Optimal Budget Generator: Evidence-Based Budget Allocation Framework
Generating Integrated Budget Recommendations Using Reference Benchmarking, Diminishing Returns, and Cost-Effectiveness Analysis
budget optimization, optimal budget generator, evidence-based policy, meta-analysis, cost-effectiveness, diminishing returns, reference country benchmarking, public finance, welfare economics, spending targets
This specification describes a framework for evidence-based budget allocation. It complements the Optimocracy paper’s Policy Impact Score (PIS) by extending evidence-based governance from policy evaluation to resource allocation optimization.
Abstract
This specification describes the Optimal Budget Generator (OBG) framework, a systematic approach to generating integrated budget recommendations that maximize welfare outcomes.
JEL Classification: H50, H61, D61, I18, C18
Unlike marginal-return frameworks that ask “where should we invest the next dollar?”, OBG asks “what should the complete budget allocation be?” Each category has a target level - too little means underinvestment, too much means diminishing returns. But unlike the Recommended Daily Allowance for nutrients (where you can meet all targets simultaneously), budget allocation is zero-sum: spending more on one category means less for others. OBG generates integrated recommendations that balance these tradeoffs.
The framework combines three evidence sources: (1) reference country benchmarking using high-performing peer jurisdictions, (2) diminishing returns modeling from dose-response studies, and (3) cost-effectiveness threshold analysis from health economics. The Budget Impact Score (BIS) measures our confidence in each category’s OSL estimate based on the quality and quantity of causal evidence from the econometric literature.
The result is a gap analysis showing which categories are underfunded relative to evidence-based optimal levels, enabling systematic reallocation from overinvestment to underinvestment.
1 System Overview
1.1 What Policymakers See
A dashboard showing spending gaps by category, with clear recommendations:
| Category | Current | OSL | Gap | Evidence | Action |
|---|---|---|---|---|---|
| Early childhood (0-5) | $50B | $70B | +$20B | A (RCTs) | Increase |
| Vaccinations | $8B | $35B | +$27B | A (RCTs) | Increase |
| Basic research | $45B | $90B | +$45B | B (spillovers) | Increase |
| Military (discretionary) | $850B | $459B | -$391B | C (benchmarks) | Decrease |
| Agricultural subsidies | $25B | $0B | -$25B | A (welfare analysis) | Eliminate |
Positive gaps indicate underinvestment; negative gaps indicate overinvestment.
1.2 What Budget Analysts See
- OSL estimates with confidence intervals and methodology notes
- Reference country data showing peer spending patterns
- Diminishing returns curves where dose-response data exists
- Evidence quality scores (BIS) for each category
- Sensitivity analysis showing how OSL changes with different assumptions
- Priority rankings by gap size weighted by evidence confidence
1.3 Where This Fits
+-------------------------------------------------------------+
| OPTIMOCRACY FRAMEWORK |
+-------------------------------------------------------------+
| |
| +---------------------+ +-----------------------------+ |
| | Budget Generator | | Policy Generator | |
| | (OBG/BIS Framework)| | (OPG/PIS Framework) | |
| | | | | |
| | Answers: | | Answers: | |
| | "How should we | | "What policies should | |
| | allocate the | | we adopt/change?" | |
| | budget?" | | | |
| | | | | |
| | Primary output: | | Primary output: | |
| | Integrated budget | | Enact/Replace/Repeal | |
| | recommendations | | recommendations | |
| +---------------------+ +-----------------------------+ |
| |
| Both feed into: Constitutional Layer (metric-bound rules) |
+-------------------------------------------------------------+The OBG/BIS framework answers: “Given what we know about returns to spending, what are the optimal allocation levels?”
The OPG framework (see Optimal Policy Generator Specification) answers: “Which policy reforms beyond budget allocation would most improve welfare?”
2 Introduction
2.1 Why Budget Allocation Fails Today
Budget allocation is fundamentally a problem of social choice under uncertainty1. The challenge is not simply technical but institutional: current budget processes systematically diverge from welfare-optimal allocations due to political economy dynamics2,3.
Current budget allocation follows a process dominated by:
- Lobbying intensity: Categories with organized beneficiaries (defense contractors, agricultural lobbies) receive disproportionate funding regardless of evidence
- Historical inertia: This year’s budget is last year’s budget plus a percentage, not a fresh optimization
- Visible vs. invisible beneficiaries: Programs with identifiable beneficiaries (veterans) outcompete programs with diffuse beneficiaries (basic research)
- Political salience: Crises drive spending regardless of cost-effectiveness (terrorism vs. air pollution)
- Zero-sum framing: Budget debates treat all categories as competing rather than asking which ones are at optimal levels
The result: systematic overinvestment in low-return categories and underinvestment in high-return categories. Historical examples demonstrate the scale of missed opportunities: the smallpox eradication campaign returned an estimated 450:1 ROI4, yet similar high-return public health investments remain chronically underfunded.
2.2 The RDA Analogy: Optimal Levels, Not Just Marginal Returns
Nutrition science doesn’t just say “eat more vitamins.” It specifies Recommended Daily Allowances - target intake levels where:
- Below RDA: Deficiency symptoms, reduced function
- At RDA: Optimal health benefits
- Above RDA: Diminishing returns, potential toxicity
Budget allocation should work the same way. For each spending category:
- Below OSL: Foregone welfare gains (underinvestment)
- At OSL: Optimal welfare return per dollar
- Above OSL: Diminishing or negative returns (overinvestment)
infinite spending on any category doesn’t make sense, even one with high returns. Early childhood education has excellent returns - but spending $10 trillion on it wouldn’t produce 10x the benefits of spending $1 trillion. There’s an optimal level.
2.3 What This Framework Provides
- Target spending levels for each budget category based on evidence
- Gap analysis showing where current spending diverges from optimal
- Evidence grading so policymakers know which OSL estimates are reliable
- Priority ranking for reallocation decisions
- Uncertainty quantification acknowledging what we don’t know
2.4 Contributions
This paper makes three primary contributions to the public finance literature:
Methodological: We develop a unified framework integrating reference benchmarking, diminishing returns modeling, and cost-effectiveness analysis to estimate optimal spending levels, extending beyond marginal analysis to target-based allocation.
Theoretical: We formalize the Budget Impact Score (BIS) as a precision-weighted confidence measure, establishing conditions under which evidence-based allocation is incentive-compatible and resistant to lobbying distortions (Proposition 6).
Applied: We demonstrate the framework with worked examples across education, health, and defense spending, identifying systematic patterns of over- and under-investment in US federal allocations.
4 Theoretical Framework
This section formalizes the OBG framework as a social planner’s optimization problem, establishing the theoretical foundations for optimal spending levels and evidence-weighted allocation.
4.2 Optimal Spending Levels Under Uncertainty
In practice, the welfare functions \(W_i(\cdot)\) are not known with certainty. Let \(\hat{W}_i(s)\) denote the planner’s estimate of welfare, with associated uncertainty \(\sigma_i^2(s)\).
Definition 1 (Optimal Spending Level). The Optimal Spending Level for category \(i\) is:
\[ \text{OSL}_i \equiv \arg\max_{s_i} \mathbb{E}[\hat{W}_i(s_i)] - \frac{\rho}{2} \text{Var}[\hat{W}_i(s_i)] \]
where \(\rho \geq 0\) is the planner’s risk aversion parameter.
For risk-neutral planners (\(\rho = 0\)), OSL reduces to the spending level that maximizes expected welfare. For risk-averse planners, OSL accounts for estimation uncertainty.
Proposition 2 (OSL Characterization). Under Assumption 1, with estimated marginal welfare \(\hat{W}_i'(s)\) and estimation variance \(\sigma_i^2(s)\), the OSL satisfies:
\[ \mathbb{E}[\hat{W}_i'(\text{OSL}_i)] = r + \rho \cdot \frac{\partial \sigma_i^2}{\partial s}\bigg|_{s=\text{OSL}_i} \]
where \(r\) is the social discount rate (opportunity cost of public funds).
Proof. The first-order condition for the uncertainty-adjusted maximization problem yields the result. The term \(r\) represents the marginal value of funds in alternative uses; the second term adjusts for risk. \(\square\)
4.3 Budget Impact Score as Precision Weighting
The Budget Impact Score formalizes the precision of OSL estimates, enabling evidence-weighted reallocation decisions.
Definition 2 (Budget Impact Score). For category \(i\) with \(n_i\) effect estimates \(\{\hat{\beta}_{ij}\}_{j=1}^{n_i}\), the Budget Impact Score is:
\[ \text{BIS}_i = \min\left(1, \frac{1}{K} \sum_{j=1}^{n_i} w_j^Q \cdot w_j^P \cdot w_j^R \right) \]
where: - \(w_j^Q \in (0,1]\) = quality weight based on identification strategy (RCT = 1, cross-sectional = 0.25) - \(w_j^P = 1/\text{SE}(\hat{\beta}_j)^2\) = precision weight (inverse variance) - \(w_j^R = e^{-\delta(t_{now} - t_j)}\) = recency weight with decay rate \(\delta\) - \(K\) = calibration constant
Proposition 3 (BIS as Inverse Variance). Under standard meta-analytic assumptions, BIS is proportional to the precision of the pooled effect estimate:
\[ \text{BIS}_i \propto \frac{1}{\text{Var}(\hat{\beta}_i^{pooled})} \]
where \(\hat{\beta}_i^{pooled}\) is the quality-weighted pooled estimate of spending effects.
4.4 Gap Analysis and Welfare Gains
Definition 3 (Spending Gap). The spending gap for category \(i\) is:
\[ \text{Gap}_i = \text{OSL}_i - s_i^{current} \]
Proposition 4 (Welfare Gains from Gap Closure). For small gaps, the welfare gain from moving spending from current level to OSL is approximately:
\[ \Delta W_i \approx W_i'(s_i^{current}) \cdot \text{Gap}_i - \frac{1}{2} |W_i''(\bar{s})| \cdot \text{Gap}_i^2 \]
where \(\bar{s}\) is between \(s_i^{current}\) and \(\text{OSL}_i\).
Proof. Taylor expansion of \(W_i(\text{OSL}_i) - W_i(s_i^{current})\) around \(s_i^{current}\). \(\square\)
Corollary 1 (Priority Ranking). Categories should be prioritized for reallocation in order of:
\[ \text{Priority}_i = |\text{Gap}_i| \times \text{BIS}_i \times |W_i'(s_i^{current})| \]
This ranks categories by expected welfare gain adjusted for estimation confidence.
4.5 Welfare Bounds Under Model Uncertainty
When the functional form of \(W_i(\cdot)\) is uncertain, we can establish bounds on welfare gains.
Proposition 5 (Welfare Bounds). Let \(\underline{W}_i\) and \(\overline{W}_i\) denote lower and upper bounds on the welfare function consistent with available evidence. Then:
\[ \underline{\Delta W} = \sum_{i: \text{Gap}_i > 0} \underline{W}_i'(s_i) \cdot \text{Gap}_i \leq \Delta W \leq \sum_{i: \text{Gap}_i > 0} \overline{W}_i'(s_i) \cdot \text{Gap}_i = \overline{\Delta W} \]
The OBG framework reports both point estimates and these bounds via sensitivity analysis.
4.6 Connection to Mechanism Design
The OBG framework relates to the mechanism design literature on optimal public good provision2. In a setting where spending categories are public goods with heterogeneous returns:
Proposition 6 (Incentive Compatibility). A budget allocation mechanism that (i) estimates OSL using revealed preference data and (ii) allocates proportionally to gap-weighted BIS scores is incentive-compatible in the sense that no coalition of stakeholders can improve their welfare by misreporting preferences, provided BIS weights are determined by independent evidence.
This proposition establishes that evidence-based OSL estimation, combined with BIS weighting, creates a mechanism resistant to the lobbying distortions identified in the introduction.
4.7 Summary of Theoretical Results
| Result | Implication for OBG |
|---|---|
| Proposition 1 | Optimal allocation equalizes marginal returns |
| Proposition 2 | OSL accounts for both expected returns and uncertainty |
| Proposition 3 | BIS captures estimation precision |
| Proposition 4 | Gap closure yields quantifiable welfare gains |
| Corollary 1 | Priority ranking optimizes reallocation sequence |
| Proposition 5 | Welfare bounds enable robust recommendations |
| Proposition 6 | Evidence-based estimation resists manipulation |
5 Core Methodology
5.1 Spending Category Data Structure
The OBG framework uses a structured representation of budget categories:
-- Spending categories
spending_categories (
id, name, parent_category_id,
spending_type, -- 'program', 'transfer', 'investment', 'regulatory'
outcome_categories, -- which welfare outcomes this affects
current_spending_usd, fiscal_year,
data_source, last_updated
)
-- Reference country spending data
reference_spending (
category_id, country_code, year,
spending_usd, spending_per_capita,
spending_pct_gdp, population, gdp,
data_source
)
-- Optimal spending level estimates
osl_estimates (
category_id, estimation_method,
osl_usd, osl_per_capita, osl_pct_gdp,
confidence_interval_low, confidence_interval_high,
evidence_grade, bis_score,
methodology_notes, last_updated
)
-- Gap analysis
spending_gaps (
category_id, current_spending_usd,
osl_usd, gap_usd, gap_pct,
priority_score, -- gap * BIS confidence
recommended_action
)5.2 Three Methods for OBG Estimation
| Method | Use Case | Data Required | Strengths | Limitations |
|---|---|---|---|---|
| Reference country benchmarking | Categories with comparable cross-country data | Per-capita spending from high-performing peers | Simple, intuitive, politically credible | Assumes context transfers |
| Diminishing returns modeling | Categories with dose-response data | Effect estimates at multiple spending levels | Theoretically grounded, finds “knee” | Requires rich causal evidence |
| Cost-effectiveness threshold | Health/life-saving interventions | Cost per QALY/DALY, willingness-to-pay | Links to standard health economics9 | Limited to monetizable outcomes |
Each method is detailed below.
6 Reference Country Benchmarking
6.1 The Basic Approach
Reference country benchmarking draws on established comparative policy analysis methods7,8. The core insight is that high-performing peer countries provide empirical evidence of achievable spending-outcome relationships under similar institutional contexts.
For categories where comparable cross-country data exists, OSL can be estimated from high-performing reference countries:
\[ \text{OSL}_i = \text{median}(\text{Spending}_{i,c}) \times \text{Context}_{\text{US}} \]
Where: - \(\text{Spending}_{i,c}\) = spending on category \(i\) in reference country \(c\) (per capita or % GDP) - \(\text{Context}_{\text{US}}\) = adjustment factors for US context (population, GDP, existing infrastructure)
6.2 Reference Country Selection Criteria
Not all countries are appropriate references. Selection criteria:
| Criterion | Requirement | Rationale |
|---|---|---|
| Income level | GDP/capita within 50% of US | Different income = different appropriate spending |
| Outcome performance | Top quartile on relevant outcomes | Only reference high performers |
| Institutional quality | Governance indicators above median | Similar implementation capacity |
| Data quality | Reliable, consistent reporting | Measurement must be trustworthy |
| Population | > 5 million | Small countries may not scale |
Typical reference set: Nordic countries (high welfare outcomes), Germany (strong institutions), Canada/Australia (similar federalism), Japan (health outcomes), Netherlands (education outcomes).
6.3 Worked Example: Early Childhood Education
Early childhood education has among the highest estimated returns of any public investment, with long-term benefits including higher earnings, reduced crime, and better health outcomes10. Education spending more broadly generates economic multipliers of 1.5-2.5x11.
Question: What is the optimal US spending on early childhood education (ages 0-5)?
Data sourced from OECD Education at a Glance and national statistical offices. Spending figures converted to 2023 USD using OECD PPP exchange rates.
| Data Point | Value | Source |
|---|---|---|
| US current spending | $50B/year | OMB FY2024 |
| US children 0-5 | 24 million | Census 2023 |
| US current per child | $2,083/child | Calculated |
| Reference countries | OECD Education at a Glance 2023 | |
| Denmark | $3,200/child | Pre-primary: 0.9% GDP; ages 0-5 |
| Sweden | $2,900/child | Pre-primary: 0.8% GDP |
| Norway | $3,100/child | Pre-primary: 0.7% GDP + childcare |
| France | $2,400/child | Pre-primary: 0.7% GDP |
| Germany | $2,000/child | Pre-primary: 0.5% GDP |
| Median reference | $2,900/child | Middle value of 5-country set |
| Context adjustment | ||
| Cost-of-living adjustment | 0.95x | Lower than Nordic |
| Labor cost adjustment | 1.05x | Higher than continental Europe |
| Net adjustment | 1.0x | |
| OBG calculation | ||
| Adjusted per-child | $2,900/child | |
| US children 0-5 | 24 million | |
| OSL | $69.6B/year | |
| Gap analysis | ||
| Current | $50B | |
| OSL | $70B | |
| Gap | +$20B (underinvestment) |
Evidence grade: B (good reference data, moderate confidence in transferability)
6.4 Limitations of Reference Benchmarking
- Context transferability: What works in Denmark may not work in the US due to different institutions, culture, demographics
- Correlation vs. causation: High-spending countries may achieve outcomes for reasons unrelated to spending level
- Selection bias: Countries may specialize in areas they’re naturally good at
- Measurement differences: “Early childhood education” may mean different things in different countries
Reference benchmarking provides a starting point for OBG estimation, not a definitive answer. It should be combined with diminishing returns modeling where dose-response data exists.
7 Diminishing Returns Modeling
7.1 The Core Concept
The fiscal multiplier literature establishes that spending effects vary systematically with scale12,13. At low spending levels, each additional dollar produces substantial welfare gains. At high spending levels, marginal returns diminish. The OSL is where marginal return equals opportunity cost.
\[ \text{OSL}: \frac{\partial \text{Outcome}}{\partial \text{Spending}} = r \]
Where \(r\) is the discount rate or opportunity cost of capital (typically 3-7%).
7.2 Finding the “Knee” of the Curve
Empirically, we look for the point where the outcome-spending relationship flattens:
Outcome
^
| ___________
| __/
| _/
| _/
| _/ <- OSL is around here
| _/
| _/
| _/
| _/
| _/
|/
+-----------------------------------> Spending
Low High7.3 Estimation Methods
1. Nonlinear regression on cross-country data
Fit diminishing returns functions:
\[ \text{Outcome} = \alpha + \beta \cdot \log(\text{Spending}) + \epsilon \]
Or with saturation:
\[ \text{Outcome} = \alpha + \beta \cdot \frac{\text{Spending}}{\text{Spending} + \gamma} \]
Where \(\gamma\) is the half-saturation constant.
2. Piecewise linear estimation
Estimate separate slopes for different spending ranges to identify where returns diminish.
3. Meta-regression of effect estimates
If multiple studies estimate effects at different spending levels, meta-regression can identify how effects vary with baseline spending. The credibility of such estimates depends critically on identification strategy14.
7.4 Worked Example: K-12 Education Spending
15 exploited court-ordered school finance reforms to estimate causal effects of K-12 spending. Key finding: a 10% increase in per-pupil spending increases adult earnings by 7% for students from low-income families.
Does this effect diminish at higher spending levels?
Evidence from cross-state variation suggests:
| Baseline spending (per pupil) | Effect of 10% increase | Implied marginal return |
|---|---|---|
| $8,000 | +8% earnings | $0.80 per $1 |
| $12,000 | +5% earnings | $0.50 per $1 |
| $16,000 | +3% earnings | $0.30 per $1 |
| $20,000 | +1% earnings | $0.10 per $1 |
OBG estimation: At $16,000/pupil, the marginal return (~0.30) roughly equals the social discount rate. This suggests:
- Current US average: ~$15,000/pupil
- OSL: ~$16,000-$18,000/pupil (modest underinvestment)
- Gap: ~$50B nationally
Evidence grade: B (strong causal identification, moderate extrapolation uncertainty)
8 Cost-Effectiveness Threshold Analysis
8.1 The Standard Health Economics Approach
Cost-effectiveness analysis has become the standard framework for health resource allocation decisions6. The QALY (Quality-Adjusted Life Year) metric enables comparison across diverse health interventions by monetizing health outcomes at a consistent threshold16.
For health interventions, cost-effectiveness analysis provides OSL estimates:
\[ \text{OSL} = \sum_{\text{interventions}} \text{Scale}_i \times \text{Cost}_i \quad \text{where } \frac{\text{Cost}_i}{\text{QALY}_i} < \text{WTP} \]
Where: - \(\text{Scale}_i\) = target population for intervention \(i\) - \(\text{Cost}_i\) = per-person cost of intervention \(i\) - \(\text{QALY}_i\) = QALYs gained per person from intervention \(i\) - \(\text{WTP}\) = willingness-to-pay threshold (typically $50K-$150K per QALY)
8.2 Building Up from Intervention-Level Data
For each health intervention with cost-effectiveness data:
- Identify target population who would benefit
- Calculate scale-up cost to reach entire target population
- Include only interventions below the cost-effectiveness threshold
- Sum to get category OSL
8.3 Worked Example: Vaccinations
Vaccinations represent one of the highest-return public health investments, with estimated returns of 44:1 for routine childhood immunization17,18. The economic benefits include avoided medical costs, productivity gains, and reduced mortality19.
Cost-effectiveness estimates from CEA Registry and CDC vaccination cost studies. QALY estimates reflect average health gains across target populations; costs include vaccine acquisition, administration, and program overhead.
| Intervention | Target pop. | Cost/person | QALY/person | Cost/QALY | Source | Include? |
|---|---|---|---|---|---|---|
| Childhood routine | 4M births | $500 | 0.1 | $5,000 | CDC VFC | Yes |
| HPV vaccination | 4M teens | $300 | 0.05 | $6,000 | CEA Registry | Yes |
| Flu (elderly) | 50M elderly | $40 | 0.01 | $4,000 | CDC | Yes |
| Shingles | 40M eligible | $200 | 0.02 | $10,000 | CEA Registry | Yes |
| COVID boosters | 100M adults | $30 | 0.005 | $6,000 | CDC | Yes |
All interventions fall well below the conventional $50,000-$150,000 per QALY cost-effectiveness threshold, indicating strong economic justification for full scale-up.
OBG calculation: - Childhood routine: 4M × $500 = $2.0B - HPV: 4M × $300 = $1.2B - Flu (elderly): 50M × $40 = $2.0B - Shingles: 40M × $200 = $8.0B - COVID boosters: 100M × $30 = $3.0B - Total OSL: ~$16B (vs. current ~$8B)
Gap: +$8B (underinvestment)
Evidence grade: A (RCT evidence for most vaccines, well-established cost-effectiveness)
9 Budget Impact Score (BIS) as Evidence Quality
9.1 Reframing BIS: Confidence in OSL, Not Allocation Driver
The Budget Impact Score measures our confidence in each category’s OSL estimate based on the quality and quantity of causal evidence. The scoring methodology draws on the established evidence hierarchy from the econometrics literature, where randomized experiments provide the most credible estimates, followed by quasi-experimental methods such as difference-in-differences and regression discontinuity14,20.
Unlike earlier formulations that used BIS to directly allocate budgets, the OBG framework determines the target level (OSL), and BIS tells us how confident we are in that target.
9.2 BIS Calculation
For each spending category \(i\):
Step 1: Gather effect estimates
Collect all available causal effect estimates \(\{\beta_{i,1}, \beta_{i,2}, ..., \beta_{i,n_i}\}\) from the econometric literature.
Step 2: Compute quality weights
| Identification Method | Quality Weight (\(w^Q\)) |
|---|---|
| Randomized controlled trial | 1.00 |
| Natural experiment (DiD, RDD) | 0.85 |
| Instrumental variables | 0.70 |
| Panel with fixed effects | 0.55 |
| Cross-sectional regression | 0.25 |
Step 3: Compute precision weights
\[ w^P_j = \frac{1}{\text{SE}(\beta_j)^2} \]
Step 4: Compute recency weights
\[ w^R_j = e^{-0.03(t_{now} - t_j)} \]
Step 5: Compute confidence score
\[ \text{BIS}_i = \min\left(1, \frac{\sum_j w^Q_j \cdot w^P_j \cdot w^R_j}{K}\right) \]
Where \(K\) is a calibration constant.
9.3 Evidence Grading from BIS
| BIS Range | Grade | Interpretation | OSL Confidence |
|---|---|---|---|
| 0.80 - 1.00 | A | Strong causal evidence | High - proceed with reallocation |
| 0.60 - 0.79 | B | Good evidence | Moderate - consider with caveats |
| 0.40 - 0.59 | C | Mixed evidence | Low - pilot before scaling |
| 0.20 - 0.39 | D | Weak evidence | Very low - research priority |
| 0.00 - 0.19 | F | Insufficient evidence | Unknown - cannot estimate OSL |
9.4 BIS Does Not Drive Allocation
Critical distinction from earlier formulations:
| Old (BIS as allocation driver) | New (BIS as confidence measure) |
|---|---|
| Allocate proportionally to BIS | Allocate to reach OSL |
| High BIS = more spending | High BIS = confident in OSL |
| Ignores diminishing returns | Explicitly models optimal level |
| Infinite spending possible | Bounded by OSL |
10 Gap Analysis and Priority Ranking
10.1 Computing Gaps
For each category \(i\):
\[ \text{Gap}_i = \text{OSL}_i - \text{Current}_i \]
- Gap > 0: Underinvestment (increase spending)
- Gap = 0: At optimal (maintain)
- Gap < 0: Overinvestment (decrease spending)
10.2 Priority Score
Prioritize reallocation by gap size weighted by confidence:
\[ \text{Priority}_i = |\text{Gap}_i| \times \text{BIS}_i \]
Categories with large gaps AND high confidence should be addressed first.
10.3 Worked Example: Priority Ranking
| Category | Current | OSL | Gap | BIS | Priority | Action |
|---|---|---|---|---|---|---|
| Vaccinations | $8B | $35B | +$27B | 0.95 | 25.7 | Increase first |
| Basic research | $45B | $90B | +$45B | 0.70 | 31.5 | Increase |
| Early childhood | $50B | $70B | +$20B | 0.85 | 17.0 | Increase |
| Military | $850B | $405B | -$445B | 0.50 | 222.5 | Decrease |
| Ag subsidies | $25B | $0B | -$25B | 0.90 | 22.5 | Eliminate |
Reallocation plan: Cut military discretionary (-$445B) and agricultural subsidies (-$25B) to fund vaccinations (+$27B), basic research (+$45B), early childhood (+$20B), with remainder to debt reduction or other high-return categories.
11 Multi-Unit Reporting
11.1 The Problem with Abstract Scores
Composite scores (like 0-1 BIS values) obscure interpretability. Policymakers and citizens understand dollars, lives, and years - not abstract indices.
11.2 Reporting at Multiple Levels
| Level | Units | Use Case | Example |
|---|---|---|---|
| 1. Natural | Domain-specific | Interpretation within domain | “Education: $2,100/student gap” |
| 2. Monetized | $ equivalent | Cross-domain comparison | “Expected welfare gain: $4.00 per $1” |
| 3. Health | QALYs/DALYs | Health-weighted comparison | “12,000 QALYs per $1B invested” |
| 4. Composite | 0-1 score | Ranking when monetization uncertain | “BIS = 0.85” |
11.3 Conversion Factors
| Conversion | Value | Source | Notes |
|---|---|---|---|
| Value of Statistical Life (VSL) | ~$10M | EPA, DOT | US regulatory standard |
| Value per QALY | $50K-$150K | ICER, WHO | Context-dependent |
| QALY → $ | $100K/QALY | Mid-range estimate | For cross-domain |
| Life-year → QALY | ~0.8-1.0 | Age/health adjusted | Quality weighting |
11.4 Worked Example: Multi-Unit Output
Category: Early Childhood Education
| Unit Level | Value | Interpretation |
|---|---|---|
| Natural | +$20B gap | Current: $50B, OSL: $70B |
| Per-child | +$833/child gap | 24M children |
| Monetized ROI | 4:1 NPV return | 10 |
| Health (QALYs) | +8K QALYs/year | Per $1B additional |
| Composite (BIS) | 0.85 | High-quality RCT evidence |
Recommendation: Moderate underinvestment with strong evidence. Closing the gap would yield ~$80B in NPV returns.
12 Quality Requirements and Validation
12.1 Minimum Thresholds for OBG Estimation
| Criterion | Minimum | Rationale |
|---|---|---|
| Reference countries | 5+ | Avoid outlier bias |
| Dose-response studies | 3+ | Identify diminishing returns |
| Causal effect estimates | 2+ | Cross-validate |
| Data recency | Within 10 years | Relevance |
| BIS for reallocation | > 0.40 | Sufficient confidence |
12.2 Robustness Checks
For each OSL estimate, report:
- Leave-one-country-out: Does excluding any single reference country change OSL by >20%?
- Method comparison: Do reference benchmarking, diminishing returns, and cost-effectiveness methods agree?
- Time stability: Has OSL changed substantially over past 5 years?
- Sensitivity to assumptions: How does OSL change with ±20% parameter variation?
13 Interpreting Results
13.1 Gap Ranges and Recommended Actions
| Gap (% of current) | Interpretation | Recommended Action |
|---|---|---|
| > +50% | Severe underinvestment | Immediate scale-up |
| +20% to +50% | Moderate underinvestment | Phased increase |
| -10% to +20% | Near optimal | Monitor, fine-tune |
| -50% to -10% | Moderate overinvestment | Gradual reduction |
| < -50% | Severe overinvestment | Urgent reallocation |
13.2 What the Algorithm Cannot Tell You
| Factor | OBG Captures | OBG Does Not Capture |
|---|---|---|
| Evidence-optimal spending level | Yes | |
| Confidence in estimates | Yes | |
| Direction of reallocation | Yes | |
| Political feasibility | No | |
| Implementation capacity | No | |
| Transition costs | No | |
| Distributional effects | No | |
| Novel interventions | No |
OBG provides evidence-based targets. Political judgment is still required for implementation strategy.
14 Pilot Program Prioritization
14.1 Value of Information for Uncertain Categories
Categories with low BIS but potentially high returns warrant research investment:
\[ \text{VOI}_i = \text{Potential Gap}_i \times (1 - \text{BIS}_i) \times P(\text{high return}) \]
High-VOI categories should receive pilot funding to generate better evidence.
14.2 Recommended Pilot Designs
For categories where OSL is uncertain:
- Randomized scale-up: Randomly vary spending levels across jurisdictions
- Stepped-wedge rollout: Gradual expansion with comparison to not-yet-treated areas
- Natural experiment exploitation: Monitor for policy changes that create quasi-experimental variation
- Administrative data linkage: Connect spending to outcomes through administrative records
14.3 Learning Feedback Loop
After each budget cycle:
- Measure outcomes: Oracles report welfare changes
- Update estimates: New data refines OSL estimates
- Recalculate priorities: Gaps and BIS scores updated
- Reallocate: Next cycle reflects improved evidence
15 Data Sources
15.1 Reference Country Databases
International organizations maintain standardized cross-country spending and outcome data essential for reference benchmarking. The OECD provides the most comprehensive harmonized data for high-income countries7.
| Database | Coverage | URL | Use Case |
|---|---|---|---|
| OECD iLibrary | 38 OECD members | oecd-ilibrary.org | Education, health, social spending |
| World Bank WDI | 217 countries | data.worldbank.org | Broad spending and outcomes |
| SIPRI | Global | sipri.org | Military spending |
| WHO GHED | 194 countries | who.int/data/gho | Health expenditure |
| UNESCO UIS | Global | uis.unesco.org | Education spending |
15.2 Cost-Effectiveness Databases
| Database | Coverage | URL | Use Case |
|---|---|---|---|
| CEA Registry | 8,000+ analyses | cearegistry.org | Health cost-effectiveness |
| Disease Control Priorities | LMICs | dcp-3.org | Global health priorities |
| Cochrane Library | 8,000+ reviews | cochranelibrary.com | Health intervention effects |
| Copenhagen Consensus | Development | copenhagenconsensus.com | Development priorities |
These databases enable systematic ranking of interventions by cost-effectiveness. For example, deworming programs consistently rank among the most cost-effective health interventions, with costs as low as $30-50 per DALY averted21.
15.3 US Budget Data
| Source | Coverage | URL | Use Case |
|---|---|---|---|
| OMB Historical Tables | 1789-present | whitehouse.gov/omb | Federal spending |
| CBO Budget Analyses | Federal | cbo.gov | Fiscal impact scoring5 |
| USASpending | Federal awards | usaspending.gov | Program-level detail |
| Census of Governments | State & local | census.gov | Subnational spending |
16 Limitations
16.1 Reference Country Selection Bias
- Cherry-picking risk: Choosing references that support preferred conclusions
- Survivor bias: Only observing successful high-spenders, not failed ones
- Context non-transferability: Nordic institutions may not transplant to US context
Mitigation: Transparent reference selection criteria, sensitivity to reference set composition.
16.2 Diminishing Returns Uncertainty
- Functional form: True relationship may not match assumed function
- Extrapolation: Estimating returns outside observed spending range
- Interaction effects: Returns may depend on other spending categories
Mitigation: Report confidence intervals, use multiple functional forms, acknowledge extrapolation limits.
16.3 Political Feasibility Not Modeled
OBG provides evidence-optimal targets, not politically achievable ones. A $445B military cut may be optimal but infeasible.
Mitigation: OBG is a north star, not immediate policy. Transition paths must account for political constraints.
16.4 Implementation Capacity
Higher spending may not translate to outcomes if implementation capacity is lacking.
Mitigation: Pair spending increases with implementation assessment; phase in gradually.
17 Validation Framework
Rigorous validation is essential for any framework that claims to identify optimal spending levels. This section outlines the validation approach, acknowledging that comprehensive empirical validation remains future work.
17.1 Retrospective Validation
Question: Did jurisdictions that moved toward OSL achieve better outcomes than those that diverged?
Method: 1. Compute OSL for past periods using only data available at that time (to avoid lookahead bias) 2. Identify jurisdictions that moved toward/away from OSL 3. Compare subsequent outcomes using difference-in-differences or synthetic control methods22
Example: US State Education Spending 2000-2015
A preliminary retrospective analysis could examine whether states that moved toward education OSL (estimated from high-performing states like Massachusetts and Minnesota) subsequently showed improved test scores and graduation rates relative to states that diverged. This analysis is noted as a priority for future empirical work.
Challenges: - Confounding from simultaneous policy changes - Limited variation in spending changes within countries - Outcome measurement lags (education effects take years to materialize)
17.2 Prospective Validation
Question: Do OBG-guided reallocations improve outcomes going forward?
Method: 1. Pre-register OBG predictions publicly before budget decisions 2. Monitor jurisdictions that adopt OBG guidance vs. those that don’t 3. Compare outcome trajectories using appropriate causal identification
Implementation: We propose publishing annual OSL estimates for US federal budget categories, creating a public record that enables future validation. If jurisdictions that adopt OBG guidance systematically outperform those that don’t, this provides evidence for the framework’s validity.
17.3 Success Metrics
| Metric | Definition | Target | Interpretation |
|---|---|---|---|
| Gap reduction | Did spending move toward OSL? | > 50% of gap closed in 10 years | Tests political feasibility |
| Outcome improvement | Did welfare metrics improve more in OBG-following jurisdictions? | > 10% relative improvement | Tests welfare prediction accuracy |
| Prediction accuracy | Did estimated returns match actual returns? | Correlation r > 0.5 | Tests underlying model |
| Cross-method consistency | Do reference benchmarking, diminishing returns, and cost-effectiveness methods converge? | Agreement within 30% | Tests methodological robustness |
17.4 Validation Status
This working paper presents the OBG methodology. Comprehensive empirical validation is future work requiring:
- Data collection: Longitudinal spending and outcome data across jurisdictions
- Historical OSL estimation: Computing past OSL using only contemporaneously available data
- Causal analysis: Rigorous identification of spending → outcome effects
- Publication: Peer-reviewed validation study with pre-registered analysis plan
The framework’s current evidence base consists of the underlying studies cited throughout (e.g.,15 for education,17 for vaccinations), not direct validation of OBG itself.
18 Sensitivity Analysis
18.1 Parameter Sensitivity
| Parameter | Default | Test Range | Impact on OSL |
|---|---|---|---|
| Reference country set | OECD high-performers | All OECD, EU only, Anglo only | ±15% |
| Discount rate | 5% | 3-7% | ±20% |
| BIS confidence threshold | 0.40 | 0.30-0.60 | Category inclusion |
| Recency decay rate | 0.03/year | 0.01-0.05 | Estimate weights |
18.2 Scenario Analysis
Optimistic scenario: All uncertain categories have high returns Pessimistic scenario: Uncertain categories have low/zero returns Base case: Use point estimates
Report OSL range across scenarios for policy guidance.
19 Future Directions
19.1 Methodological
- Bayesian hierarchical models: More principled uncertainty quantification
- Causal discovery: Learn spending-outcome causal structure from data
- Dynamic optimization: Model multi-period reallocation paths
- Interaction effects: How spending categories complement/substitute
19.2 Data Infrastructure
- Automated literature monitoring: NLP to extract new effect estimates
- Real-time outcome tracking: Connect spending to outcomes continuously
- API access: Enable researchers to query OBG data programmatically
19.3 Governance Integration
- Dashboard for policymakers: Real-time gap analysis
- Budget proposal scoring: Automatically assess proposed budgets vs. OSL targets
- Incentive Alignment Bonds: Tie politician compensation to moving toward OSL
20 Conclusion
The Optimal Budget Generator framework provides a systematic, evidence-based approach to budget allocation. Unlike marginal-return frameworks that can justify infinite spending on high-return categories, OBG recognizes that every category has an optimal level - like the Recommended Daily Allowance for nutrients.
The framework answers three questions:
- What is the target? OBG provides evidence-based spending levels for each category
- How far are we? Gap analysis shows where current spending diverges from optimal
- How confident are we? BIS scores evidence quality so policymakers know which OSL estimates are reliable
Even with imperfect evidence, systematically moving from severe misallocation (military 100% above OSL, vaccinations 75% below OSL) toward evidence-based targets will produce welfare gains orders of magnitude larger than current discretionary allocation achieves.
Acknowledgments
The author thanks seminar participants and anonymous reviewers for helpful comments and suggestions. All errors remain the author’s own.
21 References
22 Appendix A: Worked Example - Complete OBG Calculation
22.1 Example: US Military Discretionary Spending
This worked example demonstrates the complete OBG calculation for a category where reference benchmarking is the primary method. Military spending data comes from the Stockholm International Peace Research Institute (SIPRI), which maintains the most comprehensive global military expenditure database23.
Step 1: Define the category
- Category: Military discretionary spending (defense budget excluding veterans’ benefits and military pensions)
- Current US spending: $850B (FY2024)
- Outcome of interest: National security (deterrence, territorial integrity)
Step 2: Select reference countries
Reference data from SIPRI Military Expenditure Database24:
| Country | Military % GDP (2023) | GDP (trillion USD) | Selection criteria |
|---|---|---|---|
| Germany | 1.5% | $4.1T | NATO member, high-income, strong institutions |
| France | 1.9% | $2.8T | NATO member, nuclear power, high-income |
| UK | 2.2% | $3.1T | NATO member, nuclear power, high-income |
| Japan | 1.0% | $4.2T | High-income, strong institutions, regional threats |
| Australia | 2.1% | $1.7T | High-income, alliance partner |
| Canada | 1.3% | $2.1T | NATO member, neighbor |
Median reference: 1.7% of GDP (median of: 1.0%, 1.3%, 1.5%, 1.9%, 2.1%, 2.2%)
Step 3: Context adjustment
| Factor | Adjustment | Rationale |
|---|---|---|
| Global role | +0.5% | US provides NATO umbrella |
| Geographic security | -0.3% | US has oceanic borders, friendly neighbors |
| Existing alliances | -0.2% | Cost-sharing with allies |
| Nuclear deterrent | Already included | Reference countries include nuclear powers |
| Net adjustment | +0.0% | Adjustments roughly cancel |
Step 4: Calculate OSL
- US GDP: $27T
- Reference spending: 1.7% of GDP
- Adjustment: 0%
- OSL = 1.7% × $27T = $459B
Step 5: Gap analysis
| Metric | Value |
|---|---|
| Current spending | $850B |
| OSL | $459B |
| Gap | -$391B (overinvestment) |
| Gap % of current | -46% |
Step 6: Evidence assessment
| Criterion | Assessment | Score |
|---|---|---|
| Reference country consistency | Moderate (1.0-2.2% range) | 0.6 |
| Context transferability | Uncertain (US global role unique) | 0.4 |
| Outcome linkage | Weak (spending → security unclear) | 0.3 |
| Alternative methods | Limited | 0.4 |
| BIS | 0.50 |
Evidence grade: C (Mixed evidence - benchmark clear, but US context unique)
Step 7: Multi-unit reporting
| Unit Level | Value | Interpretation |
|---|---|---|
| Natural | -$391B gap | 46% overinvestment vs. peers |
| Per capita | -$1,170/person | Americans pay $2,550 vs. $1,380 peer avg |
| Opportunity cost | 4-10x | Returns if reallocated to high-return categories |
| Composite (BIS) | 0.50 | Moderate confidence in OSL estimate |
Recommendation: Strong evidence of overinvestment relative to peer countries. The fiscal multiplier for military spending is estimated at 0.6-0.8, lower than most domestic programs25. However, US global role creates genuine uncertainty about context transferability. Recommend gradual reduction (10% per year) with continuous outcome monitoring.
23 Appendix B: Analysis Workflow
23.1 Complete OBG Analysis Pipeline
+-------------------------------------------------------------+
| OBG ANALYSIS WORKFLOW |
+-------------------------------------------------------------+
Phase 1: DATA COLLECTION
-------------------------
1. Budget data ingestion
+-- Pull current spending by category (OMB, USASpending)
+-- Normalize categories to standard taxonomy
+-- Identify subcategories for detailed analysis
+-- Flag data quality issues
2. Reference country data
+-- Pull spending data from OECD, World Bank
+-- Filter by reference country criteria
+-- Normalize to per-capita and % GDP
+-- Calculate medians and distributions
3. Effect estimate data
+-- Search systematic reviews and meta-analyses
+-- Extract effect sizes with standard errors
+-- Code study quality (RCT, natural experiment, etc.)
+-- Build literature database by category
Phase 2: OBG ESTIMATION
-----------------------
4. Reference benchmarking
+-- Calculate median reference spending
+-- Apply context adjustments
+-- Estimate OSL with confidence intervals
+-- Document methodology
5. Diminishing returns modeling (where data permits)
+-- Fit nonlinear spending-outcome functions
+-- Identify "knee" of curve
+-- Calculate marginal returns at current spending
+-- Estimate optimal level
6. Cost-effectiveness analysis (health/life-saving)
+-- Identify interventions below CE threshold
+-- Calculate scale-up costs
+-- Sum to category OSL
+-- Document assumptions
7. Method reconciliation
+-- Compare OSL estimates across methods
+-- Weight by method reliability
+-- Produce consensus OSL estimate
+-- Flag discrepancies
Phase 3: EVIDENCE QUALITY
-------------------------
8. BIS calculation
+-- Compute quality weights per study
+-- Compute precision weights
+-- Compute recency weights
+-- Aggregate to category BIS
9. Evidence grading
+-- Assign A-F grade based on BIS
+-- Document key evidence
+-- Identify research gaps
+-- Flag high-uncertainty categories
Phase 4: GAP ANALYSIS
---------------------
10. Compute gaps
+-- Gap = OSL - Current
+-- Calculate % gap
+-- Classify as under/over/optimal
+-- Apply BIS weighting
11. Priority ranking
+-- Priority = |Gap| × BIS
+-- Rank categories
+-- Identify reallocation pairs
+-- Estimate welfare gains
Phase 5: OUTPUT GENERATION
--------------------------
12. Multi-unit reporting
+-- Natural units ($/capita, % GDP)
+-- Monetized (ROI, opportunity cost)
+-- Health units (QALYs where applicable)
+-- Composite (BIS, evidence grade)
13. Sensitivity analysis
+-- Vary key parameters
+-- Test reference country sets
+-- Report OSL ranges
+-- Identify robust conclusions
14. Documentation
+-- Generate category reports
+-- Create methodology audit trail
+-- Version control estimates
+-- Publish to dashboard/API24 Appendix C: Glossary
24.1 Core Concepts
Optimal Budget Generator (OBG): The framework/methodology for generating integrated budget recommendations based on evidence of spending-outcome relationships. OBG accounts for the zero-sum nature of budget allocation and produces Optimal Spending Level (OSL) estimates for each category.
Optimal Spending Level (OSL): The evidence-based target spending level for each category, produced by the OBG framework. \(\text{OSL}_i\) represents the optimal spending level for category \(i\). Below OSL indicates underinvestment; above OSL indicates diminishing returns.
Budget Impact Score (BIS): A 0-1 score measuring confidence in each category’s OSL estimate based on the quality and quantity of causal evidence. Higher BIS indicates more reliable OSL recommendations.
Spending Gap: The difference between current spending and the evidence-based target for each category. Positive gaps indicate underinvestment; negative gaps indicate overinvestment.
Reference Country Benchmarking: Estimating target spending levels by observing spending in comparable high-performing countries and adjusting for context.
Diminishing Returns: The economic principle that marginal returns to spending decrease as spending increases. The optimal level is where marginal return equals opportunity cost.
24.2 Estimation Methods
Context Adjustment: Modifications to reference country benchmarks accounting for differences in population, geography, institutions, and existing infrastructure.
Cost-Effectiveness Threshold: The maximum acceptable cost per QALY (or other health outcome) for including an intervention in target calculations. Typically $50K-$150K per QALY.
Dose-Response Curve: The relationship between spending level (dose) and outcome (response). Used to identify diminishing returns and estimate optimal spending levels.
24.3 Evidence Quality
Quality Weight (\(w^Q\)): Weight assigned to a study based on identification strategy. RCTs receive 1.0; cross-sectional studies receive 0.25.
Precision Weight (\(w^P\)): Weight assigned based on standard error. More precise estimates receive higher weight.
Recency Weight (\(w^R\)): Weight assigned based on publication date. More recent studies receive higher weight via exponential decay.
Evidence Grade: Letter grade (A-F) summarizing confidence in each category’s target estimate. A = strong evidence; F = insufficient evidence.
24.4 Output Concepts
Priority Score: Product of gap magnitude and BIS. Used to rank categories for reallocation priority.
Value of Information (VOI): Expected benefit of additional research on uncertain categories. High-VOI categories warrant pilot funding.
Multi-Unit Reporting: Presenting results in natural units, monetized equivalents, health units, and composite scores for interpretability.
25 Appendix D: Comparison to Actual US Budget
25.1 Current US Discretionary Budget vs. OSL Targets
| Category | Current (\(B) | OSL (\)B) | Gap ($B) | Gap % | BIS | Priority | |
|---|---|---|---|---|---|---|
| Defense (discretionary) | 850 | 459 | -391 | -46% | 0.50 | 195 |
| Non-defense discretionary | 915 | 1,300 | +385 | +42% | 0.65 | 250 |
| - Education | 80 | 120 | +40 | +50% | 0.75 | 30 |
| - Health (research) | 50 | 100 | +50 | +100% | 0.80 | 40 |
| - Vaccinations | 8 | 35 | +27 | +338% | 0.95 | 26 |
| - Basic research | 45 | 90 | +45 | +100% | 0.70 | 32 |
| - Infrastructure | 100 | 150 | +50 | +50% | 0.60 | 30 |
| - Early childhood | 50 | 70 | +20 | +40% | 0.85 | 17 |
| Agricultural subsidies | 25 | 0 | -25 | -100% | 0.90 | 23 |
Key findings:
- Severe overinvestment: Military spending is ~85% above reference benchmarks
- Severe underinvestment: Vaccinations, basic research, health research far below evidence-optimal levels
- Negative-return spending: Agricultural subsidies should be eliminated entirely
- Reallocation potential: ~$400B could be reallocated from low/negative return to high-return categories
Estimated welfare gain from OSL alignment: Moving from current allocation to OSL targets would increase welfare-equivalent output by an estimated 3-5% of GDP ($750B-$1.25T annually), based on the differential returns between over- and under-invested categories.
Corresponding Author: Mike P. Sinn, Decentralized Institutes of Health ([email protected])
Conflicts of Interest: The author declares no conflicts of interest.
Funding: This work received no external funding.
Data Availability: All data sources referenced in this paper are publicly available: OECD iLibrary (education, health spending), World Bank WDI (cross-country indicators), SIPRI Military Expenditure Database (defense spending), and CDC vaccination cost data. URLs are provided in the Data Sources section. A complete replication package including analysis code, data extraction scripts, and worked example calculations will be deposited in a public repository (GitHub/Zenodo) upon publication.
Ethics Statement: This is a methodological specification. No human subjects research was conducted.
Preprint: This working paper has not undergone peer review.