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---

### Model suite and purpose
- Three new models: DIG-Labor 1, DIG-Labor 2, DIG-Labor 3; extensions of DIG and DIGNAR to incorporate segmented labor markets and richer labor-market frictions.
- DIG-Labor features:
  - Formal sector: firms pay efficiency wages (EWs).
  - Agriculture: flexible wages.
  - Non-agricultural informal sector:
    - DIG-Labor 1 and 3: own-account workers; labor in informal sector earns same return as in agriculture.
    - DIG-Labor 2: wage employees; informal firms pay an EW below the formal-sector wage.
- Model applicability:
  - DIG-Labor 1: appropriate for most Low-Income Countries (LICs).
  - DIG-Labor 2: appropriate for most Middle-Income Countries (MICs) and Emerging Market Economies (EMEs).
  - DIG-Labor 3: appropriate for countries that suffer only from underemployment.
- New features across DIG-Labor models: skilled labor, public investment in human capital, maintenance investment vs. new infrastructure investment, sector-specific taxes on wages/profits/consumption.
- Models supported by Dynare + MATLAB programs, fully annotated.

### Key empirical and structural premises
- Labor markets in developing countries are highly segmented; textbook competitive flex-wage assumptions are restrictive.
- Open unemployment and underemployment are prevalent in many LICs.
- Property rights on land often insecure: "80-95percent of land is untitled in most of Sub-Saharan Africa (Doss et al., 2015; Chen, 2017)."
- Eighty percent of the equations in DIG-Labor 1 carry over to DIG-Labor 2 and DIG-Labor 3; main differences are labor-market specifications.

### Major quantitative findings on investment mix and impacts
- General-equilibrium comparisons for a 1 percent of GDP increase in public investment (steady-state effects):
  - Basic education (1 percent of GDP):
    - increases aggregate consumption by 10:2percent
    - increases real income of the poor by 10:3percent
  - Upper-level education (secondary + tertiary) (1 percent of GDP):
    - increases aggregate consumption by 9:3percent
    - increases real income of the poor by 18:1percent
  - Infrastructure (1 percent of GDP):
    - increases aggregate consumption by 4:3percent
    - increases real income of the poor by 5:4percent
- Internal rate of return (base case assumptions, partial equilibrium social IRR):
  - Basic education: 12percent
  - Upper-level education: 10percent
  - These IRRs map into partial equilibrium capital rentals ten percentage points above the rental for infrastructure in the base case.
- Sensitivity to lower IRRs:
  - Lowering IRR to 6:7percent for upper-level education and 7:6percent for basic education depresses long-run partial equilibrium capital rentals for both investments to 15percent, five percentage points below the capital rental for infrastructure.
  - Even with reduced IRRs, the share of human capital in the optimal investment program is 40-65percent when the social discount rate equals or exceeds 0:96; it drops to 0-25percent at lower discount rates, but rises to 25-50percent if education is awarded 20 basis points as a merit good in equivalent variation welfare calculations.

### Intertemporal trade-offs and fiscal implications
- Human capital investment has much larger long-run payoff but materializes with a 6- to 8-year lag; it takes 15+ years before net national income, private capital stock, real wages for the poor, formal sector employment, etc., surpass outcomes from infrastructure-focused programs.
- Big-push programs emphasizing human capital require more supporting fiscal adjustment because delayed growth delays endogenous revenue gains; increasing the share of human capital thus entails:
  - more fiscal adjustment to avoid explosive debt dynamics, and/or
  - tolerance of a higher debt trajectory for several decades.
- Optimal investment mix depends on:
  - the social discount rate,
  - the weight on distributional objectives in the social welfare function,
  - diminishing returns and complementarity between human capital and infrastructure,
  - the faster payoff of infrastructure.

### Welfare and optimal investment-share results (base-case characterization)
- Share of human capital in the optimal investment program:
  - On the order of 50-100percent in the base case.
  - Optimal investment share is 50-75percent when the social discount rate is 0:93-0:96 and the weight on distributional objectives is not extreme.
  - At social discount rates above 0:96, the share for infrastructure drops to zero.
- Distributional impacts:
  - Basic education increases growth more but reduces poverty less than upper-level education.
  - Upper-level education produces the largest gains for the ex ante poor by converting some workers from unskilled/poor into high-skill/well-paid workers and raising productivity of remaining low-skill workers through labor-market adjustments.

### Labor-market distortions, unemployment, and underemployment
- DIG-Labor distinctions:
  - Open unemployment exists in DIG-Labor 1 and 2, but not in DIG-Labor 3.
  - Involuntary unemployment pervades entire non-agricultural sector in DIG-Labor 2; in DIG-Labor 1 it is confined to the formal sector.
  - Underemployment exists in all three models; for any given unemployment rate (zero in DIG-Labor 3 possible), aggregate labor productivity increases when labor moves from informal to formal sector or from agriculture to non-agricultural sectors.
- In DIG-Labor 1 and 3, smallholder agriculture receives marginal value product plus a share of implicit land rents; insecure property rights lower marginal productivity and limit mobility-induced equalization.

### Model implementation, calibration highlights, and parameters
- DIG-Labor 1 developed and calibrated in Sections III and IV; Sections V–VII present policy experiments. DIG-Labor 2 and 3 full models accompany DIG-Labor 1 material.
- Selected baseline calibration values (preserve exactly):
  - Consumption shares: formal good 40percent, informal good 20percent, imported consumer good 10percent, agricultural good 30percent.
  - Intertemporal elasticity of substitution ρ = 0:40.
  - Elasticities of substitution: "1 = 0:50, "2 = 0:5, "3 tested at 0:5 and 5.
  - Wages: w_n = 1; w_j = :60 (mid-range formal premium = 67percent); w_s = 3.
  - Factor shares (formal): β_n = 0:50; θ_n = 0:30.
  - Informal shares: β_j = 0:20; θ_j = 0:20.
  - Agriculture shares: land 30percent, capital 20percent, high‑skill labor 5percent; shadow wage w_x = 0:36.
  - Depreciation rates ϵ = 5percent.
  - Returns and rates: concessional real rate r_d = 1:3percent; external commercial r_dc ≈ 6percent; trend growth g = :023.
  - Education IRRs and lags: basic education IRR = 12percent (lag 6 years); upper-level education IRR = 10percent (lag 8 years).
  - Q-elasticity of investment ȷ = 2:5.
  - Initial public/debt stocks: domestic debt b = 15percent of GDP; concessional external debt d = 32percent of GDP; external commercial debt dc = 6percent of GDP.
  - VAT rate h = 20percent; public investment efficiency s = 1; absorptive capacity ϵ = 0.

### Policy analysis: public investment choices, maintenance, and big-push programs
- Long-run ranking for a 1-percent-of-GDP increase:
  - Basic education strongly dominates infrastructure for long-run GDP, formal employment, and real wages (IBE raises these 2–2.5 times more than II).
  - Upper-level education also strongly dominates II in long-run effects, reduces unemployment more, and raises GDP, aggregate consumption, and poor incomes more than II.
  - Formal-good tradability ("3) matters: when "3 = 5 IUE is far more powerful; when "3 = 0:5 tax base erosion risk is larger.
- Maintenance underfunding:
  - Increasing maintenance can immediately raise Net National Product; restoring maintenance can eliminate return gaps and produce large gains.
  - Example: spending 1:64percent of GDP on maintenance eliminates return gap and increases GDP by 9:1-10percent and aggregate consumption by 8:3-9:1percent; "free‑lunch" component accounts for 35-39percent of total gains.
- Big-push programs (permanent +4percent of initial GDP):
  - Pure infrastructure much less effective long run than human-capital programs.
  - Mixed programs can dominate pure infrastructure in medium run because education returns are delayed; optimal mix depends on social discount factor and weight on poverty reduction.
  - Marginal returns decline with scale but gross complementarity across infrastructure, basic education, and upper education raises marginal return schedules of other components.
- Transition trade-offs:
  - Human-capital–heavy programs: superior long-run growth, structural transformation, and poverty reduction, but weak/negative short-run gains (first decade) and require substantial fiscal space and concessional financing.
  - Infrastructure‑heavy programs: faster short-run gains but lower long-run poverty reduction.
  - Blended programs mitigate extremes.
- Fiscal constraints and debt dynamics:
  - Limits on domestic fiscal adjustment (examples: VAT increase ≤ 2 percentage points; transfers cut ≤ 1 percentage point of GDP) make concessional external financing essential.
  - In base runs with generous concessional financing and some tax base widening, peak public debt rises to ~80percent of GDP in the human-capital–only PIP (initial 55percent) and ~70percent in the infrastructure‑only PIP; reduced concessional access would render programs infeasible.
- Welfare calculations and optimal mixes:
  - Social welfare uses weight on ex‑ante poor income parameter ψ and social discount factor _s.
  - If _s = private discount factor  = 0:93, optimal big‑push mixes include 25–50percent infrastructure.
  - If _s increases (e.g., 0:96–0:98) and/or ψ ≥ 1, optimal share of infrastructure falls to ≤ 25percent and human capital dominates.
  - If returns to human capital are lower, optimal infrastructure share rises; welfare surfaces are relatively flat so substantial pessimism is required to overturn preference for human capital.
  - Inclusion of health as distinct human capital likely raises optimal allocation to human capital.

### Policy recommendations and model uses
- For most LICs (DIG‑Labor 1 environment), prioritize human capital investment (basic + upper‑level education) over pure infrastructure for long‑run growth and poverty reduction, provided:
  - concessional financing available to bridge gestation lags, and
  - policymakers accept short‑run fiscal and growth costs from delayed returns.
- Always fund adequate maintenance: restoring underfunded maintenance yields large immediate gains and raises long‑run returns.
- Use blended programs when short‑run political constraints require visible early gains or concessional financing is limited.
- Carefully manage fiscal space and sequencing:
  - Limit VAT increases and transfer cuts in the short run; seek concessional financing and tax base widening.
  - Monitor debt dynamics: peak public debt may rise substantially (e.g., to ~80percent of GDP in illustrative runs).
- Model extensions and future research:
  - Account for unemployment/underemployment of high‑skill labor, wage/productivity gaps between estate and smallholder agriculture, binding minimum wage laws.
  - Incorporate health explicitly into human capital.

### Selected numerical long-run results (increase of one percent of initial GDP — steady-state percentage deviations)
- Infrastructure investment (ε3 = 0.5):
  - GDP 4.6; C/NNI 3.8; k 3.9; CIC 0.52; qx 4.6; qn 4.8; qj 4.6; Pn -2.3; Pj -0.2; Ln 0.6; Lj -0.1; Lx 0; u 6.0; EAPG 5.5; wn/P 2.8; wj/P 5.5; ws/P 4.3; ΔT/GDP -0.35
- Basic education (ε3 = 0.5):
  - GDP 10.1; C/NNI 10.3; k 10.6; CIC 0.98; qx 9.5; qn 10.0; qj 11.3; Pn 0.1; Pj -2.3; Ln 5.2; Lj -0.7; Lx 0; u 5.8; EAPG 10.3; wn/P 5.2; wj/P 10.0; ws/P 10.1; ΔT/GDP 0.47
- Upper-level education (ε3 = 0.5):
  - GDP 6.2; C/NNI 6.5; k 2.7; CIC 0.25; qx 3.0; qn 10.1; qj 6.6; Pn -13.6; Pj -6.2; Ln -4.2; Lj -4.4; Lx -1.6; u 5.7; EAPG 18.0; wn/P 6.3; wj/P 12.0; ws/P -29.0; ΔT/GDP -0.64
- Note: solutions other than CIC, unemployment rate, and change in transfers are percentage deviations from the initial steady state.

### Maintenance findings (selected results)
- Gains from correcting underfunded maintenance:
  - Increasing maintenance spending by 0.49% of GDP (free-lunch component):
    - ε3 = 0.5: GDP 3.3; C/NNI 3.2; k 2.8; CIC 0.69; qx 3.2; qn 3.6; qj 3.0; Pn -1.5; Pj -0.1; Ln 0.7; Δu -0.2; wn/P ≈0; wj/P 3.8; ws/P 1.9; ΔT/GDP 3.8
  - Raising maintenance to optimal level (direct net fiscal cost 1.154% of GDP):
    - ε3 = 0.5: GDP 9.1; C/NNI 8.3; k 7.7; CIC 0.63; qx 8.8; qn 9.8; qj 8.6; Pn -4.3; Pj -0.3; Ln 1.7; Δu -0.4; EAPG 0.1; wn/P -0.06; wj/P 10.7; ws/P 5.3

### Big-Push program results (increase of four percent of initial GDP — long-run percentage deviations)
- All to infrastructure (ε3 = 0.5):
  - GDP 16.2; C/NNI 12.5; k 13.2; CIC 0.44; qx 15.9; qn 16.4; qj 16.2; Pn -7.3; Pj -0.6; Ln 1.6; Lj -0.3; Lx 0.1; u 5.9; EAPG 19.5; wn/P 9.4; wj/P 19.5; ws/P 14.6; ΔT/GDP -1.7
- All to basic education (ε3 = 0.5):
  - GDP 37.5; C/NNI 37.5; k 39.2; CIC 0.9; qx 35.0; qn 36.8; qj 42.5; Pn 0.4; Pj -7.5; Ln 17.8; Lj -2.3; Lx 0; u 5.4; EAPG 38.0; wn/P 18.3; wj/P 36.8; ws/P 37.3; ΔT/GDP 1.5
- Mixed (1% infrastructure, 2% basic, 1% upper; ε3 = 0.5):
  - GDP 33.0; C/NNI 33.2; k 28.7; CIC 0.72; qx 27.7; qn 38.1; qj 35.5; Pn -15.3; Pj -10.4; Ln 6.0; Lj -6.2; Lx -1.3; u 5.4; EAPG 49.7; wn/P 20.1; wj/P 40.9; ws/P -11.5; ΔT/GDP 0.1
- Mixed variants and ε3 = 5 cases reported with larger formal-sector expansions and different price/wage responses.

### Welfare sensitivity (examples)
- With Ru = Rb = 0.30 (ε3 = 5), welfare metric examples:
  - ζ = 0, iz share 0%: βs = 0.93 → 3.8; βs = 0.98 → 17.3
  - ζ = 2, iz share 0%: βs = 0.93 → 6.4; βs = 0.98 → 22.3
- With Ru = Rb = 0.20 (ε3 = 5), welfare metric examples:
  - ζ = 0, iz share 0%: βs = 0.93 → 1.8; βs = 0.98 → 11.7
  - ζ = 2, iz share 0%: βs = 0.93 → 4.4; βs = 0.98 → 16.3
- With Ru = Rb = 0.15 (ε3 = 5), welfare metric examples:
  - ζ = 0, iz share 0%: βs = 0.93 → 0.8; βs = 0.98 → 8.5
  - ζ = 2, iz share 0%: βs = 0.93 → 3.4; βs = 0.98 → 13.0

### Appendix A — Formal-sector wage premium and informal vs agriculture gaps
- Reported magnitudes of formal-sector wage premium in literature:
  - Low end: 10-30percent
  - Middle: 30-70percent
  - High end: 70-150percent
- Typical measurement: coefficient on formal employment dummy controlling for firm size and industry; wage variable often gross base wage or net of taxes/social security when data allow.
- Measurement distinctions:
  - Wage premium computed from formal dummy alone or including firm-size and industry dummies; the latter preferable because EW effects operate via firm size and industry.
  - Employer labor cost comparisons require pre-tax wage plus non-wage benefits; non-wage benefits can add 40-90percent of base wage in many countries (examples listed).
- Evidence on unobservable heterogeneity and compensating differentials (short answer: No — they do not explain most of the large formal premium):
  - Panel studies tracking movers across sectors affirm very large formal premiums (example: Funkhouser (1997b) finds 61:4percent for females and 107 percent for males in El Salvador).
  - High correlations of inter-industry wage differentials across occupations consistent with EW models.
  - Workplace conditions generally better in formal sector; inclusion of workplace controls often has no effect or increases measured premium.
- Heterogeneity of informal sector:
  - Two segments: salaried workers and self-employed.
  - Self‑employment accounts for 70-90percent of informal employment in most LICs.
  - In MICs and EMEs the two segments often equal in size or wage employment predominates.
- Evidence for efficiency wages in formal sector: Very strong. EWs also present in wage-employment sub-sector of informal sector.
- Agriculture vs informal productivity:
  - Gollin et al. (2014): mean APG for poorest quartile = 3.
  - Adjusted studies show smaller but meaningful gaps (e.g., average productivity gap in four countries = 1:58; Malawi/Uganda/Tanzania average = 1:82).
- Involuntary unemployment in LDCs: substantial, especially urban; unemployment reductions in EW models generate substantial welfare gains.

### Appendix A — study summaries and selected quantitative findings (selected examples)
- Badaoui et al. (2010): formal sector, net wage 0 controlling for firm size; 35.1% with firm size effect.
- Funkhouser (1997b): formal sector, unskilled labor premium 107% for males; 61.4% for females.
- Tansel and Kan (2012): net wage gap including firm size effect 28.9%; including firm size effects and payroll taxes 72.1%.
- Gollin et al. (2014): ratio of labor productivity non-agriculture vs agriculture — poorest quartile = 3.0; third quartile = 1.9; average = 2.6 (National Accounts data); average = 2.2 (microeconomic data).
- Multiple studies report firm-size premiums ranging widely (examples: Mizala and Romaguera 66.4% medium vs small; Teal 2017 reported 34-81%).

*Source: wpiea2020102-print-pdf (IMF).*

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

### wpiea2020102-print-pdf - References .............................................................................................................

### Model suite and purpose
- Presents three new models: DIG-Labor 1, DIG-Labor 2, and DIG-Labor 3, extending the DIG and DIGNAR frameworks to incorporate segmented labor markets and richer labor-market frictions.
- DIG-Labor features:
  - Formal sector: firms pay efficiency wages (EWs).
  - Agriculture: flexible wages.
  - Non-agricultural informal sector:
    - DIG-Labor 1 and 3: populated by own-account workers; labor in informal sector earns same return as in agriculture.
    - DIG-Labor 2: populated by wage employees; informal firms pay an EW below the formal-sector wage.
- Model applicability:
  - DIG-Labor 1: appropriate for most Low-Income Countries (LICs).
  - DIG-Labor 2: appropriate for most Middle-Income Countries (MICs) and Emerging Market Economies (EMEs).
  - DIG-Labor 3: appropriate for countries that suffer only from underemployment.
- New features across DIG-Labor models: skilled labor, public investment in human capital, maintenance investment vs. new infrastructure investment, sector-specific taxes on wages/profits/consumption.
- The models are supported by Dynare + MATLAB programs that are fully annotated and user friendly.

### Key empirical and structural premises
- Labor markets in developing countries are highly segmented; the textbook model of competitive, flex-wage labor markets applies in some cases but not broadly.
- Open unemployment and underemployment are prevalent in many LICs; perfect wage flexibility and integrated labor market assumptions in earlier DIG models are restrictive.
- Property rights on land are often insecure or non-existent; note: "80-95percent of land is untitled in most of Sub-Saharan Africa (Doss et al., 2015; Chen, 2017)."
- Eighty percent of the equations in DIG-Labor 1 carry over to DIG-Labor 2 and DIG-Labor 3; the main differences are labor-market specifications.

### Major quantitative findings on investment mix and impacts
- Partial-equilibrium and general-equilibrium comparisons for a 1 percent of GDP increase in public investment:
  - Investing 1 percent of GDP in basic education:
    - increases aggregate consumption by 10:2percent
    - increases real income of the poor by 10:3percent across steady states
  - Investing 1 percent of GDP in upper-level education (secondary + tertiary):
    - increases aggregate consumption by 9:3percent
    - increases real income of the poor by 18:1percent across steady states
  - Investing 1 percent of GDP in infrastructure:
    - increases aggregate consumption by 4:3percent
    - increases real income of the poor by 5:4percent across steady states
- Internal rate of return (base case assumptions):
  - Partial equilibrium (social) IRR for basic education: 12percent
  - Partial equilibrium (social) IRR for upper-level education: 10percent
  - Note: these IRRs map into partial equilibrium capital rentals ten percentage points above the rental for infrastructure in the base case.
- Sensitivity to lower IRRs:
  - Lowering IRR to 6:7percent for upper-level education and 7:6percent for basic education depresses long-run partial equilibrium capital rentals for both investments to 15percent, five percentage points below the capital rental for infrastructure.
  - Even with these reduced IRRs, the share of human capital in the optimal investment program is 40-65percent when the social discount rate equals or exceeds 0:96; it drops to 0-25percent at lower discount rates, but rises to 25-50percent if education is awarded 20 basis points as a merit good in equivalent variation welfare calculations.

### Intertemporal trade-offs and fiscal implications
- Investment in human capital has much larger long-run payoff but materializes with a 6- to 8-year lag; it takes 15+ years before net national income, the private capital stock, real wages for the poor, formal sector employment, etc., surpass outcomes from programs investing mainly in infrastructure.
- Big-push programs that emphasize human capital require more supporting fiscal adjustment because delayed growth delays endogenous revenue gains; increasing the share of human capital thus entails:
  - more fiscal adjustment to avoid explosive debt dynamics, and/or
  - tolerance of a higher debt trajectory for several decades.
- The optimal investment mix depends on:
  - the social discount rate,
  - the weight placed on distributional objectives in the social welfare function,
  - diminishing returns and complementarity between human capital and infrastructure,
  - the faster payoff of infrastructure.

### Welfare and optimal investment-share results (base-case characterization)
- The share of human capital in the optimal investment program:
  - Is on the order of 50-100percent in the base case.
  - In the base case, the optimal investment share is 50-75percent when the social discount rate is 0:93-0:96 (i.e., no more than three percentage points above the private discount rate (0:93)) and the weight on distributional objectives is not extreme.
  - At social discount rates above 0:96, the share for infrastructure drops to zero.
- Distributional impacts:
  - Investing in basic education increases growth more but reduces poverty less than investing in upper-level education.
  - Investing in upper-level education produces the largest gains for the ex ante poor because it converts some workers from unskilled/poor into high-skill/well-paid workers and raises productivity of those remaining low-skill through labor-market adjustments.

### Labor-market distortions, unemployment, and underemployment
- DIG-Labor 1-3 differ in distortions:
  - Open unemployment exists in DIG-Labor 1 and 2, but not in DIG-Labor 3.
  - Involuntary unemployment pervades the entire non-agricultural sector in DIG-Labor 2; in DIG-Labor 1 it is confined to the formal sector.
  - Underemployment exists in all three models: for any given unemployment rate (zero in DIG-Labor 3), aggregate labor productivity increases when labor moves from the informal to the formal sector or from agriculture to either non-agricultural sector.
- In DIG-Labor 1 and 3, labor in smallholder agriculture receives its marginal value product plus a share of implicit land rents; insecure property rights lower marginal productivity in agriculture and limit mobility-induced equalization.

### Policy implications and recommendations
- Policy makers evaluating big-push public investment programs should:
  - Account for the structure of the labor market (segmentation, EWs, unemployment, underemployment) when assessing macroeconomic effects of public investment scale-ups.
  - Consider the composition of investment (maintenance vs. new infrastructure vs. human capital) because composition affects growth, debt dynamics, inequality, poverty, and the supply of good jobs.
  - Recognize trade-offs between short/medium-term payoffs (infrastructure) and larger long-run gains (human capital), balancing fiscal adjustment needs against desired distributional outcomes.
  - Use the DIG-Labor suite (with accompanying Dynare + MATLAB tools) to quantify macroeconomic and distributional impacts tailored to country-specific labor-market structures.

### Model implementation and extensions
- Sections III and IV develop and calibrate DIG-Labor 1; Sections V-VII present policy experiments.
- DIG-Labor 1 material (and the DIG-Labor 2 and 3 full models) are accompanied by Dynare + MATLAB code; DIG-Labor 2 calibration guidance for MICs and EMEs is discussed.
- Possible future extensions include other labor market structures and a separate treatment of health in human capital; prior DIG extensions include energy sector, maintenance costs, climate-resilient infrastructure, and security spending.

*Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020102-print-pdf.pdf*

### Appendix A contains capsule summaries of 38 empirical estimates of the formal sector wage pre-

### wpiea2020102-print-pdf - Appendix A contains capsule summaries of 38 empirical estimates of the formal sector wage pre-

### Formal‑sector wage premium: evidence and magnitude
- The literature reports a ubiquitous and large formal sector wage premium with magnitudes reported as:
  - 10-30percent at the low end,
  - 30-70percent in the middle, and
  - 70-150percent at the high end.
- Typical empirical approach: coefficient on a dummy for formal employment controlling for firm size and industry category; wage variable typically gross base wage or net of taxes and employee social security contributions when data allow.
- Many studies report divergent results across countries and even across studies of the same country or same author; nevertheless the weight of evidence supports a large and common premium.

### Measurement, interpretation, and common misreadings
- Key measurement distinctions:
  - “Wage premium” can be computed from the formal dummy alone or from the formal dummy plus the firm‑size and industry dummies. The authors argue the latter is preferable because EW (efficiency wage) effects operate strongly via firm size and industry.
  - For allocative efficiency and firm cost comparisons, a second wage premium measure is needed: the pre‑tax wage plus all non‑wage benefits financed by the firm. Non‑wage benefits can add up to 40-90percent of base wage in many countries (examples cited: Egypt, Mexico, Colombia, Brazil, India, Zimbabwe, South Africa, Panama, and Bolivia).
- Examples that illustrate misinterpretation:
  - Matching/formal–informal propensity score methods may show the formal premium disappears, but adding firm size and payroll taxes can produce much larger employer labor cost gaps (examples: Argentina, Ecuador, Turkey).

### Evidence on unobservable heterogeneity and compensating differentials (Question 2)
- Short answer: No — unobservable heterogeneity and workplace conditions do not explain most of the large formal premium (subject to standard empirical uncertainty).
- Three types of rebutting evidence:
  - Panel studies tracking movers across sectors (the “gold standard”) affirm very large formal premiums (example: Funkhouser (1997b) finds low‑skill premium in El Salvador of 61:4percent for females and 107 percent for males).
  - High correlations of inter‑industry wage differentials across occupations are consistent with EW models but not with compensating differentials being the dominant cause.
  - Direct and indirect evidence shows workplace conditions generally better in the formal sector (access to phones, electricity, restroom facilities, running water, stability of income, lower injury rates); inclusion of workplace controls often has no effect or increases the measured formal premium (examples: Zimbabwe, Peru, Brazil).

### Heterogeneity of the informal sector (Question 3)
- The informal sector is heterogeneous with at least two segments:
  - Salaried workers (wage employment) and
  - Self-employed (micro‑enterprise owners, independent professionals, own‑account workers).
- Relative importance:
  - Self‑employment accounts for 70-90percent of informal employment in most LICs.
  - In MICs and EMEs, the two segments are often equal in size or wage employment predominates.
- Preferences and earnings:
  - Salaried informal workers typically prefer formal employment due to higher pay and better conditions.
  - Self‑employed responses are mixed; many in Latin America voluntarily work informally to maximize earnings or independence, but in many African countries self‑employed earn less than wage employees.

### Efficiency wages (EWs) and stylized facts (Questions 4–5)
- Strength of evidence for EWs in the formal sector: Very strong.
  - Empirical wage‑curve studies and stylized facts across many LDCs support EW models (firm‑size wage premiums starting at 5+ employees; stable inter‑industry differentials; high correlation of industry premiums across occupations; large formal vs informal premia; lower quit rates and longer tenure in formal sector).
- Are there EWs in the informal sector? Yes, but only in the wage‑employment sub‑sector.
  - Wage curves operate in both sectors but informal wages are generally more responsive to unemployment than formal wages (more flexible but not frictionless).
  - Firm‑size effects start very small (2-5 employees).
  - Empirical labor dynamics (e.g., Mexico, Argentina, Brazil) show large flows into/out of unemployment from salaried informal employment; in some countries (South Africa) job rationing in the informal sector is directly observed (80percent of unemployed report they could not find any work).
  - Minimum wage evidence: Contrary to a simple competitive story, raising minimum wages often does not flood the informal sector with laid‑off workers; informal sector employment often decreases and informal real wages typically increase (the “lighthouse effect”), consistent with EWs.

### Agriculture vs informal sector productivity (Question 6)
- Short answer: Probably — marginal value product of labor is likely lower in agriculture than in the informal sector, but recent research raises measurement doubts.
- Structural transformation literature and decomposition:
  - Gollin et al. (2014) find mean APG (agricultural productivity gap) for the poorest quartile = 3.
  - Newer work (Arthi et al. (2018), McCullough (2017)) questions large APG estimates due to overstated agricultural hours in surveys; adjusted evidence suggests smaller but still meaningful gaps (e.g., average productivity gap in four countries = 1:58; Malawi/Uganda/Tanzania average = 1:82).
- Implications and calculations:
  - Using illustrative parameters (e.g., `\`j = 0:8, PGAP_fj = 2, \`= 0:8-1`), an APG of 2 yields MVPL gaps in the range 1:33-1:67 consistent with country micro estimates.
- Unresolved puzzle: Why limited rural–urban migration and arbitrage if MVPL gaps are large? Explanations include social/family norms as exit barriers, transport/transactions costs, risk aversion & information asymmetries, low labor demand outside agriculture, and measurement issues. The literature remains unsettled.

### Involuntary unemployment in LDCs (Question 7)
- Short answer: A lot, especially in urban areas.
- Many LDCs show high unemployment rates concentrated in urban areas; some countries have national, rural, and urban unemployment rates all >10percent.
- Debate over “luxury unemployment”: semantic issue — unemployment may be voluntary relative to low informal wages but involuntary relative to formal wages. The important result: reductions in unemployment in EW models generate substantial welfare gains (first‑order), unlike trivial gains under frictionless markets.

### DIG‑Labor 1 model: key features (overview)
- Three sectors: tradables (x, agriculture), informal non‑tradable (j), formal non‑tradable (n).
- Inputs: capital k, low‑skill labor L, high‑skill labor S, public infrastructure z, sector‑specific land H for agriculture.
- Efficiency wages apply in the formal sector via effort function:
  - e_n;t = g_0 + g_1 ln(w_n;t / P_t) − g_2 ln(w_j;t / P_t) + g_3 u_t,
  - Firms choose w_n to satisfy Solow condition: @e_n/@ (w_n/P) * (w_n/P)/e_n = 1, yielding constant e_n in GE.
- Labor market structure:
  - Segmented: w_n > w_j ≥ w_x with rationing of formal jobs; agriculture/informal sector form an integrated flexible‑wage market.
  - Underemployment and open unemployment coexist: wages flexible in j and x, rigid in n.
- Public sector includes investment in infrastructure and human capital with lags:
  - Basic education lag = 6 years; upper‑level education lag = 8 years.
  - Public investment efficiency parameter s in [0,1] and absorptive capacity parameter ϵ for implementation cost overruns.

### Calibration highlights (base case and parameter choices)
- Consumption shares: formal good 40percent, informal good 20percent, imported consumer good 10percent, agricultural good 30percent.
- Intertemporal elasticity of substitution ρ = 0:40.
- Elasticities of substitution: "1 = 0:50, "2 = 0:5, "3 tested at 0:5 and 5 (affects tradability of formal good).
- Wage calibration:
  - Formal low‑skill wage w_n = 1; informal w_j = :60 (implies a mid‑range formal premium = 67percent).
  - Skilled wage w_s = 3.
- Factor shares (formal): β_n (capital share) = 0:50; θ_n (high‑skill share) = 0:30.
- Informal sector shares: β_j = 0:20; θ_j = 0:20 (yields high‑skill share ~6:3percent and informal share in non‑agricultural employment = 74:1percent).
- Agriculture shares: land 30percent, capital 20percent, high‑skill labor 5percent; shadow wage in agriculture w_x = 0:36 vs w_j = 0:60; agriculture employment share 59:5percent.
- Depreciation rates ϵ = 5percent (applies to private and public capital).
- Returns and rates:
  - Concessional + semi‑concessional loan real rate r_d = 1:3percent.
  - External commercial loan real rate r_dc ≈ 6percent.
  - Trend growth g = :023.
  - Base case formal sector premium mid‑range = 67percent (w_n = 1; w_j = :60).
- Education investment returns and lags:
  - Base IRRs: basic education IRR = 12percent (lag 6 years); upper‑level education IRR = 10percent (lag 8 years). Calibrated via R_b and R_u consistent with equations linking returns to general equilibrium responses.
- Q‑elasticity of investment ȷ = 2:5 (used to calibrate adjustment cost parameter v).
- Initial public/debt stocks:
  - Domestic debt b = 15percent of GDP (median LIC 2016).
  - Concessional + semi‑concessional external debt d = 32percent of GDP; external commercial debt dc = 6percent of GDP.
- Assumptions on tax base and VAT:
  - VAT rate h = 20percent; parameters g_j = 0:3 and g_x = 0:1 reflect limited VAT reach in informal/agriculture; g_m = 1 in base case.
- Maintenance and absorptive capacity:
  - Efficiency of public investment s = 1 (base case); absorptive capacity ϵ = 0 (no scaling constraint).

### Policy analysis: Public investment choices, maintenance, and big‑push programs
- Long‑run ranking of one‑percent of GDP increases in public investment:
  - Investment in basic education (IBE) strongly dominates investment in infrastructure (II) for long‑run GDP, formal employment, and real wages: IBE raises GDP, formal employment, and wages 2–2.5 times more than II.
  - Investment in upper‑level education (IUE) also strongly dominates II in long‑run effects; IUE reduces unemployment more and raises GDP, aggregate consumption, and poor incomes more than II.
  - Tradability of the formal good ("3) matters: when "3 = 5 (formal good highly substitutable with imports), IUE is far more powerful (formal sector expands and endogenous revenues can cover more of investment costs); when "3 = 0:5 (formal good non‑tradable), tax base erosion risk is larger.
- Maintenance underfunding: “free lunch” and large costs
  - Increasing maintenance can immediately raise Net National Product (NNP). Underfunding maintenance (e.g., raising depreciation to 7:46percent by cutting maintenance) makes return on maintenance R_mz > return on new investment and creates large gains from restoring maintenance.
  - Example: spending 1:64percent of GDP on maintenance eliminates the return gap and increases GDP by 9:1-10percent and aggregate consumption by 8:3-9:1percent; the “free‑lunch” component accounts for 35-39percent of total gains.
- Big‑push programs (permanent +4percent of initial GDP):
  - Pure infrastructure is much less effective in the long run than programs focused on human capital.
  - Mixed programs (some infrastructure + human capital) can dominate pure infrastructure in the medium run because education returns are delayed; the optimal mix depends on the policymaker’s social discount factor and weight on poverty reduction.
  - Marginal returns decline with scale but gross complementarity across infrastructure, basic education, and upper education raises the marginal return schedules of the other components.
- Transition path trade‑offs:
  - Human capital–heavy programs produce superior long‑run growth, structural transformation, and poverty reduction, but produce weak or negative short‑run development gains (first decade) and require substantial fiscal space and concessional financing because returns are delayed by lags (6–8 years).
  - Infrastructure‑heavy programs deliver faster short‑run gains but lower long‑run poverty reduction.
  - Blended programs mitigate extremes: less short‑run stagnation than pure human capital and better long‑run gains than pure infrastructure.
- Fiscal constraints and debt dynamics:
  - Limits on domestic fiscal adjustment (VAT increase ≤ 2 percentage points; transfers cut ≤ 1 percentage point of GDP in examples) make concessional external financing essential for feasibility of large PIPs.
  - In the base runs with generous concessional financing and some tax base widening, peak public debt rises to ~80percent of GDP in the human‑capital–only PIP (initial 55percent) and ~70percent in the infrastructure‑only PIP; reduced concessional access would render programs infeasible.
- Welfare calculations and optimal mixes:
  - Social welfare function used includes weight on ex‑ante poor income (EAPY) with parameter ψ and social discount factor _s.
  - Key results (baseline returns to education):
    - If social discount factor _s = private discount factor  = 0:93, optimal big‑push mixes include 25–50percent infrastructure.
    - If _s increases (e.g., 0:96–0:98) and/or policymaker places higher weight on poverty reduction (ψ ≥ 1), optimal share of infrastructure falls to ≤ 25percent and human capital dominates.
  - If returns to human capital are lower (IRRs reduced), optimal infrastructure share rises; but welfare surfaces are relatively flat so substantial pessimism is required to overturn preference for human capital.
  - Inclusion of health as a distinct component of human capital likely raises the optimal allocation to human capital due to complementarity and higher marginal returns.

### Policy recommendations and model uses
- For most LICs (DIG‑Labor 1 environment with EWs in formal sector only), prioritize human capital investment (basic + upper‑level education) over pure infrastructure for long‑run growth and poverty reduction, provided:
  - concessional financing is available to bridge long gestation lags, and
  - policymakers accept the short‑run fiscal and growth costs associated with delayed returns.
- Always fund adequate maintenance: restoring underfunded maintenance yields large immediate gains (free‑lunch component) and raises long‑run returns.
- Use blended programs (some infrastructure + human capital) when:
  - short‑run political constraints require visible early gains, or
  - access to concessional financing is limited.
- Carefully manage fiscal space and sequencing:
  - Limit VAT increases and transfers cuts in the short run; seek concessional financing and tax base widening to finance scaling up.
  - Monitor debt dynamics: peak public debt may rise substantially (e.g., to ~80percent of GDP in illustrative runs) and feasibility depends on concessional inflows and market access.
- Model extensions and future research priorities:
  - Expand DIG‑Labor family to account for unemployment/underemployment of high‑skill labor, wage/productivity gaps between estate and smallholder agriculture, and binding minimum wage laws.
  - Incorporate health explicitly into human capital to capture complementarities with education and to better estimate returns in LICs.

*Source: wpiea2020102-print-pdf (IMF).*

### References

### wpiea2020102-print-pdf - References

### Major datasets and empirical sources
- Unemployment rates: country-level and urban/rural breakdowns for multiple less-developed countries (Table 2). Example values preserved exactly:
  - Algeria 2013: National 9.8, Rural 8.1, Urban 10.6
  - Botswana 2010: National 17.9, Urban 9.8
  - Brazil 2009: National 8.4, Rural 3.4, Urban 9.3
  - India 2014: National 4.9, Rural 5.5, Urban 4.7
  - Mozambique 2012: National 22.6
  - Namibia 2014: National 28.1, Rural 30.2, Urban 26.2
  - South Africa 2012: National 24.7, Rural 28.0, Urban 24.3
  - Zambia 2012: National 7.8, Rural 3.3, Urban 14.2
- Sources cited for statistics: International Labor Office, World Economic Outlook, World Bank, CIA World Factbook, and National Statistical Offices (Labor Force Surveys, Censuses, Poverty Surveys, AIDS Surveys, and Household Surveys).

### Model structure and variants (DIG-Labor)
- DIG: two sectors, integrated labor market, full wage flexibility and full employment; no open unemployment or under-employment.
- DIG-Labor 1:
  - Involuntary unemployment in formal sector only.
  - EW → open unemployment.
  - Flex-wage; labor paid marginal value product plus share of land rents.
  - Own account workers: wage equals agricultural earnings.
- DIG-Labor 2:
  - Involuntary unemployment in entire non-agricultural sector.
  - EW → open unemployment.
  - Flex-wage; wage employees face an EW below formal sector wage → open unemployment.
  - Wage exceeds agricultural earnings.
- DIG-Labor 3:
  - EW, no open unemployment.
  - Flex-wage; own account workers: wage equals agricultural earnings.
- All DIG-Labor variants:
  - Underemployment: "For any given unemployment rate (even zero in DIG-Labor 3), aggregate labour productivity rises if labor moves from informal to formal sector or from agriculture to non-agriculture."
- Note: EW refers to Efficiency Wages.

### Calibration of the baseline model (selected parameters from Table 3)
- Consumption shares: γn = 0.40, γm = 0.10, γj = 0.20, γx = 0.30
- Intertemporal elasticity of substitution (τ) = 0.40
- Elasticities of substitution: ε1 = 0.5, ε2 = 0.5, ε3 = 0.5 (5)
- Wages: ws = 3, wn = 1, wj = 0.6
- Factor shares—formal sector: αn = 0.50, θn = 0.30
- Factor shares—informal sector: αj = 0.20, θj = 0.20
- Factor shares—agriculture: χ = 0.30, αx = 0.20, θx = 0.05
- Depreciation rates: δ = δz = δb = δu = 0.05
- Real interest rates: concessional rd = 0.013, external commercial rdc = 0.06, domestic bonds r = 0.10, private foreign loans rf = 0.10
- Trend growth rate (g) = 0.023
- Ratio of maintenance spending to GDP (Pzm/GDP) = 0.01644
- Ratio of infrastructure investment to GDP (Pziz/GDP) = 0.06
- Ratios of investment in education to GDP: Psi_b/GDP = 0.028, Psi_u/GDP = 0.012
- Ratio of domestic public debt to GDP (b/GDP) = 0.15
- Initial external debt ratios: bf/GDP = 0, d/GDP = 0.32, dc/GDP = 0.06
- q-elasticity of investment spending (Ω) = 2.5
- Share of new high-skill workers from low-skill pool Δxj = 0.80; fraction of new formal jobs filled from sector x-j ξ = 0.5
- Unemployment rate (u) = 0.06
- Elasticities of wages: g2 = 0.1, g3 = 0.5
- Returns to education: Ru = 0.30, Rb = 0.30
- Efficiency of public investment (s) = 1; absorptive capacity constraint (φ) = 0
- Return on infrastructure (Rz) = 0.20
- Interest elasticity of private capital flows (Γ) = 1
- Long-run debt targets: btarget = b0, dctarget = dc0
- Division of fiscal adjustment between expenditure cuts and tax increases (λ) = 0.5
- Residual financing of the fiscal gap (λdc) = 0.30
- Notes:
  - "Recall that the consumption VAT proxies for all indirect tax rates."
  - "For the assumed time lags, the internal rate of return is 12% for basic education and 10% for upper-level education."

### Long-run effects of increasing one component of public investment (Table 4) — Increase of One Percent of Initial GDP
- (a) Infrastructure investment (comparison for ε3 = 0.5 and ε3 = 5)
  - ε3 = 0.5:
    - GDP 4.6; C/NNI 3.8; k 3.9; CIC 0.52; qx 4.6; qn 4.8; qj 4.6; Pn -2.3; Pj -0.2
    - Ln 0.6; Lj -0.1; Lx 0; u 6.0; EAPG 5.5; wn/P 2.8; wj/P 5.5; ws/P 4.3; ΔT/GDP -0.35
  - ε3 = 5:
    - GDP 5.1; C/NNI 4.3; k 4.8; CIC 0.65; qx 4.1; qn 6.5; qj 5.0; Pn -1.7; Pj 0.2
    - Ln 2.3; Lj 0.6; Lx -0.4; u 5.9; EAPG 5.4; wn/P 2.7; wj/P 5.2; ws/P 5.4; ΔT/GDP -0.24
- (b) Investment in basic education (ε3 = 0.5 and ε3 = 5)
  - ε3 = 0.5:
    - GDP 10.1; C/NNI 10.3; k 10.6; CIC 0.98; qx 9.5; qn 10.0; qj 11.3; Pn 0.1; Pj -2.3
    - Ln 5.2; Lj -0.7; Lx 0; u 5.8; EAPG 10.3; wn/P 5.2; wj/P 10.0; ws/P 10.1; ΔT/GDP 0.47
  - ε3 = 5:
    - GDP 10.1; C/NNI 10.2; k 10.5; CIC 0.97; qx 9.6; qn 9.9; qj 11.3; Pn 0.1; Pj -2.4
    - Ln 5.1; Lj -0.8; Lx 0.1; u 5.8; EAPG 10.3; wn/P 5.2; wj/P 10.0; ws/P 10.0; ΔT/GDP 0.47
- (c) Investment in basic education with Rb = Rz = 0.20
  - ε3 = 0.5:
    - GDP 7.3; C/NNI 7.1; k 7.6; CIC 0.70; qx 6.8; qn 7.1; qj 8.6; Pn 0.1; Pj -1.7
    - Ln 3.6; Lj -0.1; Lx -0.2; u 5.9; EAPG 7.4; wn/P 3.8; wj/P 7.2; ws/P 7.3; ΔT/GDP 0.03
  - ε3 = 5:
    - GDP 7.3; C/NNI 7.0; k 7.5; CIC 0.70; qx 6.8; qn 7.0; qj 8.5; Pn 0.1; Pj -1.7
    - Ln 3.5; Lj -0.2; Lx -0.1; u 5.9; EAPG 7.4; wn/P 3.8; wj/P 7.2; ws/P 7.3; ΔT/GDP 0.03
- (d) Investment in upper-level education (ε3 = 0.5 and ε3 = 5)
  - ε3 = 0.5:
    - GDP 6.2; C/NNI 6.5; k 2.7; CIC 0.25; qx 3.0; qn 10.1; qj 6.6; Pn -13.6; Pj -6.2
    - Ln -4.2; Lj -4.4; Lx -1.6; u 5.7; EAPG 18.0; wn/P 6.3; wj/P 12.0; ws/P -29.0; ΔT/GDP -0.64
  - ε3 = 5:
    - GDP 9.1; C/NNI 9.3; k 8.4; CIC 0.77; qx 0.4; qn 20.8; qj 9.2; Pn -10.7; Pj -4.3
    - Ln 6.9; Lj -0.3; Lx -4.2; u 5.3; EAPG 18.1; wn/P 6.5; wj/P 10.7; ws/P -24.1; ΔT/GDP 0.02
- (e) Investment in upper-level education with Ru = Rz = 0.20 (ε3 = 0.5 and ε3 = 5)
  - ε3 = 0.5:
    - GDP 4.7; C/NNI 4.6; k 2.1; CIC 0.19; qx 2.2; qn 7.4; qj 5.4; Pn -10.4; Pj -4.6
    - Ln -3.2; Lj -2.9; Lx -1.3; u 5.8; EAPG 14.0; wn/P 4.7; wj/P 8.9; ws/P -22.6; ΔT/GDP -0.74
  - ε3 = 5:
    - GDP 6.9; C/NNI 6.7; k 6.4; CIC 0.59; qx 0.2; qn 15.4; qj 7.4; Pn -8.0; Pj -3.2
    - Ln 5.4; Lj 0.3; Lx -3.3; u 5.5; EAPG 13.9; wn/P 4.7; wj/P 7.8; ws/P -18.5; ΔT/GDP -0.23
- Note: "Solutions for all variables other than the crowding-in coefficient (CIC), the unemployment rate, and the change in transfers are percentage deviations from the initial steady state."

### The high cost of neglecting maintenance (Table 5)
- Gains are calculated relative to initial equilibrium where maintenance spending equals zero. Initial unemployment = 6.06% when ε3 = .5 and 6.19% when ε3 = 5.
- (a) "Gains from eating the free lunch" — increase in maintenance spending equals 0.49% of GDP when maintenance is at its optimal level (i.e., increase in maintenance spending is 49% as large as in Table 3).
  - ε3 = 0.5: GDP 3.3; C/NNI 3.2; k 2.8; CIC 0.69; qx 3.2; qn 3.6; qj 3.0; Pn -1.5; Pj -0.1
    - Ln 0.7; Δu -0.2; EAPG 0.1; wn/P ≈0; wj/P 3.8; ws/P 1.9; ΔT/GDP 3.8; o ≈0
  - ε3 = 5: GDP 3.6; C/NNI 3.4; k 3.5; CIC 0.84; qx 2.9; qn 4.8; qj 3.3; Pn -1.1; Pj 0.1
    - Ln 2.1; Δu 0.3; EAPG -0.3; wn/P ≈0; wj/P 3.7; ws/P 1.9; ΔT/GDP 3.6; o ≈0
- (b) "Maintenance spending increases to its optimal level"
  - Direct net fiscal cost equals 1.154% of GDP when maintenance at optimal level. Adjusting for endogenous tax revenue, net fiscal cost is 0.28% (0.38%) less than fiscal cost of increasing new infrastructure investment by 1% of initial GDP when ε3 = 0.5 (ε3 = 5) in Table 3.
  - ε3 = 0.5: GDP 9.1; C/NNI 8.3; k 7.7; CIC 0.63; qx 8.8; qn 9.8; qj 8.6; Pn -4.3; Pj -0.3
    - Ln 1.7; Δu -0.4; EAPG 0.1; wn/P -0.06; wj/P 10.7; ws/P 5.3; ΔT/GDP 10.6; o 8.4; ΔT/GDP -0.05
  - ε3 = 5: GDP 10.0; C/NNI 9.1; k 9.6; CIC 0.78; qx 7.9; qn 13.3; qj 9.4; Pn -3.1; Pj 0.3
    - Ln 5.6; Δu 1.0; EAPG -0.8; wn/P -0.19; wj/P 10.3; ws/P 5.2; ΔT/GDP 10.0; o 10.8; ΔT/GDP 0.18

### Long-run effects of Big-Push programs (Table 6) — Increase of Four Percent of Initial GDP
- (a) All investment to infrastructure
  - ε3 = 0.5: GDP 16.2; C/NNI 12.5; k 13.2; CIC 0.44; qx 15.9; qn 16.4; qj 16.2; Pn -7.3; Pj -0.6
    - Ln 1.6; Lj -0.3; Lx 0.1; u 5.9; EAPG 19.5; wn/P 9.4; wj/P 19.5; ws/P 14.6; ΔT/GDP -1.7
  - ε3 = 5: GDP 17.8; C/NNI 14.0; k 16.5; CIC 0.56; qx 14.4; qn 22.5; qj 17.7; Pn -5.6; Pj 0.4
    - Ln 8.0; Lj 1.9; Lx -1.4; u 5.7; EAPG 19.0; wn/P 9.4; wj/P 18.6; ws/P 18.8; ΔT/GDP -1.3
- (b) All investment to basic education
  - ε3 = 0.5: GDP 37.5; C/NNI 37.5; k 39.2; CIC 0.9; qx 35.0; qn 36.8; qj 42.5; Pn 0.4; Pj -7.5
    - Ln 17.8; Lj -2.3; Lx 0; u 5.4; EAPG 38.0; wn/P 18.3; wj/P 36.8; ws/P 37.3; ΔT/GDP 1.5
  - ε3 = 5: GDP 37.4; C/NNI 37.4; k 38.9; CIC 0.9; qx 35.1; qn 36.3; qj 42.4; Pn 0.3; Pj -7.6
    - Ln 17.3; Lj -2.4; Lx 0.1; u 5.4; EAPG 38.0; wn/P 18.3; wj/P 36.9; ws/P 37.0; ΔT/GDP 1.4
- (c) Investment in basic and upper-level education (2.67% and 1.33% of initial GDP)
  - ε3 = 0.5: GDP 35.5; C/NNI 36.4; k 31.0; CIC 0.72; qx 28.8; qn 41.4; qj 39.2; Pn -16.6; Pj -12.8
    - Ln 6.5; Lj -7.6; Lx -2.0; u 5.2; EAPG 54.5; wn/P 22.0; wj/P 44.7; ws/P -18.6; ΔT/GDP 0.3
  - ε3 = 5: GDP 40.2; C/NNI 40.8; k 39.8; CIC 0.92; qx 25.0; qn 58.0; qj 43.3; Pn -13.1; Pj -10.6
    - Ln 21.3; Lj -2.9; Lx -5.2; u 4.7; EAPG 55.1; wn/P 22.5; wj/P 42.7; ws/P -11.6; ΔT/GDP 1.3
- (d) Mixed: infrastructure, basic education, upper-level education increases of 1%, 2%, 1%
  - ε3 = .5: GDP 33.0; C/NNI 33.2; k 28.7; CIC 0.72; qx 27.7; qn 38.1; qj 35.5; Pn -15.3; Pj -10.4
    - Ln 6.0; Lj -6.2; Lx -1.3; u 5.4; EAPG 49.7; wn/P 20.1; wj/P 40.9; ws/P -11.5; ΔT/GDP 0.1
  - ε3 = 5: GDP 37.2; C/NNI 37.1; k 36.6; CIC 0.92; qx 24.2; qn 53.1; qj 39.1; Pn -12.1; Pj -8.4
    - Ln 19.8; Lj -1.8; Lx -4.3; u 4.9; EAPG 50.0; wn/P 20.1; wj/P 39.1; ws/P -4.6; ΔT/GDP 1.1
- (e) Mixed: increases 1.6%, 1.6%, 0.8% of initial GDP (infrastructure, basic, upper)
  - ε3 = .5: GDP 30.7; C/NNI 30.3; k 26.5; CIC 0.70; qx 26.3; qn 35.0; qj 32.6; Pn -14.3; Pj -8.8
    - Ln 5.5; Lj -5.3; Lx -1.0; u 5.5; EAPG 45.5; wn/P 18.5; wj/P 37.8; ws/P -7.0; ΔT/GDP -0.1
  - ε3 = 5: GDP 34.5; C/NNI 33.9; k 33.8; CIC 0.89; qx 23.1; qn 48.7; qj 35.9; Pn -11.2; Pj -6.9
    - Ln 18.3; Lj -1.1; Lx -3.8; u 5.0; EAPG 45.5; wn/P 18.8; wj/P 36.1; ws/P -0.2; ΔT/GDP 0.8

### Comparison of welfare gains (Tables 7–9) — sensitivity to returns to education and parameters
- Table 7: Base case Ru = Rb = 0.30 (ε3 = 5). Welfare metric with diminishing marginal utility; varying ζ (0,1,2), iz share (%) and βs values.
  - Examples (ζ = 0, iz share 0%): βs = 0.93 → 3.8; βs = 0.98 → 17.3
  - ζ = 2, iz share 0%: βs = 0.93 → 6.4; βs = 0.98 → 22.3
- Table 8: Ru = Rb = 0.20 (ε3 = 5). Welfare metric; examples:
  - ζ = 0, iz share 0%: βs = 0.93 → 1.8; βs = 0.98 → 11.7
  - ζ = 2, iz share 0%: βs = 0.93 → 4.4; βs = 0.98 → 16.3
  - Notes: when iz share equals zero, runs set ceiling on VAT at 0.22 and allow transfers to decrease by 1.5% of initial GDP; otherwise transfers cannot decrease more than 1% of initial GDP.
- Table 9: Ru = Rb = 0.15 (ε3 = 5). Welfare metric; examples:
  - ζ = 0, iz share 0%: βs = 0.93 → 0.8; βs = 0.98 → 8.5
  - ζ = 2, iz share 0%: βs = 0.93 → 3.4; βs = 0.98 → 13.0
  - Same debt-sustainability VAT and transfers constraints as Table 8.

### Transition-path figures (listed)
- Figures illustrate:
  - Figure 1: "Correcting Sub-Optimal Maintenance Is a Free Lunch."
  - Figure 2: "Relationship Between Marginal General Equilibrium Returns and the Impact of the Investment Mix on Long-Run Output."
  - Figure 3: "Transition Paths for All-Infrastructure and All-Human Capital (Education) Investment Programs." (Variables expressed as percentage deviations from initial steady state.)
  - Figure 4: "Transition Paths for All-Infrastructure and Mixed Investment Programs." (Variables expressed as percentage deviations from initial steady state.)

*Source: wpiea2020102-print-pdf - References (IMF working paper PDF content unit).*

### Appendix A.

### Appendix A. Formal Sector Wage Premium and the Earnings Gap Between the Informal Sector and Agriculture.

### Study summaries and estimation techniques
- Badaoui et al. (2010) — Ecuador, 1994. Excludes farmers and self-employed individuals. Propensity Score Matching.
- Heintz and Slonimczyk (2007) — Ghana, 1998-1999. Mincer earnings functions; no controls for selection bias.
- Schaffner (1998) — Peru, 1985-1986. Urban males. Earnings functions; no controls for selection bias. Controls for minimum wage law and unionization.
- Funkhouser (1997b) — El Salvador, 1991-1992. Urban workers. Panel data with premium computed for job changers vs. job stayers.
- Jaffry et al. (2006) — Pakistan, 1990/91-2003/04. Earnings functions; no control for self-selection. Estimates control for firm size.
- Mizala and Romaguera (1998) — Chile, 1985-1991. Earnings functions with firm size dummy variables.
- Funkhouser (1998) — Guatemala, 1989-1990. Private firms with 10+ workers in the capital city. Earnings functions.
- Tansel and Kan (2012) — Turkey, 2006-2009. Panel data set. Fixed effects estimates. Controls for self-selection, observable job and worker characteristics and unobservable individual effects.
- Funkhouser (1997a) — Guatemala, 1989. Earnings functions with and without Heckman 2-stage correction for selection bias.
- Gong and van Soest (2002) — Mexico, 1992-1993. Employment surveys. Dynamic random effects estimator controls for time-invariant heterogeneity.
- Kingdon et al. (2005) — Tanzania, South Africa, Ghana, Nigeria, and Kenya, 1992-2001. Labor force and household surveys. Earning function with controls for human capital characteristics.
- Heintz and Posel (2008) — South Africa, 2004. Earnings functions; no control for selection bias.
- Perry et al. (2007) — Latin America. Labor force surveys.
- Alcaraz et al. (2011) — Mexico, 2001-2004. Panel data restricted to urban workers in services and industry. Wage premium computed from job changers vs. stayers.
- Baskaya and Hulagu (2011) — Turkey, 2005-2009. Propensity Score Matching.
- Harati (2013) — Egypt, 2006. Sample restricted to wage earners. Earnings functions; no correction for selection bias.
- Gunther and Launov (2012) — Côte d’Ivoire, 1998. Urban population. Finite mixed regressions with controls for selection bias.
- Carneiro and Henley (2001) — Brazil, 1997. Nationally representative household survey. Earnings functions with Heckman 2-stage correction for selection bias.
- Fafchamps and Soderbom (2006) — 9 countries in SSA + Morocco, 1996-1998. Matched employer-employee data. Sample restricted to firms with 6+ employees.
- Lachaud (1995) — Burkina Faso, Cameroon, Mali, Côte d’Ivoire, 1986-1992. Household survey for large urban areas. Earnings functions with controls for human capital characteristics and selection bias.
- Kingdon et al. (2005) — South Africa, 1993-2002. Nationally representative household surveys. Earnings functions with correction for selection bias.
- Soderbom et al. (2005) — Kenya and Ghana, 1995-2000. Panel data for manufacturing. Fixed effects estimator; one-step GMM for Ghana.
- Pratap and Quintin (2006) — Argentina, 1993-1995, urban households in Greater Buenos Aires area. Propensity Score Matching.
- Thomas and Vallee (1996) — Cameroon. Controls for self-selection through multinomial logit first stage.
- Soderbom and Teal (2004) — Ghana, 1991-97. 7-year panel of plant-level data. Controls for human capital and firm characteristics.
- Aigbokhan (2011) — Nigeria, 1998-2000. Mincer earnings functions; no controls for selection bias.
- Falco et al. (2011) — Ghana and Tanzania, urban labor. Panel data with controls for endogenous sorting.
- Velenchik (1997) — Zimbabwe, manufacturing, 1993. Matched employer-employee data. Controls for compensating differentials and human capital characteristics.
- Teal (2017) — Ghana, firm-level panel data for 1962-2014. Controls for human capital characteristics and time-invariant unobservable effects.
- Gollin et al. (2014) — 72 LDCs. Controls for labor in agriculture doing non-agricultural work (and vice versa) and for differences in hours worked, human capital, cost of living, and public amenities.
- Bargain and Kwenda (2014) — Brazil, Mexico, and South Africa, urban males aged 15-65. Panel data. Fixed effects and propensity score matching.
- Tansel et al. (2015) — Egypt, 1998-2012. Panel data.
- Maloney and Ribeiro (1999) — Mexico, 1992. 2SLS with controls for firm characteristics and human capital (including training).
- Beagle et al. (2011) — Tanzania, 1992-2004. Data tracks migrants’ income and consumption. 2SLS with controls for many sources of unobserved heterogeneity.
- Manda (2002) — Kenya, 1993-1995. Manufacturing sector. Numerous controls for work conditions and observable firm and worker characteristics.
- Glinskaya and Lokshin (2005) — India, 1990-2000. Representative national survey restricted to wage employees. Three estimation methods including Propensity Score Matching.
- Marcelle and Strobl (2003) — Trinidad and Tobago, 1996-1998. National household survey. Sample: full-time private sector workers aged 15-70.
- Botelho and Ponczek (2011) — Brazil, 1995-2001. Panel data for six major metropolitan areas. Fixed-effect estimates.

### Reported wage premia and key quantitative findings
- Badaoui et al. (2010)
  - Formal sector, net wage: 0 controlling for firm size; 35.1% with firm size effect.
  - Formal sector, gross wage: 26.9% controlling for firm size; 47% with firm size effect.
- Heintz and Slonimczyk (2007)
  - Formal sector vs. informal wage: 73.7-111%.
  - Formal sector vs. agriculture, self-employment: 91.4-129%.
  - Formal sector vs. agriculture, wage employment: 148-335%.
  - Informal sector vs. agriculture (all workers): 31%.
- Schaffner (1998) — Firm size effect (%) vis-à-vis microenterprise
  - Blue Collar, Small: 15.0-19.8
  - Blue Collar, Medium: 23.9
  - Blue Collar, Large: 41.3-52.2
  - White Collar, Small: 39.2-53.3
  - White Collar, Medium: 70.1-92.5
  - White Collar, Large: 71.4-117.0
  - All, Small vs microenterprise: 28.3
  - All, Medium: 51.0
  - All, Large: 73.3
- Funkhouser (1997b)
  - Formal sector, unskilled labor: 107% for males; 61.4% for females.
- Jaffry et al. (2006)
  - Industry vs. agriculture: 35-49%.
  - Industry vs. services and food + textiles: 24-27%.
- Mizala and Romaguera (1998)
  - Firm size premium: Medium vs. small = 35%; Large vs. small = 66.4%.
- Funkhouser (1998)
  - Firm size premium: 26-50 employees = 4.8%; 51-100 employees = 36.9%; 101-500 employees = 10.4%; 500+ employees = 21.0%
  - Union wage premium = 43.5-57.3%.
- Tansel and Kan (2012)
  - No formal-informal sector wage gap for wages net of taxes payroll taxes when controlling for firm size.
  - Net wage gap including firm size effect: 28.9%
  - Wage gap including firm size effects and payroll taxes: 72.1%.
- Funkhouser (1997a)
  - Formal sector premium: No correction for selection: 69.6%. Heckman 2-stage correction: 77.9%.
- Gong and van Soest (2002)
  - Formal sector wage premium for educated workers:
    - High: male = 89%, female = 96%
    - Mid-level: male = 21%, female = 49.5%
  - No wage premium for low-education workers in the formal sector.
- Kingdon et al. (2005) (multiple countries)
  - Union wage premium: 3% in Kenya, 14% in Nigeria, 21% in Tanzania, 23% in South Africa, and 28% in Ghana.
  - Firm-size premium adds 37% in Ghana, 17% in Kenya, 30% in Nigeria, and 15% in Tanzania.
- Heintz and Posel (2008)
  - Formal vs. informal sector: 83.8-131.2%
  - Formal vs. agriculture: 143.8-172.6%
  - Informal vs. agriculture: 38.7-46.1%
- Perry et al. (2007)
  - Great majority of wage employees in the informal sector prefer work in the formal sector.
  - 30% of self-employed informal workers also prefer formal sector employment.
  - Colombia: great majority of both wage and self-employed informal workers prefer formal sector employment.
- Alcaraz et al. (2011)
  - Formal sector premium = 13.4%.
- Baskaya and Hulagu (2011)
  - Firm size premium: 10-24 employees = 17.8%; 25-49 employees = 19.7%; 50-249 employees = 28.3%; 250-499 employees = 36.8%; 500+ employees = 47.7%; Average = 30.1%
  - Formal sector premium controlling for firm size = 21.5% (2009).
  - Premium with average firm size effect = 51.6%.
- Harati (2013)
  - Formal sector premium = 38.8%.
- Gunther and Launov (2012)
  - Two-tiered informal labor market: fraction of workers who would be better off in formal sector twice the sector’s employment share.
- Carneiro and Henley (2001)
  - Union wage premium = 16% in the formal sector and 17.6% in the informal sector.
- Fafchamps and Soderbom (2006)
  - Doubling of employment increases wages 8-9%.
- Lachaud (1995)
  - Formal sector premium: Burkina Faso = 57.1%; Côte d’Ivoire = 40.9%; Cameroon = 60.3%; Mali = 9.6%.
- Kingdon et al. (2005) — South Africa, 1993-2002
  - Formal sector premium = 64%.
- Soderbom et al. (2005)
  - Firm size premium for 50 vs. 10 employees: Kenya = 13%; Ghana = 27.1%
- Pratap and Quintin (2006)
  - Firm size premium = 19.4-30.8%.
  - Size premium + payroll taxes paid by formal firms = 37-48.3%.
- Thomas and Vallee (1996)
  - Minimum wage laws generate wage gap in formal vs. informal sector of 38-65%.
- Soderbom and Teal (2004)
  - Wage premium for average firm size vs. micro firms (5 or fewer employees) = 47.6-59.3%.
- Aigbokhan (2011)
  - Firm size premium vs. micro enterprises:
    - Small = 28.6-47.1%
    - Medium = 83.2-109.6%
    - Large = 103.9-133.2%
- Falco et al. (2011)
  - Elasticity of earnings = .44-.46 with respect to firm size and .38-.50 with respect to number of employees.
- Velenchik (1997)
  - Firm size premium vs. small enterprises (1-10 employees):
    - Medium = 46.5%
    - Large = 76%
    - Very Large = 91.7%
- Teal (2017)
  - Firm size premium = 34-81%.
- Gollin et al. (2014)
  - Ratio of labor productivity in non-agriculture vs. agriculture:
    - Poorest quartile of LDCs = 3.0
    - Third quartile of LDCs = 1.9
    - Average = 2.6, National Accounts data
    - Average = 2.2, microeconomic data
- Bargain and Kwenda (2014)
  - Formal sector wage premium for two poorest quantiles:
    - In South Africa: 33.4-60%
    - In Mexico: 14-20%
    - In Brazil: 6.7-12%
- Tansel et al. (2015)
  - Formal sector premium = 20.7% (70.2% counting social security contributions of employers).
  - Premium for educated male workers = 27.8% (80.2% counting social security contributions of employers).
- Maloney and Ribeiro (1999)
  - At the 50th percentile, the firm size premium equals 39.1% for skilled workers and 75.1% for unskilled workers.
- Beagle et al. (2011)
  - Earnings premium for non-agriculture vs. agriculture = 41%.
- Manda (2002)
  - Firm-size premium vs. micro enterprises:
    - Small = 18-19%
    - Medium = 47-49%
    - Large = 59-68%
    - Very Large = 88-172%
- Glinskaya and Lokshin (2005)
  - Private formal sector wage premium vis-à-vis informal wage employment = 102-157%. (Informal sector = firms with less than ten employees.)
- Marcelle and Strobl (2003)
  - Firm-size effect raises the wage for unskilled workers 30% and the wage for skilled workers 61% (1-9 employees vs. 10+ employees).
- Botelho and Ponczek (2011)
  - Formal sector premium = 16% for the poorest quartile and 8.1% for the second quartile. No premium for the third and fourth quartiles. (Wage variable is net of taxes and estimates control for firm size.)

*Source: wpiea2020102-print-pdf - Appendix A.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020102-print-pdf.pdf_