## _wp0960 — References / Chapter 2: Application Outcomes Under Universal Knowledge

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---

### I. Introduction and Methodology
- Participation decomposed into stages: KNOW, APPLY, ACCEPT.
- Targeting performance evaluated using household consumption and a Bergson-Samuelson social welfare index (λ); welfare weights βh = (yh/k)ε with ε capturing aversion to inequality. Normalization chosen so λ(NEUTRAL)=1 for a universal uniform transfer.
- Sequential program scenarios evaluated:
  - NEUTRAL: universal uniform transfer.
  - KNOW: all households with knowledge receive uniform transfer.
  - APPLY: all households applying receive uniform transfer.
  - ACCEPT: all accepted households receive uniform transfer.
  - DEMOG: current program with transfers differentiated by demographic structure (Table 2).
- Contribution(ACCEPT) computed as [λ(ACCEPT)-λ(APPLY)] / [λ(DEMOG)-λ(NEUTRAL)].
- Inequality aversion parameter varied; reported λ results for "1.05.0ε≤≤" (verbatim from source).
- Equivalence scale applied: consumption / household size^γ with baseline γ=1 and alternative γ=0.7.

### II. Program and Data Description
- Program: Mexico’s “Oportunidades” expansion (2002) from rural Progresa to small/medium urban localities.
- Urban targeting: information campaign (self-selection) → administrative proxy-means testing at program offices → verification home visits.
- Proxy-means discriminant score variables and coefficients shown in Table 1.
- Transfer schedule (pesos per month, 2002) (Table 2): monthly food transfer 150 pesos; caps: 1680 pesos if household has children attending high school, 915 otherwise; education transfers by grade and gender as specified in Table 2.
- Data: Urban Evaluation Survey of Oportunidades (2002) baseline (Sep–Dec 2002):
  - Census survey: 149 stratified blocks, 20,859 households.
  - Sample survey: 10,527 sampled, 9,817 completed SAMPLE questionnaires.
  - Sampling strata: beneficiaries, poor nonbeneficiaries, quasi-poor nonbeneficiaries, non-poor nonbeneficiaries.
- Households classified by proxy-means score into: Poor, Quasi-Poor, Non-poor.
- Program eligibility under rural Progresa: 80 percent of households in eligible rural localities deemed program eligible.

### III. Key Participation and Targeting Results
- Unconditional participation probabilities (population):
  - P(KNOW) = 63 percent.
  - P(APPLY) = 47 percent.
  - P(ACCEPT) = 30 percent.
- Conditional application and acceptance patterns:
  - Conditional on KNOW: bottom income quintile ~87 percent apply; top income quintile ~45 percent of those who know apply. Overall only 8 percent of top quintile apply.
  - Conditional acceptance rates (conditional on applying): bottom quintile 74 percent, top quintile 51 percent.
- Targeting performance (λ) increases across stages for all reported ε values ("1.05.0ε≤≤").
- Contributions of stages to targeting gains:
  - KNOW contribution decreases rapidly with higher ε.
  - ACCEPT contribution increases with ε; administrative proxy-means selection crucial for reducing program coverage while retaining lowest-welfare households.
  - DEMOG contribution often exceeds ACCEPT and increases with ε due to negative correlation between household size and per capita consumption.
  - DEMOG contribution numerics:
    - Under per capita welfare (γ=1), DEMOG contribution reported as 22–37 percent across various ε.
    - With economies of scale γ=0.7, DEMOG contribution falls to 9–18 percent across various ε.
- Bootstrapping (2,000 draws) inference:
  - Targeting performance increases across stages in all draws.
  - Targeting performance increases with ε in all draws.
  - Stage λ lines fan out as ε increases in almost all draws.

### IV. Policy Reform Simulations and Trade-offs (Table 3 highlights)
- Baseline participation and subgroup rates (selected exact figures):
  - Total Participation Rate: NEUTRAL 100; KNOW 63; APPLY 47; ACCEPT 30.
  - “Poor” Participation Rate (PPR): NEUTRAL 100; KNOW 78; APPLY 66; ACCEPT 47.
  - “Non-poor” Participation Rate (NPR): NEUTRAL 100; KNOW 54; APPLY 36; ACCEPT 21.
  - Average Beneficiary Transfer (pesos per month): NEUTRAL 145; KNOW 246; APPLY 344; ACCEPT 534.
  - Transfer share of “Poor”: NEUTRAL 30; KNOW 40; APPLY 47; ACCEPT 52.
  - Welfare Impact (transfer share × PPR): NEUTRAL 30; KNOW 25; APPLY 22; ACCEPT 16.
  - Targeting Differential (TD=PPR-NPR): NEUTRAL 0.00; KNOW 0.24; APPLY 0.30; ACCEPT 0.26.
- Universal Knowledge scenario (top panel reproduced):
  - Total Participation Rate: NEUTRAL 100; KNOW 100; APPLY 79; ACCEPT 30.
  - “Poor” Participation Rate (PPR): NEUTRAL 100; KNOW 100; APPLY 97; ACCEPT 52.
  - “Non-poor” Participation Rate (NPR): NEUTRAL 100; KNOW 100; APPLY 68; ACCEPT 18.
  - Average Beneficiary Transfer (pesos per month): NEUTRAL 145; KNOW 145; APPLY 199; ACCEPT 534.
  - Transfer share of “Poor”: NEUTRAL 30; KNOW 30; APPLY 40; ACCEPT 57.
  - Welfare Impact (transfer share × PPR): NEUTRAL 30; KNOW 30; APPLY 32; ACCEPT 17.
  - Targeting Differential (TD=PPR-NPR): NEUTRAL 0.00; KNOW 0.00; APPLY 0.29; ACCEPT 0.34.
- Trade-offs and simulation insights:
  - Under existing knowledge, PPR falls from 100 to 47 percent across stages while poor’s share of transfers rises from 30 to 52 percent.
  - Total undercoverage of the poorest three deciles = 53 percent: 22 percent lost at KNOW, 12 percent at APPLY, 19 percent at ACCEPT.
  - Welfare impact can decline when program size falls even if targeting improves (observed decreases at APPLY and ACCEPT).
  - Universal knowledge increases applications (47 → 79 percent) and increases PPR for APPLY from 66 to 97 percent but decreases transfer share of the poor for APPLY from 47 to 40 percent.
  - At fixed program size, moving to universal knowledge shifts ACCEPT-stage composition: poorest three deciles’ coverage increases from 47 to 52 percent and their share of transfers increases from 52 to 57 percent; λ ranges shift from 1.32–2.28 to 1.39–2.44 across ε.
  - Applying proxy-means score strictly to ration places yields marginal improvement: λ from 1.39–2.44 to 1.41–2.57; poorest three deciles coverage from 52 to 53 percent.
  - Re-estimating a proxy score by regressing per capita consumption on the same variables yields λ = 1.52–3.00 and poorest three deciles coverage increases to 60 percent.
- Benefit differentiation and participation responsiveness:
  - Reduced-form participation regression: P(PART) = 0.1195 t - 0.0649 t^2 (t in thousand pesos); coefficients significant at 5 percent.
  - Estimated impact: a 100 peso/month reallocation from a non-poor household at 450 pesos to a poor household increases participation gap by 1.2 percent (0.6 percent effect per 100 peso change on one household → switching increases gap from zero to 1.2 percent).
  - Differentiating transfers can: (i) shift budget toward lower-income households, (ii) alter application behavior favorably, (iii) reduce processing costs for non-poor applications.
  - Risk: linking transfers to scores increases incentives to misreport; need for effective verification (home visits, verifiable characteristics).

### V. Policy Conclusions and Recommendations
- Administrative selection (proxy-means) is effective at reducing overall program coverage while maintaining high coverage of lowest-welfare households relative to self-selection.
- Relying on knowledge-based self-selection reduces leakage to highest-welfare households but does little to concentrate transfers on lowest-welfare households; reliance on ignorance for targeting is undesirable.
- Demographic differentiation of transfers substantially concentrates resources on the poorest because poorer households have larger numbers of children and young adults.
- Reducing undercoverage requires:
  - Addressing knowledge constraints (but noting that broader knowledge may increase applications among non-poor).
  - Strengthening administrative selection and improving the proxy-means algorithm to better correlate with welfare.
- Tying transfer levels to poverty scores can improve targeting and reduce processing costs but raises misreporting incentives; effective verification is essential.
- Expansion to reduce remaining undercoverage implies an adverse targeting trade-off; this can be alleviated by a better proxy-means algorithm and by linking transfers to scores with verification.

### VI. Appendix — Estimation and Simulation Details (Heckman results and universal knowledge simulation)
- Estimation approach: Heckman two-step linear probability model; block poverty rate used as exclusion restriction for KNOW equation.
- Key unconditional and conditional coefficients (selected exact values):
  - Head of Household Education (years):
    - P(KNOW): Coefficient 0.0007, t-statistic 1.98
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.0030, t-statistic 2.62
    - Consumption regression: Coefficient 0.0042, t-statistic 3.74
  - Children 6-11yrs:
    - P(KNOW): Coefficient 0.0165, t-statistic 2.85
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.1945, t-statistic 10.32
    - Consumption regression: Coefficient 0.2199, t-statistic 11.79
    - Consumption model: Coefficient -28.79, t-statistic -6.60
  - Family Size:
    - P(KNOW): Coefficient -0.0144, t-statistic -3.22
    - P(APPLY|KNOW) selection P(KNOW): Coefficient -0.0808, t-statistic -5.63
    - Consumption regression: Coefficient -0.1047, t-statistic -7.32
    - Consumption model: Coefficient -74.92, t-statistic -22.92
  - Vehicle:
    - P(KNOW): Coefficient 0.1744, t-statistic 6.04
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.5134, t-statistic 7.64
    - Consumption regression: Coefficient 0.7308, t-statistic 9.66
    - Consumption model: Coefficient -210.77, t-statistic -13.00
  - Transfer level (transfers are in thousands of pesos):
    - P(APPLY|KNOW) selection P(APPLY): Coefficient 0.0975, t-statistic 2.03
    - Consumption regression: Coefficient 0.3804, t-statistic 2.33
  - Constants (selected):
    - P(KNOW): Constant 0.8189, t-statistic 15.11
    - P(ACCEPT|APPLY): Constant -0.5753, t-statistic -2.31
    - Consumption regression: Constant 1377.23, t-statistic 38.13
- Model fit and diagnostics:
  - No. of observations: 6017; 9666; 5332; 9666; 9666 (as reported).
  - R-squared: 0.31.
  - Inverse Mills Ratio: -0.1395 (t=-5.23); -0.0613 (t=-1.63).
  - rho: -0.4328; -0.1464.
- Simulation of universal knowledge (selected exact results, Appendix Table 2):
  - Full Sample: All Households share 100.0.
  - KNOW=0: Households 3649, Share (%) 37.8100; predicted APPLY rates: t=0.5 → 80.5; t=0.886 → 68.3.
  - KNOW=1: Households 6017, Share (%) 62.2100; predicted APPLY rates: t=0.5 → 94.5; t=0.886 → 88.6.
  - All (aggregate predicted applying): t=0.5 → 89.2; t=0.886 → 81.0.
  - Subsample KNOW=1 by prior APPLY status:
    - APPLY=0: Households 685, Share (%) 11.4100; t=0.5 → 83.7; t=0.886 → 72.6.
    - APPLY=1: Households 5332, Share (%) 88.6100; t=0.5 → 95.8; t=0.886 → 90.8.
  - Calibration thresholds:
    - Using t=0.5 threshold: all households apply (all predicted probabilities above 0.6).
    - Using average application rate for selected sample (t=0.886): 88.6 percent of households that knew actually applied; simulating universal knowledge yields 89.2 percent applying overall.
    - Alternative threshold t=0.908 chosen by trial and error so post-reform proportion of previously-knowledgeable households applying equals pre-reform rate (88.6 percent). Under t=0.908:
      - Proportion of all households that apply under universal knowledge: 81 percent.
      - Nearly 91 percent of those who previously applied now apply; 68 percent of those who previously did not acquire knowledge now apply.
- Acceptance under constrained program size:
  - Acceptance modeled with program size binding at 30 percent of the population; 30 percent of households with highest P(ACCEPT|APPLY) assumed to participate; newly applying households can "bump out" previously selected households.
  - Selection rules compared: acceptance regression P(ACCEPT|APPLY), proxy-means score, alternative proxy from consumption regression.
  - Acceptance regression findings: block poverty rate positive and highly significant in application selection; transfer effect positive and decreasing (transfer squared negative); probability of acceptance higher for lower proxy-means scores; number of children of primary school age positive for acceptance; number of rooms negatively associated with acceptance.
- Notes and assumptions:
  - Transfers reported in thousands of pesos in regression tables.
  - Consumption quintile dummies included in Heckman acceptance regression were insignificant.
  - Program officials reported that once beneficiary quota reached verification visits were suspended; verification-rate variable included to capture budget constraint intensity.

*Source: IMF Working Paper — Chapter "2. Application Outcomes Under Universal Knowledge" (Urban Evaluation Survey of Oportunidades, 2002) — _wp0960*

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

### _wp0960 - References

### Tables
- 1. Variables and Weights Used to Estimate the Discriminant Proxy-Means Score ..................6
- 2. Transfer Levels by Grade and Gender (pesos per month, 2002) ...........................................7
- 3. Trade-off Between Vertical Targeting Performance and Program Coverage .....................18

### Figures
- 1. Unconditional Probabilities .................................................................................................13
- 2. Conditional Probabilities .....................................................................................................14
- 3. Targeting Performance by Stage..........................................................................................15
- 4. Share of Targeting Performance by Stage ...........................................................................16
- 5. Share of Targeting Performance by Stage ...........................................................................17

### Appendix
- Details of Simulations Estimating Targeting Implications of Universal Knowledge..............24

### Appendix Tables
- 1. Results for Conditional Application and Acceptance Outcomes and Consumption  
Model...................................................................................................................................26

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0960.pdf*

### 2. Application Outcomes Under Universal Knowledge ..........................................................28

### 2. Application Outcomes Under Universal Knowledge ..........................................................28

### I. Introduction
- Many safety net programs in developing countries are poorly targeted; large benefit leakage to higher income households and exclusion of many poor households.
- This chapter compares two common targeting methods: self-selection by households and administrative selection by program officials.
- Participation process decomposed into stages: knowledge of program (KNOW), application (APPLY), acceptance (ACCEPT).
- Targeting performance evaluated using household consumption as welfare measure and a Bergson-Samuelson social welfare index (λ) that increases as transfers are more concentrated on lower-welfare households.
- Welfare weights βh derived from a constant elasticity social welfare function βh = (yh/k)ε with ε capturing aversion to inequality; normalization chosen so λ(NEUTRAL)=1 for a universal uniform transfer.

### II. Program and Data Description
- Program: Mexico’s “Oportunidades” expansion (2002) from rural Progresa to small/medium urban localities.
- Urban targeting approach: preliminary self-selection (information campaign) followed by administrative proxy-means testing at program offices and verification home visits.
- Proxy-means discriminant score (variables and coefficients shown in Table 1) used to classify households; 80 percent of households in eligible rural localities were deemed program eligible under rural Progresa.
- Transfer schedule (Table 2): education transfers (pesos per month, 2002) by grade and gender; monthly food transfer of 150 pesos; caps: 1680 pesos if household has children attending high school, 915 otherwise.
- Data: Urban Evaluation Survey of Oportunidades (2002) baseline collected Sep–Dec 2002 by INSP:
  - Census survey: 149 stratified blocks, 20,859 households.
  - Sample survey: stratified subsample (10,527 sampled, 9,817 completed SAMPLE questionnaires); sampling strata: beneficiaries, poor nonbeneficiaries, quasi-poor nonbeneficiaries, non-poor nonbeneficiaries.
  - Focus: targeting performance within sampled very poor urban blocks.
- Households classified by proxy-means score into: Poor, Quasi-Poor, Non-poor.

### III. Methodology
- Social welfare impact: W = Σh βh ∂Vh/∂mh dmh ≡ Σh βh θh where θh is share of budget to household; λ index derived independent of transfer scale.
- Evaluate targeting performance (λ) for sequential “programs”:
  - NEUTRAL: universal uniform transfer.
  - KNOW: all households with knowledge receive uniform transfer.
  - APPLY: all households applying receive uniform transfer.
  - ACCEPT: all accepted households receive uniform transfer (administrative selection).
  - DEMOG: actual program—transfers differentiated by demographic structure (Table 2).
- Contribution of each stage to total improvement: e.g., Contribution(ACCEPT) = [λ(ACCEPT)-λ(APPLY)] / [λ(DEMOG)-λ(NEUTRAL)].
- Welfare weights parameter ε (>0) varied to capture inequality aversion; ε→∞ corresponds to Rawlsian focus on poorest. Results normalized so λ(NEUTRAL)=1.
- Economies of scale in welfare measure also considered using equivalence scale household consumption / household size^γ with baseline γ=1 and alternative γ=0.7.

### IV. Results — Participation and Targeting Performance
- Unconditional participation probabilities (population):
  - P(KNOW) = 63 percent.
  - P(APPLY) = 47 percent.
  - P(ACCEPT) = 30 percent.
- Interpretation: program desired size proximate to 30 percent coverage → bottom three income quintiles treated as target population.
- Figure findings (descriptive):
  - Unconditional probabilities KNOW, APPLY, ACCEPT decrease with income; knowledge slope drives much of the pattern.
  - Conditional on KNOW: bottom income quintile ~87 percent apply; top income quintile ~45 percent of those who know apply. But only 8 percent of top quintile apply overall.
  - Conditional acceptance rates: 74 percent for bottom quintile, 51 percent for top quintile (conditional on applying).
- Targeting performance across stages (λ increases across stages for all ε in reported range):
  - Presented for inequality aversion values reported as "1.05.0ε≤≤" (verbatim from source).
  - DEMOG stage substantially increases targeting relative to uniform transfers, especially at higher ε.
- Contributions of stages to targeting gain (qualitative and quantified highlights):
  - KNOW contribution decreases rapidly with higher ε — knowledge reduces leakage to highest income households but less important for concentrating transfers on bottom half.
  - ACCEPT contribution increases with ε — administrative proxy-means selection crucial for reducing program coverage while maintaining coverage of lowest welfare households.
  - DEMOG contribution (differentiated transfers by demographics) increases with ε and often exceeds ACCEPT; due to strong negative correlation between household size and per capita consumption (more children in poorer households).
  - Numerics on demographic contribution:
    - Under per capita welfare (γ=1), DEMOG contribution reported as 22–37 percent across various ε.
    - Allowing for economies of scale with γ=0.7, DEMOG contribution falls to 9–18 percent across various ε.
- Statistical inference:
  - Bootstrapping (2,000 draws) tests show:
    - Targeting performance increases across stages in all draws.
    - Targeting performance increases with ε in all draws.
    - Lines for stages fan out as ε increases in almost all draws.

### V. Policy reform simulations and trade-offs
- Table 3 (key simulated quantitative outcomes; percentages and pesos preserved exactly as in source):
  - Baseline (NEUTRAL / KNOW / APPLY / ACCEPT / Current Program) — selected entries:
    - Total Participation Rate: NEUTRAL 100; KNOW 63; APPLY 47; ACCEPT 30.
    - “Poor” Participation Rate (PPR): NEUTRAL 100; KNOW 78; APPLY 66; ACCEPT 47.
    - “Non-poor” Participation Rate (NPR): NEUTRAL 100; KNOW 54; APPLY 36; ACCEPT 21.
    - Average Beneficiary Transfer (pesos per month): NEUTRAL 145; KNOW 246; APPLY 344; ACCEPT 534.
    - Transfer share of “Poor”: NEUTRAL 30; KNOW 40; APPLY 47; ACCEPT 52.
    - Welfare Impact (transfer share × PPR): NEUTRAL 30; KNOW 25; APPLY 22; ACCEPT 16.
    - Targeting Differential (TD=PPR-NPR): NEUTRAL 0.00; KNOW 0.24; APPLY 0.30; ACCEPT 0.26.
  - Universal Knowledge scenario (top panel reproduced as “Universal Knowledge”):
    - Total Participation Rate: NEUTRAL 100; KNOW 100; APPLY 79; ACCEPT 30.
    - “Poor” Participation Rate (PPR): NEUTRAL 100; KNOW 100; APPLY 97; ACCEPT 52.
    - “Non-poor” Participation Rate (NPR): NEUTRAL 100; KNOW 100; APPLY 68; ACCEPT 18.
    - Average Beneficiary Transfer (pesos per month): NEUTRAL 145; KNOW 145; APPLY 199; ACCEPT 534.
    - Transfer share of “Poor”: NEUTRAL 30; KNOW 30; APPLY 40; ACCEPT 57.
    - Welfare Impact (transfer share × PPR): NEUTRAL 30; KNOW 30; APPLY 32; ACCEPT 17.
    - Targeting Differential (TD=PPR-NPR): NEUTRAL 0.00; KNOW 0.00; APPLY 0.29; ACCEPT 0.34.
- Key trade-offs and simulation insights:
  - Under existing knowledge, PPR falls from 100 to 47 percent across stages while poor’s share of transfers rises from 30 to 52 percent; total undercoverage of poorest three deciles = 53 percent: 22 percent lost at KNOW, 12 percent at APPLY, 19 percent at ACCEPT.
  - Welfare impact (transfer share × PPR) can decline when program size falls even if targeting performance improves (observed decrease at APPLY and ACCEPT stages).
  - Universal knowledge increases applications (47 → 79 percent) and increases PPR for APPLY stage from 66 to 97 percent but decreases transfer share of the poor for APPLY from 47 to 40 percent (due to higher proportional application increases among higher-income groups).
  - At fixed program size, acceptance-stage composition changes: poorest three deciles’ coverage increases from 47 to 52 percent and their share of transfers increases from 52 to 57 percent; λ ranges shift from 1.32–2.28 to 1.39–2.44 across ε.
  - Applying the proxy-means score strictly to ration places yields only marginal improvement: λ increases from 1.39–2.44 to 1.41–2.57; coverage of poorest three deciles increases from 52 to 53 percent.
  - Re-estimating a proxy score by regressing per capita consumption on the same variables yields λ = 1.52–3.00 and poorest three deciles coverage increases to 60 percent — suggesting room for improved correlation by refining the algorithm.
- Benefit differentiation linked to poverty scores:
  - Reduced-form participation regression estimated: P(PART) = 0.1195 t - 0.0649 t^2 (t in thousand pesos); coefficients significant at 5 percent.
  - Estimated impact: a 100 peso/month reallocation from a non-poor household at 450 pesos to a poor household increases participation gap by 1.2 percent (0.6 percent effect per 100 peso change on one household → switching increases gap from zero to 1.2 percent).
  - Differentiating transfers helps: (i) shift budget toward lower-income households, (ii) alter application behavior favorably, (iii) reduce processing costs for non-poor applications.
  - Risk: linking transfers to scores increases incentives to misreport; Martinelli and Parker (2006) find misreporting widespread but marginal relationship between transfer level and misreporting magnitude; reinforces need for effective verification (home visits, verifiable characteristics).
- Expansion of program size reduces undercoverage but tends to worsen targeting performance; trade-off can be mitigated by:
  - Improving proxy-means algorithm to better correlate with welfare.
  - Linking transfers to proxy-means scores, conditional on effective verification, to lower budget cost of reducing undercoverage.

### VI. Summary — main policy-relevant conclusions
- Administrative selection (proxy-means) is especially effective at reducing overall program coverage while maintaining high coverage of the lowest-welfare households, relative to self-selection at the application stage.
- Knowledge-based self-selection reduced coverage among the highest-welfare households but played little role in concentrating transfers on the lowest-welfare households; reliance on ignorance for targeting is undesirable.
- Demographic differentiation of transfers substantially concentrates resources on the poorest households because poorer households have larger numbers of children and young adults.
- Reducing undercoverage requires addressing knowledge constraints (which may increase applications among non-poor) and strengthening administrative selection and the proxy-means algorithm to improve correlation with welfare.
- Tying transfer levels to poverty scores can improve targeting and reduce processing costs but increases misreporting incentives; effective verification mechanisms are essential.
- Expansion to reduce remaining undercoverage implies an adverse targeting trade-off; this can be alleviated by a better proxy-means algorithm and by linking transfers to scores with verification.

### Appendix — Simulations of Universal Knowledge
- Participation decomposition: P(PART) = P(KNOW) × P(APPLY|KNOW) × P(ACCEPT|KNOW,APPLY).
- Estimation challenges: sample selection bias when estimating P(APPLY|KNOW) and P(ACCEPT|KNOW,APPLY) because KNOW and APPLY reflect household decisions.
- Identification strategy: include block poverty rate (proxy for intensity of advertising concentrated in poorer blocks) in KNOW equation to provide exclusion restriction for Heckman selection correction.
- Estimation approach: Heckman two-step linear probability model; block poverty rate positive and highly significant in knowledge equation; inverse Mills’ ratio significant indicating sample selection correction needed.

*Source: IMF Working Paper (Urban Evaluation Survey of Oportunidades, 2002) — chapter "2. Application Outcomes Under Universal Knowledge" as provided in the source content.*

### Appendix Table 1. Results for Conditional Application and Acceptance Outcomes and Consumption Model

### Appendix Table 1. Results for Conditional Application and Acceptance Outcomes and Consumption Model

### Heckman application and acceptance regressions — key coefficient estimates
- Head of Household
  - Education (years)
    - P(KNOW): Coefficient 0.0007, t-statistic 1.98
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.0030, t-statistic 2.62
    - P(ACCEPT|APPLY): Coefficient -0.0001, t-statistic -0.14
    - Consumption regression (consumption model): Coefficient 0.0042, t-statistic 3.74
    - Consumption model (other column): Coefficient -0.630, t-statistic -2.31
  - Gender
    - P(KNOW): Coefficient 0.0037, t-statistic 0.37
    - P(APPLY|KNOW) selection P(KNOW): Coefficient -0.1483, t-statistic -4.26
    - P(ACCEPT|APPLY): Coefficient 0.0464, t-statistic 3.29
    - Consumption regression: Coefficient -0.1319, t-statistic -3.86
    - Consumption model: Coefficient -11.49, t-statistic -1.39
  - Age (years)
    - P(KNOW): Coefficient -0.0007, t-statistic -1.43
    - P(APPLY|KNOW) selection P(KNOW): Coefficient -0.0064, t-statistic -3.93
    - P(ACCEPT|APPLY): Coefficient 0.0006, t-statistic 0.82
    - Consumption regression: Coefficient -0.0074, t-statistic -4.54
    - Consumption model: Coefficient 1.34, t-statistic 3.40
  - Indigenous
    - P(KNOW): Coefficient 0.0003, t-statistic 0.03
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.2066, t-statistic 4.26
    - P(ACCEPT|APPLY): Coefficient 0.0238, t-statistic 1.31
    - Consumption regression: Coefficient 0.2007, t-statistic 4.30
    - Consumption model: Coefficient -35.31, t-statistic -3.18

- Household characteristics (selected)
  - Number of rooms
    - Consumption regression: Coefficient -0.0364, t-statistic -4.55
    - Consumption model: Coefficient 28.98, t-statistic 7.50
  - Children 0-5yrs
    - P(KNOW): Coefficient 0.0182, t-statistic 2.68
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.1205, t-statistic 5.19
    - P(ACCEPT|APPLY): Coefficient 0.0021, t-statistic 0.22
    - Consumption regression: Coefficient 0.1520, t-statistic 6.63
    - Consumption model: Coefficient -30.55, t-statistic -5.80
  - Children 6-11yrs
    - P(KNOW): Coefficient 0.0165, t-statistic 2.85
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.1945, t-statistic 10.32
    - P(ACCEPT|APPLY): Coefficient 0.0267, t-statistic 3.11
    - Consumption regression: Coefficient 0.2199, t-statistic 11.79
    - Consumption model: Coefficient -28.79, t-statistic -6.60
  - Children 12-17yrs
    - P(KNOW): Coefficient 0.0094, t-statistic 1.27
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.1087, t-statistic 4.37
    - P(ACCEPT|APPLY): Coefficient 0.0104, t-statistic 1.11
    - Consumption regression: Coefficient 0.1178, t-statistic 4.79
    - Consumption model: Coefficient -6.81, t-statistic -1.32
  - Family Size
    - P(KNOW): Coefficient -0.0144, t-statistic -3.22
    - P(APPLY|KNOW) selection P(KNOW): Coefficient -0.0808, t-statistic -5.63
    - P(ACCEPT|APPLY): Coefficient -0.0098, t-statistic -1.55
    - Consumption regression: Coefficient -0.1047, t-statistic -7.32
    - Consumption model: Coefficient -74.92, t-statistic -22.92
  - Disabled
    - P(KNOW): Coefficient 0.0190, t-statistic 0.61
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.0282, t-statistic 0.28
    - P(ACCEPT|APPLY): Coefficient -0.0102, t-statistic -0.23
    - Consumption regression: Coefficient 0.0541, t-statistic 0.53
    - Consumption model: Coefficient -103.08, t-statistic -4.21
  - Vehicle
    - P(KNOW): Coefficient 0.1744, t-statistic 6.04
    - P(APPLY|KNOW) selection P(KNOW): Coefficient 0.5134, t-statistic 7.64
    - P(ACCEPT|APPLY): Coefficient 0.0084, t-statistic 0.17
    - Consumption regression: Coefficient 0.7308, t-statistic 9.66
    - Consumption model: Coefficient -210.77, t-statistic -13.00
  - Other durables and amenities (selected consumption-model coefficients)
    - Number of rooms: Coefficient 28.98, t-statistic 7.50
    - Health Insurance: Coefficient 144.40, t-statistic 4.52
    - Fridge: Coefficient 62.35, t-statistic 8.28
    - Washing Machine: Coefficient 96.53, t-statistic 9.61
    - Gas Heater: Coefficient 48.39, t-statistic 5.43
    - No Bath: Coefficient -78.53, t-statistic -8.51
    - Bath w/o water: Coefficient -25.04, t-statistic -1.95
    - Dirt Floor: Coefficient -22.13, t-statistic -2.84

- Consumption and transfers (selection and consumption equations)
  - Consumption
    - P(APPLY|KNOW) selection P(APPLY): Coefficient -0.0002, t-statistic -3.84
    - P(ACCEPT|APPLY): Coefficient -0.0015, t-statistic -11.80
    - Consumption regression: Coefficient -0.0018, t-statistic -13.67
  - Consumption Sqd.
    - Consumption regression: Coefficient 0.0059e-05, t-statistic 3.23
    - Consumption model: Coefficient 0.3700e-06, t-statistic 7.91
    - Other consumption-model column: Coefficient 0.0046e-04, t-statistic 9.63
  - Transfer level (transfers are in thousands of pesos)
    - P(APPLY|KNOW) selection P(APPLY): Coefficient 0.0975, t-statistic 2.03
    - P(ACCEPT|APPLY): Coefficient 0.1734, t-statistic 1.05
    - Consumption regression: Coefficient 0.3804, t-statistic 2.33
  - Transfer Sqd.
    - P(APPLY|KNOW) selection P(APPLY): Coefficient -0.0508, t-statistic -2.02
    - P(ACCEPT|APPLY): Coefficient -0.0981, t-statistic -1.13
    - Consumption regression: Coefficient -0.2023, t-statistic -2.36
  - Transfer*Cons
    - P(APPLY|KNOW) selection P(APPLY): Coefficient -0.0263e-03, t-statistic -0.74
    - P(ACCEPT|APPLY): Coefficient -0.1000e-04, t-statistic -0.10
    - Consumption regression: Coefficient -0.0001, t-statistic -0.55

- Proxy-means classification (consumption model column coefficients and t-statistics)
  - Extreme Poor: Coefficient 0.3213, t-statistic 11.41
  - Poor: Coefficient 0.3125, t-statistic 12.49
  - Quasi-poor: Coefficient 0.2722, t-statistic 12.18
  - Non-poor: Coefficient 0.1113, t-statistic 5.01

- Block Poverty Rate and distance
  - Block Poverty Rate
    - Consumption regression: Coefficient 2.0203, t-statistic 22.98
    - Consumption model (another column): Coefficient 1.8658, t-statistic 21.42
    - Consumption model (acceptance-related column): Coefficient -220.15, t-statistic -10.19
  - Distance to office
    - P(KNOW): Coefficient 0.0006, t-statistic 2.34
    - P(APPLY|KNOW) selection P(KNOW): Coefficient -0.0015, t-statistic -1.70
    - P(ACCEPT|APPLY): Coefficient 0.0003, t-statistic 0.82
    - Consumption regression: Coefficient -0.0003, t-statistic -0.35
  - Verification rate
    - Consumption model: Coefficient 1.1506, t-statistic 5.03

- Constants (selected)
  - P(KNOW): Constant 0.8189, t-statistic 15.11
  - P(APPLY|KNOW) selection P(KNOW): Constant -0.2899, t-statistic -1.68
  - P(ACCEPT|APPLY): Constant -0.5753, t-statistic -2.31
  - Consumption regression: Constant 1377.23, t-statistic 38.13

### Model fit, sample sizes, and selection diagnostics
- No. of observations: 6017; 9666; 5332; 9666; 9666
- R-squared: 0.31 (reported)
- Inverse Mills Ratio
  - -0.1395 (t=-5.23)
  - -0.0613 (t=-1.63)
- rho: -0.4328; -0.1464

### Simulation of universal knowledge counterfactual — application outcomes (Appendix Table 2)
- Sample shares and predicted % applying under different thresholds
  - Full Sample: All Households share 100.0
  - KNOW=0: Households 3649, Share (%) 37.8100
    - t=0.5: 80.5
    - t=0.886: 68.3
  - KNOW=1: Households 6017, Share (%) 62.2100
    - t=0.5: 94.5
    - t=0.886: 88.6
  - All (aggregate)
    - t=0.5: 89.2
    - t=0.886: 81.0
  - Subsample KNOW=1 by prior APPLY status
    - APPLY=0: Households 685, Share (%) 11.4100
      - t=0.5: 83.7
      - t=0.886: 72.6
    - APPLY=1: Households 5332, Share (%) 88.6100
      - t=0.5: 95.8
      - t=0.886: 90.8
- Key calibration and thresholds discussed in text
  - Using t=0.5 threshold: all households apply (all predicted probabilities above 0.6).
  - Using average application rate for selected sample (t=0.886): 88.6 percent of households that knew actually applied; simulating universal knowledge yields 89.2 percent applying overall.
  - Alternative threshold chosen so that post-reform proportion of previously-knowledgeable households applying equals pre-reform rate (88.6 percent): threshold found by trial and error as 0.908. Under t=0.908:
    - Proportion of all households that apply under universal knowledge: 81 percent.
    - Pattern across subgroups: nearly 91 percent of those who previously applied now apply; 68 percent of those who previously did not acquire knowledge now apply.

### Acceptance selection under constrained program size and targeting implications
- Acceptance modeled as administrative selection with program size binding at 30 percent of the population.
- Selection rules/simulations:
  - 30 percent of households with highest P(ACCEPT|APPLY) (conditional on applying) are assumed to participate; newly applying households can "bump out" previously selected households.
  - Comparisons made between:
    - Selection based on estimated P(ACCEPT|APPLY) (Heckman acceptance regression).
    - Selection based only on proxy-means score.
    - Selection based on alternative proxy-means algorithm from the consumption regression (final two columns).
- Acceptance regression findings (Columns 5–8 summary)
  - Block poverty rate: positive and highly significant in the application selection equation.
  - Transfer effect: significantly positive and decreasing (transfer level positive, transfer squared negative).
  - Probability of acceptance: much higher for those with lower proxy-means scores (consistent with score used to ration places).
  - Number of children of primary school age: significantly positive coefficient for acceptance.
  - Housing conditions (number of rooms): negatively associated with acceptance (fewer rooms → higher acceptance probability), suggesting program officials may weigh housing more than the official score.
  - Inverse Mills’ ratio: significant only at around the 90 percent level (selection correction only weakly significant).

### Notes, assumptions, and implementation details
- Transfers are in thousands of pesos.
- Consumption quintile dummies were included in the Heckman acceptance regression but were all insignificant.
- Application probability relationship used: P(APPLY)=P(KNOW)P(APPLY|KNOW); P(APPLY) is estimated on full sample to get unbiased estimate of P(ACCEPT|APPLY) for all households.
- The level of benefits a household would receive if accepted is included in the selection (application) equation but not the acceptance equation; it also serves as an instrumental variable in the application selection equation.
- Program officials reported that once the quota for beneficiaries was reached, verification visits were suspended; a verification-rate variable is included to capture intensity of the budget constraint.

*Source: Appendix Table 1 and Appendix Table 2, _wp0960 - Appendix Table 1. Results for Conditional Application and Acceptance Outcomes and Consumption Model*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0960.pdf_