we-solve (beta)

Econ-579 · economics · Economics

Aid that builds lasting capacity

LLM status Open unverified

Statement

Original subject group: Development and poverty

Audit classification: Background; proposed extension. Full published version and metadata checked. Positive eleven-year results already exist; residual support continued, so these are not estimates after complete donor withdrawal.

Definitions and precise research target

Complete editorial problem. Fix a set of aid-eligible communities and a program with a precisely declared withdrawal path beginning at date $t_0$. Let $p$ specify funding, local participation, implementer, public-service responsibilities, and withdrawal rules. Let $K_{it}(p)$ measure locally maintained administrative or productive capacity and $Y_{it}(p)$ household economic welfare. For a declared horizon $T>t_0$, define $\tau_K(T,p)=E[K_{iT}(p)-K_{iT}(0)]$ and $\tau_Y(T,p)=E[Y_{iT}(p)-Y_{iT}(0)]$. Capacity must be measured using verified service delivery, staffing, maintenance, or collective-action outputs, rather than continued external spending. Estimate whether aid complements state and community investment or substitutes for it, allowing political incentives and nonbeneficiary spillovers. Randomized introduction identifies offer effects; withdrawal comparisons need credible timing variation and controls for concurrent shocks. Separate temporary assets from institutional changes by measuring outcomes after each specified support component ends. Determine which program features predict durable gains and can be transported to other delivery systems. A known long-run null or positive result in one setting is a partial answer. The present statement proposes a general identification and design extension; no exact primary passage establishing this complete question as open was verified in the supporting long-run aid study.

Definitions and admissible scope. Communities, rather than households alone, are the assignment units for capacity outcomes. Let $K_{jt}$ be an independently measured vector of maintenance, staffing, tax collection, and service outputs, with a declared scalar index only when needed. Distinguish withdrawal of grants, withdrawal of facilitators, and withdrawal of all donor-paid personnel. The complete regime includes any residual support after $t_0$. A post-withdrawal contrast requires both treatment and comparator to have specified support paths; calendar time since program launch is not equivalent to time since complete withdrawal. The research problem is identifying durable program effects and comparing delivery arrangements, not denying the positive long-run results already found in Sierra Leone. Let communities be indexed $j$ with a fixed baseline household sample within each community. The community capacity target is $\tau_K=E[K_{jT}(p)-K_{jT}(0)]$, componentwise for vector $K$, and the household welfare target uses a declared household weighting law. The index $i$ in the introductory shorthand is replaced by $j$ for capacity units. Fix $t_0<T<\infty$ and support paths for grants, facilitators, and personnel in both arms. For a scalar durability criterion choose a fixed $v(K)$ and compare $E[v(K_{jT}(p))-v(K_{jT}(0))]$; no ordering of a vector is assumed silently. Introduction and withdrawal assignment, follow-up selection, and community interference are explicit inputs.

Variants and assumption changes

  1. Observed long-run aid version (source-based scope): retain the actual support history of the Sierra Leone program and compare its treated and control communities after eleven years. This is an existing estimated contrast, not a newly open question.
  2. Withdrawal design (editorial): randomize or credibly instrument grant and technical-assistance withdrawal dates separately. Measure locally funded maintenance and state service provision after each support component ends.

References and source audit

Support and access. Full published version and metadata checked. Positive eleven-year results already exist; residual support continued, so these are not estimates after complete donor withdrawal. Locator: Published 2023 paper, abstract and Section 3, pp. 1368--1369.
  1. Katherine Casey; Rachel Glennerster; Edward Miguel; Maarten J. Voors. 2023. Long-Run Effects of Aid: Forecasts and Evidence from Sierra Leone. The Economic Journal 133(652), 1348--1370; abstract and Section 3. https://emiguel.econ.berkeley.edu/wordpress/wp-content/uploads/2023/09/uead001.pdf. DOI: https://doi.org/10.1093/ej/uead001.

Common conventions: Source mathematical conventions

These conventions apply to each entry unless explicitly replaced.

Models and identification. A primitive model $m$ specifies all probability laws, feasible choices, information, equilibrium and measurement rules used by its target. The admissible class $\mathcal M$ is fixed independently of outcomes. If $P_O(m)$ is its observable probability law and $\tau(m)$ the target, its identified set at observable law $P$ is \[ \mathcal I_\tau(P)=\{\tau(m):m\in\mathcal M,\ P_O(m)=P\}. \] Point identification means that this set is a singleton. An empty set signals incompatibility of data and assumptions. Coordinate bounds need not describe the joint set. Bounds are sharp only if every retained target is attainable or arbitrarily approachable by compatible models. Finite bounds require explicit restrictions on unobserved quantities; unrestricted confounding, hidden wealth, extrapolation or arbitrary equilibrium selection can yield uninformative sets.

Causal interventions. A potential outcome $Y_i(p)$ is the outcome under a complete policy regime $p$, including timing, financing, information and market spillovers. The target population and units are fixed before treatment. With interference, use the complete assignment vector or a justified exposure mapping; individual no-interference notation alone cannot identify an economy-wide intervention. A difference of mean potential outcomes does not require the cross-world joint distribution. Conditioning on post-treatment migration, survival, enrollment or employment changes the estimand and needs separate justification.

Statistical statements. An estimator, confidence set, forecast or test specifies a sampling law, model class and loss/coverage criterion. Uniform $(1-\alpha)$-coverage means $\inf_{m\in\mathcal M}\Pr_m\{\tau(m)\in C_n\}\geq1-\alpha$, or an explicitly asymptotic version. The whole parameter space trivially has coverage, so informativeness requires a stated width, risk or power objective. A forecasting improvement is relative to a named benchmark, information set and evaluation population.

Equilibrium and optimization. An equilibrium comprises feasible plans, optimality, beliefs where needed, budget constraints and all market/resource clearing. The primitives or a stated benchmark define each correspondence $\mathcal E(p;m)$. Nonemptiness is assumed or proved, never inferred just from compact policy sets. A selected-equilibrium target uses a declared selection rule; a robust target quantifies over all permitted equilibria. Use suprema or infima unless attainment is established. An $\varepsilon$-optimal policy is feasible and within $\varepsilon$ of the finite optimum value. Report an empty feasible set separately.

Welfare and accounting. Normative utility, interpersonal normalization, social weights, numeraire, discounting and the use of public receipts are primitives. Behavioral utility need not coincide with the welfare criterion. Household welfare includes ownership income and rents once; adding profits again to compensating variation generally double-counts them. A monetary equivalent is defined by an explicit transfer and price convention, with monotonicity and range conditions. Average effects, mechanism contributions, transfers and welfare losses are different targets. Infinite sums require convergence and dynamic feasible plans require terminal or no-Ponzi conditions.

Source versions. A working-paper date, revision date and journal publication year are distinguished. A DOI for a journal version is not automatically the DOI of an earlier manuscript. Locators refer to the stated version and printed pages where specified. A metadata-only check does not verify a claim about a full-text conclusion. Every entry's source subsection narrows the provenance claim accordingly.

Statement licence: CC-BY-4.0 · Source file

Contributions 1

Econ-579-A1 · Exploration · LLM-generated · gpt 6 astra ultra ·

GPT 6 Astra Ultra attempt on Econ-579

Aid that builds lasting capacity: separating temporary assets from effects after complete withdrawal

GPT 6 Astra Ultra October 9, 2026
Target and timing.
For fixed eligible communities and a fully specified support history $p$, the catalogue asks about independently measured capacity and household welfare: \[ \tau_K(T,p)=\mathbb E[K_T(p)-K_T(0)],\qquad \tau_Y(T,p)=\mathbb E[Y_T(p)-Y_T(0)]. \] The positive long-run Sierra Leone findings of Casey and coauthors [aid] concern an actual support history that included continuing support; their description distinguishes later grants and continued facilitation. They do not eliminate the need to define complete withdrawal. This note derives how assets, local investment crowd-out, and permanent institutional improvement enter a post-withdrawal trajectory, then proves a nonidentification result when grants cease but facilitators remain. These mechanisms are a proposed benchmark, not estimates or a reanalysis of that study.
Capacity and local choice.
Communities are the units. Within each community the baseline household weights are fixed, including households that later move; there is no interference between communities in this benchmark. Independently inspected productive or administrative capacity $K_t\geq0$ follows \[ K_{t+1}=\rho K_t+e_t+g_t,\qquad 0<\rho<1. \tag{1} \] Here $g_t\geq0$ is donor-financed real investment, and $e_t\geq0$ is locally financed investment. $K_t$ measures verified service-producing capacity, not a donor expenditure ledger. A fixed physical conversion normalizes one unit of real investment to one unit of installed capacity; depreciation includes failed maintenance. The household income index is $Y_t=\omega K_t$, with known $\omega>0$. This restrictive linear index connects the two targets without claiming that income exhausts household welfare.

A short-lived local authority chooses investment to maximize the current political-service payoff \[ (v+h+\chi f_t)(e_t+g_t) -\frac d2(e_t+g_t)^2-\frac{e_t^2}{2\kappa}. \tag{2} \] Parameters satisfy $v,d,\kappa>0$, $h,\chi\geq0$. Facilitation intensity $f_t\geq0$ changes the current return to local action; $h$ is a permanent institutional change induced by the program, held fixed after it occurs. Investment resources and the convex effort cost are locally funded under a tax budget large enough for all choices considered. Donor resources finance $g_t$ and facilitation separately. Equation (2) is a specified political objective, not an aggregate welfare accounting identity. There is no hidden donor transfer in $e_t$.

Assume bounded grant and facilitation paths, bounded $h$, and $v+h+\chi f_t>dg_t$ at every evaluated date. This ensures interior nonnegative investment; outside this domain the optimal rule must be truncated at zero. Write $D=d+1/\kappa$.

Proposition (Crowd-out and net capacity formation): The unique optimal local investment is \[ e_t=\frac{v+h+\chi f_t-dg_t}{D}. \tag{3} \] Conditional on the other primitives, a unit increase in the grant reduces local investment by $d/D\in(0,1)$ but increases total capacity formation $e_t+g_t$ by $1-d/D>0$.
Proof: The derivative of (2) with respect to $e_t$ is $v+h+\chi f_t-dg_t-De_t$, and the second derivative is $-D<0$. The assumed inequality puts its unique zero above zero, proving the global maximizer (3). Differentiate (3) and add the direct grant contribution to get the two comparative statics. Bounded paths and $\rho<1$ also bound the resulting capacity sequence, so all finite-horizon contrasts exist. ∎

Partial crowd-out is therefore compatible with positive short-run capacity effects. Observing that a grant-funded building survives does not by itself establish a permanent change in the local institution that maintains it.

Theorem (Exact trajectory after complete withdrawal): Compare a treated community with a no-program community sharing the same $v,d,\kappa,\rho$. The control has $g_t=f_t=h=0$. Suppose that from date $t_0$ onward all external grants and facilitation in the treated community are zero, and its institutional increment is a constant $h\geq0$. Let $\Delta K_{t_0}$ be their capacity difference at withdrawal. Then for every integer $j\geq0$, \[ \Delta K_{t_0+j} =\rho^j\Delta K_{t_0} +\frac{h}{D}\frac{1-\rho^j}{1-\rho}. \tag{4} \] The limiting capacity difference is $h/[D(1-\rho)]$, and the corresponding income contrasts are $\omega$ times (4).
Proof: After complete withdrawal (3) gives treated investment $(v+h)/D$ and control investment $v/D$. Subtracting their versions of (1) yields $\Delta K_{t+1}=\rho\Delta K_t+h/D$. Iterating for $j$ steps gives the geometric sum (4), including $j=0$. Since $0<\rho<1$, its transient term tends to zero and its accumulated institutional term has the stated limit. The income assertion follows from the defined linear index. ∎

When $h=0$, a finite follow-up can still show a positive asset effect, even though the limiting effect vanishes. When $h>0$, convergence need not be monotone upward: a large initial asset difference can decline toward a strictly positive permanent effect. Thus the sign of a short-run trend alone does not classify durability.

Proposition (Grant withdrawal does not identify complete-withdrawal gains): Fix $x>0$ and a common observed initial capacity at date $t_0$. Suppose grants are zero and facilitators remain at $f_t=1$ throughout an observation window. If $h$ and $\chi$ are unobserved, the data $(e_t,K_t,Y_t)$ throughout that window do not distinguish a model with $(h,\chi)=(x,0)$ from one with $(h,\chi)=(0,x)$. After facilitation is also withdrawn, their limiting effects relative to no program are respectively $x/[D(1-\rho)]$ and zero.
Proof: In both models $h+\chi f_t=x$ during the observation window, so (3) yields identical investment. The common initial capacity and recursion (1) imply identical capacity and income at every observed date. Both satisfy the interior condition because $v+x>0$ and $g=0$. After $f=0$, the permanent increments are different; applying (4) to each model proves the distinct limits. Their pre-window histories need not be identified by this specified observation law. ∎
A design implication with a precise comparator.
Among communities sharing a specified program prefix, randomize grant continuation and facilitator continuation separately at $t_0$, with positive probabilities for all four paths and complete fixed-cohort follow-up. Under consistency and no cross-community interference, each conditional mean at $T$ equals the potential mean under that path: randomization makes the path independent of its potential outcomes. Their differences identify effects of withdrawing each component after the shared prefix, including their interaction. They do not identify the effect of program introduction versus never receiving aid, because every community in that experiment shares the prefix. A separate introduction comparison is needed for that target.
Remaining gap.
The catalogue allows political incentives, state substitution, vector capacity, and spillovers; this benchmark fixes one local objective and a scalar service index. Endogenous withdrawal dates, selective survival of administrative units, unknown depreciation, and transport to other delivery systems are not solved by (4). A full empirical answer requires verified outputs after each actual support component ends and credible comparisons for the relevant histories. The result establishes exactly why continued facilitation and permanent institutions cannot be separated from the stated post-grant data alone.

Completion Estimate

41%

This is a post hoc, heuristic estimate for the full catalogue target. The attempt solves local investment crowd-out and post-withdrawal capacity trajectories, and proves that continued facilitation cannot be distinguished from permanent institutional improvement in the stated data. Durable aid effects still require credible introduction and withdrawal comparisons, verified vector capacity and household welfare, and treatment of political incentives, state substitution, spillovers and transport.

References

  • [aid] K. Casey, R. Glennerster, E. Miguel, and M. J. Voors (2023), "Long-Run Effects of Aid: Forecasts and Evidence from Sierra Leone," Economic Journal 133(652), 1348--1370. Published paper on the author's site.

Go to contribution →