## 2.1    Data

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---

### Data sources, sample, and definitions
- Main data source: Pesquisa Nacional por Amostra de Domicílios (PNAD), 1996-2012.
- Sample restrictions and measures:
  - Individuals aged between 18-54.
  - One job per worker (main job in the reference week).
  - Monthly gross labor earnings (excluding social transfers and pensions), deflated by the CPI and expressed in 2012 terms.
  - A worker is informal if they do not have a signed working permit (Carteira de Trabalho Assinada).
  - Self-employment is excluded from the main analysis (results can be interpreted as a lower bound on total effects when including self-employment).
- Institutional note:
  - The federal minimum wage imposes a nation-wide floor on monthly nominal earnings of formal workers.
  - Since Lei Complementar No. 103 on July 14, 2000, five out of the 27 states instituted state-specific wage floors: Rio de Janeiro and Rio Grande do Sul since 2001, Paraná since 2006, São Paulo since 2007, and Santa Catarina since [text truncated].
- Alternative measures and robustness:
  - Alternative definitions of informality (including self-employed) do not alter qualitative findings.
  - Hourly earnings adjustment (minimum wage adjusted to full-time 44 hours/week) yields similar results.

### Descriptive statistics and stylized facts (Brazil, 1996–2012)
- Informality and composition:
  - Informal workers constitute 35% of the labor force (summary elsewhere reports 39.1% in 1996 and 30.9% in 2012).
  - Informal workers tend to earn less and be substantially less educated than formal workers.
  - Within-industry informal share ranges from 17% in Manufacturing to 70% in Domestic Services.
  - Unemployment rate around 7.5% (varied 9% to 6%), much lower than the informal share.
- Table 1 summary moments (selected exact values):
  - Share (1996): Formal 60.9, Informal 39.1
  - Share (2012): Formal 69.1, Informal 30.9
  - Mean earnings (1996): Formal 1,387, Informal 673, Difference 714***
  - Mean earnings (2012): Formal 1,388, Informal 840, Difference 548***
  - Share with HS (1996): Formal 31.5, Informal 14.6, Difference 16.9***
  - Share with HS (2012): Formal 61.2, Informal 38.4, Difference 22.8***
  - Age (1996): Formal 32.5, Informal 31.0, Difference 1.5***
  - Age (2012): Formal 33.7, Informal 33.5, Difference .2**
  - Male (1996): Formal 63.8, Informal 55.2, Difference 8.6***
  - Male (2012): Formal 58.6, Informal 50.0, Difference 8.7***
  - Notes: Earnings are deflated by CPI and expressed in 2012 values. ***p<1%, **p<5%, *p<10%.

### Inequality facts
- Evolution of variance of log earnings (1996–2012):
  - Strong and steady reduction in overall inequality: 2.3% per year.
  - Formal sector inequality fell at 4.5% per year.
  - Informal sector variance of log earnings remained roughly constant, fluctuating around 0.65 log points.
  - The gap between formal and informal earnings inequality widened consistently through the 2000s.
- Decomposition:
  - Aggregate variance Vt decomposed into within and between components.
  - The within-component explains over 80% of the level of aggregate earnings inequality and over 83% of its reduction over the sample period.

### Minimum wage facts (1996–2012)
- Two measures of minimum-wage evolution:
  - Minimum wage as fraction of median earnings: increased from 45% in 1996 to 73% in 2012.
  - Share of formal workers receiving exactly the minimum wage: increased from 8% in 1996 to 16% in 2012.
- The bulk of the increase in minimum-wage restrictions occurs after 1999.

---

### Reduced-form evidence: identification and main empirical results
- Identification and empirical strategy:
  - Leverages state-level heterogeneity in initial exposure to the minimum wage (1999 share of formal workers binding at the national wage floor).
  - Brazil’s 27 states ranked and split into 9 treatment groups; comparisons between the 3 most exposed states (Piauí, Sergipe, Bahia) and the 3 least exposed states (São Paulo, Santa Catarina, Distrito Federal).
  - Event-study / differences-in-differences specifications with state and year fixed effects and controls for age, gender, race, education composition; standard errors clustered at the state level.
- Event-study mean post-1999 coefficients (β_9) — point estimates and standard errors:
  - log(VAll): 0.200 (0.077)**
  - log(VF): -0.253 (0.063)***
  - log(VI): 0.316 (0.078)***
  - log(Inf Share): 0.073 (0.032)**
- Interpretation (most-exposed vs least-exposed states):
  - 25.3 percentage points (p.p.) stronger reduction in formal inequality (matches log(VF) coefficient).
  - 31.6 p.p. larger increase in informal inequality (matches log(VI) coefficient).
  - 7.3 p.p. larger increase in the informal share of labor (matches log(Inf Share) coefficient).
  - Joint effect: 20 p.p. relative increase in overall inequality in the most-exposed states (matches log(VAll) coefficient).
- Group-level Diff-in-diff patterns:
  1. Minimum wages reduce inequality in the formal sector, effects stronger in more-exposed states.
  2. Minimum wages increase informal inequality and the informal share mainly in the most restricted states (groups 8 and 9).
  3. Net effect on overall inequality varies by treatment intensity (e.g., group 2: 14.2 p.p. stronger decrease relative to group 1; groups 8–9: 20 p.p. stronger increase).
- Robustness:
  - Alternative definitions of informality, hourly earnings, alternative splits, different TWFE estimators produce qualitatively similar patterns.
  - Kaitz-regression checks: marginal coefficients (ρ) (H.1) — Formal (log(Variance)): -0.985*** (0.085); Informal (log(Variance)): 0.172** (0.081); Aggregate (log(Variance)): -0.151* (0.076); log(Informal share): 0.162*** (0.051).
  - Using share-at-minw as treatment (Table H.2) shows Formal (log(Variance)): -1.382*** (0.264); Informal (log(Variance)): 0.897*** (0.286); Aggregate (log(Variance)): 0.730*** (0.210); log(Informal share): 0.445** (0.208).

---

### Theoretical environment and mechanisms (monopsonistic competition with informality)
- Model primitives and agents:
  - Unit measure of ex-ante homogeneous households supply one unit of inelastic labor.
  - Individual utility V_i(j) = A_i(j) w(j), with A_i(j) iid Fréchet with shape parameter η.
  - Firm productivity z ∼ F over [z_0 > 0, ∞), f(z) > 0 ∀ z.
  - Goods market: perfect competition; labor market: monopsonistic competition.
- Formal sector (minimum wage w):
  - Formal firm optimal wage: w_form(z) = max( η/(η+1) z, w ).
  - Formal firm profit: π_form(z) = W^{-η} [ max( η/(η+1) z, w ) ]^η [ z − max( η/(η+1) z, w ) ].
  - Minimum wage acts as a fixed production cost for low productivity firms; below a cutoff firms have negative profits if formal.
- Informal sector (detection cost ρ):
  - Informal optimal wage: w_inf(z) = η/(η+1) (1−ρ) z.
  - Informal profit: π_inf(z) = W^{-η} [ η^η / (η+1)^{η+1} ] (1−ρ)^{η+1} z^{η+1}.
  - Absence of fixed costs implies positive profits for all informal firms; informality is a profitable outside option for unproductive firms.
- Partial-equilibrium firm selection (Proposition 1):
  - Two thresholds z and z̄ with z satisfying η^η / (η+1)^{η+1} (1−ρ)^{η+1} z^{η+1} − w^η z + w^{η+1} = 0 and z̄ = (η+1)/η w.
  - Firms with z < z operate informally; z ∈ [z, z̄] are formal but wage-restricted; z > z̄ are formal and unrestricted.
  - ∂z/∂ρ < 0, ∂z/∂w > 0, ∂^2 z / ∂ρ ∂w < 0, and ∂(z/w)/∂w = 0.
  - Intuition: larger minimum wages and smaller detection costs increase informality.
- Aggregate wage index:
  - W = η/(η+1) [ ∫_{z_0}^z [ (1−ρ) z ]^η f(z) dz + [ F(z̄) − F(z) ] z̄^η + ∫_{z̄}^∞ z^η f(z) dz ]^{1/η}.

### Inequality effects with the informal margin (Proposition 2)
- Marginal decomposition of ∂V/∂w:
  - ∂V/∂w = ∂V_form/∂w (formal response, FR)
    + ∂L_inf/∂w × [ (E_inf − E_form)^2 + V_inf − V_form ] (informal response, IR)
- Key implications:
  - The minimum wage compresses formal-sector earnings distribution (FR < 0).
  - If the informal margin is activated (∂L_inf/∂w > 0) and (E_inf − E_form)^2 + V_inf − V_form is sufficiently large, the IR term can dominate and ∂V/∂w > 0.
  - If firm productivity z ∼ Pareto(ν > η) and informality levels are low, increasing the minimum wage can increase overall earnings inequality.
- Worker welfare and labor demand (Proposition 3):
  - Worker expected utility proportional to aggregate wage index: E[U] = Γ((η−1)/η) W.
  - Without informality, increasing the minimum wage reduces inequality and can increase worker welfare.
  - With informality, the informal margin can reduce worker welfare and even reduce aggregate labor demand; in Pareto case, increasing the minimum wage can reduce worker welfare.

---

### Quantitative calibration, validation, and counterfactual experiments (Brazil)
- Calibration targets and parameters (selected exact calibrated values):
  - Labor supply elasticity η: 4.52 (1996), 4.22 (2012).
  - Elasticity of substitution ε: 1.875.
  - Productivity parameters: σ = 1.01 (1996), σ = 1.29 (2012); κ = 6.02 (1996), κ = 6.33 (2012).
  - Minimum wage parameter w: 4.04 (1996), 8.87 (2012).
  - Informality cost ρ: 0.26 (1996), 0.32 (2012).
  - Payroll tax multiplier τ = 71.4%.
  - Worker valuation wedges ςh: gap between nominal and real value of formal wages 30% for no-degree workers and 24% for tertiary workers.
- Fit and external validation:
  - Model replicates targeted moments well except some tension matching informal-sector inequality.
  - Selected model vs data moments (exact values):
    - Overall variance of log earnings: 1996 Data 0.78 vs Model 0.78; 2012 Data 0.50 vs Model 0.46.
    - Formal variance: 1996 Data 0.65 vs Model 0.58; 2012 Data 0.33 vs Model 0.33.
    - Informal variance: 1996 Data 0.66 vs Model 0.73; 2012 Data 0.62 vs Model 0.51.
    - Formal fraction at minimum wage: 1996 Data 7.7 vs Model 7.7; 2012 Data 15.8 vs Model 15.8.
    - Informal share overall: 1996 Data 0.39 vs Model 0.39; 2012 Data 0.31 vs Model 0.31.
- Counterfactual design:
  - Change one parameter at a time from 1996 calibrated level to 2012 value: w, ρ, Nh, ξh(z).
  - Counterfactual w = 6.6 calculated assuming all increase in formal bunching (7.7% → 15.8%) driven solely by minimum wage.
- Quantified effects of the minimum wage spike in the 2000s (holding other factors constant):
  - Overall inequality (variance of aggregate log earnings) increased by 6.4%.
  - Formal-sector wage inequality decreased by 12.1%.
  - Net increase in overall inequality driven by substantial informalization and inequality increases within the informal sector.
- Detailed counterfactual entries (selected exact values from Table 5):
  - Variance of log earnings (overall): 1996 = 0.78; w → 0.83; ρ → 0.78; Nh → 0.79; ξh(z) → 0.98; 2012 = 0.46.
  - Fraction at w (Formal): 1996 = 7.7; w → 15.2; ρ → 8.3; Nh → 3.6; ξh(z) → 14.0; 2012 = 15.8.
  - Min/mean wage: 1996 = 0.26; w → 0.33; ρ → 0.26; Nh → 0.21; ξh(z) → 0.24; 2012 = 0.47.
  - Informal share: 1996 = 0.39; w → 0.73; ρ → 0.28; Nh → 0.23; ξh(z) → 0.61; 2012 = 0.31.
- Welfare and distributional spillovers:
  - Minimum wage increase improves welfare only for tertiary-educated workers (0.7% increase).
  - Raising the minimum wage increases percentile ratios in the formal distribution: p10p90 by 21.8%, p20p90 by 12.4%, p50p90 by 3.5% (Figure 11).
- Firm types and informality responses:
  - Under 2012 minimum wage:
    - Type 1 (cannot cope with 2012 minimum wage): 25.8% of workers employed.
    - Type 2 (productive enough to be formal under 2012 minimum wage but choose informality): 9.9% of labor force.
    - 27.7% of labor force that becomes informal in response to minimum wage work in firms that could be formal if forced.
- Effects of enforcement (informality cost ρ):
  - An increase of at least 85% in the cost of informality would have been required for the minimum wage to reduce overall inequality.
  - Estimated 24% increase in informality costs (calibrated) → 28% decrease in informal share; little change in aggregate earnings inequality due to offsetting forces.
- Skill composition and SBTC:
  - Improvement in skill composition reduces informality by 41% (other summaries report 30%); improvements raise low-skill wages and the costs of being informal.
  - Skill-biased technical change (model-implied): increases the share of the informal workforce by 50% and increases overall earnings inequality by 26%.
- Joint counterfactuals:
  - ∆ρ = 24% does little to offset minimum wage’s effect on informality and aggregate inequality.
  - ∆ρ = 85% would offset minimum wage’s effect on aggregate inequality.
  - Improvements in skill composition reduce informal share (e.g., by 30–41%) and can complement minimum wage policies in reducing overall earnings inequality.

---

### Policy-relevant conclusions and implications
- Primary finding for Brazil (1996–2012):
  - Large minimum wage increases in the 2000s reduced formal-sector inequality but increased aggregate earnings inequality by 6.4% due to substantial informality responses and increased informal inequality.
- Mechanisms and takeaways:
  - Minimum wage increases compress formal-sector earnings but can induce reallocation to informality where wage gaps and within-informal variance may increase aggregate inequality.
  - Strong informal margins of adjustment can produce unintended consequences of labor-market policies aimed at reducing inequality.
  - Complementary policies matter:
    - Formalization/enforcement increases can mitigate unintended informality responses; an 85% increase in enforcement (relative to 1996) would offset the minimum wage’s effect on aggregate inequality in the model.
    - Improvements in skill composition reduce informality and can complement minimum wage increases in lowering aggregate inequality.
- Broader relevance:
  - Policy design of federal minimum wages should consider local informality and enforcement conditions.
  - Results inform assessment of minimum-wage effects where agents can operate outside labor legislation (e.g., gig economy arrangements).

*Italic source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024159-print-pdf.pdf*

### 2.1    Data  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  . 

### 2.1    Data

### Section headings and nearby table of contents entries
- 2.1    Data  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .8
- 2.2    Stylized facts on the informal sector, inequality, and the minimum wage .  .  .  .  .  .9
- 2.3    Reduced-form evidence: minimum wage, inequality, and informality    .  .  .  .  .  .  .    12
- 3    Informality and the effects of the minimum wage18
  - 3.1    Labor supply  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    18
  - 3.2    Labor demand  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    19
  - 3.3    Equilibrium    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    20
  - 3.4    Inequality, minimum wage, and the informal sector .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    21
  - 3.5    The effects of the minimum wage on worker welfare   .  .  .  .  .  .  .  .  .  .  .  .22
- 4    Quantitative extension24
  - 4.1    Labor supply  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    24
  - 4.2    Labor demand  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    25
  - 4.3    Equilibrium    .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    26
- 5    Calibration and validation27
  - 5.1    Labor supply  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    27
  - 5.2    Labor demand  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    28
  - 5.3    Government   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .    29

*Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024159-print-pdf.pdf*

### 5.4    Discussion and external validation   .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .  .

### 5.4    Discussion and external validation

### Key empirical findings (Brazil, 1996-2012)
- Informal workers constitute 35% of the labor force.
- Between 1996 and 2012:
  - Variance of log earnings in the formal sector fell from 0.65 to 0.33.
  - Inequality in the informal sector remained constant at 0.65.
- The share of formal workers at the minimum wage:
  - Stable around 7% until 1999.
  - Increased to 16% by 2006 and stabilized thereafter.
- Heterogeneous state-level exposure to the minimum wage (measured by share of formal minimum wage workers in 1999) yields reduced-form differences:
  - Most exposed states experienced a 25.3 percentage points (p.p.) stronger reduction in the variance of log earnings in the formal sector relative to least exposed states.
  - Most exposed states experienced a 31.6 p.p. larger increase in informal inequality relative to least exposed states.
  - Most exposed states experienced a 7.3 p.p. larger increase in the informal share relative to least exposed states.
  - Jointly, these led to a 20 p.p. relative increase in overall inequality in the states where the minimum wage binds the most.
- The effect of the minimum wage on overall inequality varies across states:
  - Minimum wage increases inequality in the most exposed states but decreases it in less exposed ones.

### Stylized theoretical results (monopsonistic competition with informality)
- Model setup:
  - Heterogeneous firms compete for labor, can operate formally or informally, and formal firms face the minimum wage.
  - Firms trade off minimum wage restrictions (if formal) versus revenue losses due to government inspections (if informal).
  - In equilibrium: most productive firms operate formally; within formal firms, the least productive bunch at the minimum wage.
- Analytical insights:
  - A higher minimum wage compresses the formal-sector earnings distribution.
  - Some formal workers lose jobs and transition to informality; the informal response depends on:
    - Elasticity of the informal sector to the minimum wage.
    - Differences in means and variances between formal and informal wage distributions.
  - When firm productivity follows a Pareto distribution and informality levels are low, increasing the minimum wage can increase overall earnings inequality.
  - Policy aimed at reducing inequality can have unintended inequality-increasing consequences when informal margins of adjustment are strong.

### Quantitative calibration and counterfactuals (Brazil)
- Calibration targets and validation:
  - The calibrated framework replicates the observed distribution of wages in the aggregate economy, within each sector, and within each skill group for 1996 and 2012.
- Quantified effects of the minimum wage spike in the 2000s (holding other factors constant):
  - Overall inequality (variance of aggregate log earnings) increased by 6.4%.
  - Formal-sector wage inequality decreased by 12.1%.
  - The net increase in overall inequality is driven by substantial informalization and inequality increases within the informal sector.
- Interaction with formal enforcement, skill composition, and skill-biased technical change:
  - An increase of at least 85% in the cost of informality would have been required for the minimum wage to reduce overall inequality.
  - Improvement in skill composition:
    - Reduces informality by 41%.
    - Informal firms are more intensive in low-skill workers; improvements in skills raise low-skill wages and the costs of being informal.
    - Skill-composition improvements can complement minimum wage policies in reducing overall earnings inequality in contexts with a large informal sector.
  - Model-implied skill-biased technical change:
    - Increases the share of the informal workforce by 50%.
    - Increases overall earnings inequality by 26%.

### Data and definitions used for validation
- Main data source: Pesquisa Nacional por Amostra de Domicílios (PNAD), 1996-2012.
- Sample restrictions and measures:
  - Individuals aged between 18-54.
  - One job per worker (main job in the reference week).
  - Monthly gross labor earnings (excluding social transfers and pensions), deflated by the CPI and expressed in 2012 terms.
  - A worker is informal if they do not have a signed working permit (Carteira de Trabalho Assinada).
  - Self-employment is excluded from the main analysis (results can be interpreted as a lower bound on total effects when including self-employment).
- Institutional note:
  - The federal minimum wage imposes a nation-wide floor on monthly nominal earnings of formal workers.
  - Since Lei Complementar No. 103 on July 14, 2000, five out of the 27 states instituted state-specific wage floors: Rio de Janeiro and Rio Grande do Sul since 2001, Paraná since 2006, São Paulo since 2007, and Santa Catarina since [text truncated].

### Implications for validation and external checks
- Reduced-form state-level heterogeneity provides external validation for the model mechanism: larger formal-sector minimum wage exposure is associated with stronger informal-sector responses and higher aggregate inequality.
- Calibration replicates sectoral and skill-group wage distributions, supporting external validity of quantitative counterfactuals on:
  - Aggregate inequality effects of minimum wage increases.
  - The role of enforcement and skill composition in mediating those effects.

*Source: IMF Working Paper excerpt (file: wpiea2024159-print-pdf; content covering Introduction, Table of Contents, and Empirical motivation sections for 1996-2012 Brazil).*

### 2010.  However, these state-specific wage floors are not considered in the analysis, as the federal

### Minimum Wages, Inequality, and the Informal Sector

### Stylized facts on the informal sector, inequality, and the minimum wage
- Informal workers constitute a substantial share of the labor force and tend to earn less and be substantially less educated than formal workers.
- Table 1: Summary statistics by formality status (1996 and 2012)
  - Share (1996): Formal 60.9, Informal 39.1
  - Share (2012): Formal 69.1, Informal 30.9
  - Mean earnings (1996): Formal 1,387, Informal 673, Difference 714***
  - Mean earnings (2012): Formal 1,388, Informal 840, Difference 548***
  - Share with HS (1996): Formal 31.5, Informal 14.6, Difference 16.9***
  - Share with HS (2012): Formal 61.2, Informal 38.4, Difference 22.8***
  - Age (1996): Formal 32.5, Informal 31.0, Difference 1.5***
  - Age (2012): Formal 33.7, Informal 33.5, Difference .2**
  - Male (1996): Formal 63.8, Informal 55.2, Difference 8.6***
  - Male (2012): Formal 58.6, Informal 50.0, Difference 8.7***
  - Notes: Earnings are deflated by CPI and expressed in 2012 values. ***p<1%, **p<5%, *p<10%. Sources: 1996/2012 PNAD.
- Key movements 1996–2012:
  - The informal share fell from 39.1% to 30.9%.
  - The share of workers with at least a high school diploma rose:
    - Formal: from 31.5% to 61.2%
    - Informal: from 14.6% to 38.4%
  - Aggregate improvements in education substantially explain the reduction in informality (shift-share analysis referenced).
- Additional empirical notes:
  - Informality is widespread across industries; within-industry informal share ranges from 17% in Manufacturing to 70% in Domestic Services.
  - The unemployment rate was much lower than the informal share (around 7.5%) and varied less (9% to 6%) over the sample, implying a lower role for unemployment margins versus informality margins.

### Facts on inequality
- Evolution of variance of log earnings (1996–2012):
  - Strong and steady reduction in overall inequality: 2.3% per year.
  - Formal sector inequality fell at 4.5% per year.
  - Informal sector variance of log earnings remained roughly constant, fluctuating around 0.65 log points.
  - The gap between formal and informal earnings inequality widened consistently through the 2000s.
- Decomposition of aggregate inequality:
  - Aggregate variance Vt decomposed into:
    - Within component: employment-weighted average of inequality within formal and informal sectors.
    - Between component: employment-weighted sum of squared distances between sector means and the overall mean.
  - The within-component (weighted sum of formal and informal inequality) explains over 80% of the level of aggregate earnings inequality and over 83% of its reduction over the sample period.

### Facts on the minimum wage
- Two measures of minimum-wage evolution (1996–2012):
  - Minimum wage as fraction of median earnings: increased from 45% in 1996 to 73% in 2012.
  - Share of formal workers receiving exactly the minimum wage: increased from 8% in 1996 to 16% in 2012.
- The bulk of the increase in minimum-wage restrictions occurs after 1999; prior to 1999 there was a small decrease in the share of formal minimum-wage workers.

### Reduced-form evidence: minimum wage, inequality, and informality
- Empirical approach:
  - Leverages state-level heterogeneity in initial exposure to the minimum wage (measured by 1999 share of formal workers binding at the national wage floor).
  - Brazil’s 27 states are ranked and split into 9 treatment groups; comparisons made between the 3 most exposed states (Piauí, Sergipe, Bahia) and the 3 least exposed states (São Paulo, Santa Catarina, Distrito Federal).
  - Event-study specification:
    - ysgt = α + Σh,1 Σk,1999 βkh · I g=h · I t=k + δs + δt + X′st Γ + εst
    - ysgt: outcome in state s, treatment group g, year t
    - δs: state fixed effects; δt: year fixed effects; Xst: controls for age, gender, race, education composition
    - Year 1999 and group 1 omitted as baseline
- Main empirical findings (states most exposed vs least exposed):
  - Formal inequality: stronger declines in most-exposed states (60% decline) versus least-exposed states (40% decline).
  - Informal inequality: 40% increase in most-exposed states.
  - Aggregate inequality: milder declines in most-exposed states (10% decline) versus least-exposed states (40% decline).
  - Informal share of labor: states with largest share of formal minimum-wage workers experienced milder decreases in informality (13.6% decrease) versus least-exposed states (33.6% decrease).
- Interpretation:
  - The minimum wage can decrease inequality within the formal sector while increasing inequality overall, due to adverse effects on the informal sector (rising informal inequality and a relatively higher informal share).

*Source: IMF Working Paper excerpt (1996–2012 PNAD data presented).*

### 1999.  The identification assumption is that of parallel trends:  absent the sharp increase in the

### wpiea2024159-print-pdf - 1999.  The identification assumption is that of parallel trends:  absent the sharp increase in the

### Identification and empirical strategy
- Identification assumption: parallel trends — absent the sharp increase in the minimum wage after 1999, the relative evolution of outcomes in states belonging to different treatment groups would not change.
- Estimation: differences-in-differences / event-study using states grouped by exposure to the 1999 minimum wage increase. Regression:
  - y_sgt = α + Σ_{h,1} β_h · I_{g=h} · I_{t>1999} + δ_s + δ_t + X'_st Γ + ε_st
- Data: 1996-2012 PNAD. Standard errors clustered at the state level.

### Empirical results — most treated vs least treated (Figure 5 & Table 2)
- Event-study mean effects in the post-1999 period (β_9):
  - log(VAll): 0.200 (0.077)**
  - log(VF): -0.253 (0.063)***
  - log(VI): 0.316 (0.078)***
  - log(Inf Share): 0.073 (0.032)**
- Interpretation (most vs least exposed states):
  - 25.3 p.p. stronger reduction in formal inequality (matches β for formal: -0.253).
  - 31.6 p.p. larger increase in informal inequality (matches β for informal: 0.316).
  - 7.3 p.p. stronger increase in the informal share of labor (matches β for informal share: 0.073).
  - Joint effect: 20 p.p. stronger increase in overall inequality (matches β for overall: 0.200).
- Table 2 additional covariate coefficients (with standard errors and significance):
  - Fraction high skill: 0.485 (0.177)** ; log(VF): 0.447 (0.373) ; log(VI): 0.582 (0.254)** ; log(Inf Share): -0.466 (0.106)***
  - Fraction under 30: -0.561 (0.165)*** ; log(VF): -0.511 (0.320) ; log(VI): -0.742 (0.198)*** ; log(Inf Share): 0.219 (0.143)
  - Fraction white: -0.083 (0.165) ; log(VF): -0.233 (0.204) ; log(VI): -0.200 (0.172) ; log(Inf Share): 0.052 (0.064)
  - Fraction female: 0.218 (0.147) ; log(VF): 0.446 (0.269) ; log(VI): 0.558 (0.220)** ; log(Inf Share): -0.059 (0.226)
  - Unemployment rate: -0.343 (0.521) ; log(VF): -1.689 (0.723)** ; log(VI): -0.042 (0.668) ; log(Inf Share): 0.253 (0.336)
  - State FE: ✓ ; Year FE: ✓
  - Observations: 405 for each regression
  - R^2: log(VAll) 0.854 ; log(VF) 0.891 ; log(VI) 0.642 ; log(Inf Share) 0.966

### Diff-in-diff across treatment groups (Figure 6)
- Three empirical patterns across treatment groups:
  1. Minimum wages reduce inequality in the formal sector, with effects stronger in states more exposed.
  2. Minimum wages are associated with significant increases in informal inequality and in the informal share only in the most restricted states (groups 8 and 9).
  3. Net effect on overall inequality varies by treatment intensity: e.g., relative to group 1, states in group 2 experienced a 14.2 p.p. stronger decrease in overall inequality, whereas states in groups 8 and 9 experienced a 20 p.p. stronger increase in overall inequality.
- Conclusion: increasing the minimum wage increases overall earnings inequality when there is a strong, inequality-increasing effect on the informal sector.

### Robustness checks
- Alternative definitions of informality:
  - Including self-employed individuals in the definition of informality does not alter the qualitative findings (Figures A.8–A.10).
- Hours adjustment:
  - Using hourly earnings (minimum wage adjusted to full-time 44 hours/week) yields similar results (Figures A.11–A.12), suggesting hours adjustment is not consequential.
- Alternative splits and levels:
  - Splitting states by median 1999 share of formal minimum wage workers preserves event-study patterns but yields noisier estimates (Figure A.13).
  - Analysis in levels shows positive and significant relationship between minimum wages and overall and informal earnings inequality, and a positive but insignificant relationship with informal share (Figure A.14).
- Recent TWFE estimator concerns:
  - Implementations of Borusyak et al. (2021), de Chaisemartin and D’Haultfœuille (2020), and Callaway and Sant’Anna (2020) produce event-study coefficients qualitatively and quantitatively similar to OLS (Figures A.15–A.16).
- Kaitz-regression style checks:
  - Following the literature using the Kaitz index yields persistent findings: minimum wages correlate negatively with formal inequality, positively with informal inequality and the informal share, which act as counteracting forces for overall inequality (online Appendix H).
- Treatment intensity insight:
  - Reconciliation with Derenoncourt et al. (2021): displacement into informality occurs in the poorest, most binding states (e.g., Piauí, Sergipe, Bahia); less-treated states did not experience a relative increase in the informal sector (online Appendix J).

### Model — environment and mechanisms
- Agents and preferences:
  - Unit measure of ex-ante homogeneous households; supply one unit of inelastic labor.
  - Individual utility: V_i(j) = A_i(j) w(j), with A_i(j) drawn i.i.d. Fréchet with shape parameter η.
  - Firm-level labor supply: l(j) = Prob_i(j) = [ w(j) / W ]^η, with W ≡ [ ∫_{j′∈Ω} w(j′)^η dj′ ]^{1/η}.
- Firms and production:
  - Exogenous mass of firms heterogeneous in productivity z ∼ F over [z_0 > 0, ∞), with f(z) > 0 ∀ z and lim_{b→∞} ∫_{z_0}^b z^η dF(z) < ∞.
  - Goods market: perfect competition; labor market: monopsonistic competition.
- Formal sector (minimum wage w):
  - Formal firm profit problem:
    - π_form(z) = max_{l,w} [ z l − w l | l = (w/W)^η, w ≥ w ].
  - Optimal solutions:
    - w_form(z) = max( η/(η+1) z, w )
    - l_form(z) = W^{-η} [ max( η/(η+1) z, w ) ]^η
    - π_form(z) = W^{-η} [ max( η/(η+1) z, w ) ]^η [ z − max( η/(η+1) z, w ) ]
  - Minimum wage acts as a fixed production cost for low productivity firms; firms with productivity below the minimum-wage-implied cutoff have negative profits if formal.
- Informal sector (detection cost ρ):
  - Detection probability ρ; penalty: loss of all revenues if detected (alternative parametrization discussed in footnote).
  - Informal firm problem:
    - π_inf(z) = max_{l,w} [ (1−ρ) z l − w l | l = (w/W)^η ].
  - Optimal solutions:
    - w_inf(z) = η/(η+1) (1−ρ) z
    - l_inf(z) = W^{−η} [ η/(η+1) (1−ρ) z ]^η
    - π_inf(z) = W^{−η} [ η^η / (η+1)^{η+1} ] (1−ρ)^{η+1} z^{η+1}
  - Absence of fixed costs implies positive profits for all informal firms; informality is a profitable outside option for unproductive firms.

### Equilibrium and firm selection
- Equilibrium definition: W such that aggregate labor demand equals aggregate labor supply:
  - L_D(W) ≡ ∫_{z_0}^∞ l(z) f(z) dz = 1 = L_S.
- Partial equilibrium firm selection (Proposition 1):
  - There exist two thresholds z and z̄:
    - z satisfies: η^η / (η+1)^{η+1} (1−ρ)^{η+1} z^{η+1} − w^η z + w^{η+1} = 0 (expression shown in text)
    - z̄ = (η+1)/η w
  - Characterization:
    1. w ≤ z < z̄
    2. Firms with z < z operate informally; z ∈ [z, z̄] are formal but restricted by w; z > z̄ are formal and unrestricted by w.
    3. ∂z/∂ρ < 0, ∂z/∂w > 0, and ∂^2 z / ∂ρ ∂w < 0.
    4. ∂(z/w)/∂w = 0.
  - Intuition: low-productivity firms select into informality because the labor-cost savings from avoiding the minimum wage outweigh productivity losses; larger minimum wages and smaller detection costs (ρ) increase informality.

- Aggregate wage index expression:
  - W = η/(η+1) [ ∫_{z_0}^z [ (1−ρ) z ]^η f(z) dz + [ F(z̄) − F(z) ] z̄^η + ∫_{z̄}^∞ z^η f(z) dz ]^{1/η}

### Inequality, minimum wage, and the informal margin (Proposition 2)
- Setup: compare economy without informality (ρ = 1) vs with informality (ρ < 1). Consider minimum wages w ∈ (w_0, w_0 + ε) with small ε where a marginal increase generates the first units of informal labor.
- Marginal decomposition of the effect of minimum wage on variance of log earnings V (Proposition 2):
  - ∂V/∂w =
    - ∂V_form/∂w | formal sector response (FR)
    - + ∂L_inf/∂w | workers become informal
    - × [ (E_inf − E_form)^2 | wage differential + V_inf − V_form | pre↑w variances ] | informal sector response (IR)
- Key implication:
  - If z ∼ Pareto(ν > η), then the informal margin can dominate: increasing the minimum wage can increase overall earnings inequality when firms can avoid the minimum wage by operating informally.
  - Intuition: the minimum wage reduces formal-sector dispersion (FR) but induces reallocation to the informal sector (IR) where wage differentials and higher within-informal variance can raise overall inequality.
- Policy-relevant insight:
  - Presence of an informal sector implies potential unintended consequences: policies aimed to reduce inequality via minimum wage increases might increase overall inequality if the informal margin is a significant adjustment channel.

_Italic source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024159-print-pdf.pdf_

### 1.  Without informality, increasing the minimum wage reduces inequality:

### 1.  Without informality, increasing the minimum wage reduces inequality:

### Main propositions and formal results
- Proposition 2 (informality and inequality):
  - Without informality, increasing the minimum wage reduces inequality:
    - ∂V/∂w = ∂V_form/∂w < 0.
  - With informality, increasing the minimum wage increases inequality:
    - ∂V/∂w > 0.
  - Proof. See online Appendix E for details.

- Proposition 3 (minimum wage and worker welfare; effect on labor demand):
  - Notation: l_inf(z) and l_w denote labor allocation at informal and minimum-wage firms.
  - Assume the minimum wage (w) is such that w < z0 < z < z̄z. Then the marginal effect of the minimum wage on labor demand (L_D) is:
    - ∂L_D/∂w =
      - [F(z̄) − F(z)] | Firms at MW
        - ∂l_w/∂w | L_D increase | formal sector response (FR > 0)
      - − [l_w − l_inf(z)] | L_D drop (MW → inf)
        - f(z) | firms at cutoff
        - ∂z/∂w | cutoff response
      - Informal sector response (IR > 0)
  - If z ∼ Pareto(ν > η) then:
    1. Without informality, increasing minimum wage increases worker welfare:
       - ∂L_D/∂w > 0.
    2. With informality, increasing the minimum wage reduces worker welfare:
       - ∂L_D/∂w < 0.
  - Proof. See online Appendix E for details.

### Mechanisms and interpretation
- Decomposition of the marginal effect of the minimum wage on the variance of log earnings:
  - Component 1: Effects on formal sector earnings inequality — typically negative (reduces inequality) and is the object of the conventional minimum wage literature.
  - Component 2: Informal margin of adjustment — depends on:
    - the responsiveness of the informal sector to the increase in the minimum wage,
    - how “spread apart” the earnings distribution in both sectors are.
  - Net effect on aggregate inequality is ambiguous: which component dominates matters.

- Special case: Pareto-distributed firm productivity
  - When firm productivity is Pareto-distributed, the net effect of a marginal increase in the minimum wage on inequality is positive.
  - In a model without informality, inequality goes down as the minimum wage increases.
  - However, with informality, workers that become informal spread out the earnings distribution, raising inequality levels beyond the inequality-reducing effects in the formal sector.

### Effects of the minimum wage on worker welfare (discussion)
- Worker expected utility is proportional to the aggregate wage index:
  - E[U] = Γ(η−1/η) W.
  - Γ(·) denotes the gamma function.
- Because aggregate labor supply is inelastic, policies that increase aggregate labor demand increase the wage index and improve worker welfare.
- Two components shape the minimum wage effect on worker welfare:
  - Formal sector response:
    - Minimum wage reduces firms’ monopsony power; firms must set wages at the minimum rather than a markdown over marginal product, increasing labor demand.
  - Informal margin of adjustment:
    - Increase in the minimum wage raises the informality cutoff; firms at the cutoff become informal, reset wages as a markdown over discounted productivity, and adjust their labor demand downward.
- The formal and informal responses counteract; the net effect depends on which dominates.
- If F is Pareto, the informal margin of adjustment can be too strong (many firms concentrated around the informality cutoff), so increasing the minimum wage may reduce workers’ welfare. The presence of the informal sector thus can fundamentally alter welfare consequences relative to a model without informality.

### Quantitative extension — model features summarized
- Purpose: extend the model to quantify general equilibrium effects of the minimum wage, consistent with empirical evidence for Brazil.
- Household side:
  - Workers differ in skill level: H different skill levels; N_h denotes fraction of workers of skill level h.
  - Utility of worker i of skill h at firm j:
    - V_ih(j) = A_i(j) · (1 + ς_h(j)) w(j),
    - where ς_h(j) = 0 if firm j is informal and ς_h(j) = ς_h if formal.
    - Allows wedge between nominal and perceived wage due to valuation of labor legislation (vacation stipend, unemployment and retirement benefits, etc.).
  - Labor supply curve firm j faces for skill h:
    - l_h(j) = N_h [ (1 + ς_h(j)) w_h(j) / W_h ]^η,
    - W_h = [ ∫_{j∈Ω} [(1 + ς_h(j)) w_h(j)]^η dj ]^{1/η}.
  - Worker welfare for skill h is proportional to wage index W_h.

- Firm side:
  - Productivity z = ν θ, drawn independently from distributions F_ν and F_θ.
  - Labor markets segmented by skill; firms compete monopsonistically in each skill market.
  - Firms aggregate skills via CES to produce a homogeneous good under perfect competition.
  - Timing: firms draw ν; decide formal vs informal status; then draw θ (z realized); conditional on z maximize profits subject to skill-specific labor supply and sector constraints.
  - Formal firm profits:
    - π_form(z) = max_{ {l_h(z), w_h(z)}_h } { z ℓ − (1 + τ) Σ_h w_h(z) l_h(z) }
    - s.t. ℓ = [ Σ_h ξ_h(z) l_h(z)^{(ε−1)/ε} ]^{ε/(ε−1)}, l_h(z) = N_h [ (1 + ς_h) w_h(z) / W_h ]^η, w_h(z) ≥ w ∀ h,
    - where τ is payroll tax rate, ε is elasticity of substitution across skills, ξ_h(z) are skill-specific demand shifters.
  - Proposition 4:
    - Conditional on z, unique solution: wages are either constrained at the minimum or reflect a markdown over marginal product of labor.
    - Proof. See online Appendix E for details.
  - Informal firm profits:
    - Informal firms not subject to minimum wages nor payroll taxes; face government detection probability ρ that leads to losing all revenue.
    - π_inf(z) = max_{ {l_h(z), w_h(z)}_h } { (1 − ρ) z ℓ(z) − Σ_h w_h(z) l_h(z) }
    - s.t. ℓ(z) = [ Σ_h ξ_h(z) l_h(z)^{(ε−1)/ε} ]^{ε/(ε−1)}, l_h(z) = N_h [ w_h(z) / W_h ]^η ∀ h = 1,...,H.
  - Proposition 5 (closed-form informal solution):
    - π_inf(z) = W(z)^(−η/η) (η+1)^(η/(η+1)) (1−ρ)^(η+1) z^(η+1)
      - (as presented: π_inf(z) = W(z)^{−η/η η(η+1)^{η+1} (1−ρ)^{η+1} z^{η+1}; preserve original notation)
    - Wording in source for informal profits and labor/wage allocations:
      - w_inf_h(z) = [ ξ_h(z)^{ε} / N_h ]^{1/(η+ε)} [ W_h / W(z) ]^{η/(η+ε) * η/(η+1) } (1−ρ) z,
      - l_inf_h(z) = N_h [ w_inf_h(z) / W_h ]^η.
    - W(z) denotes the cost index a firm with productivity z faces:
      - W(z) ≡ [ Σ_h ξ_h(z)^{ε/(η+ε)} (1+η) [ W_h / N_h^{1/η} ]^{η/(η+ε)} (1−ε) ]^{(η+ε)/η 1/(1−ε)}.
    - Proof. See online Appendix E for details.

- Formality decision:
  - Firms operate formally iff expected formal profits exceed expected informal profits:
    - V_form(ν) ≡ ∫_{θ∈Θ} π_form(νθ) dF_θ(θ) ≥ ∫_{θ∈Θ} π_inf(νθ) dF_θ(θ) ≡ V_inf(ν).
  - Two implications:
    - Generates overlap in productivity distributions across formal and informal sectors → overlap in wage distributions.
    - Exit of formal firms that are not productive enough (low θ draw) to operate with positive profits.

- Equilibrium condition:
  - Wage indices W_h for all h = 1,...,H such that aggregate labor demand equals aggregate labor supply:
    - ∫_0^∞ l_h(z) dF(z) = N_h, ∀ h = 1,...,H.
  - Further market clearing in goods markets calculated in online Appendix F.

*Source: IMF Working Paper (section text provided).*

### Appendix G details the algorithm used to numerically solve for the equilibrium.

### Appendix G: Algorithm used to numerically solve for the equilibrium

### Calibration and validation (Section 5)
- Calibration period and focus:
  - Parameters calibrated to Brazilian data spanning 1996 and 2012 values unless noted otherwise.
  - Targets: labor supply, labor demand, government parameters; internal calibration matches model moments to data moments.
- Validation:
  - External validation compares untargeted moments (earnings distributions overall, within sector, within skill groups).
  - Model delivers realistic earnings distributions and captures bunching at the minimum wage in the formal sector.

### Labor supply (Section 5.1)
- Skill mapping:
  - H = 4 education groups: no degree (4 years or less), primary (5-8 years), secondary (9-11 years), tertiary (over 12 years).
  - Share changes: no-degree share (N1) fell from 38% in 1996 to 16% in 2012 (Figure 7, PNAD).
- Earnings heterogeneity:
  - Workers with tertiary degrees earn on average 4 times more than non-degree workers (Figure A.17).
- Firm-level labor supply elasticity (internally calibrated):
  - η = 4.52 for 1996 and η = 4.22 for 2012.
  - Interpretation: η influences slope of firm-level wages with respect to firm productivity; estimated values are stable over time and align with literature.

### Labor demand (Section 5.2)
- Skill-biased technology:
  - Demand shifters ξh(z) = zφh / Σj zφj, with Σh φh = 0 (equation 27).
  - φh > 0 ⇒ more productive firms are more intensive in skill h.
  - φh parameters internally calibrated to match ratios of mean earnings across skills relative to no degree (Figure 8).
  - Finding: demand coefficients for skill groups 3 and 4 increase over time, indicating skill-biased technical change (SBTC).
- Elasticity of substitution:
  - ε = 1.875 (value from Fernández and Messina (2018) range 1.16 to 2.51).
- Firm productivity distribution:
  - ν ∼ Log-Normal with underlying Normal mean zero and standard deviation σ.
  - θ ∼ Pareto with shape parameter κ.
  - Calibrated values: σ = 1.01 (1996), σ = 1.29 (2012); κ = 6.02 (1996), κ = 6.33 (2012).
  - Interpretation: σ increased (greater dispersion of base productivity); κ increased (decrease in tail).

### Government and labor legislation (Section 5.3)
- Internally calibrated:
  - Minimum wage parameter w = 4.04 (1996), w = 8.87 (2012).
  - Informality cost ρ = 0.26 (1996), ρ = 0.32 (2012).
  - Model-implied 120% increase in the minimum wage vs observed 106% increase in the real minimum wage.
  - Calibrated model delivers a 23% increase in the informality cost.
- Payroll and perceived wages:
  - Formal firms face total labor cost multiplier τ = 71.4% (estimated from Souza et al. (2012) methodology; assumed constant).
  - Workers value each Real of gross formal wages at 1 + ςh; ςh estimated from legislation (Figure 9).
    - Findings: ςh > 0 for all h; gap between nominal and real value of formal wages is 30% for no-degree workers and 24% for tertiary workers (progressive taxation effects).
- Internal calibration objective:
  - Parameter vector Θ∗ = {φ∗1, φ∗2, φ∗3, σ∗, κ∗, η∗, ρ∗, w∗} minimizes mean absolute percentage distance between model and targeted data moments:
    - Θ∗ = argminΘ Σi=1^8 |mi(Θ)/ˆmi − 1| (Table 3 summary of parameters and targets).

### Fit and external validation (Section 5.4)
- Model fit:
  - Replicates targeted moments well except inequality in the informal sector.
  - Tension: matching within-sector inequality versus correct size of informal sector—tradeoff across 1996 and 2012.
  - Less heterogeneity in model’s informal share within skill groups than in data.
- Earnings distributions:
  - Model-generated histograms of log earnings relative to minimum wage (Figure 10) show:
    - Aggregate distribution: similar higher moments (beyond mean and variance).
    - Pareto-LogNormal productivity assumption approximates lower and upper tails well.
    - Formal sector: model captures bunching at minimum wage.
    - Informal sector: model produces less bunching than data (consistent with literature).
- Table 4: Selected model vs data moments (1996 and 2012)
  - Mean earnings ratios (Data vs Model):
    - Formal/Informal: 1996 Data 2.06 vs Model 2.11; 2012 Data 1.65 vs Model 1.67.
    - Primary/No degree: 1996 Data 1.39 vs Model 1.39; 2012 Data 1.19 vs Model 1.19.
    - Secondary/Primary: 1996 Data 1.46 vs Model 1.49; 2012 Data 1.21 vs Model 1.21.
    - Tertiary/Secondary: 1996 Data 2.49 vs Model 2.41; 2012 Data 2.15 vs Model 2.15.
  - Variance of log-earnings (selected):
    - Overall: 1996 Data 0.78 vs Model 0.78; 2012 Data 0.50 vs Model 0.46.
    - Formal: 1996 Data 0.65 vs Model 0.58; 2012 Data 0.33 vs Model 0.33.
    - Informal: 1996 Data 0.66 vs Model 0.73; 2012 Data 0.62 vs Model 0.51.
  - Minimum wage binding (Formal Fraction at w):
    - 1996 Data 7.7 vs Model 7.7; 2012 Data 15.8 vs Model 15.8.
  - Informal share (Overall):
    - 1996 Data 0.39 vs Model 0.39; 2012 Data 0.31 vs Model 0.31.

### Counterfactuals (Section 6)
- Counterfactual minimum wage:
  - Counterfactual w = 6.6 calculated assuming all increase in formal bunching (7.7% → 15.8%) driven solely by minimum wage.
- Counterfactual experiment design:
  - Change one parameter at a time from 1996 calibrated level to its 2012 value: w, ρ, Nh, ξh(z).
  - Table 5 reports resulting outcomes across counterfactuals (selected entries reproduced as exact values):
    - Mean earnings ratios under counterfactuals (examples):
      - Form/Inf: 1996 Data 2.11; Counterfactual w → 1.70; ρ → 2.37; Nh → 2.52; ξh(z) → 1.90; 2012 Data 1.67.
    - Variance of log earnings (overall):
      - 1996: 0.78; w: 0.83; ρ: 0.78; Nh: 0.79; ξh(z): 0.98; 2012: 0.46.
    - Fraction at w (Formal):
      - 1996: 7.7; w: 15.2; ρ: 8.3; Nh: 3.6; ξh(z): 14.0; 2012: 15.8.
    - Min/mean wage:
      - 1996: 0.26; w: 0.33; ρ: 0.26; Nh: 0.21; ξh(z): 0.24; 2012: 0.47.
    - Informal share:
      - 1996: 0.39; w: 0.73; ρ: 0.28; Nh: 0.23; ξh(z): 0.61; 2012: 0.31.
- Effects of increasing the minimum wage:
  - No effect on skill earnings premia (first three rows of w column), but:
    - Substantial decrease in formal wage premium (formal/informal), driven by productive formal firms becoming informal and increased share of minimum-wage workers.
    - Minimum wage accounts for 28% of observed decrease in formal inequality.
    - Spillovers up to the 75th percentile of the formal earnings distribution (Figure 11):
      - Raising the minimum wage increases percentile ratios: p10p90 by 21.8%, p20p90 by 12.4%, p50p90 by 3.5%.
  - Aggregate unintended consequence:
    - Minimum wage increase raised overall earnings inequality by 6.4% because increases in informality and informal inequality offset formal-sector reductions.
  - Welfare effects:
    - Minimum wage increase improves welfare only for tertiary-educated workers (0.7% increase).
- Firm types and informality:
  - Firm classification under 2012 minimum wage:
    - Type 1 (cannot cope with 2012 minimum wage): 25.8% of workers employed.
    - Type 2 (productive enough to be formal under 2012 minimum wage but choose informality): 9.9% of labor force.
    - 27.7% of labor force that becomes informal in response to minimum wage work in firms that could be formal if forced.
  - Policy implication: Formalization policies paired with minimum wage adjustments can deter a large share of increased informality without causing firm exit.
- Effects of increased informality cost (ρ):
  - Estimated 24% increase in informality costs → 28% decrease in informal share; little change in aggregate earnings inequality due to offsetting forces:
    - Formal earnings premium increases by 12.3% (increases cross-sector inequality).
    - Informal inequality decreases.
- Joint counterfactuals (Table 7):
  - Jointly changing minimum wage and informality cost:
    - ∆ρ = 24% (estimated) does little to offset minimum wage’s effect on informality and aggregate inequality.
    - ∆ρ = 85% would offset minimum wage’s effect on aggregate inequality.
  - Jointly changing minimum wage and skill composition:
    - Improvement in skill composition reduces informal share by 30% and helps complement minimum wage policies in reducing overall earnings inequality.
- Skill composition and SBTC:
  - Improvement in skill composition:
    - Reduces informal labor share by 30%.
    - Raises scarcity and wages of low-skilled factors; increases formal inequality by 6.4% and decreases informal inequality by 11.1%, leaving aggregate inequality nearly unaffected.
  - Skill-biased technical change (ξh(z) shifts):
    - Welfare changes (Table 6 wage indices W h):
      - No degree: 1996 W = 0.967; ξh(z) counterfactual W = 0.690.
      - Primary: 1996 W = 1.240; ξh(z) W = 1.066.
      - Secondary: 1996 W = 1.730; ξh(z) W = 1.902.
      - Tertiary: 1996 W = 3.687; ξh(z) W = 3.952.
    - SBTC increases informal share from 39% to 61% and increases aggregate earnings inequality by 26% (inequality rises within both sectors).
- Unemployment margin (Online Appendix I):
  - Adding unemployment following Caliendo et al. (2019) and re-calibrating shows the primary margin of adjustment to the minimum wage is between formal and informal sectors, not employment-unemployment transitions (due to relative positions of unemployment benefits vs minimum wage).

### Key quantitative moments and parameters (selected exact values from calibration and results)
- Labor supply elasticity η: 4.52 (1996), 4.22 (2012).
- Elasticity of substitution ε: 1.875.
- Productivity distribution parameters:
  - σ: 1.01 (1996), 1.29 (2012).
  - κ: 6.02 (1996), 6.33 (2012).
- Government and wage parameters:
  - w (minimum wage parameter): 4.04 (1996), 8.87 (2012).
  - ρ (informality cost): 0.26 (1996), 0.32 (2012).
  - τ (payroll tax multiplier): 71.4%.
  - ςh: positive for all skills; gap between nominal and real formal wages: 30% for no-degree workers, 24% for tertiary workers.
- Distribution and inequality moments (selected):
  - Formal/Informal mean earnings: 2.06 (1996 Data), 2.11 (1996 Model); 1.65 (2012 Data), 1.67 (2012 Model).
  - Overall variance of log earnings: 0.78 (1996 Data & Model), 0.50 (2012 Data), 0.46 (2012 Model).
  - Formal fraction at minimum wage: 7.7% (1996 Data & Model), 15.8% (2012 Data & Model).
  - Informal share overall: 0.39 (1996 Data & Model), 0.31 (2012 Data & Model).

### Main conclusions and policy-relevant insights (Section 7)
- Primary finding:
  - In the Brazilian context, the large increase in the minimum wage during the 2000s reduced formal-sector inequality but increased aggregate earnings inequality by 6.4% due to substantial informality responses and increased informal inequality.
- Mechanisms and implications:
  - Minimum wage increases have spillovers across the formal earnings distribution (up to the 75th percentile) due to imperfect substitution across skills.
  - Strong informal margins of adjustment can produce unintended consequences of labor-market policies aimed at reducing inequality.
  - Complementary policies matter:
    - Formalization/enforcement increases can mitigate unintended informality responses; an 85% increase in enforcement (relative to 1996) would offset the minimum wage’s effect on aggregate inequality in the model.
    - Improvements in skill composition reduce informality and can complement minimum wage increases in lowering aggregate inequality.
- Broader relevance:
  - Results highlight the need to consider local informality and formalization policies when setting federal-level minimum wages.
  - Findings are relevant for assessing minimum-wage effects in contexts where agents can operate outside labor legislation (e.g., gig economy arrangements).

*Source: Appendix G and related sections from the IMF Working Paper "Minimum Wages, Inequality, and the Informal Sector" (calibration, validation, and counterfactual exercises summarized from the supplied content).*

### References

### References

### Primary research themes
- Empirical and theoretical work on minimum wages, wage inequality, and spillover effects into low-wage and informal sectors.
- Studies of informality, labor regulation enforcement, and the interaction between labor market institutions and firm behavior.
- Research on trade shocks, international trade, and their effects on labor markets, earnings distribution, and sectoral reallocation.
- Analyses of wage distribution modeling and income distribution dynamics.
- Investigations of racial and regional inequality, geographic development patterns, and productivity implications of tax and informal-sector interactions.

### Methodological approaches represented
- Difference-in-differences and event-study designs, including recent work on robust estimation with multiple time periods and heterogeneous treatment effects.
- General equilibrium and heterogeneous-firm models linking trade shocks to labor market outcomes.
- Density discontinuity and regression-discontinuity-style approaches for estimating minimum-wage impacts.
- Compensating-differentials, bargaining (Roy-Rosen) frameworks, rent sharing, and models of labor market sorting.
- Combination of administrative data, household surveys, and matched employer-employee datasets underpinning empirical findings.

### Geographic and sectoral focus
- Significant attention to Brazil and Latin America, including studies of formal and informal employment dynamics and changes in wage inequality.
- Evidence and case studies from the United States, including low-wage sectors and minimum-wage case studies.
- Cross-country and macro perspectives connecting trade, commodities booms, and structural wage changes.

### Recurring policy-relevant topics
- The role of minimum wages in shaping wage inequality and distributional outcomes.
- Enforcement of labor regulations as a determinant of informality and formal-sector employment.
- Trade policy and external shocks as drivers of within-country labor-market reallocation and inequality.
- Tax collection, productivity, and the incentives for formalization.

*Source: References (wpiea2024159-print-pdf)*

### Introduction of Minimum Wages to a Low Wage Sector,”Journal of the European Economic Asso-

### wpiea2024159-print-pdf - Introduction of Minimum Wages to a Low Wage Sector,”Journal of the European Economic Asso- ciation, 2003,1(1), 154–180.

### Appendices overview (A–G) and data comparisons
- Appendix A: Additional figures and tables referenced in the main text; comparisons across surveys:
  - Figure A.1: Comparison between RAIS and PNAD data sets, 1996-2012 (formal earnings distributions).
  - Figure A.2: Comparison between ECINF and PNAD data sets, 1997 and 2003 (informal earnings distributions).
  - Figure A.3: Share of formal/informal workers with more than one job, 1996-2012 (Sources: 1997-2012 PNAD).
  - Figure A.4 and A.5: Shift-share decompositions of informality across education groups and industries, 1996-2012 (Sources: 1996-2012 PNAD).
  - Figure A.6: Informality and unemployment, 1996-2012 (Sources: 1996-2012 PNAD).
  - Figure A.7: Decomposition of overall variance of log earnings into within and between terms (Sources: 1996-2012 PNAD).
- Table A.1: Informal share in different industries (data restricted to 2001-2012; sample weights used). Selected entries:
  - Manufacturing: Share informal 16.5; Share of total employment 18.1
  - Commerce and repair: Share informal 24.5; Share of total employment 18.2
  - Construction: Share informal 43.5; Share of total employment 6.5
  - Domestic services: Share informal 69.4; Share of total employment 11.7
  - Agriculture: Share informal 61.6; Share of total employment 7.8
  - Notes: Second column shows share of employment that is informal; third column shows size of each industry.

### Empirical event study and difference-in-differences results
- Table A.3: Diff-in-diff results (complete table) — outcomes: log(VAll), log(VF), log(VI), log(Inf Share). Selected coefficients (standard errors in parentheses; standard clustering at state level; significance markers preserved):
  - β2: -0.142 (0.058)** ; -0.203 (0.046)*** ; -0.080 (0.073) ; 0.046 (0.037)
  - β8: 0.213 (0.052)*** ; -0.261 (0.075)*** ; 0.297 (0.093)*** ; 0.055 (0.021)**
  - Fraction high skill: 0.485 (0.177)** ; 0.447 (0.373) ; 0.582 (0.254)** ; -0.466 (0.106)***
  - Fraction under 30: -0.561 (0.165)*** ; -0.511 (0.320) ; -0.742 (0.198)*** ; 0.219 (0.143)
  - Observations: 405 (for all reported regressions)
  - R2: 0.854 ; 0.891 ; 0.642 ; 0.966
- Event study figures (A.10, A.12, A.13, A.14): OLS coefficients of Equation (2) plotted for most-treated groups and variants (incl. self-employed; hourly earnings; two groups above/below median); outcomes include log(Variance) across Formal/Informal/Overall and log(Informal share). Standard errors clustered at the state level.
- Robustness figures (A.15, A.16): Comparisons across TWFE estimators: OLS; Chaisemartin and D'Haultfoeuille (2020); Callaway and Sant'Anna (2020); Borusyak et al. (2021). Outcomes plotted include log(Overall variance), log(Informal share), log(Formal variance), log(Informal variance).

### Key descriptive distributions and inequality patterns
- Figures A.8 and A.11: Earnings inequality (variance of log earnings, 1996=1) by 3 most binding states (Piauí, Sergipe, Bahia) vs 3 least binding states (São Paulo, Santa Catarina, Distrito Federal), for aggregate, formal, and informal sectors (including self-employed and hourly earnings variants).
- Figure A.9: Informal share of labor (1996=1) — evolution in most exposed vs least exposed states.
- Figure A.17: Earnings distribution relative to the minimum wage: densities for 1996 and 2012 by education (No degree, Primary, Secondary, Tertiary).
- Figure A.18: Mean earnings relative to non-degree mean earnings, 1996-2012 — mean earnings as multiples of lowest skill’s (Primary, Secondary, Terciary).

### Payroll tax / valuation calculations (Appendix B)
- Methodology: Estimation of total labor cost of hiring a formal worker at a nominal monthly wage of 100 Brazilian Reais; apply labor legislation to each PNAD observation and average wedges across educational groups to produce worker valuation wedges ς_h.
- Table B.1: Calculating τ (payroll tax rate) — illustration for Nominal wage (A)=100. Key line-items and computed values:
  - 13th salary (A.1) = A/12 = 8.33
  - Vacation (A.2) = (A/3)/12 = 2.78
  - Advance notice = (A+A.1+A.2)*dismiss prob. = 3.33  (dismiss prob = 3%)
  - Raw total (B) = 114.44
  - FGTS contribution (B.1) = 8% of B = 9.16
  - FGTS fund (B.2) = B.1 * duration = 304.33  (duration = 33 months)
  - Severance payment = B.2/2 * dismiss prob. = 4.56
  - INSS employer = 20% of B = 22.89
  - Other contributions = 5.3% of B = 6.07
  - Total with contributions (C) = 157.12
  - Vacation adjustment = C/11 = 14.28
  - Total cost (D) = 171.40
  - Payroll tax rate: τ = D/A - 171.4%
  - Notes: Calculations made under dismissal probability of 3% and expected duration of employment of 33 months (Haanwinckel, 2020).
- Table B.2: Calculating ς_h (worker valuation wedges) — 1996 mean earnings by education and resulting overall valuation and worker wedge (values shown for four skill groups):
  - Nominal wage (A) — Means: No degree 306 ; Primary 382 ; Secondary 534 ; Tertiary 1323
  - Raw total (B): No degree 350.2 ; Primary 437.2 ; Secondary 611.1 ; Tertiary 1514.1
  - INSS deduction (over B): -31.5 ; -39.3 ; -67.2 ; -105.3
  - Income tax (over B): 0.0 ; 0.0 ; 0.0 ; -92.1
  - Valuation of FGTS (50% of firm contribution): 14.0 ; 17.5 ; 24.4 ; 60.6
  - Severance payment (40% FGTS fund * dismiss prob.): 11.2 ; 14.0 ; 19.5 ; 48.3
  - Accident insurance (2% of B): 7.0 ; 8.7 ; 12.2 ; 30.3
  - Total (pre-vacation adjustment): 350.9 ; 438.0 ; 600.1 ; 1455.8
  - Vacation adjustment (vacation cost paid by firm): 43.7 ; 54.6 ; 76.3 ; 189.0
  - Overall valuation: 394.6 ; 492.6 ; 676.4 ; 1644.8
  - Worker wedge (%): 28.9% ; 28.9% ; 26.7% ; 24.3%
  - Notes: Calculations under dismissal probability of 3% and expected duration of employment of 33 months (Haanwinckel, 2020).

### Analytical model appendices (C–E): key derivations and propositions
- Appendix C: Fréchet calculations (labor supply at firm level and worker welfare)
  - Utility U_i(j) = A_i(j) w(j); A_i(j) iid Fréchet with shape η, scale 1, location 0.
  - Worker share choosing firm j: l(j) = w(j)^η / ∫_{j'} w(j')^η (Equation (37) form).
  - Expected utility E[U] = Γ((η−1)/η) · W, where W = [∫_{j'} w(j')^η]^{1/η} (Equation (44)).
- Appendix D: Monopolistic competition extension
  - CES demand and goods market power introduced (elasticity σ).
  - Labor supply and demand expressions modified but threshold characterization (low-productivity firms choose informal sector) unchanged.
  - Adjusted markdown ̃η ≡ (σ−1)/σ · ησ/(η+σ); real wage ̃W ≡ W/P; informal labor allocation l_inf(z) expressed as function of ̃W, ̃η, (1−ρ), z (Equations (53)-(54)).
- Appendix E: Theory proofs — concise highlights
  - Proposition 1: Existence of threshold z (w ≤ z < ̄z) separating firms that operate informally from those formal; ∂z/∂ρ < 0; ∂z/∂w > 0; ratio z/w determined by η and ρ (Equations (55)-(59) and derivatives in (57)-(58)).
  - Proposition 2: Variance decomposition and effects of minimum wage on earnings variance:
    - Decomposition V = L_I V_I + L_F V_F + between-group terms (Equation (64)-(66)).
    - In Pareto case, increasing minimum wage reduces aggregate variance in absence of informality (derived from formulas (69)-(74)).
    - When informality present, formal sector variance response FR = 0; informal share ∂L_I/∂w > 0 and aggregate variance increases at the margin (detailed derivations through (75)-(103)).
  - Proposition 3: Aggregate labor demand response to minimum wage (Equations (60)-(63)); in Pareto case minimum wage increases reduce aggregate wage index ̃W (Equation (62)-(63)).
  - Proposition 4 and 5: Characterization of formal and informal firm optimization problems with CES labor aggregates; existence and uniqueness of formal firm solution (fixed point S* for operator T(S)) (Equations (110)-(116)); informal firm labor and profit formulas (Equations (107)-(109)).
- Appendix F: Walras’ Law — goods market clearing condition:
  - C + Π_form + Π_inf + ρ Q_inf = ∫_j q(j) dj = Q (Equation (122)).
  - Aggregate production allocated to consumption, formal/informal profits, and government revenue from fiscalized informal units.
- Appendix G: Computation of the quantitative model
  - Discretization of firm state space:
    - Productivity component 1 (log-Normal): grid between 0.0001 and 100 with 112 points concentrated over 1 (ν ∈ V).
    - Productivity component 2 (Pareto): grid between 1 and 100 with 93 points concentrated over 1 (θ ∈ Θ).
    - Final grid size: 10,416 points (z ∈ Z = V × Θ).
  - Computational algorithm described (algorithm steps not included in supplied excerpt).

### Model calibration / identification notes
- Identification of calibrated parameters shown in Figure A.20: objective function defined as Σ_{i=1}^8 |m_i(Θ)/ˆm_i − 1|; local identification plots for 1996 and 2012 vary parameters around calibrated values; ξ_h parameters varied collectively for brevity.

*INTERNATIONAL MONETARY FUND — IMF WORKING PAPERS: Minimum Wages, Inequality, and the Informal Sector*

### 1.  Guess a vector of wage indicesW

### 1.  Guess a vector of wage indicesW

### Algorithm steps for computing wage indices
- Step 1: Guess a vector of wage indices W0h for h = 1,...,H.
- Step 2: Calculate formal and informal profits, labor, and wages over for each firm productivity z ∈ Z following the details in the main text.
- Step 3: Update the vector of wage indices:
  - W1h ≡ [∑z∈Z (1 + ςh(z)) η w h(z) η ]1/η, ∀h = 1,...,H
- Step 4: Compare W0h and W1h for all h, update and iterate until convergence.

### Kaitz index empirical framework (Kaitz analysis)
- Definition:
  - Kaitzst ≡ log( wt / w50,Fst ). (Equation (123))
- Regression specification:
  - yst = β1 · Kaitzst + β2 · Kaitz2st + α(s,t) + εst. (Equation (124))
  - α(s,t) represents controls at the state and year level (e.g., state fixed effects and state-specific quadratic time trends in preferred specification).
  - Marginal coefficient on the minimum wage evaluated at the employment-weighted median Kaitz index: ρ = β̂1 + 2 β̂2 kaitz.

### Reduced-form empirical findings (Table H.1)
- Each cell represents a separate regression (405 observations: 27 states by 15 years). Standard errors clustered at state level. Sources: 1996/2012 PNAD.
- Estimated marginal coefficients (ρ) on outcomes:
  - Formal (log(Variance)): -0.985*** (standard error 0.085)
  - Informal (log(Variance)): 0.172** (standard error 0.081)
  - Aggregate (log(Variance)): -0.151* (standard error 0.076)
  - log(Informal share): 0.162*** (standard error 0.051)
- Interpretation:
  - Negative and significant relationship between the minimum wage and formal inequality (-0.985***).
  - Positive and significant relationship between the minimum wage and informal earnings variance (0.172**).
  - Increase in the minimum wage associated with increases in the informal share of labor (0.162***).
  - Aggregate inequality relationship is negative but smaller in magnitude than the formal-sector relationship (-0.151* vs. -0.985***), consistent with counteracting informal-sector forces.

### Robustness checks and alternative specifications
- Alternative controls and specifications considered (Figure H.1):
  - Controlling for unemployment rate.
  - State-specific linear time trends.
  - No state fixed effects (as in Lee (1999)).
  - State-specific linear time trends + national quadratic time trends (as in Haanwinckel (2020)).
- Two strategies to address endogeneity of Kaitz index:
  - Use share of formal workers at the minimum wage as the measure for how binding the minimum is.
  - 2SLS IV following Autor et al. (2016): first stage projects Kaitz index and square on log minimum wage, its square, and interaction with state’s overall median earnings.
- Results with share-at-minw as main measure (Table H.2):
  - Formal (log(Variance)): -1.382*** (0.264)
  - Informal (log(Variance)): 0.897*** (0.286)
  - Aggregate (log(Variance)): 0.730*** (0.210)
  - log(Informal share): 0.445** (0.208)
  - Notes: Each cell reports marginal coefficient from yst = β · atminwst + αs + αt + εst. All regressions employment-weighted, 405 observations.

### Comparison with Engbom and Moser (2021) (Figure H.2)
- Replication exercises:
  - Rows include Engbom & Moser (2021) reported effect, PNAD replication, sample including female workers, excluding self-employed, combined ("Both"), and "Both + IV" (2SLS).
- Finding:
  - Applying similar sample restrictions can yield a null relationship between the minimum wage and informal share, consistent with sensitivity to sample and specification choices.

### Model extension: adding unemployment
- Model modification (Appendix I):
  - Households face unemployment benefits b and draw a Fréchet-distributed taste shock for being unemployed.
  - Share of households of skill h that opt out of labor force: Uh = Nh [b / Wh]η.
  - Aggregate wage indices now:
    - Wh = [ bη + ∫j∈Ω [(1 + ς(j)) w(j)]η dj ]1/η. (Equation (125))
- Calibration procedure:
  - Additional parameter b is endogenously chosen to match aggregate unemployment U = ∑h Uh in 1996 and 2012.
  - Table I.1 reports calibration results (model with unemployment) — parameters chosen to match targets in 1996 and 2012.
- Calibration results (Table I.1; selected entries):
  - w Minimum wage: 1996 = 3.985, 2012 = 8.623 (Target: Share at min wage)
  - ρ Probability of detection: 1996 = 0.269, 2012 = 0.327 (Target: Informal share)
  - b Unemployment benefits: 1996 = 0.620, 2012 = 1.237 (Target: Unemployment rate)
  - η Labor supply elast.: 1996 = 4.856, 2012 = 4.121 (Target: Formal wage premium)
  - σ Standard deviation: 1996 = 0.957, 2012 = 1.324 (Target: Formal inequality)
  - κ Pareto tail: 1996 = 6.523, 2012 = 6.236 (Target: Informal inequality)
- Data vs. model comparison (Table I.2; selected moments)
  - Mean earnings ratios:
    - Formal/Informal: Data 1996 = 2.06, Model 1996 = 2.13; Data 2012 = 1.65, Model 2012 = 1.68
    - Primary/No degree: Data 1996 = 1.39, Model 1996 = 1.39; Data 2012 = 1.19, Model 2012 = 1.20
    - Secondary/Primary: Data 1996 = 1.46, Model 1996 = 1.45; Data 2012 = 1.21, Model 2012 = 1.21
    - Tertiary/Secondary: Data 1996 = 2.49, Model 1996 = 2.49; Data 2012 = 2.15, Model 2012 = 2.15
  - Variance of log-earnings:
    - Overall: Data 1996 = 0.78, Model 1996 = 0.73; Data 2012 = 0.50, Model 2012 = 0.46
    - Formal: Data 1996 = 0.65, Model 1996 = 0.52; Data 2012 = 0.33, Model 2012 = 0.33
    - Informal: Data 1996 = 0.66, Model 1996 = 0.66; Data 2012 = 0.62, Model 2012 = 0.51
  - Formal bunching at min wage: Data 1996 = 0.077, Model 1996 = 0.077; Data 2012 = 0.158, Model 2012 = 0.159
  - Informal share of labor: Data 1996 = 0.390, Model 1996 = 0.386; Data 2012 = 0.299, Model 2012 = 0.299
  - Unemployment share: Data 1996 = 0.065, Model 1996 = 0.065; Data 2012 = 0.062, Model 2012 = 0.062
- Counterfactual: increase in minimum wage (Table I.3)
  - Scenario: All parameters at 1996 values, except:
    - ∆w = 120% (minimum wage)
    - ∆ρ = 23% (enforcement)
    - Nh (skill composition)
  - Variance of log earnings:
    - overall: 0.730 → 0.810 (∆w=120%), 0.720 (∆ρ=23%), 0.71 (Nh)
    - formal: 0.520 → 0.430 (∆w=120%), 0.520 (∆ρ=23%), 0.56 (Nh)
    - informal: 0.660 → 0.810 (∆w=120%), 0.650 (∆ρ=23%), 0.58 (Nh)
  - Fraction at w: 0.077 → 0.211 (∆w=120%), 0.072 (∆ρ=23%), 0.045 (Nh)
  - Informal share: 0.390 → 0.871 (∆w=120%), 0.275 (∆ρ=23%), 0.205 (Nh)
  - Unemployment rate: 0.065 → 0.071 (∆w=120%), 0.073 (∆ρ=23%), 0.016 (Nh)
- Interpretation:
  - Increasing the minimum wage generates strong informal-sector responses and also increases the unemployment rate (e.g., unemployment rate increases by 9% in one counterfactual).
  - The predominant margin of adjustment to a minimum wage increase remains between the formal and informal sectors, not between employment and unemployment, even when unemployment is explicitly modeled.

### Discussion reconciling Derenoncourt et al. (2021)
- Specification tested (Equation (126)):
  - yst = α + β · Treateds · It>1999 + δs + δt + X′st Γ + εst.
  - Treateds indicates states above median treatment in pre-period average.
  - Analysis includes self-employed workers in the definition of informality (results invariant to including/excluding self-employed).
- Findings (Table J.1):
  - Using fraction of workers bunched at minimum before 1999 or the Kaitz index as treatment measures:
    - Columns (1) and (3): relative to below-median treatment states, above-median treatment states did not experience a larger increase in the share of the informal sector after 1999, confirming Derenoncourt et al. (2021).
    - Treatment heterogeneity matters — columns (2) and (4) highlight heterogeneity in treatment effects.
  - Table J.1 reports multiple β coefficients; Observations = 405; R-squared reported (0.973–0.977). Standard errors clustered at state level. Significance: ***p<1%, **p<5%, *p<10%.

_International Monetary Fund — Minimum Wages, Inequality, and the Informal Sector (Working Paper No. WP/2024/159)_

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_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024159-print-pdf.pdf_