### Key empirical findings (programmed responses)
- Representative aggregate results:
  - "70 percent of aid is programmed to be absorbed and more than 80 percent is programmed to be spent over just two years."
- One-year OLS estimates (sample restricted to aid increases):
  - Programmed spending ≈ "49.4 percent" (reported "0.494***").
  - Programmed absorption ≈ "47.8 percent" (reported "0.478***").
  - Observations: spending regression "186," absorption regression "176"; R-squared 0.209 and 0.135 respectively.
- Two-year smoothing (pooled OLS with lagged aid):
  - Absorption (example column): contemporaneous Δ aid = "0.561***"; lagged Δ aid = "0.127**"; sum ≈ "69 percent" absorbed in two years ("56 percent" in first year; "13 percent" from the lagged change).
  - Spending (example column): contemporaneous Δ aid = "0.578***"; lagged Δ aid = "0.258***"; sum ≈ "84 percent" spent in two years (about "58 percent" in first year; about "26 percent" in the following year).
  - Alternative specifications note feedback effects could lower two-year spending to ~"70 percent" in one specification.
- Treatment of decreases:
  - Programs do not request immediate downward adjustment in spending when aid is expected to decrease, supporting expenditure smoothing.
  - Eventual absorption (sum of same-year and lagged effects) remains about "0.72."
  - Eventual spending remains about "0.82."

### Regression controls and selected quantitative coefficients
- Selected control effects (programming year and two-year effects preserved exactly):
  - Lagged overall fiscal deficit: a one percent of GDP higher lagged deficit implies programmed fiscal deficit net of aid is about "0.2 percent of GDP" lower.
  - Lagged inflation: "one percent higher inflation implies a lower increase in the deficit by 0.1 percent of GDP" over two years.
  - Lagged reserves coverage: a positive difference in reserves equivalent to one month of imports induces an increase in the programmed current account deficit net of aid by about "0.2 percent of GDP."
- Examples of pooled regression coefficients (preserved from source tables):
  - Absorption pooled coefficients: Δ aid values include "0.478***", "0.500***", "0.561***", "0.702***", etc.; Δ aid lagged include "0.165***", "0.127**", "0.163***", etc.
  - Spending pooled coefficients: Δ aid values include "0.494***", "0.512***", "0.578***", "0.647***", etc.; Δ aid lagged include "0.154**", "0.258***", "0.250***", etc.
  - Tests of two-year sums and long-run multipliers reported across specifications with varying Prob values.

### Thresholds in programming (grid-search results and implications)
- General finding: "little evidence of simple threshold effects"; R-squared surfaces not concave and many local maxima → weak evidence for simple universal thresholds.
- Reserve coverage threshold (illustrative result noted):
  - Threshold identified: "2.9 months of imports."
  - Interaction coefficient on coverage > 2.9: "0.355*" (significant at the 10 percent level).
  - Implied two-year absorption:
    - If reserve coverage < "2.9 months": two-year absorption = "46 percent" (sum of coefficient on aid and lagged aid).
    - If coverage ≥ "2.9 months": two-year absorption increases to "81 percent."
  - R-squared reported for absorption regression with threshold: "0.277."
- Inflation threshold for spending (grid-search result):
  - Grid indicates highest R-squared corresponds to threshold of "15.7 percent" inflation.
  - Interaction coefficient for inflation > "15.7": "-0.349***".
  - Implied spending:
    - If inflation ≤ "15.7 percent": spending ≈ "87 percent."
    - If inflation > "15.7 percent": spending ≈ "53 percent."
  - R-squared reported for spending regression with threshold: "0.382."
- Levels specification alternative:
  - Evidence of an inflation threshold at "3 percent" in levels model:
    - Long-run spending would be full if inflation ≤ "3"; long-run spending ≈ "66 percent" if inflation > "3."

### Actual versus programmed inflows and use
- Programmed vs. actual aid inflows (same-year regressions, percent of GDP):
  - Dependent variable: Actual BOP aid received — Programmed aid inflow coefficient = "0.731***"; Constant = "1.591***"; Observations = "237"; R-squared = "0.693."
  - Dependent variable: Actual fiscal aid received — Programmed aid inflow coefficient = "0.705***"; Constant = "1.464***"; Observations = "235"; R-squared = "0.598."
- Summary comparison:
  - Programmed BOP aid inflows were on average "1.4 percent of GDP higher than actual inflows."
  - Programmed fiscal aid inflows were on average "0.7 percent of GDP higher than actual inflows."
  - Pattern: IMF programs tend to be overly pessimistic when projecting low levels of aid and overly optimistic when projecting large aid inflows.
- Actual use findings (Table 7 and Appendix III):
  - Estimated actual absorption of aid received in the first programming year: "32 percent" (lower than programmed).
  - Actual spending of same-year aid is full in regressions using the entire period (Table 7, column 4); other specifications show high actual spending coefficients.
  - Presence of a PRGF-supported program: interaction term not significantly different from zero — "neither actual spending nor actual absorption are significantly affected by the presence of a PRGF-supported program."
  - Aid surprises are absorbed and spent to the same extent as expected aid in several specifications.

### Robustness, alternative specifications, and heterogeneity
- Levels model robustness checks:
  - Same-year spending ≈ "76 percent" of same-year programmed aid.
  - Long-run spending ≈ "73 percent" (calculated as sum of coefficients on aid and lagged aid "0.40" divided by "1 − coefficient on lagged deficit net of aid (0.55)").
  - Same-year absorption ≈ "50 percent"; full absorption over the long run.
  - No consistent evidence for reserves coverage threshold in levels specification.
- Cross-country heterogeneity:
  - Standard deviation of absorption coefficients from country regressions ≈ "0.8."
  - Standard deviation of spending coefficients from country regressions ≈ "4."
  - Fixed effects and country-specific regressions alter absorption results somewhat but not spending results.
  - Sensitivity: excluding a few countries (e.g., Guyana, Lesotho, Nicaragua) materially affects some absorption estimates in fixed-effects specifications.

### Representative quantitative summaries (preserved)
- Programmed two-year absorption: "70 percent" (representative average).
- Programmed two-year spending: more than "80 percent" over two years.
- One-year programmed spending: "49 percent" (one-year OLS).
- One-year programmed absorption: "48 percent" (one-year OLS).
- Actual first-year absorption: "32 percent."
- Levels specification same-year spending: "76 percent"; long-run spending: "73 percent."
- Levels specification same-year absorption: "50 percent"; full in the long run.
- Reserve coverage threshold: "2.9 months."
- Inflation thresholds: "15.7 percent" (difference in programming), "3 percent" (levels model).
- Interaction coefficient for inflation > "15.7": "-0.349***."
- Spending if inflation ≤ "15.7": "87 percent"; if > "15.7": "53 percent."
- Spending if inflation ≤ "3": full; if > "3": "66 percent."

### Conclusions and policy implications
- Main conclusions:
  - PRGF-supported programs generally accommodate the spending and absorption of most available aid increases for low-income recipient countries while smoothing use of aid over time.
  - Evidence of smoothing is supported by the significance of lagged aid effects in regressions.
  - Program design does not appear to follow simple universal thresholds; rather, program responses reflect country-specific circumstances and a complex array of influences, though certain extreme vulnerability levels (e.g., high inflation above "15.7 percent" or low reserves) are associated with more cautious programmed use.
  - Actual spending and actual absorption do not systematically differ between countries with and without PRGF-supported programs.
- Policy implications highlighted:
  - Smoothing of aid supports effective multi-year projects and stabilizes spending in the face of aid volatility (aid volatility measured at about "5 percentage points of GDP" average deviation).
  - Program design instruments (floors on reserve buildup, ceilings on fiscal financing measures) commonly allow higher spending for unanticipated aid windfalls but do not require full offsetting of aid shortfalls via immediate spending cuts.
  - Attention to inflation and reserve indicators is warranted: high inflation and very low reserves can lead to programmatic constraints on spending and absorption to safeguard macroeconomic stability.

*Source: IMF staff paper content as provided in the supplied PDF extract.*

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

### _wp08237 - References

### Introduction
- For developing countries, aid provides an opportunity to reduce poverty and enhance growth.
- Aid can finance an expansion of infrastructure, the provision of services such as health and education, and other spending aimed at poverty reduction.
- Several factors can impair effective use of aid:
  - If aid is volatile, initiating long term projects that require steady financing could generate financial difficulties in the future.
  - When capacity constraints are acute, an increase of expenditures might exceed productive capacity of the economy, to the point where inflation could rise.
  - In case of severe economic vulnerabilities or instability, poverty reduction and growth may be most effectively achieved if aid is first used to address these vulnerabilities and instabilities, and then to expand spending.

### Research questions and objectives
- These considerations raise questions on the advice the IMF gives to member countries about the timing and extent of using aid.
- Further questions are how aid volatility, capacity constraints, or macroeconomic stability shape these recommendations.
- The IMF has recently clarified the principles for its advice on the use of aid: the IMF supports the full use of aid over time, taking into account the need to safeguard macroeconomic stability and limits on productive spending. 2
- This paper studies the extent to which the Fund’s actual advice to countries receiving aid aligns with that supportive approach, focusing on countries with programs supported under the IMF’s Poverty Reduction and Growth Facility (PRGF).

### Scope and specific aims
- The objective of this paper is to study the extent to and pace at which PRGF-supported programs allow aid to be used over time.
- Specifically, the paper studies:
  - The extent to which an increase in aid is allowed to be spent through an increase in the fiscal deficit (net of aid).
  - The extent to which an increase in aid is absorbed through an increase in the current account deficit (net of aid).
  - How considerations about macroeconomic stability influence programmed spending and absorption of aid.
- The paper takes both a short and a long run perspective and studies whether programs allow to spend and absorb aid immediately, or to smooth it over time.
- The paper focuses mainly on the programmed spending and absorption (i.e., the plans for spending and absorbing aid yet to be received) and also looks at actual spending and absorption of aid.

### Data and empirical approach
- The paper uses data from IMF program documents to estimate reduced forms models.
- The dataset was constructed by collecting data from all the staff reports for the request or a review of all PRGF-supported programs approved since the inception of the PRGF in 1999, until end-

*_wp08237 - References_*

### 2007. The dataset allows tracking Fund’s projections and economic programming for 378

### _wp08237 - 2007. The dataset allows tracking Fund’s projections and economic programming for 378

### Key findings
- On average, "70 percent of aid is programmed to be absorbed and more than 80 percent is programmed to be spent over just two years."
- Simple one-year OLS estimates: programmed spending is about "49 percent" and programmed absorption is about "48 percent" of an anticipated aid increase (Table 1).
- Two-year smoothing estimates:
  - "69 percent of a programmed increase in aid is absorbed in two years" (56 percent in the first year; 13 percent from the lagged change).
  - "84 percent of a programmed increase in aid is allowed to be spent in two years" (about 58 percent in the first year; about 26 percent in the following year).
- Programs do not request immediate downward adjustment in spending when aid is expected to decrease, supporting expenditure smoothing for volatile aid inflows.
- Weak evidence for thresholds shaping programmed use of aid; the strongest result is that "programmed spending may drop once inflation exceeds 15 percent."
- On average, actual spending and absorption are "roughly the same in countries with and without a PRGF-supported program."

### Background and data definitions
- Aid is defined on a cash basis as "the net transfer of financial resources from donors to recipient countries," including:
  - "all official net transfers and loans," net official borrowing added to official transfers/grants, with interest payments to official creditors deducted;
  - the flow component of exceptional financing (the part of debt relief not used for clearing arrears).
- Aid volatility: "On average, a PRGF-eligible country can expect that aid will vary about 5 percentage points of GDP with respect the average aid that it received in the previous 5 year, and the average deviation is higher than 10 percentage points of GDP for about one in four countries."
- PRGF context:
  - The PRGF is "the main vehicle by which the IMF provides concessional financial support to countries’ poverty reduction and growth strategies."
  - "Currently, 77 countries are eligible to access resources under the PRGF."
  - "During 1999-2007, generally, each year a PRGF arrangement was in place in between 25 and 40 countries."

### IMF programs and program projections
- PRGF arrangements:
  - "A PRGF arrangement typically covers a three-year period and sets macroeconomic objectives for the medium-term."
  - Program documents include quantitative fiscal and balance of payments projections and program conditions; program reviews are "conducted, in principle, every half-year."
- Program projections implicitly define the programmed use of expected aid inflows via floors on reserve buildup and ceilings on fiscal financing measures.
- Program mechanisms commonly:
  - allow higher spending in case of unanticipated aid windfalls (especially grants);
  - "do not require lower spending to offset all of aid shortfalls—generally through higher domestic financing."

### Conceptual framework: spending and absorption
- Two ratios:
  - Absorption ratio: degree to which an aid increase finances a widening of the current account deficit (excluding aid) vs. increasing net foreign assets.
  - Spending ratio: degree to which an aid increase channeled through the government budget finances a widening of the fiscal deficit (excluding aid) vs. substitution for domestic financing.
- Distinct outcomes:
  - If fiscal deficit moves with the current account deficit, "the spending and absorption are the same."
  - If central bank sells more aid-based foreign exchange than needed for government spending, "absorption is greater than spending."
  - If fiscal deficit increases while aid is kept as reserves, "spending is greater than absorption."
- Optimal timing depends on aid volatility, spending capacity, national priorities, and macroeconomic vulnerabilities; smoothing over time is often desirable for multi-year commitments or volatile aid.

### Methodology and dataset
- Scope: all PRGF program staff reports approved over "1999–2007."
- Observational unit: country-document; dataset comprises observations from "369 documents, pertaining to 51 countries." (The content unit header references "378 episodes" as context for tracking projections and programming.)
- Data span: collected available years "spanning 1996–2010" from each document.
- Measurement:
  - Aid constructed as "net foreign financing including grants, debt relief, and the flow component of exceptional financing."
  - Current account deficit net of aid: current account deficit minus current account components of aid (official transfers net of interest payments).
  - Fiscal deficit net of aid: fiscal deficit minus grants net of interest payments on external debt.
  - All deficits and aid expressed as shares of GDP.
- Econometric approach:
  - Reduced-form pooled regressions (panel techniques considered less reliable for the data structure).
  - Models include contemporaneous and lagged changes in aid to capture smoothing over time; controls for inflation, reserves, lagged deficits, PPP-GDP per capita, SSA dummy, and other macro variables.

### Regression results and interpretation
- Simple OLS one-year regressions (sample restricted to aid increases):
  - Spending regression coefficient on aid increase: "0.494***" (49.4 percent).
  - Absorption regression coefficient on aid increase: "0.478***" (47.8 percent).
  - Observations: spending regression "186," absorption regression "176"; R-squared 0.209 and 0.135 respectively.
- Pooled OLS with lagged aid (summary Table 2):
  - Absorption (column 1): contemporaneous Δ aid = "0.561***"; lagged Δ aid = "0.127**"; sum ≈ "69 percent" absorbed in two years.
  - Spending (column 4): contemporaneous Δ aid = "0.578***"; lagged Δ aid = "0.258***"; sum ≈ "84 percent" spent in two years (noting feedback effects could lower this to ~70 percent in one specification).
  - Two-year cumulative regressions (column 3 and 6) generally confirm high two-year spending (over "80 percent") though two-year absorption regressions are less credible due to operational significance.
- Controls and thresholds:
  - Lagged overall fiscal deficit: a one percent of GDP higher lagged deficit implies programmed fiscal deficit net of aid is about "0.2 percent of GDP" lower.
  - Lagged inflation: does not affect programmed fiscal deficit net of aid in the programming year, but "one percent higher inflation implies a lower increase in the deficit by 0.1 percent of GDP" over two years.
  - Lagged reserves coverage: a positive difference in reserves equivalent to one month of imports induces an increase in the programmed current account deficit net of aid by about "0.2 percent of GDP."
  - Evidence on simple thresholds (inflation or reserves) is weak; IEO (2007) earlier estimated same-year absorption nearly full only when reserves > "2.5 months of imports" and spending complete only when inflation < "5 percent"; this paper finds the most robust threshold effect around inflation exceeding "15 percent" lowering programmed spending.

### Complementarity with earlier studies
- The paper complements:
  - Berg et al (2007) by using a new comprehensive dataset and multi-year perspective.
  - IEO (2007) by extending analysis beyond same-year use and controlling for additional variables.
  - Aiyar and Ruthbah (2008) by estimating programmed (not only actual) spending and absorption and analyzing both increases and decreases in aid.

*Source: IMF staff paper content as provided.*

### Box 1: Control variables

### Box 1: Control variables

### Spending regressions — control variables
- Lagged change in the deficit net of aid: captures indirect effect of past aid or concerns about keeping deficit stable.
  - Positive coefficient implies persistence in the increase in the deficit net of aid (aid affects next year’s deficit directly and indirectly).
  - Negative coefficient implies programs aim at keeping the deficit net of aid stable over time, programming a reduction after an expansion.
- Lag of the overall fiscal deficit: captures concerns about fiscal consolidation.
  - Negative coefficient implies the reduction in the deficit net of aid is programmed to be larger the greater was the overall fiscal deficit in the past.
- Real GDP growth: captures the cyclicality of fiscal policy.
  - Negative coefficient implies that higher deficit is programmed when growth slows down.
- Lag of the inflation rate: captures concerns about the impact of fiscal policy on internal macroeconomic stability.
  - Negative coefficient implies that the higher past inflation is, the larger the programmed reduction in the fiscal deficit.
- All pertinent variables are expressed in percent of GDP.

### Absorption regressions — control variables
- Lagged change in the current account deficit net of aid (analogous interpretation to fiscal balance in spending equation).
- Lag of the overall current account deficit (analogous to lag of overall fiscal deficit in spending equation).
- Lag change in the terms of trade: captures concerns about adjusting to past exogenous shock.
  - Negative coefficient implies that past shocks are allowed to be passed to the economy through an increase in the current account deficit net of aid.
- Change in the overall fiscal deficit: captures concerns about effects of fiscal policy on external macroeconomic stability (negative coefficient), or demand pressures generated by fiscal policy on the current account (positive coefficient).
- Per capita GDP relative to that of the US: captures concerns about a country’s vulnerability.
  - Positive coefficient implies a larger increase in the current account deficit is programmed for countries of higher income.
- Lag of reserve coverage in terms of months of imports: captures concerns about external stability, in particular reserve adequacy.
  - Positive coefficient implies a larger increase in the current account deficit is programmed for countries where the reserve position is higher.
- All pertinent variables are expressed in percent of GDP.

### Findings on regional and country-specific effects
- No evidence of differences in spending and absorption for countries of Sub-Saharan Africa: coefficient of interaction between aid increase and an SSA dummy is not significantly different from zero (Table 2, columns 2 and 5).
- Country specific effects:
  - Do not alter results for spending.
  - Do somewhat alter results for absorption (see Appendix III for details).

### Treatment of positive and negative changes in aid — summary of approach
- Aid volatility implies both increases and decreases should be considered; less-than-complete adjustments in both directions allow smoothing and stabilization.
- The treatment of decreases is controlled by interacting expected change in aid with a dummy equal to one if the expected change is negative.

### Treatment of positive and negative changes in aid — empirical findings
- Eventual absorption (sum of same-year and lagged effects) remains about 0.72.
- Eventual spending remains about 0.82 (Table 3, columns 1 through 3).
- Coefficients below 1 imply program design does not ask for an immediate full adjustment of current account or fiscal deficits, smoothing the adjustment over time.
- Absorption response to increases and decreases in aid appears symmetric: interaction term not significant.
- Spending response is asymmetric over a one-year horizon but symmetric over a two-year horizon (Table 3, columns 2 and 3).
  - Negative sign of the interaction term suggests an expansive asymmetry: if aid is expected to fall, the programmed tightening of the fiscal deficit net of aid is smaller than the expansion allowed when aid increases.
- Sensitivity note: for absorption, results are highly sensitive to inclusion of some countries (excluding Guyana, Lesotho, and Nicaragua increases overall absorption in fixed effects to about 0.59).

### Selected coefficients and statistics from Table 3 (Absorption regression, pooled OLS)
- Δ aid 2/: 0.568***
- Δ aid * dummy aid decrease 2/: -0.203
- Δ aid lagged 2/: 0.163***
- Δ deficit net of aid, lagged 2/: 0.033
- Overall CA deficit, lagged: -0.077***
- Δ terms of trade, lagged: 0.342
- Real GDP growth: 0.013
- Lagged inflation: -0.025*
- PPP - GDP per capita: 0.084
- Lagged coverage: 0.135
- Constant: 1.034***
- Observations: 260
- R-squared: 0.315

- (Additional columns reported in the source show alternative pooled OLS specifications with Δ aid = 0.591*** and Δ aid = 0.824*** in the two-year specification, and other coefficient variations; see source tables for full detail.)

### Aid projections — key findings and regressions
- Programmed aid is estimated to follow an upward trend: the positive constant in regressions corresponds to an estimated upward trend in projected aid close to 1 percent of GDP for the program year.
- Lagged change in aid has a negative coefficient: aid changes are not considered fully permanent; expectations are revised upward after an increase, but not in full, and aid inflows are expected to fluctuate around a revised long-run average with fluctuations diminishing over time.
- For balance of payments aid, this relationship is weak (very low R-squared).

Table of programmed vs. lagged aid changes (percent of GDP):
- Change in aid used in absorption regressions (Aid from BOP)
  - Δ aid, lagged 2/: -0.211***
  - Constant: 1.023***
  - Observations: 359
  - R-squared: 0.07
- Change in aid used in spending regressions (Aid from Fiscal)
  - Δ aid, lagged 2/: -0.327***
  - Constant: 0.789***
  - Observations: 339
  - R-squared: 0.187

Illustrative interpretation (from source footnote):
- Example for fiscal aid: if past aid rose to 10 percent of GDP from 0, the aid inflows expected for the first year of the program would be 7.5 percent of GDP (coefficient -0.33 times lagged change 10, plus constant 0.8), producing oscillation around an increasing trend.

### Actual vs. programmed aid inflows (same-year regressions)
Table 5 (percent of GDP):
- Dependent variable: Actual BOP aid received
  - Programmed aid inflow 2/: 0.731***
  - Constant: 1.591***
  - Observations: 237
  - R-squared: 0.693
- Dependent variable: Actual fiscal aid received
  - Programmed aid inflow 2/: 0.705***
  - Constant: 1.464***
  - Observations: 235
  - R-squared: 0.598

Summary statement from the source:
- During 1999-2007 under PRGF programs, programmed BOP aid inflows were on average 1.4 percent of GDP higher than actual inflows; programmed fiscal aid inflows were on average 0.7 percent of GDP higher than actual inflows.
- IMF programs tend to be overly pessimistic when projecting low levels of aid and overly optimistic when projecting large aid inflows (pattern holds for both fiscal and BOP data).

### Thresholds in programming the use of aid
- Question: whether inflation or reserve coverage thresholds trigger systematic changes in programmed spending and absorption.
- Method: include interaction between increase in aid and dummy that equals one if inflation (or coverage) is above threshold; conduct grid search to maximize R-squared.
- Result: little evidence of simple threshold effects; R-squared functions are not concave, have many local maxima, and little variability across maxima — suggesting weak evidence for existence of such thresholds.
- Weak evidence noted for a coverage threshold:
  - Apparent weak evidence of a threshold for coverage of 2.9 months of imports.
  - Grid search suggests threshold that maximizes R-squared is 6.6 months of imports.
  - However, at that threshold the coefficient of the interaction term is not significantly different from zero (see column 6 of Table III.3 in the source).

*Source: Box 1: Control variables (extracted from the supplied IMF PDF content).*

### Appendix III). However, the left panel of Figure 4 shows that the second-highest R-squared

### _wp08237 - Appendix III). However, the left panel of Figure 4 shows that the second-highest R-squared

### Thresholds in Program Design and Their Estimated Effects
- Reserve coverage threshold:
  - Threshold identified: 2.9 months of imports.
  - Interaction coefficient on coverage > 2.9: 0.355* (positive, different from zero; significant at the 10 percent level).
  - Implied two-year absorption:
    - If reserve coverage is below 2.9 months of imports: two year absorption is 46 percent (the sum of the coefficient on aid and lagged aid).
    - If coverage is above 2.9 months of imports: two year absorption increases to 81 percent.
  - Table 6 reported R-squared for absorption regression: 0.277.
- Inflation threshold for spending:
  - Grid indicates highest R-squared corresponds to a threshold of 15.7 percent (inflation).
  - Interaction coefficient for inflation > 15.7: -0.349*** (significantly different from zero).
  - Implied spending:
    - If inflation is below 15.7 percent: spending would be about 87 percent.
    - If inflation is above 15.7 percent: spending drops to 53 percent.
  - Table 6 reported R-squared for spending regression: 0.382.
- Interpretation:
  - Results indicate program design is not based on simple rules, but certain levels of vulnerability indicators (coverage, inflation) raise heightened concern and can lead to a more cautious stance in programmed macroeconomic policies.

### Actual versus Programmed Spending and Absorption
- Main regression findings (entire period 1996-2007, Table 7):
  - Actual spending of same-year aid is full, and there is no smoothing of aid (Table 7, column 4).
  - Estimated actual absorption of aid received in the first programming year is lower than programmed absorption: 32 percent; no evidence of smoothing (Table 7, column 1).
  - Presence of a program (interaction term between aid and program dummy) has a coefficient not different from zero: neither actual spending nor actual absorption are significantly affected by the presence of a PRGF-supported program (Table 7, columns 2 and 5).
  - Aid surprises (unexpected increases in aid) are absorbed and spent to the same extent as expected aid (Table 7, columns 3 and 6).
- Table 7 reported R-squared values across columns: 0.118, 0.129, 0.145, 0.328, 0.329, 0.371.
- Observations reported in Table 7 vary by specification (examples): 132, 132, 881, 651, 651, 107 (as listed under Observations 3/...).

### Alternative Model in Levels (Robustness Check)
- When estimating spending and absorption using levels (percent of GDP) rather than changes:
  - Estimated same-year spending: about 76 percent of same-year programmed aid.
  - Long-run spending (accounting for persistence using formula (3) of Appendix II): estimated to be 73 percent.
    - Footnote calculation: this is the sum of the coefficients on aid and lagged aid (0.40) divided by one minus the coefficient on the lagged deficit net of aid (0.55).
  - Evidence of an inflation threshold at 3 percent:
    - Long-run spending would be full if inflation is below 3 percent.
    - Long-run spending would be 66 percent if inflation is above 3 percent (Table 8).
  - Estimated absorption in levels:
    - About 50 percent of the same-year programmed aid.
    - Full absorption over the long run.
  - No evidence for a reserves coverage threshold affecting programmed absorption in the levels specification.
- Table 8 reported high R-squared values across specifications (examples): 0.715, 0.720, 0.589, 0.891, 0.805.
- Observations reported in Table 8 examples: 327, 327, 434, 297, 409 (as listed under Observations 3/...).

### Comparative Evidence and Context
- Comparison to other studies:
  - Aiyar and Ruthbah (2008) findings (contrasted with results here):
    - Actual spending 56 percent in the short run and above 100 percent in the long run; absorption 50 in the short run and 83 percent in the long run.
  - Case studies in Berg et al (2007) align with the finding that, in many cases, aid is spent but not absorbed.
- Interpretation of program constraints:
  - For absorption: standard program design sets a floor on reserve accumulation, allowing monetary authorities to raise reserves further and thereby limit actual absorption to be less than programmed.
  - For spending: program limits may not be binding on expansion of the broader non-aid fiscal deficit; program limits could nonetheless guide financing choices to help ensure debt sustainability and avoid crowding out or monetary financing.

### Key Quantitative Summaries and Ranges
- Typical estimated eventual spending and absorption ratios generally range between 0.6 and 0.9 across specifications.
- Representative point estimates highlighted:
  - Programmed two-year absorption (average finding): 70 percent of aid increases programmed to be absorbed.
  - Programmed two-year spending: more than 80 percent programmed to be spent over two years.
  - Actual absorption first programming year: 32 percent (lower than programmed).
  - Levels specification: same-year spending ~76 percent; long-run spending ~73 percent.
  - Levels specification: same-year absorption ~50 percent; full in the long run.
- Threshold-specific values preserved:
  - Reserve coverage threshold: 2.9 months.
  - Coverage interaction coefficient: 0.355*.
  - Inflation thresholds: 15.7 percent (spending drop) and 3 percent (levels model threshold).
  - Interaction coefficient for inflation > 15.7: -0.349***.
  - Spending if inflation ≤ 15.7: 87 percent; if > 15.7: 53 percent.
  - Spending if inflation ≤ 3 (levels): full; if > 3: 66 percent.

### Conclusions and Policy Implications
- Overall conclusions:
  - PRGF-supported policy programs have accommodated the spending and absorption of most or almost all available aid or aid increases by low-income recipient countries, while smoothing the use of aid over time.
  - Evidence of smoothing is confirmed by the significance of lagged aid in regressions (gradual use of aid over time).
  - Expenditure smoothing stabilizes use of aid over time in the face of high aid volatility and is beneficial because large swings in expenditures can undermine spending effectiveness.
  - Very weak evidence of simple inflation or reserves coverage thresholds points to a more complex array of influences on program design reacting to specific country circumstances.
  - Actual spending and actual absorption do not depend on whether a country has a PRGF-supported program.

*Source: _wp08237 - Appendix III). However, the left panel of Figure 4 shows that the second-highest R-squared*

### Appendix II: The Model

### Appendix II: The Model

### Model specification for aid changes
- Variables and notation:
  - e_tY: programmed level of the endogenous variable for year t and document i (current account deficit net of aid, or fiscal deficit net of aid, in percent of GDP).
  - tY: actual level of the endogenous variable at year t.
  - e_tX and tX: expected and actual level of aid at year t.
  - tZ: vector of explanatory variables.
  - tω: zero-mean i.i.d. error term.
- Baseline dynamic specification (difference form):
  - Equation (1):
    - YY e tt − , XX e tt − , XZY ttt , and parameters 1γ , 2γ , 3γ , 11γ , 12γ , 2γ , δω appear in the formal expression:
      - (e)tt tttt tt YYX XX XZY Yγγγ γδω −−−−−−− −=+ − + − + + − +  (expression as presented).
  - Interpretation:
    - 1γ represents spending (or absorption) of aid in the first programming year.
    - 2γ represents spending (or absorption) of aid in the second programming year.

### Alternative level formulation and dynamics
- Level model (equation (2)):
  - 0121311 ee tttttt YXXZYuββ β β θ −−− =+ + + + +  (notation preserved from source).
  - t u: zero-mean i.i.d. error term.
- Short-run and multi-year partial derivatives (as given):
  - Short run: ∂e_tY/∂e_tX = β1.
  - Next programming year: ∂∂ = β1 + θβ1 + θβ2 (as presented in the source's symbolic expression).
  - Following year: ∂/∂ = θβ1 + θβ2 (symbolic as in source).
  - General jth year: ∂/∂ = θ^(j-1)β1 + θ^(j-1)β2 (symbolic representation preserved).
- Long-run cumulative effect:
  - Given by (β1 + β2)/(1 − θ). (Source expression: 12 1 ββ θ + − .)
  - If (β1 + β2)/(1 − θ) = 1 (i.e., 12 1ββθ+=− in the source notation), there is full spending/absorption of aid over the long run.
- Error-correction representation:
  - Subtracting lagged dependent variable and re-arranging yields an ECM form where the deviation from equilibrium appears within square brackets.
  - The source shows the transformed equation and notes: "The expression within square brackets is the deviation of the actual from equilibrium."

### Estimation approach and diagnostics (Appendix III summary relevant to the model)
- Software and estimation:
  - STATA was used; analysis based on pooled estimations.
- Data characteristics and estimator choice:
  - Preliminary analysis indicates a high degree of heterogeneity in spending and absorption relationships across countries.
  - Country-by-country regressions were run as a first step.
  - Due to heterogeneity and an unbalanced dataset, pooling with simple OLS was preferred; panel regressions with homogeneous coefficients are likely unreliable and dataset does not make feasible panel regressions that allow heterogeneous coefficients (e.g., Swamy estimator).
  - Fixed effects estimates are also reported.
- Diagnostic issues and remedies:
  - Evidence of heteroskedastic errors in some regressions → robust variances estimated for all pooled regressions.
  - For fixed effects estimations, robust option not used because standard STATA commands do not allow the F-test that fixed effects equal zero with robust option.
  - Ramsey specification test performed for pooled regressions of programmed spending and absorption.
  - Test that fixed effects are equal to zero conducted on all fixed effects regressions.
  - Serial correlation testing limited by data: "only in few countries there are enough sequenced observations."
  - Tests performed include:
    - Sum of coefficient on the increase in aid and the lagged increase in aid.
    - Test on the long run effect of a change in aid (as defined in Appendix II).
- Sample size drivers and exclusions:
  - Lagged change in aid requires data for two years preceding programming year → loss of about 10 observations in absorption regressions and 30 in spending regressions.
  - Observations with programmed aid declines excluded; about 130 observations with negative programmed change in aid excluded.
  - Outliers: observations where programmed change in overall deficit and aid exceeded their respective averages by two standard deviations were dropped → about 30 outliers dropped for absorption regressions and 38 for spending regressions.
  - Programmed variables observed twice a year on average while actual variables observed once a year → differences in number of observations between regressions.

### Key empirical findings and reported coefficients (selected highlights from tables)
- Cross-country dispersion (from country regressions):
  - Standard deviation of absorption coefficients: about 0.8.
  - Standard deviation of spending coefficients: about 4.
- Table III.1 — Average of coefficients of country regressions (values preserved):
  - Absorption regressions:
    - Programmed change in aid: Simple average 0.442; Standard deviation -0.018; Weighted average (Stein rule) 0.444.
    - Lagged change in aid: Simple average -0.018; Standard deviation 1.212; Weighted average (Stein rule) -0.160.
  - Spending regressions:
    - Programmed change in aid: Simple average 1.289; Standard deviation 4.344; Weighted average (Stein rule) 1.280.
    - Lagged change in aid: Simple average -1.189; Standard deviation 13.852; Weighted average (Stein rule) -1.180.
- Representative pooled regression coefficient magnitudes (selected from Tables III.2–III.8, preserving exact reported coefficients and significance):
  - Spending of aid increases (Table III.2):
    - Δ aid: coefficients range reported, e.g., 0.494***, 0.512***, 0.578***, 0.550***, 0.647***, 0.566*, 0.847***, 0.639*** with standard errors shown in parentheses.
    - Δ aid lagged: reported coefficients include 0.154**, 0.258***, 0.250***, 0.228***, 0.266*** (with respective standard errors).
    - Tests:
      - Test Δaid + Δaid lagged = 0.85: multiple reported test statistics and probabilities (e.g., Prob of rejecting 0.072, 0.899, 0.677, 0.822, 0.953 for various regressions).
      - Test long run abs. = 0.70: reported probabilities include 0.915, 0.954, 0.726, 0.965 (various regressions).
  - Absorption of aid increases (Table III.3):
    - Δ aid: coefficients such as 0.478***, 0.500***, 0.561***, 0.414***, 0.702***, 0.545***, 0.340**, 0.411***, 0.455*** with standard errors.
    - Δ aid lagged: coefficients include 0.165***, 0.127**, 0.079, 0.119*, 0.119**, 0.118* (with standard errors).
    - Tests:
      - Test Δaid + Δaid lagged = 0.7: reported test statistics and Prob of rejecting include 0.731, 0.933, 0.118, 0.791, 0.118 (various regressions).
      - Test long run abs. = 0.76: reported probabilities include 0.929, 0.036, 0.937, 0.130 (various regressions).
  - Treatment of increases and decreases in aid (Table III.4):
    - Δ aid: 0.568***, 0.438***, 0.591***, 0.594***, 0.824***, 0.609*** (with standard errors).
    - Δ aid * dummy aid decrease: coefficients reported include -0.203, -0.028, -0.227*, -0.174, -0.256, 0.084 (with standard errors).
    - Δ aid lagged: 0.163***, 0.128***, 0.243***, 0.259*** (with standard errors).
  - Actual absorption and spending (Tables III.5 and III.6):
    - Table III.5 (actual absorption of aid increases):
      - Δ aid: 0.308**, 0.324**, 0.496***, …, 0.332*, 0.594 (with standard errors).
      - Δ overall fiscal deficit: 0.069**, 0.068**, 0.064* in certain regressions.
    - Table III.6 (actual spending of aid increases):
      - Δ aid: 0.710***, 0.714***, 0.751***, …, 0.819***, 0.809* (with standard errors).
      - Unexpected aid: positive and significant in some specifications (e.g., 0.776***, 0.758**).
      - Expected aid: positive and significant in some specifications (e.g., 0.585**, 0.737**).
  - Spending using level of aid inflows (Table III.7):
    - Aid: 0.787***, 0.747***, 0.768***, 0.580***, 0.914***, 0.894***, 0.954*** across regressions.
    - Lagged aid: mixed signs (e.g., 0.050, -0.366**, -0.194***, -0.364***, 0.043, 0.144*).
    - Fiscal deficit net of aid, lagged: 0.450***, 0.327***, 0.442*** in some specifications.
    - Tests:
      - Test aid + aid lagged = 0.7: multiple reported test statistics and probabilities (e.g., Prob of rejecting 0.202, 0.025, 0.000, 0.053, 0.000, 0.000).
      - Test long run abs. = 0.7: reported probabilities include 0.813, 0.108, 0.016, 0.000, 0.000.
  - Absorption using level of aid inflows (Table III.8):
    - Aid: 0.919***, 0.720***, 0.501***, 0.476***, 0.349***, 0.204*** across regressions.
    - Lagged aid: 0.241***, -0.237**, -0.126**, -0.114, -0.100** in different specifications.
    - CA deficit net of aid, lagged: 0.749***, 0.490***, 0.743***, 0.371*** in some specifications.
    - Tests:
      - Test aid + aid lagged = 1: reported test statistics and probabilities include e.g., Prob of rejecting 0.350, 0.000, 0.000, 0.000, 0.000.
      - Test long run abs. = 1: reported probabilities include 0.623, 0.001, 0.608, 0.000.

### Empirical implications (as reflected in the reported results)
- Programmed increases in aid are generally associated with positive and statistically significant coefficients for both spending and absorption in many pooled specifications (e.g., multiple Δ aid coefficients significant at *** , ** , and * levels as reported).
- Lagged aid often contributes additional positive effects in several specifications but signs and significance vary across models and dependent variables.
- Tests of long-run absorption/spending (as defined by the model’s long-run multiplier) yield mixed results across specifications; several pooled regressions reject or fail to reject particular long-run values depending on sample and controls.
- Heterogeneity across countries is substantial (standard deviations reported), motivating pooled OLS with robust standard errors and reporting of fixed effects where applicable.

*Source: Appendix II: The Model (and supporting estimation notes and tables) from the provided IMF content unit.*

### References

### References

### Cited works

- Adam, Christopher, Stephen O’Connell, Edward Buffie, and Catherine Pattillo, 2007, Monetary Policy Rules for Managing Aid Surges in Africa, Working Paper No. 07/180 (Washington: International Monetary Fund).
- Aiyar, Shekkar and Ummul Ruthbah, 2008, Where did all the Aid go? A Macroeconomic Investigation of the Uses of Aid, Working Paper No. 08/34 (Washington: International Monetary Fund).
- Baltagi, Badi H., George Bresson, and James M. Griffin, 2003, Homogenous, Heterogeneous or Shrinkage Estimators? Some Empirical Evidence from French Regional Gasoline Consumption, Empirical Economics, Vol. 28, pp. 795–811.
- Baltagi, Badi H. and James M. Griffin, 1997, Pooled Estimators v.s. Their Heterogeneous Counterparts in the Context of Dynamic Demand for Gasoline, Journal of Econometrics, Vol. 77, pp. 303–327.
- Berg, Andrew, Shekhar Aiyar, Mumtaz Hussain, Shaun K. Roache, Tokhir N. Mirzoev, Amber Mahone, 2007, The Macroeconomics of Scaling Up Aid: Lessons from Recent Experience, Occasional Paper No. 253 (Washington: International Monetary Fund).
- Bulir, Ales and A. Javier Hamann, 2006, Volatility of Development Aid: From the Frying Pan into the Fire? Working Paper No. 06/65 (Washington: International Monetary Fund).
- Gupta, Sanjeev, Gerd Schwartz, Shamsuddin Tareq, Richard Allen, Isabell Adenauer, Kevin Fletcher, and Duncan Last, 2008, Fiscal Management of Scaled-up Aid (Washington: International Monetary Fund).
- Heller, Peter, Manachem Katz, Xavier Debrun, Theo Thomas, Taline Koranchelian, and Isabell Adenauer, 2006, Making Fiscal Space Happen: Managing Fiscal Policy in a Word of Scaled-Up Aid, Working Paper No. 06/270 (Washington: International Monetary Fund).
- Independent Evaluation Office (IEO) of the International Monetary Fund, 2007, The IMF and aid to Sub-Saharan Africa (Washington: International Monetary Fund).
- International Monetary Fund, 2005, The Macroeconomics of Managing Aid Inflows: Experiences of Low-Income Countries and Policy Implications.
- International Monetary Fund, 2007, Aid Inflows—The Role of the Fund and Operational Issues for Program Design.
- International Monetary Fund and World Bank, 2007, Heavily Indebted Poor Countries (HIPC) Initiative and Multilateral Debt Relief Initiative (MDRI) – Status of Implementation.
- Isard, Peter, Leslie Lipschitz, Alexandros Mourmouras, Boriana Yontcheva, 2006, The Macroeconomic Management of Foreign Aid: Opportunities and Pitfalls (Washington: International Monetary Fund).
- Roberston, Donald and James Symons, 1992, Some Strange Properties of Panel Data Estimators, Journal of Applied Econometrics, Vol. 7, pp. 175–189.

*Source: _wp08237 - References*

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