## 2.1 Institutional Background (wpiea2026126-source-pdf)

## Source details

**Canonical URL:** [2.1 Institutional Background (wpiea2026126-source-pdf)](https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026126-source-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2026/english/wpiea2026126-source-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2026/english/wpiea2026126-source-pdf.pdf.json)

---

### Institutional reforms and minimum-wage policy
- Minimum wage set annually by the tripartite Comisión Nacional de los Salarios Mínimos (CONASAMI).
- 2016 constitutional reform decoupled the minimum wage from non-labor indexation uses (fines, loans, and collective bargaining provisions).
- Minimum-to-median wage ratio:
  - 29 percent in 2016.
  - Ratio raised to 60 percent through double-digit increases after 2018, including a 16.2 percent increase in 2019 and continued double-digit increases through 2025.
- Northern Border Free Zone (ZLFN):
  - Minimum wage doubled in the ZLFN; zone comprises 43 municipalities along the U.S. border.
  - ZLFN accounted for 7 percent of total employment in 2024.
  - ZLFN increase accompanied by tax incentives.
- Additional labor reforms:
  - 2019: transformed labor relations (secret-ballot union elections, independent labor courts, Federal Center for Labor Conciliation and Union Registration, legitimation of collective bargaining agreements by worker vote).
  - USMCA (effective 2020): strengthened labor provisions including requirements to maintain laws on minimum wages.
  - 2021: reform essentially banned domestic outsourcing.

### Data used in the analysis
- Primary data source: Encuesta Nacional de Ocupación y Empleo (ENOE), household labor market survey.
- Sample period: 2015Q1–2025Q4, excluding 2020 and excluding states in the Northern Border Free Zone (ZLFN).
- Sample restricted to respondents aged 16–55.
- Formal employment defined by enrollment in IMSS or ISSSTE as reported in ENOE.
- Income measurement and imputation:
  - Minimum wage defined at daily level; daily income calculated following Kumler et al.(2020) (details in Appendix A.1).
  - Non-response to income addressed using hotdeck imputation following Campos Vázquez(2013) (Appendix A.2).

### Empirical strategy and identification
- Treatment variation: differences in intensity of treatment across states ("bite") rather than statutory minimum-wage differences.
- Bite definition:
  - Bite_st = (Formal Workers Reporting Income ≤ Minimum Wage_st) / (Formal Workers_st).
- Initial-bite measure (gBite_s):
  - Constructed from 2016–17 income distribution compared with a hypothetical minimum wage at the 2019 minimum-to-median wage ratio; incomes inflated so each quarter has an aggregate median equal to the aggregate median income in 2019 (excluding NBFZ).
- Estimation equation (difference-in-differences with two-way fixed effects):
  - Y_st = α_s + γ_t + ∑_{y≠2017} β_y [gBite_s × 1_{ft=yg}] + X_st + ε_st.
  - α_s and γ_t are state and year-quarter fixed effects; β_y are year-specific coefficients; X_st is vector of baseline controls.
- Baseline controls and robustness devices:
  - Drought severity (state-quarter share of municipalities in moderate-or-worse drought).
  - Bartik-style manufacturing export-demand index (state 2013 industry mix and US industrial production growth).
  - Indicator for seven Special Economic Zones (active in 2018) and indicator for four southern-border states receiving VAT-rate reduction from 2021 onward.
  - Leave-one-out (LOO) shift-share controls aggregated from industry×occupation×age×sex×education cells using state's 2016–17 cell shares.
- Scaling and interpretation:
  - Outcomes other than the bite rescaled by IQR(gBite).
  - Rates in percentage points; log wages in log points.
  - Year-y coefficient on gBite × 1_{ft=yg} interpretable as effect of moving from 25th to 75th percentile of initial bite distribution.

### Geographic representation and 2020 survey suspension
- ENOE representative at state level; finer geographic distinctions not used.
- ENOE suspended in 2020Q2 and replaced by phone-based ETOE with different sampling; year-specific coefficients isolate yearly effects to avoid 2020 contamination.

### Key empirical findings: link between initial and realized bite
- By 2025, a one percentage point higher initial bite is associated with a 1.7 percentage point larger realized bite.

---

### Key empirical findings: labor-market quantities

- Employment measures:
  - Labor force participation, employment rate, and hours worked show no strong systematic relationship with minimum wage exposure overall, though some deterioration in labor force participation and hours appears by end of sample.
- Formalization:
  - Moving from the 25th to the 75th percentile of the initial bite distribution implies roughly a 0.25 percentage point decline in the formalization rate (marginally negative effect in later years; imprecise, small magnitudes).
- Population and migration:
  - Relative decline in population in more-exposed states starting in 2022; pattern consistent with either low-bite states attracting workers or high-bite states losing them.
  - Migration may ease local labor-market pressure; continued expansion of realized bite in high-exposure states suggests migration does not fully undo treatment.
- Subgroup heterogeneity:
  - Effects on formalization systematic only for women, with effect sizes roughly double the baseline.
- Robustness:
  - Main results confirmed using commuting zones as geographic unit (Online Appendix D.1).

---

### Key empirical findings: wages

- Bottom-decile formal-sector wages:
  - By 2025, moving from the 25th to the 75th percentile of the initial bite distribution is associated with roughly a 4 percent increase in the bottom-decile mean wage.
  - Estimates noisy but consistent across specifications.
- Decile effects (2025):
  - Minimum wage raised incomes for the first three deciles with little effect on higher deciles; effects similar across the bottom three deciles rather than concentrated at the very bottom.
- Wage distribution and sub-minimum reporting:
  - Income mass shifted from below minimum wage toward higher levels between 2018 and 2024, but substantial mass remains below the minimum wage.
  - Even among formal workers, many report sub-minimum-wage earnings.
  - Sub-minimum reporting more prevalent among individuals with lower educational attainment, employment in micro or unregistered firms, and work in agriculture or trade.
- Enforcement counterfactual:
  - Replacing sub-minimum-wage values with the minimum wage ("MW enforcement") increases estimated effects:
    - Effects on the bottom decile are more than two times as large.
    - Effects on the second decile are about 1.5 times as strong.
  - Interpretation: incomplete enforcement may explain muted concentration of wage effects at the very bottom and muted effects on labor-market quantities.
- Informal-sector spillovers:
  - Informal wages rise across the distribution (around 2 to 4 percent), but responses among informal employees are statistically indistinguishable from zero; broad-based gains concentrated among the self-employed and partly reflect fewer hours rather than higher wage rates.

---

### Modeling approach and calibration (overview)

- Purpose: interpret empirical findings and assess consequences of further increases via a quantitative general equilibrium model with heterogeneous firms, monopsony power, and endogenous selection into informality.
- Key model features (preserved notation and structure):
  - Households supply labor to firms; formal firms face payroll tax τ_L and corporate tax τ_Π and must pay at least the minimum wage W_t; informal firms avoid taxation and minimum wages but incur productivity losses captured by ϖ_h and size-dependent visibility (L_hit/L_h0t)^{-ϑ}.
  - Government collects taxes to finance exogenous expenditure G_t and lump-sum transfers T_t; of output lost by informal firms, share τ_I is collected as fines and fees.
  - Entry and exit: potential entrants pay φ_Et units of output; exit fraction ε; free entry condition φ_Et = 1 / ∑_{s=0} [(1-ε)/(1+r)]^s E_t[Π_it+s].
  - Equilibrium definitions: Competitive Equilibrium and Steady-State Competitive Equilibrium (constant inputs and constant prices/quantities).
- Partial equilibrium lemma:
  - Informal firms and unconstrained formal firms: employment elasticity with respect to minimum wage = 0.
  - Supply-constrained formal firms: elasticity = ε.
  - Demand-constrained formal firms: elasticity = −1/(1−ζ) (notation preserved).
- Key calibration values (representative household):
  - IES  = 2.00
  - Aggregate labor supply elasticity φ = 0.30
  - Firm-level labor supply elasticity ε = 2.00
  - Returns to scale 
 = 0.50
  - Interest rate r = 0.07
  - Exit rate  = 0.08
  - Detection elasticity  = 0.05
  - Corporate tax rate  = 0.30
  - Labor taxes W = 0.10
  - Personal income tax ~W = 0.10
  - Informality cost parameter I = 0 (baseline)
  - Government consumption G_t = 0
- Internal calibration results (representative household):
  - Pareto tail parameter  = 1.98
  - Taste for productivity  = 1.22
  - Informal disutility shifter !I = 1.07
  - Detection intercept  = 0.11
  - Entry costs φ_E = 9.72
- Moment targets matched exactly:
  - Top Employment Share: Target 0.32, Model 0.32
  - Top Wage Share: Target 0.58, Model 0.58
  - Informality Rate: Target 0.55, Model 0.55
  - Formal wage premium: Target 0.01, Model 0.01

---

### Counterfactual analysis: minimum wage scenarios and quantitative results

- Two exercises:
  - Current minimum wage: set W to match minimum wage coverage of 8% in the formal sector (2024 Mexico).
  - +20% productivity-adjusted minimum wage: increase by 20 percent (Plan México target through 2030 adjusted for 4% labor productivity growth).
- Reporting setups: with and without free entry; with fixed sectoral distribution (short vs long adjustment horizons).
- Key results (Table 2; differences from baseline reported in percent except shares which are percentage points):

  - Constant Types, No Entry, Current vs +20%:
    - Output: 0.02 ; 0.58
    - Consumption: 0.02 ; 0.90
    - Productivity: -0.02 ; -0.50
    - Employment: 0.08 ; 2.18
    - Informality Rate: -0.10 ; -2.15
    - Minimum Wage Bite: 8.85 ; 39.68
    - Wages: 0.07 ; 1.95

  - Constant Types, Free Entry, Current vs +20%:
    - Output: -0.06 ; -1.06
    - Consumption: -0.02 ; -0.49
    - Productivity: -0.08 ; -1.18
    - Employment: 0.04 ; 0.25
    - Informality Rate: 0.30 ; 4.50
    - Minimum Wage Bite: 8.00 ; 28.38
    - Wages: 0.06 ; 0.96

  - Flexible Types, Free Entry, Current vs +20%:
    - Output: -0.10 ; -1.67
    - Consumption: -0.04 ; -0.85
    - Productivity: -0.08 ; -1.22
    - Employment: 0.04 ; 0.20
    - Informality Rate: 0.30 ; 4.66
    - Minimum Wage Bite: 8.05 ; 28.8
    - Wages: 0.03 ; 0.47

- Interpretation of +20% scenario (flexible sector assignment):
  - Informal share rises by 5 percentage points.
  - Minimum wage coverage among remaining formal workers reaches 28.4 percent (minimum wage bite in Table 2).
  - Output and consumption decline by around 1 percent; productivity falls by about 1.2 percent in some specifications due to lower average productivity as firms migrate to informality.
  - Overall employment rises by 0.5 percent driven by expansion of supply-constrained formal firms and a wealth effect inducing households to work more; part of new employment shifts into informal sector.
  - Wages rise: 7 percent formal, 2.4 percent informal (aggregate wage growth 0.9 percent); informal wage increase reflects compositional shifts rather than competitive spillovers.
  - Inequality increases: compression in the formal sector more than offset by rising inequality within the expanding informal sector.
  - Welfare falls by 1.6 percent in consumption-equivalent terms (representative household) in the flexible, +20% scenario.

- Mechanism highlighted:
  - Many marginal firms find formality costlier and switch into informality as the minimum wage rises; informality provides an escape margin but finite capacity leads to strong deterioration at higher wage floors.
  - When firms cannot switch into informality (constant sector assignment), higher minimum wages increase output and worker welfare because supply-constrained firms expand hiring—informality therefore limits gains from minimum wage policy.

---

### Welfare, distributional outcomes, and heterogeneity

- Aggregate welfare:
  - Representative-household welfare loss from +20% scenario about 1.6 percent (consumption-equivalent).
- Heterogeneous-household results (four education types):
  - Welfare losses largest for households at extremes of the skill distribution (low- and high-education).
  - Intermediate-education households:
    - Experience wage gains and increased employment but still net welfare declines because higher labor income does not fully offset lower transfers and profits; consumption falls.
  - Low-education households:
    - Largely informal and do not benefit from wage increases; they lose from falling transfers.
  - High-education households:
    - Earn well above the minimum wage but suffer indirectly as expanding informality erodes tax base and transfers.
  - Net effect: welfare declines for all types, with regressivity—low-skill households gain no wage increase yet lose from fiscal contraction.

---

### Robustness checks, alternative assumptions, and mechanisms

- Monopsony power (ε):
  - Recalibration with ε = 4 (weaker monopsony) yields smaller welfare losses from higher minimum wages.
- No informal sector:
  - Without informality, employment increases more strongly and wage inequality declines; output and productivity fall by more; aggregate welfare losses similar in magnitude but incidence shifts toward capitalists.
- Informality penalties as redistributable tax (I = 1):
  - If informality penalties are fines redistributed by government, welfare losses attenuate: output falls less and transfers decline less.
- Wealth effects:
  - General equilibrium wealth effects substantially shape outcomes: declining profits and transfers induce households to work more, attenuating output declines but amplifying employment responses.
- Quantitative sensitivity (selected table entries preserved from Table G.6):
  - Impact of distortions (differences from baseline; preserved entries):
    - Output: 0.78, -19.94, 47.0, 17.6
    - Consumption: -2.42, -9.52, 59.14, 44.4
    - Productivity: 5.32, 0.00, 5.32, 25.32
    - Employment: 1.68, 6.75, 3.79, 10.7
    - Informality Rate: -55.0, 0.00, -55.0, -55.0
    - Wages: -6.64, 12.56, 3.08, 3.4
    - Representative Household welfare: -2.12, -12.85, 8.03, 8.0
    - Workers: 3.18, 7.89, 38.15, 59.5
    - Capitalists: -9.94, -40.08, 87.61, 2.6
- Empirical robustness:
  - Results robust to commuting-zone analyses where feasible; ENOE representativeness caveats noted.
  - ENOE vs IMSS comparison:
    - ENOE (Daily): fraction earning ≤ 1 MW rises from close to 1% in 2016 to around 10% in 2024; IMSS remains stable around 1%.
    - ENOE and IMSS fractions earning ≤ 2 MW converge by 2024; ENOE increases faster from below 20% to coincide with IMSS near 60%.
    - Quarterly ENOE jumps in Q1 align with statutory January minimum wage increases; IMSS shows smaller, more stable jumps.
  - Interpretation: patterns consistent with reporting differences and partial non-compliance; no direct proof of misreporting source.

---

### Main takeaways

- Informality constrains minimum wage policy through limited coverage (many low-wage workers are informal) and an escape margin for firms.
- At current minimum wage levels, the escape margin is narrow and labor market effects are muted.
- Substantial increases (e.g., +20 percent productivity-adjusted) can:
  - Raise informality by ~5 percentage points.
  - Reduce productivity by ~1.2 percent in some specifications.
  - Raise employment modestly (about 0.2–0.5 percent) but shift jobs into lower-productivity informal arrangements.
  - Increase inequality and lower welfare (representative-household welfare loss ~1.6 percent).
- Distributional outcome is regressive: low-skill households (primarily employed informally) do not benefit from higher wage floors and lose from reduced transfers as informality erodes the tax base.
- Policy implication: effective redistribution in economies with large informal sectors may require complementary policies that expand formal employment or strengthen support for informal workers; the informality margin limits the gains from minimum wage increases.

*Source: Excerpt from "2.1 Institutional Background" and "3.2 Equilibrium" (wpiea2026126-source-pdf).*

### 2.1  Institutional Background

### 2.1 Institutional Background

### Institutional reforms and minimum-wage policy
- Minimum wage set annually by the tripartite Comisión Nacional de los Salarios Mínimos (CONASAMI).
- A 2016 constitutional reform decoupled the minimum wage from non-labor indexation uses (fines, loans, and collective bargaining provisions), allowing it to function as an independent labor policy instrument.
- With the minimum-to-median wage ratio at 29 percent in 2016, policy shifted toward raising its real value.
- CONASAMI accelerated adjustments after the 2018 election, raising the national minimum wage by 16.2 percent in 2019 and maintaining double-digit increases through 2025, bringing the ratio to 60 percent.
- Northern Border Free Zone (ZLFN): the minimum wage doubled in the ZLFN; the zone comprises 43 municipalities along the U.S. border and accounted for 7 percent of total employment in 2024. The ZLFN increase was accompanied by tax incentives.
- Additional labor reforms:
  - 2019 reform transformed the labor relations system (guaranteeing secret-ballot union elections and establishing independent labor courts; creation of the Federal Center for Labor Conciliation and Union Registration and mandated legitimation of existing collective bargaining agreements through worker votes).
  - USMCA (effective 2020) strengthened labor provisions relative to NAFTA, including requirements to maintain laws on minimum wages.
  - 2021 reform essentially banned domestic outsourcing.

### Data used in the analysis
- Primary data source: Encuesta Nacional de Ocupación y Empleo (ENOE), household labor market survey.
- Sample period: 2015Q1–2025Q4, excluding 2020 due to Covid-related survey disruptions and excluding states in the Northern Border Free Zone (ZLFN).
- Sample restricted to respondents aged 16–55.
- Formal employment defined by enrollment in the IMSS or ISSSTE social security systems, as reported in ENOE.
- Income measurement:
  - Minimum wage defined at daily level while income reported monthly; daily income calculated following Kumler et al.(2020) (details in Appendix A.1).
  - Non-response to income questions addressed using hotdeck imputation following Campos Vázquez(2013) (Appendix A.2).

### Empirical strategy and identification
- Treatment variation exploited: differences in intensity of treatment across states (minimum-wage "bite") rather than cross-state differences in the statutory minimum wage.
- Bite definition:
  - Bite_st = (Formal Workers Reporting Income ≤ Minimum Wage_st) / (Formal Workers_st). (Equation (1))
- Initial-bite measure (gBite_s):
  - Constructed from 2016–17 income distribution for each state compared with a hypothetical minimum wage at the 2019 minimum-to-median wage ratio; held constant throughout estimation.
  - In practice, incomes in the 2016–17 sample are inflated so each quarter has an aggregate median equal to the aggregate median income in 2019 (excluding the NBFZ), then compared to the actual 2019 minimum wage.
- Estimation equation (difference-in-differences with two-way fixed effects):
  - Y_st = α_s + γ_t + ∑_{y≠2017} β_y [gBite_s × 1_{ft=yg}] + X_st + ε_st. (Equation (2))
  - α_s and γ_t are state and year-quarter fixed effects; β_y are year-specific coefficients; X_st is vector of baseline controls.
- Baseline controls and robustness devices:
  - Controls for non-policy shocks: drought severity (state-quarter share of municipalities in moderate-or-worse drought) and a Bartik-style manufacturing export-demand index (state 2013 industry mix and US industrial production growth).
  - Controls for confounding policies: indicator for seven Special Economic Zones (2016–19 program, active in 2018) and indicator for four southern-border states that received a VAT-rate reduction from 2021 onward.
  - Leave-one-out (LOO) shift-share controls: for each state s, construct cell-level (industry×occupation×age×sex×education) shifts using national outcomes excluding s, then aggregate using the state's 2016–17 cell shares. Outcomes covered: employment rates, hours worked, formality rates, full-time formality rates, and formal-sector log wages. Preferred specification (baseline) adds these LOO controls to X_st.
- Scaling and interpretation:
  - Outcomes other than the bite are rescaled by the interquartile range of the initial bite distribution, IQR(gBite).
  - Rates are expressed in percentage points; log wage outcomes are in log points.
  - The year-y coefficient on gBite × 1_{ft=yg} is interpretable as the effect of moving from the 25th to the 75th percentile of the initial bite distribution.
- Additional robustness: interactions of initial state characteristics (shares young, low-skilled, urban, average age) with year fixed effects (Appendix D.2); grouped design allowing non-linear dose-response (Online Appendix F). Effects concentrated among most-exposed states, consistent with nonlinearity.

### Controls for potential bias and geographic representation
- ENOE only representative at the state level; finer geographic distinctions not used because of representativeness constraints.
- 2020 ENOE suspension: ENOE suspended in 2020Q2 and replaced by phone-based ETOE with different sampling; year-specific coefficients isolate each year's effect to avoid contamination from 2020 spillovers.

### Key empirical findings: labor market quantities
- The initial bite strongly predicts the realized bite; by 2025, a one percentage point higher initial bite is associated with a 1.7 percentage point larger realized bite.
- Employment measures (labor force participation, employment rate, hours worked) show no strong systematic relationship with minimum wage exposure, though some deterioration in labor force participation and hours appears by end of sample.
- Formalization: marginally negative effect in later years; estimates imprecise and magnitudes small:
  - Moving from the 25th to the 75th percentile of the initial bite distribution implies roughly a 0.25 percentage point decline in the formalization rate.
- Population: relative decline in population in more-exposed states starting in 2022; pattern consistent with either low-bite states attracting workers or high-bite states losing them. Migration may ease local labor-market pressure; continued expansion of realized bite in high-exposure states suggests migration does not fully undo treatment.
- Subgroup analysis (Appendix A.4): effects on formalization are systematic only for women, with effect sizes roughly double the baseline.
- Robustness: main results confirmed using commuting zones as geographic unit (Online Appendix D.1).

### Key empirical findings: wages
- Bottom-decile formal-sector wages:
  - Higher minimum wage exposure associated with faster growth in the bottom-decile mean wage; estimates noisy.
  - By 2025, moving from the 25th to the 75th percentile of the initial bite distribution is associated with roughly a 4 percent increase in the bottom-decile mean wage.
  - Results consistent across specifications.
- Decile analysis (2025): minimum wage raised incomes for the first three deciles with little effect on higher deciles; effects similar across the bottom three deciles rather than concentrated at the very bottom.
- Wage distribution and sub-minimum reporting:
  - Figure evidence: shift of income mass from below the minimum wage toward higher levels between 2018 and 2024, but a substantial mass remains below the minimum wage.
  - Even among formal workers, many report sub-minimum-wage earnings.
  - Sub-minimum-wage reporting more prevalent among individuals with lower educational attainment, employment in micro or unregistered firms, and work in agriculture or trade (Table A.4).
- Enforcement counterfactual:
  - Replacing sub-minimum-wage values with the minimum wage ("MW enforcement" line) increases estimated effects:
    - Effects on the bottom decile are more than two times as large.
    - Effects on the second decile are about 1.5 times as strong.
  - Interpretation: incomplete enforcement may explain muted concentration of wage effects at the very bottom and muted effects on labor-market quantities.
  - Model-based counterfactuals assume full enforcement and thus describe effects of a binding minimum wage.
- Informal sector spillovers:
  - Informal wages rise across the distribution, but responses among informal employees are statistically indistinguishable from zero.
  - Broad-based gains concentrated among the self-employed and partly reflect fewer hours rather than higher wage rates (Appendix A.5).

### Modeling approach (overview)
- Purpose: interpret empirical findings and assess consequences of further increases via a quantitative general equilibrium model with heterogeneous firms, monopsony power, and endogenous selection into informality.
- Key features:
  - Households:
    - Countable set H of representative households indexed by h, each with mass s_h of workers.
    - Households supply labor L_hit to a mass M_t of firms indexed by i.
    - Firms operate in informal sector M_Iht or formal sector M_Fht.
    - Workers earn firm-specific wages W_hit and pay tax rate ~τ on formal sector labor income; informal sector avoids taxation.
    - Households own shares ζ_h of firms with associated profits Π_t and receive share ~s_h of government transfers T_t.
    - Per-worker consumption C_ht financed by transfers, profits, and labor income net of taxes: s_h × C_ht = ~s_h × T_t + ζ_h × Π_t + ∫_{M_Iht} W_hit × L_hit di + (1-~τ_L) ∫_{M_Fht} W_hit × L_hit di. (Equation (3))
    - Utility: King-Plosser-Rebelo form with labor supply elasticity φ, labor supply shifter !_Lh, intertemporal elasticity of substitution ψ, labor disutility v(L_ht) specified with CES aggregation across firm-level employment and parameters ε (labor supply elasticity across firms) and ζ (preference for high-productivity firms); informal sector weight !_Ih. (Equation (4))
  - Firms:
    - Production: Y_it = ∑_h Y_hit with Y_hit = A_it × ϖ_h × L_hit (Equation (5)).
    - Productivity A_it Pareto-distributed with location parameter A_0t and shape parameter κ: F(A_it) = 1 - (A_0t / A_it)^κ. (Equation (6))
    - Formal firms:
      - Face payroll tax τ_L and corporate tax τ_Π; must pay at least the minimum wage W_t.
      - Formal profits: Π^F_hit = (1-τ_Π) × max{ Y_hit - (1+τ_L) × W_hit × L_hit s.t. L_hit ≤ L_S^F_ht(W_hit) and W_hit ≥ W_t }. (Equation (7))
    - Informal firms:
      - Face no taxation or minimum wages but lose fraction 1 - (1-ϖ_h)(L_hit/L_h0t)^{-ϑ} of output (L_h0t employment at smallest informal firm).
      - Baseline rate ϖ_h captures common losses (inspections, detection avoidance, limited contract enforcement, restricted finance).
      - Size-dependent visibility term (L_hit/L_h0t)^{-ϑ} captures larger firms being more visible; less productive firms sort into informality.
      - Informal profits: Π^I_hit = max{ (1-ϖ_h)(L_hit/L_h0t)^{-ϑ} × Y_hit - W_hit × L_hit s.t. L_hit ≤ L_S^I_ht(W_hit) }. (Equation (8))
    - Sector choice: Π_it = ∑_h max{Π^F_hit, Π^I_hit}. (Equation (9))
  - Government and budget constraint:
    - Government collects taxes to finance exogenous expenditure G_t and redistributes remainder as lump-sum transfers T_t.
    - Of output lost by informal firms, share τ_I is collected as fines and fees; the rest is deadweight loss.
    - Transfers and government budget: T_t + G_t = τ_Π (1-τ_Π) × ∑_h ∫_{M_Fht} Π_hit di + (~τ_L + τ_L) × ∑_h ∫_{M_Fht} W_hit × L_hit di + τ_I × ∑_h ∫_{M_Iht} (1 - (1-ϖ_h)(L_hit/L_h0t)^{-ϑ}) Y_hit di. (Equation (10))
  - Entry, exit, and market clearing:
    - Potential entrants pay φ_Et units of output to draw productivity; fraction ε of firms exit exogenously.
    - Free entry condition: φ_Et = 1 / ∑_{s=0} [(1-ε)/(1+r)]^s E_t[Π_it+s]. (Equation (11))
    - Law of motion for firms: M_{t+1} = (1-ε) M_t + M_Et. (Equation (12))
    - Product market clearing accounts for informality losses and entry costs (Equation (13)).
  - Equilibrium definitions:
    - Competitive Equilibrium: vector of prices {W_ht, W_hit}_i∈M_t and quantities that satisfy optimization and market clearing for given sequences {G_t, W_t, A_it} and initial conditions {M_0, A_0}.
    - Steady-State Competitive Equilibrium: competitive equilibrium with constant inputs {G, W, A_i} and constant prices and quantities over time.

*Source: Excerpt from "2.1 Institutional Background" (wpiea2026126-source-pdf).*

### 3.2  Equilibrium

### 3.2 Equilibrium

### Equilibrium characterization and assumptions
- Assumption 1: The parameters satisfy f; ; 
+g2(0;1).
- Market structure: Firms choose formality/informality and hiring given a minimum wage; profit maximization is concave under the maintained parameter assumptions.
- Informality occurs only among the least productive firms; formal firms split into three types by productivity:
  - Demand-constrained formal firms: productivity too low to hire all workers willing to work at the minimum wage.
  - Supply-constrained formal firms: pay the minimum wage, hire all willing workers, with employment exceeding the unconstrained optimum.
  - Unconstrained formal firms: pay above the minimum wage and exercise monopsony power.

### Key propositions and lemma
- Proposition 1:
  - There exist productivity thresholds A_F h;t and A_F h;t such that formal firms are:
    - labor demand constrained for A_it  A_F h;t,
    - labor supply constrained for A_it 2 (A_F h;t ; A_F h;t),
    - unconstrained for A_it  ; A_F h;t,
  - Expressions:
    - A_F ht = (1 + L  h 
A (1
) 0t )^{1/(1(1
))} (W_t)^{(1+ε(1
))/(1(1
))} (W_ht (1~L))^{-ε(1
)/(1(1
))}
    - A_F ht = (1 + 1/ε)^{1/(1(1
))} 
A_F ht
  - There exists a threshold A_I;t such that all firms below the threshold choose to operate informally.
  - All thresholds are weakly increasing in the minimum wage.
- Proposition 2:
  - At least some firms choose to operate informally if
    1 1 (1 ) 1~ 
 (T_L ! I ) ~ with T_L = 1 + L 1~L and ~
 = 1 + 1/ε .
- Lemma 1 (partial equilibrium elasticities of employment wrt the minimum wage, holding aggregates and cutoffs constant):
  - Informal firms: elasticity = 0
  - Unconstrained formal firms: elasticity = 0
  - Supply-constrained formal firms: elasticity = ε
  - Demand-constrained formal firms: elasticity = 1/(1 )

### Partial equilibrium implications (illustrated by Figures 7–8)
- In the informal sector, employment and wages are log-linear in productivity.
- In the formal sector, the minimum wage generates a piecewise employment policy across the three firm types described above.
- Employment-productivity gradient ordering: steepest for demand-constrained, shallowest for unconstrained.
- Supply-constrained firms hire more than the level implied by interpolating unconstrained firms—minimum wage raises labor demand for these firms.
- Minimum wage increases from low levels:
  - First create supply-constrained firms (employment strictly increasing in minimum wage in partial equilibrium).
  - Demand-constrained firms exist only if supply-constrained firms exist (given monopsony power).
  - Informality shifts rightward, expanding the informal sector via selection; the effect on formal employment is ambiguous (rising for supply-constrained, falling for demand-constrained); formal wages rise unambiguously.

### Pareto properties for unconstrained formal firms (calibration targets)
- Proposition 3 (shares of formal employment and wage bill for top P percent of unconstrained formal firms):
  - L_P = P^{11/(1+ /ε) (1+1/ε
)}
  - W B_P = P^{11/(1+1/ε+ /ε) (1+1/ε
)}
- Special case  = 0 yields:
  - ε = (1ln(L_P/P)) / (ln(L_P/P)ln(W B_P/P))
- Use of these moments plus 
 and ε pins down  and ; allowing  > 0 helps match observed dispersion.

### Calibration (representative and heterogeneous households)
- Household setups:
  - Representative household.
  - Heterogeneous households with four education types; parameters differing by type: relative skill supplies {_h}, detection intercepts {_h}, relative disutility of informality {!Ih}, labor supply intercepts {!Lh}.
  - Normalizations: _1 = 1 and !L1 = 0:3.
- External calibration choices and values (representative household):
  - Intertemporal elasticity of substitution  = 2.00
  - Aggregate labor supply elasticity φ = 0.30
  - Firm-level labor supply elasticity ε = 2.00 (markdown estimates for Mexican firms)
  - Aggregate labor supply shifter φ = 0.30
  - Returns to scale 
 = 0.50 (consistent with Mexico's labor share of 35 percent in 2017 and markdown)
  - Interest rate r = 0.07
  - Exit rate  = 0:08
  - Detection elasticity  = 0:05 (implies returns to scale in informal sector 10% lower)
  - Corporate tax rate  = 0.30
  - Labor taxes W = 0.10
  - Personal income tax ~W = 0.10
  - Informality cost parameter I = 0 (baseline so cost of informality reflects productivity losses rather than tax enforcement)
  - Government consumption G_t = 0
- Internal calibration (representative household) — Table 1 panel B highlights:
  - Pareto tail parameter  = 1.98
  - Taste for productivity  = 1.22
  - Informal disutility shifter !I = 1.07 (moment matching)
  - Detection intercept  = 0.11 (moment matching)
  - Entry costs φ_E = 9.72
- Moment targets (Table 1 panel A) — exact matches:
  - Top Employment Share: Target 0.32, Model 0.32
  - Top Wage Share: Target 0.58, Model 0.58
  - Informality Rate: Target 0.55, Model 0.55
  - Formal wage premium: Target 0.01, Model 0.01
- Heterogeneous household calibration: household shares s_h match ENOE; relative parameters calibrated to match relative employment rates, wages, informality rates, and wage premia across education groups. Firm ownership and transfer shares set to match capital-income and transfer incidence by education in ENIGH. Mass of firms normalized to 1; entry costs set to satisfy free-entry/resource constraint.

### Counterfactual analysis: minimum wage scenarios
- Two exercises:
  - Current minimum wage: set W to match minimum wage coverage of 8% in the formal sector (2024 Mexico).
  - +20% productivity-adjusted minimum wage: increase by 20 percent (Plan México target through 2030 adjusted for 4% labor productivity growth).
- Reporting setups: with and without free entry; with fixed sectoral distribution of firms (short vs long adjustment horizons).
- Key results (Table 2; differences from baseline reported in percent except for shares which are percentage points):
  - Constant Types, No Entry, Current vs +20%:
    - Output: 0.02 ; 0.58
    - Consumption: 0.02 ; 0.90
    - Productivity: -0.02 ; -0.50
    - Employment: 0.08 ; 2.18
    - Informality Rate: -0.10 ; -2.15
    - Minimum Wage Bite: 8.85 ; 39.68
    - Wages: 0.07 ; 1.95
  - Constant Types, Free Entry, Current vs +20%:
    - Output: -0.06 ; -1.06
    - Consumption: -0.02 ; -0.49
    - Productivity: -0.08 ; -1.18
    - Employment: 0.04 ; 0.25
    - Informality Rate: 0.30 ; 4.50
    - Minimum Wage Bite: 8.00 ; 28.38
    - Wages: 0.06 ; 0.96
  - Flexible Types, Free Entry, Current vs +20%:
    - Output: -0.10 ; -1.67
    - Consumption: -0.04 ; -0.85
    - Productivity: -0.08 ; -1.22
    - Employment: 0.04 ; 0.20
    - Informality Rate: 0.30 ; 4.66
    - Minimum Wage Bite: 8.05 ; 28.8
    - Wages: 0.03 ; 0.47
- Interpretation of +20% scenario (flexible sector assignment):
  - Informal share rises by 5 percentage points.
  - Minimum wage coverage among remaining formal workers reaches 28.4 percent (reported as minimum wage bite in Table 2).
  - Output and consumption decline by around 1 percent (productivity falls ~1.2 percent in some specifications) due to lower average productivity as firms migrate to informality.
  - Overall employment rises by 0.5 percent driven by:
    - Expansion of supply-constrained formal firms.
    - Wealth effect: falling consumption/transfers/profits induces households to work more, shifting labor partly into informal sector.
  - Wages rise: 7 percent formal, 2.4 percent informal (aggregate wage growth 0.9 percent) — the informal wage increase reflects compositional shifts, not strong competitive spillovers.
  - Inequality increases: compression in formal sector more than offset by rising inequality within the expanding informal sector.
  - Welfare falls by 1.6 percent in consumption-equivalent terms (substantially larger loss than at current levels). Free entry yields similar qualitative results with slightly larger losses.
- Mechanism: as minimum wage rises, many firms near the margin simultaneously find formality costlier and switch into informality; informality provides an escape margin but finite capacity leads to strong deterioration at higher wage floors.
- Comparison: When firms cannot switch into informality (constant sector assignment), higher minimum wages increase output and worker welfare at the expense of profits because supply-constrained firms expand hiring; the informality margin therefore limits gains from formal labor market policy.

### Welfare and distributional outcomes
- Aggregate welfare loss from +20% scenario is about 1.6 percent (representative household).
- Heterogeneous-household (four education types) results:
  - Welfare losses are largest for households at extremes of the skill distribution (low- and high-education), contrary to intended targeting of minimum wage.
  - Intermediate-education households:
    - Experience wage gains and increased employment, but still net welfare declines because higher labor income does not fully offset lower transfers and profits—consumption falls.
  - Low-education households:
    - Largely informal and do not benefit from wage increases; they lose from falling transfers.
  - High-education households:
    - Earn well above the minimum wage but suffer indirectly as expanding informality erodes tax base and transfers.
  - Net effect: welfare declines for all types, with regressivity—low-skill households gain no wage increase yet lose from fiscal contraction.

### Robustness checks and alternative assumptions
- Monopsony power (ε):
  - Recalibration with ε = 4 (weaker monopsony) yields smaller welfare losses from higher minimum wages.
  - Explanation: weaker monopsony implies smaller profit margins; profits and transfers decline less; weaker wealth effects; consumption falls less.
- No informal sector:
  - Absent informality, employment increases more strongly and wage inequality declines (supply-constrained firms expand and fully comply).
  - Output and productivity fall by more because additional labor goes to lower-productivity firms with diminishing returns.
  - Aggregate welfare losses are similar in magnitude but incidence shifts—capitalists bear larger share of loss.
  - Under free entry, minimum wages raise employment and labor share but can cause large welfare costs via firm exit.
- Informality penalties as redistributable tax (I = 1):
  - If informality penalties are fines redistributed by government, welfare losses attenuate: output falls less and transfers decline less.
  - Baseline (I = 0) may be an upper bound on welfare costs.
- Wealth effects:
  - General equilibrium wealth effects substantially shape outcomes: declining profits and transfers induce households to work more, attenuating output declines but amplifying employment responses.
- Additional robustness variations:
  - Larger formal wage premium, lower formal wage dispersion, higher returns to scale (
), higher detection elasticity (): main conclusions persist (muted effects at current levels; substantial welfare losses from larger increases; regressive incidence).

### Main takeaways
- Informality constrains minimum wage policy through limited coverage (low-wage workers are disproportionately informal) and an escape margin for firms.
- At current minimum wage levels, escape margin is narrow and labor market effects are muted.
- Substantial increases (e.g., +20 percent productivity-adjusted) can raise informality by ~5 percentage points, reduce productivity, raise employment modestly but shift jobs into lower-productivity informal arrangements, increase inequality, and lower welfare (representative-household welfare loss ~1.6 percent).
- The informality margin limits the gains from minimum wage increases and produces regressive distributional outcomes because fiscal erosion (from firms exiting formality) reduces transfers that low- and high-skill households rely on.

*Source: wpiea2026126-source-pdf - 3.2  Equilibrium — https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026126-source-pdf.pdf*

### 1.6 percent. These losses would be distributed regressivelylow-skill households are

### wpiea2026126-source-pdf - 1.6 percent. These losses would be distributed regressivelylow-skill households are

### Main findings on minimum wage impacts and distributional consequences
- The modeled welfare losses reach "1.6 percent."  
- Losses are distributed regressively: "low-skill households are primarily employed informally and thus do not benet from higher wage oors yet lose from reduced transfers as informality erodes the tax base."
- The informal sector buffers modest minimum wage increases, but this buffering "capacity is nite." As the wage oor rises, "welfare costs mount and may fall disproportionately on those the policy aims to help."
- Effective redistribution in economies with large informal sectors may require complementary policies that "expand formal employment or strengthen support for informal workers."

### Empirical approach, data, and constructed variables
- Educational attainment coded by years of schooling (anios_esc): "08 Years: Less than High-school; 911 Years: Highschool; 1215 Year: College; and 16+ Year: Graduate."
- Full-time employment: indicator for "whether respondent worked at least 40 hours last week."
- Formal employment: "Respondent contributing to IMSS or ISSSTE according toimssissste."
- Days worked last week: defined as the ceiling of Hours worked last week / 8:5, "capped at a maximum of 7."
- Daily income (baseline): defined via Monthly Income / (4:3 weeks × hours worked last week) × 8.
- Alternative daily income measures:
  - Daily income using days worked last week = ceiling(hours worked last week / 8.5), capped at 7, then Monthly Income / (4:3 weeks × days worked last week).
  - Monthly minimum-wage comparison by multiplying the daily minimum wage by "25" to obtain a monthly minimum wage.
- Shift-share controls constructed from state's initial exposure to gender-5-year age groups and industry-occupation groups; leave-one-out aggregates and an instrument ^X_st defined as ^X_st = Σ_g ω_gs × (X_gst leave-one-out).
- Drought severity measured with Mexican Drought Monitor categories D0–D4; indicator d1+ equals municipality classified as "D1 or worse."
- Manufacturing export-demand index: Bartik-style index using 2013 SAIC state weights ω_sk = e_sk;2013 / e_s;2013 and shifters g_kt = lnIP_kt − lnIP_k;t−1; contemporaneous shock shock_st = Σ_k ω_sk × g_kt and cumulative export_index_st = Σ_τ≤t shock_sτ, normalized to zero in the first observed quarter.
- ZEE indicator (Special Economic Zones): equal to one in "2018" for seven states (Chiapas, Guerrero, Michoacán, Oaxaca, Tabasco, Veracruz, and Yucatán) and zero otherwise; incentives took effect in "2018" and program dismantled in "2019."
- Southern-border fiscal stimulus indicator VAT_st: equal to one for four states (Campeche, Chiapas, Quintana Roo, and Tabasco) from "2021" onward reflecting VAT rate lowered from "16 to 8 percent" and corporate tax reductions in 23 municipalities.

### Income measurement and handling of missing wages
- Baseline hourly-to-daily conversion follows Kumler et al.(2020): hourly income = monthly income / (4:3 weeks × hours worked last week), then × 8 to get daily income.
- Two alternative daily income measures constructed (described above); baseline uses the first measure and robustness checks confirm similar results.
- Two methods for missing wages:
  - Hotdeck imputation with a four-level hierarchical grouping:
    1. Commuting zone, full-time status
    2. State, full-time status
    3. Commuting zone
    4. State
    - Hotdeck replaces imputed wages by lower hierarchies if the selected hierarchy has "less than 3 people" and a lower hierarchy has "3 or more observations."
  - Re-weighting: redistribute observation weight for missing wages proportionally to similar workers with non-missing wages using the same hierarchy; if none, move to next lower hierarchy.
- Both methods increase first and second moments of wage distribution; "both adjustment methods lead to very similar wages across the income distribution."

### Summary statistics for wage measures in 2024 (values in Mexican pesos)
- A. Daily Income
  - Unadjusted: Observations "348,481", Total Weight "104,148", Mean "466", Standard Deviation "599", 10th percentile "163", 50th percentile "333", 90th percentile "827"
  - Hotdeck: Observations "523,739", Total Weight "165,552", Mean "499", Standard Deviation "640", 10th percentile "173", 50th percentile "349", 90th percentile "907"
  - Reweighted: Observations "348,481", Total Weight "165,554", Mean "500", Standard Deviation "656", 10th percentile "173", 50th percentile "349", 90th percentile "914"
- B. Alternative Daily Income
  - Unadjusted: Observations "348,481", Total Weight "104,148", Mean "434", Standard Deviation "451", 10th percentile "159", 50th percentile "329", 90th percentile "775"
  - Hotdeck: Observations "523,739", Total Weight "165,552", Mean "467", Standard Deviation "500", 10th percentile "167", 50th percentile "333", 90th percentile "837"
  - Reweighted: Observations "348,481", Total Weight "165,554", Mean "468", Standard Deviation "499", 10th percentile "167", 50th percentile "333", 90th percentile "837"
- C. Monthly Income
  - Unadjusted: Observations "359,854", Total Weight "107,114", Mean "9,153", Standard Deviation "8,589", 10th percentile "2,580", 50th percentile "7,740", 90th percentile "16,000"
  - Hotdeck: Observations "523,932", Total Weight "165,609", Mean "9,862", Standard Deviation "9,627", 10th percentile "2,580", 50th percentile "7,740", 90th percentile "17,200"
  - Reweighted: Observations "359,854", Total Weight "165,615", Mean "9,904", Standard Deviation "9,766", 10th percentile "2,580", 50th percentile "7,950", 90th percentile "17,200"

### Below minimum wage incidence (shares reporting earnings below minimum wage in 2024; all values in percent)
- Baseline (None restriction, Baseline income measure): "14.5"
- Baseline (None restriction, Alternative Daily): "14.5"
- Baseline (None restriction, Monthly): "18.8"
- Formal workers (Baseline income): "10.9"
- Formal workers (Alternative Daily): "10.0"
- Formal workers (Monthly): "9.4"
- Formal + Full-time (Baseline): "12.6"
- Formal + Full-time (Alternative Daily): "11.4"
- Formal + Full-time (Monthly): "9.4"
- Tax-adjusted minimum wage (assumes income tax rate "5.5 percent" that workers adjust for when reporting income): All workers Baseline "9.7", Alternative Daily "9.9", Monthly "5.7"
- Interpretation: "consistently above 14 percent of workers report below minimum wage income" across all workers; this "shrinks to above 9 percent" for formal or full-time formal workers; tax-adjustment shrinks share to "5.69.7 percent" (table reports "9.7", "9.9", "5.7").

### Predictors of reporting below minimum wage (sample: formal workers within 0.5 log points above minimum wage; coefficients rescaled by sample mean)
- Demographics
  - Age <25: Coefficient "-0.025" (Standard Error "(0.030)")
  - Age >55: Coefficient "0.160" (Standard Error "(0.049)")
  - Female: Coefficient "0.018" (Standard Error "(0.025)")
- Years of Schooling
  - 0–9 Years: Coefficient "0.156" (Standard Error "(0.040)")
  - 10–12 Years: Coefficient "0.011" (Standard Error "(0.026)")
- Firm Type
  - Micro: Coefficient "0.077" (Standard Error "(0.043)")
  - SME: Coefficient "0.061" (Standard Error "(0.025)")
  - Unregistered: Coefficient "0.050" (Standard Error "(0.033)")
- Sector/Industry
  - Agriculture: Coefficient "0.137" (Standard Error "(0.065)")
  - Manufacturing: Coefficient "-0.186" (Standard Error "(0.027)")
  - Construction: Coefficient "-0.187" (Standard Error "(0.073)")
  - Services: Coefficient "0.156" (Standard Error "(0.026)")
  - Tourism: Coefficient "-0.072" (Standard Error "(0.041)")
  - Retail or Wholesale Trade: Coefficient "0.144" (Standard Error "(0.030)")
  - Public Sector: Coefficient "-0.040" (Standard Error "(0.048)")
- Summary interpretation: "older workers and those with less schooling are more likely to report below minimum wage" and "workers in micro enterprises or unregistered rms" are more likely; workers in manufacturing, construction, and public sector are less likely; retail and wholesale trade show positive association.

### Results for vulnerable groups and heterogeneity
- Employment-rate estimates by demographic groups are presented separately for: all groups; Age 25 or younger; 9 Years or Less of Schooling; Women. (Figures report estimates from 2015–2025 with "No controls" and "Baseline" specifications and 95% confidence intervals.)
- Formalization-rate estimates analogous to employment-rate figures are reported for the same demographic splits.

### Spillovers into the informal sector and sectoral wage distributions (2025)
- Formal-sector gains concentrated in bottom deciles: "roughly 4 to 5 percent" gains fading to zero by the median.
- Informal-sector wages respond broadly: "around 2 to 4 percent" across the entire distribution rather than a pronounced bottom spike.
- Pooled distribution (all sectors) exhibits positive gains throughout: "near 3 to 4 percent" in lower deciles easing toward "2 percent" at the top.
- Evidence suggests broad informal gains are driven by the self-employed rather than informal employees:
  - Informal employees restricted sample yields estimates "close to and statistically indistinguishable from zero across most of the distribution," turning negative only in the top decile.
- Within the informal sector, a divergence between daily wage measures and unadjusted monthly measures at the bottom deciles: unadjusted monthly measure falls to "roughly −3 percent" at the first decile while daily measures rise, consistent with firms reducing hours of marginal workers (self-employed, informal subcontractors), containing costs along the intensive rather than the extensive margin.
- Figure notes: coefficients for log mean wage within each decile are scaled by IQR(g_Bite) and interpretable as effect of moving from 25th to 75th percentile of initial bite distribution.

*Source: wpiea2026126-source-pdf - 1.6 percent. These losses would be distributed regressivelylow-skill households are*

### 5. Shaded areas report 95% condence intervals based on robust standard errors.

### wpiea2026126-source-pdf - 5. Shaded areas report 95% condence intervals based on robust standard errors.

### Model derivations and labor supply / firm behavior
- Household and firm first-order conditions yield two sector-specic labor supply curves (equation (B.1)) distinguishing formal (i ∈ M_Fht) and informal (i ∈ M_Iht) sectors with elasticities and sector shifters preserved.
- Equilibrium hiring for informal firms (equation (B.2)):
  - L_hit = (A_it / A_0t)^{1+~ζ / (1-(ψ-ξ))+1/ε} * ((1-μ_ξ_h) ψ A_0t ι_h ! I_h W_ht (1 + 1/ε))^{1/(1-ψ+1/ε)} (expression preserved in source).
- Equilibrium wage bill for informal firms (equation (B.3)) preserves normalized-parameter notation (~· = ·/(1 + 1/ε)).
- Pre-tax revenue Y_hit and after-tax revenue expressions given explicitly (textual forms preserved).
- After-tax profits for informal firms: Π_{I;it} = (1-~ψ)·(A_0t·ι_h)^{1/(1-~)}·(1-μ_ξ_h)^{1/(1-~)}·( ~! I_h ·W_t )^{~/(1-~)}·(A_it / A_0t)^{1/(1-(~ψ-~ξ))}·A_0t^{1/(1-~)} (expression preserved).

- Formal firms can have up to three employment segments depending on productivity and minimum wage binding (equation (B.4)):
  - Bottom segment: A_it ≤ A_Fht → excess supply, employment formula given.
  - Middle segment: A_Fht < A_it ≤ ͠A_Fht → firms hire all labor available at minimum wage.
  - Top segment: ͠A_Fht < A_it → minimum wage non-binding; firms internalize wage impact.
- Cut-offs:
  - A_Fht = ( (1 + ξ_L) ι_h · A_0t^{ζ(1-ψ)} )^{1/(1-ζ(1-ψ))} · (W_t)^{(1+ε(1-ψ))/(1-ζ(1-ψ))} · ( W_ht (1-~ξ_L) )^{-ε(1-ψ)/(1-ζ(1-ψ)) } (preserved form)
  - ͠A_Fht = (1 + 1/ε)^{1/(1-ζ(1-ψ))} · A_Fht (equation (B.5)).

- Profits:
  - Formal constrained, unconstrained, and informal profits given in equations (B.6) and subsequent expressions; profits are strictly increasing in productivity.
- Lemmas:
  - Lemma 2: For ξ > 0, there is a unique threshold A_It where formal profits exceed informal profits above the threshold (uniqueness argued via elasticities: formal sector elasticities 1/(1-ψ) and 1/(1-~ψ) vs informal 1/(1-~ψ + ~ξ)).
  - Lemma 3: Profits and employment are continuous around cutoffs within the formal sector (Maximum Theorem, compact/continuous constraints, strict quasi-concavity).

- Steady state and entry:
  - Free entry condition simplifies to φ_E = (1 + r)/(r + δ) · E[Π_it].
  - Constant mass of firms: M_Et = δ·M_t.
  - Net profits from corporate sector: M_t · δ · E[Π_it] - φ_E·M_Et = M_t · r(1-δ)/(r+δ) · E[Π_it].

### Disutility for the underemployed (labor aggregation)
- Labor disutility decomposition (section B.2):
  - L_t^{1+1/ε} = ∫_{M_t} L_it · L_it^{1/ε} di = ∫_{M_t} L_it^{1+1/ε} di (structure preserved).
- Two extremes:
  - Wasted effort assumption (benchmark): L_it = L_S_t for both quantity and per-unit disutility → L_t = M_t · (L_S_t)^{1+1/ε}.
  - Perfect selection (no waste): L_t = ∫_{M_t} L_it^{1+1/ε} di → much smaller utility impact since L_S_t > L_it for demand-constrained firms.
- Benchmark chosen: wasted effort in involuntary unemployment.

### Solution algorithm and calibration (multi-household model)
- Solution algorithms:
  - Three separate algorithms: entry vs no-entry, calibration vs counterfactuals.
  - Calibration algorithm: inner loop solves firms' policies conditional on aggregates; intermediate loop iterates wage index via labor disutility to clear labor market; outer loop updates consumption via budget constraint.
  - No-entry counterfactual: same algorithm but allow profits to change while keeping deadweight loss from entry constant.
  - Free-entry counterfactual: additional outer loop over M_t using free entry condition.
  - Numerical methods: bisection when possible; otherwise smooth updating via geometric averaging.

- Calibration moments and parameter values (Table C.5 preserved):
  - Moments (Targets / Model): Top Employment Share 0.32 / 0.32 (INEGI); Top Wage Share 0.58 / 0.58 (INEGI); Wage Premia {0.07,0.25,0.74}; Informality Rates {0.80,0.59,0.43,0.31}; Formal wage premia {0.01,0.01,0.02,0.05}; Employment Shares {0.32,0.24,0.20}.
  - External parameters:
    - IES: 2.00
    - Agg. labor supply elas. φ: 0.30
    - Firm-level labor supply elas. ε: 2.00
    - Returns to scale ψ: 0.50
    - Interest rate r: 0.07
    - Exit rate δ: 0.08
    - Detection elasticity ξ: 0.05
    - Corporate tax rate _: 0.30
    - Labor taxes _W: 0.10
    - Personal income tax ~_W: 0.10
  - Internal (matching / direct):
    - Pareto tail parameter : 1.98
    - Taste for Productivity : 1.22
    - Labor supply shifters φ_h: {0.30,0.31,0.30,0.31}
    - Relative productivities ι_h: {1.00,1.28,1.34,2.01}
    - Informal disutility shifters !I_h: {1.07,1.07,1.05,1.00}
    - Detection intercepts ξ_h: {-0.04,0.09,0.15,0.20}
    - Entry costs φ_E: 27.1

### Empirical results — commuting zone (CZ) and state analyses
- CZ-level caveat: ENOE is representative at state level but not at CZ level; analysis focuses on commuting zones with consistently 15 or more respondents per quarter.
- CZ results (Figures D.4–D.6, D.7):
  - Annual coefficient estimates for wages in 1st decile of formal and full-time formal wage distributions presented; shaded areas report 95% confidence intervals.
  - Labor-market quantity estimates over 2015–2025 for Minimum Wage Bite, Labor Force Participation Rate, Employment Rate, Hours Worked, Formalization Rate, and Population — charts control variations: No controls, Baseline, Initial share × Year controls.
- Formal wage distribution (Figure E.8):
  - Kernel densities for daily wage in MXP (log) in 2024:
    - Unadjusted and adjusted (residualized for education, state, and age). Horizontal lines report medians.
- State-group design (Figures F.9–F.12):
  - 1st decile wage estimates for most exposed state group and across exposure groups in 2024; shaded areas report 95% confidence intervals.
  - Group heterogeneity across exposure groups for Minimum Wage Bite, Labor Force Participation, Employment, Hours, Formalization Rate, Population.

### Comparing survey (ENOE) and administrative (IMSS) data on minimum-wage coverage
- Key documented patterns (Figures F.13–F.14):
  - Panel (a): Fraction earning ≤ 1 MW — ENOE (Daily) rises from close to 1% in 2016 to around 10% in 2024; IMSS remains stable at around 1% throughout sample.
  - Panel (b): Fraction earning ≤ 2 MW — IMSS starts near 40% and increases to 60%; ENOE starts below 20% and increases faster to coincide approximately in 2024.
  - Quarterly jump pattern: large jumps in ENOE coverage in Q1 coinciding with statutory January minimum wage increases; IMSS jumps smaller and more stable.
  - ENOE (mechanical) series (advancing threshold while holding reported wages fixed and netting assumed 2% nominal drift plus tax wedge) closely matches realized ENOE jumps.
- Interpretation and potential mechanisms:
  - Possible reasons: ENOE self-reported incomes (recall error, misreporting) vs IMSS employer-reported SBC; collusion/misreporting in IMSS to reduce contributions; ENOE respondents potentially unaware or misreporting.
  - Data is consistent with formal-sector statutory minimum wage not effectively binding (IMSS reports cannot fall below minimum wage technically), but no direct evidence—only consistency with implications.

### Quantitative results — role of informality, distortions, and robustness
- Informality as a limit on policy (Figure G.15):
  - Comparative counterfactuals: Baseline vs NoInformality; Baseline w/ Entry vs NoInf. w/ Entry — impacts on Output, Employment, LaborShare, Welfare plotted against MinimumWage (coverage axis 0.90, 0.95, 1.0, 1.05, 1.1, 1.15, 1.2).
- Impact of distortions (Table G.6 — differences from baseline):
  - Columns: Informality, Monopsony, Taxation, Combined.
  - Selected entries (preserved exactly):
    - Output: 0.78, -19.94, 47.0, 17.6
    - Consumption: -2.42, -9.52, 59.14, 44.4
    - Productivity: 5.32, 0.00, 5.32, 25.32
    - Employment: 1.68, 6.75, 3.79, 10.7
    - Informality Rate: -55.0, 0.00, -55.0, -55.0
    - Wages: -6.64, 12.56, 3.08, 3.4
    - Formal Sector: -38.21, 2.57, 7.86, 21.3
    - Representative Household welfare: -2.12, -12.85, 8.03, 8.0
    - Workers: 3.18, 7.89, 38.15, 59.5
    - Capitalists: -9.94, -40.08, 87.61, 2.6
  - Notes: Table reports impacts or turning of distortions individually and jointly. Differences from baseline in percent except shares in percentage points. Minimum wage bite is share of formal workers at minimum wage. Informality rate is share of workers in informal sector.
- Robustness to alternative calibrations (Tables G.7–G.8):
  - Alternative calibrations: Low Wage Disp., High Formal Premium, High ψ, High ξ, High ε, _I = 1, No Inf.
  - Selected parameter variations preserved (examples):
    - Firm-level labor supply elas. ε: baseline 2.00; High ε column: 4.00.
    - Returns to scale ψ: alternative values 0.75 in High ψ column.
    - Detection elasticity ξ: {0.05, 0.07, 0.10} across columns.
    - Entry costs φ_E vary across calibrations (e.g., 8.70, 9.65, 3.97, 9.98, 7.57).
  - Impact of enforcing minimum wage 20% above current levels (Table G.8) — selected preserved outcomes:
    - Baseline column:
      - Output: -1.67
      - Consumption: -0.85
      - Productivity: -1.22
      - Employment: 0.20
      - Informality Rate: 4.66
      - Minimum Wage Bite: 28.8
      - Wages: 0.47
      - Formal Sector: 6.73
      - Informal Sector: 1.99
      - Std. of log wages: 0.79
      - Representative Household welfare: -1.02
      - Workers: -0.84
      - Capitalists: -1.10
    - No Inf. column (model without informality) example:
      - Output: -0.70
      - Employment: 5.39
      - Minimum Wage Bite: 41.5
      - Wages: -2.10
      - Representative Household: -1.55
      - Workers: 1.12
      - Capitalists: -5.48
  - Notes: Table reports counterfactuals with free entry; differences from baseline in percent except shares in percentage points.

### General equilibrium / wealth effects and distributional implications
- Wealth effects matter:
  - Partial equilibrium (PE Pure) vs PE (Labor Market) vs General Equilibrium (GE) comparisons (Figures G.16–G.17).
  - In baseline with informality (Figure G.16):
    - PE (Pure): rising minimum wages increase employment and wages; output and consumption fall due to rising informality and falling productivity.
    - PE (Labor Market): adjusting L_ht to clear labor market but not updating C_ht dampens employment effects and marginally increases wages due to households demanding compensation for higher employment costs.
    - GE: additional wealth effects from falling consumption push employment up as households increase labor supply to offset income losses; consumption and output impacts dampened. Kink in marginal effects occurs when some firms become demand constrained.
  - Without informality (Figure G.17):
    - PE: wages initially fall (composition effect) then rise; output and consumption increase strongly in PE.
    - GE: attenuated impacts on output, consumption, employment; initial decline in wages muted by rise in wage intercept.
- Minimum wage and informal wage distribution (Figure G.18):
  - Model reproduces empirical pattern of no competitive transmission from formal to informal wages:
    - At current minimum wage (Panel A): informal wage distribution essentially unchanged; formal distribution shifts only near threshold.
    - 20 percent increase (Panel B): informal distribution does not rise via cross-sector competition; it moves only through composition as marginal firms reallocate across sectors.
  - Mechanism: reallocation concentrated among firms near productivity threshold, so formal-sector wage increases do not transmit to informal wages.

*Minimum Wages and the Informality Constraint — Working Paper No. WP/2026/126*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2026/english/wpiea2026126-source-pdf.pdf_