## wpiea2019257-print-pdf

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---

### Data description and definitions of informality
- Data sources and sample
  - National Employment Survey (ENOE): nationally representative, rotating panel (each household followed for five consecutive quarters); samples over one hundred thousand households per quarter; focuses on workers aged 14 to 65 who report being employed.
  - Mexican Economic Census (INEGI): establishment-level census compiled every five years; waves used: 1998, 2003, 2008, and 2013; includes the universe of non-agricultural formal and informal Mexican firms with fixed establishments in urban areas.
  - For model estimation (section 5), firms that make any social security contribution are classified as formal when reporting moments from census data.
- Definitions of formality and informality
  - Firm-side (ENOE context): informal firms include subsistence agriculture, domestic work, and firms classified as informal by INEGI based on reported name, family ownership, and accounting practices. All other firms are classified as formal.
  - Worker-side (following INEGI): informal workers include those at non-agricultural informal firms, self-employed agricultural workers, unpaid workers, non-salaried workers (at both formal and informal firms), and workers without access to social security health services in both formal and informal firms. None of these workers have access to Mexican Social Security Institute (IMSS). All other workers are defined as formal.
  - Important feature: firms classified as formal employ a substantial share of workers in non-salaried informal contractual relationships; workers in non-salaried contractual relationships at formal firms are included in the informal worker category.
- ENOE measurement advantages
  - Rotating panel permits documentation of transitions between formal and informal worker status and into/out of formal firms.
  - Allows estimation of formal-informal wage gaps accounting for worker fixed effects.

### Informality levels and worker transitions
- Informality levels and trends in Mexico
  - Share of formal employment: 42 percent in 2005; 44 percent by 2019.
  - Under ENOE definition: 44 percent of workers are fully formal; around 22 percent of workers work at formal firms without reporting access to full benefits (i.e., informal contractual relationships within formal firms).
  - Mexico’s current level of employment informality is slightly above the Latin American average and well above levels observed in advanced economies.
  - The large role of non-formal contractual relationships at formal firms has remained significant throughout the period of study.
- Worker characteristics and formal-informal transitions
  - Informal workers earn less and are less educated than formal ones (ENOE 2013 comparisons).
  - Education prevalence: 21 percent of educated workers work at informal firms; 17 percent have informal contractual relationships at formal firms.
  - Wage distributions: variance of log wages = 0.74 among formal workers; 0.65 among informal workers.
  - Formality wage premiums:
    - Formal workers earn a premium of 41 log points in the raw data and 47 log points once sectoral differences are accounted for.
    - Controlling for education and age reduces the gap from 47 to 23 log points.
    - Controlling for individual fixed effects lowers the formality premium from 23 to 4 log points (relative to specification with only observable demographics).
    - Differences in worker composition (observable and fixed unobservable characteristics) account for 92 percent of the overall wage gap.
  - Informal workers at formal firms:
    - Tend to report wages lower than informal workers at informal firms on average; controlling for age and sector reduces the gap between informal workers at formal and informal firms from -21 to -3 log points.
  - Transition flows (quarterly):
    - Around four percent of workers move from formality to informality in a given quarter, and a similar proportion move from informality to formality.
    - Most common transitions are between holding formal and informal jobs within formal firms.
  - Interpretation: modest short-term wage premiums from formality and bidirectional flows motivate modeling Mexican market duality as an equilibrium with free worker movement and wages reflecting marginal product.

### Firm characteristics, productivity, and hiring strategies
- Firm counts and sizes (2013 Mexican Economic Census)
  - Over three hundred thousand formal firms with reported employees.
  - Three million informal firms with reported employees.
  - Firm size (workers per establishment, 2013 averages): formal firms = 21.4 workers per establishment; informal firms = 2.7 workers per establishment.
- Productivity gaps and dispersion
  - Productivity gaps (value added per worker, logs): raw gap = 141 log points; controlling for sector fixed effects = 105 log points; controlling for firm size = 85 log points; controlling for share of workers hired formally = 36 log points.
  - Dispersion: 90th-10th percentile ratio in value added per worker (logs) = 3.7 in the informal sector; 2.6 in the formal sector.
  - Significant overlap in productivity distributions across formal and informal firms; both sectors contain very productive and very unproductive firms.
- Intensive margin within formal firms
  - Formal firms with 1-5 workers hire 19 percent of them in non-salaried informal contracts.
  - Firms with 51+ workers hire 7 percent of their workers in non-salaried informal contracts.
- Focus: how distortions affecting the extensive margin (more informal firms) and the intensive margin (more informal workers within formal firms) influence observed productivity distributions and aggregate productivity.

### Regulatory drivers of informality
- Social security and hiring costs
  - IMSS social insurance contributions can comprise around 30 percent of the wage and are mandatory for fully formal salaried employees.
  - Non-compliance fines: in the range of 20-350 daily minimum wages per non-registered worker.
  - Limited net benefits from IMSS membership; features include non-contributory social insurance providing free benefits and bundled social security benefits with minimum contribution requirements (e.g., minimum requirement of ten contributing years to obtain retirement benefits through IMSS).
  - Levy (2018) estimates an implicit tax on salaried contracts of 12 percent when considering benefits and costs of social security systems.
- Severance / dismissal costs
  - Implicit cost from severance pay regulations estimated at around 3.2 percent of wages.
  - 2017 and 2019 labor reforms have limited firing costs and aimed to facilitate dispute resolution.
- Taxation and withholding
  - State payroll taxes between 2 to 3 percent of wages apply only to salaried workers.
  - Federal income taxes apply to all workers at formal firms, but firms are only required to withhold income taxes for formal salaried workers—leading to widespread evasion by non-salaried workers.
  - Non-salaried workers pay about one-fourth of the expected contributions based on aggregate estimates.
  - Levy (2018) reports tax collections from salaried workers account for 2.5 percent of GDP while tax collections from non-salaried employment account for 0.1 percent.
- Entry costs and administrative burdens
  - Starting a business involves multiple steps and fees; Mexico ranks 94th out of 190 economies in costs and procedural burdens of starting a business (Doing Business (2019)); cost of starting a business is estimated at 17 percent of income per capita.
- Regimes and enforcement
  - Small Contributor Regime (Repeco) absorbs 93 percent of firms, 52 percent of labor, and 25 percent of capital of the economy.
  - Imperfect enforcement favors small informal firms with lower probability of penalties.
- Minimum wages: relatively low in Mexico but are expected to double in the next five years.

### Modeling approach (overview)
- Framework builds on Ulyssea (2018): heterogeneous firms choose to be formal or informal (extensive margin); formal firms choose numbers of formal and informal workers to hire (intensive margin).
- Firms face regulatory and idiosyncratic barriers that distort input and formality choices, producing misallocation of inputs across firms and lowering aggregate productivity.
- Simplifying assumption: workers are homogeneous and indifferent between being informal and formal.
- Production and distortions (model primitives)
  - Production: y_i = θ_i l_i^α, with α < 1.
  - Informal firms face r_I(l_i) = (1 + l_i / b_I), idiosyncratic τ_Ii, overhead c_I = w^γ_I, and profits π_Ii = max_{l_i} θ_i l_i^α − (1 + τ_Ii) r_I(l_i) w l_i − c_I.
  - Formal firms face r_F(l_i) piecewise (threshold l̃ = τ_w^2 / (2 b_F)), idiosyncratic τ_Fi, overhead c_F = w^γ_F, a constant wedge τ_w, and profits π_Fi = max_{l_i} θ_i l_i^α − (1 + τ_Fi) r_F(l_i) w l_i − c_F.
  - Marginal revenue productivities: MRP_Ii = (1/α) (1 + τ_Ii) (1 + 2 l_i / b_I) w; formal MRP similar with b_F or (1 + τ_w) factor above threshold.
- Entry and equilibrium
  - Continuum of entrepreneurs of mass M enter each period; observe noisy signal ν_i then choose sector paying E_I or E_F or not enter.
  - Firms exit with probabilities δ_I and δ_F.
  - Stationary equilibrium: labor market clears L_I + L_F = L̄; free entry; sector sizes constant.
- Aggregate productivity and misallocation measured via TFP ≡ Y / L̄; TFPR dispersion driven by idiosyncratic distortions and regulatory distortions that vary with firm size.

### Estimation, calibration, and identification
- Calibration (first step) highlights
  - τ_w set equal to .348 (computed as sum of: estimated net tax from contributory programs (.12), net payroll tax on salaried employment (.01), benefits from non-contributory programs (.162), and net tax from evasion of income taxes (.056)).
  - δ_F chosen to match exit rate of formal firms in Mexican Census between 2008 and 2013.
  - γ_F chosen so overhead costs for formal firms equal half the monthly wage.
  - ν_0 set so size of an informal firm with no distortion and θ = ν_0 equals 1.
- Parameters estimated (second step SMM, 12 parameters): {b_F, b_I, δ_I, γ_I, ξ, E_F, E_I, α, σ, ̄τ_F, σ_I, σ_F}.
- Estimation targets 16 data moments from the 2013 Mexican Census informative on extensive and intensive margins and misallocation.
- Identification insights summarized:
  - ̄τ_F identified from value-added per worker gap.
  - σ_F and σ_I determine within-sector dispersion.
  - b_I and b_F shape how informality varies with firm size.
  - ξ, σ, and α determined by firm size distributions; strong decreasing returns to scale (low α) estimated to prevent excessive overlap of firm size distributions.
  - E_F and relative entry costs affect left tails and relative sector sizes.
  - δ_I and γ_I affect survival and left tail of informal size distribution.

### Parameter estimates & model fit
- Calibrated parameters (Table 5)
  - τw = 0.35
  - δF = 0.08
  - ν0 = 1,188
  - γF = 0.45
- Estimated parameters (Table 5)
  - bF = 2.35
  - bI = 4.58
  - δI = 0.27
  - γI = 0.19
  - ξ = 1.57
  - EF = 93,193
  - EI = 8
  - α = 0.32
  - σ = 0.27
  - ̄τF = 1.01
  - σI = 1.30
  - σF = 0.99
- Model fit (selected moments, Table 6)
  - Share of informal workers out of total workers: Data = 56.5% ; Model = 55.4%
  - Share of firms that are informal: Data = 89.0% ; Model = 92.8%
  - Informal firms with ≤5 workers: Data = 94.0% ; Model = 95.8%
  - Informal workers within formal firms of size 1-5: Data = 21.0% ; Model = 23.3%
  - Formal firms with ≤5 workers: Data = 52.0% ; Model = 52.0%
  - Median value-added per worker in formal vs informal: Data = 1.05 ; Model = 0.99
  - 90-10 ratio of value-added per worker within informal: Data = 3.49 ; Model = 2.36
  - 90-10 ratio of value-added per worker within formal: Data = 2.64 ; Model = 2.11
- Fit assessment
  - Model matches most targeted moments, especially size distributions of firms in both sectors.
  - Model understates productivity dispersion within formal and informal sectors despite large variation in idiosyncratic distortions and labor distortions τw.
  - Labor distortions account for a small share of overall misallocation; most variation stems from idiosyncratic distortions.
  - Some observed dispersion likely reflects transitory factors and mismeasurement not captured by the model.

### Policy experiments and counterfactuals (Sections 6–7 summary)
- Counterfactuals considered
  - Reduce τw from 0.35 to 0.23 (removing net tax from contributory programs).
  - Set τw = 0 (remove formal sector regulatory wedge entirely).
  - Reduce formal sector entry costs by 2/3.
  - Eliminate formalization entry costs (set formal entry cost = informal entry cost).
  - Reduce dispersion in informal-sector wedges σI to the level observed in the formal sector (holding average informal distortion unchanged).
- Aggregate effects (Table 7, selected)
  - Aggregate TFP: Baseline = 1.00 ; No contributory programs = 1.01 ; No labor wedges = 1.02 ; 2/3 reduction in entry costs = 1.08 ; No entry costs = 1.29 ; Reduced dispersion in inf. wedges = 1.04.
  - Informal Share of Firms: Baseline = 92.8% ; No contributory programs = 92.2% ; No labor wedges = 90.9% ; 2/3 reduction in entry costs = 76.6% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 92.2%.
  - Informal Share of Employment: Baseline = 55.4% ; No contributory programs = 51.6% ; No labor wedges = 43.7% ; 2/3 reduction in entry costs = 45.5% ; No entry costs = 19.3% ; Reduced dispersion in inf. wedges = 46.6%.
  - Informal Share of Output: Baseline = 36.5% ; No contributory programs = 35.0% ; No labor wedges = 31.8% ; 2/3 reduction in entry costs = 24.3% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 35.0%.
  - VA/Worker Dispersion (aggregate): Baseline = 88.1% ; No contributory programs = 86.6% ; No labor wedges = 84.0% ; 2/3 reduction in entry costs = 88.8% ; No entry costs = 78.6% ; Reduced dispersion in inf. wedges = 78.0%.
  - Tax Revenues (share of output): Baseline = 15.6% ; No contributory programs = 16.9% ; No labor wedges = 19.7% ; 2/3 reduction in entry costs = 19.1% ; No entry costs = 28.2% ; Reduced dispersion in inf. wedges = 18.7%.
- Selected model moments under counterfactuals (Table 8, selected)
  - Share of informal workers: Baseline = 55.4% ; No contributory programs = 51.6% ; No labor wedges = 43.7% ; 2/3 reduction in entry costs = 45.5% ; No entry costs = 19.3% ; Reduced dispersion in inf. wedges = 46.6%.
  - Intensive margin — Informal workers within formal firms of size 1-5: Baseline = 23.3% ; No contributory programs = 15.3% ; No labor wedges = 0.0% ; 2/3 reduction in entry costs = 30.0% ; No entry costs = 39.7% ; Reduced dispersion in inf. wedges = 22.9%.
  - Formal firms with ≤5 workers: Baseline = 52.0% ; No contributory programs = 50.8% ; No labor wedges = 50.7% ; 2/3 reduction in entry costs = 79.1% ; No entry costs = 96.8% ; Reduced dispersion in inf. wedges = 50.1%.
  - Median value-added per worker in formal vs informal: Baseline = 0.99 ; No contributory programs = 0.93 ; No labor wedges = 0.73 ; 2/3 reduction in entry costs = 1.07 ; No entry costs = 0.00 ; Reduced dispersion in inf. wedges = 1.02.
  - 90-10 ratio of VA/worker within informal: Baseline = 2.36 ; No contributory programs = 2.37 ; No labor wedges = 2.41 ; 2/3 reduction in entry costs = 2.38 ; No entry costs = 0.00 ; Reduced dispersion in inf. wedges = 1.55.
- Main policy findings and interpretation
  - Reducing τw (formal sector regulatory wedge)
    - Removing τw entirely would decrease informal employment share from 55 to 44 percent and informal output share from 37 to 32 percent, while fiscal revenues (interpreting τw as a tax) would increase from 16 to 20 percent.
    - Intensive margin of informality disappears in this counterfactual.
    - Aggregate productivity increases modestly by 2 percent.
    - Distributional effect: larger formal firms benefit most; small informal firms face increased competition.
  - Reducing entry costs by 2/3
    - Aggregate productivity increases by 8 percent.
    - Informal firms share falls from 93 to 77 percent.
    - Informal employment share falls by 10 percentage points.
    - Formal share of output rises from 80 to 97 percent.
    - Mechanism: affects extensive margin (formalization), reallocating firms into the less misallocated formal sector.
  - Eliminating formalization entry costs
    - All firms choose to be formal.
    - Aggregate productivity increases by 29 percent.
    - Informal employment share falls by 36 percentage points to 19 percent.
    - Formal firms still hire many informal workers, so some informal employment remains via intensive margin.
    - Small formal firms gain most due to entry cost composition; newly formalized firms experience large gains while unproductive informal firms lose from competition.
  - Reducing dispersion in informal-sector wedges σI to formal-sector level
    - Leads to significant formalization along the intensive margin; informal employment reduces from 47 percent in the relevant comparison.
    - Aggregate productivity increases by 4 percent due to reduced misallocation in informal sector.
- Policy implications emphasized
  - Both intensive and extensive margins of informality matter quantitatively in Mexico.
  - Reducing labor costs induced by payroll taxes and contributory social security systems could substantially increase formal employment but yield only moderate aggregate productivity gains.
  - Reducing formalization (entry) costs can lead to larger aggregate productivity gains by affecting the extensive margin and increasing the number of formal firms.
  - Much misallocation is attributed to idiosyncratic distortions (some possibly from heterogeneous enforcement), whose causes remain unidentified and warrant further research.
  - Authorities should focus on reducing formalization costs and addressing structural shortcomings that prevent the development of larger productive firms regardless of formality status.

*Source: wpiea2019257-print-pdf — Sections 2.1–4.1 and 5.2 with related results from Sections 6–7.*

### 2.1    Data description and definitions of informality

### 2.1    Data description and definitions of informality

### Data sources and sample
- National Employment Survey (ENOE): nationally representative, rotating panel (each household followed for five consecutive quarters); samples over one hundred thousand households per quarter; focuses on workers aged 14 to 65 who report being employed.
- Mexican Economic Census (INEGI): establishment-level census compiled every five years; waves used: 1998, 2003, 2008, and 2013; includes the universe of non-agricultural formal and informal Mexican firms with fixed establishments in urban areas.
- For model estimation (section 5), firms that make any social security contribution are classified as formal when reporting moments from census data.

### Definitions of formality and informality
- Firm-side definition (ENOE context): informal firms include subsistence agriculture, domestic work, and firms classified as informal by INEGI based on reported name, family ownership, and accounting practices. All other firms are classified as formal.
- Worker-side definition (following INEGI): informal workers include those at non-agricultural informal firms, self-employed agricultural workers, unpaid workers, non-salaried workers (at both formal and informal firms), and workers without access to social security health services in both formal and informal firms. None of these workers have access to Mexican Social Security Institute (IMSS). All other workers are defined as formal.
- Important feature: firms classified as formal employ a substantial share of workers in non-salaried informal contractual relationships; workers in non-salaried contractual relationships at formal firms are included in the informal worker category.

### ENOE measurement advantages
- Rotating panel permits documentation of transitions between formal and informal worker status and into/out of formal firms.
- Allows estimation of formal-informal wage gaps accounting for worker fixed effects.

---

### 2.2    Informality levels and trends in Mexico

- Share of formal employment:
  - 42 percent in 2005
  - 44 percent by 2019
- Under ENOE definition:
  - 44 percent of workers are fully formal
  - Around 22 percent of workers work at formal firms without reporting access to full benefits (i.e., informal contractual relationships within formal firms)
- Mexico’s current level of employment informality is slightly above the Latin American average and well above levels observed in advanced economies.
- The large role of non-formal contractual relationships at formal firms has remained significant throughout the period of study.

---

### 2.3    The role of worker characteristics and formal-informal transitions

- Informal workers earn less and are less educated than formal ones (ENOE 2013 comparisons).
- Prevalence by education (high-level findings):
  - Significant share of educated workers work at informal firms (21 percent) or have informal contractual relationships at formal firms (17 percent).
- Wage distributions:
  - Variance of log wages: 0.74 among formal workers; 0.65 among informal workers.
  - Substantial overlap in wage distributions across sectors, even after controlling for observable demographics (age, education, gender).
- Estimated formality wage premiums (from Table 2 and text):
  - Formal workers earn a premium of 41 log points in the raw data and 47 log points once sectoral differences are accounted for.
  - Controlling for education and age reduces the gap from 47 to 23 log points.
  - Controlling for individual fixed effects lowers the formality premium from 23 to 4 log points (relative to specification with only observable demographics).
  - Differences in worker composition (observable and fixed unobservable characteristics) account for 92 percent of the overall wage gap.
- Informal workers at formal firms:
  - Tend to report wages lower than informal workers at informal firms on average; controlling for age and sector reduces the gap between informal workers at formal and informal firms from -21 to -3 log points.
- Transition flows (quarterly):
  - Around four percent of workers move from formality to informality in a given quarter, and a similar proportion move from informality to formality.
  - Most common transitions are between holding formal and informal jobs within formal firms.
- Interpretation: modest short-term wage premiums from formality and bidirectional flows suggest differences in productivity and pay are not primarily due to frictions preventing worker movement; motivates modeling Mexican market duality as an equilibrium with free worker movement and wages reflecting marginal product.

---

### 2.4    The role of firm characteristics and hiring strategies

- Firm counts (2013 Mexican Economic Census):
  - Over three hundred thousand formal firms with reported employees
  - Three million informal firms with reported employees
- Firm size (workers per establishment, 2013 averages):
  - Formal firms: 21.4 workers per establishment
  - Informal firms: 2.7 workers per establishment
- Productivity gaps (value added per worker, logs):
  - Raw productivity gap between formal and informal firms: 141 log points
  - Reduced to 105 log points after introducing sector fixed effects
  - Reduced to 85 log points after controlling for firm size
  - Reduced to 36 log points after controlling for the share of workers hired formally
- Dispersion:
  - 90th-10th percentile ratio in value added per worker (logs): 3.7 in the informal sector; 2.6 in the formal sector
  - Significant overlap in productivity distributions across formal and informal firms; both sectors contain very productive and very unproductive firms
- Intensive margin within formal firms:
  - Formal firms with 1-5 workers hire 19 percent of them in non-salaried informal contracts
  - Firms with 51+ workers hire 7 percent of their workers in non-salaried informal contracts
- Focus of paper: how distortions affecting the extensive margin (more informal firms) and the intensive margin (more informal workers within formal firms) influence observed productivity distributions and aggregate productivity.

---

### 3    Regulatory drivers of informality

- Social security and hiring costs:
  - IMSS social insurance contributions can comprise around 30 percent of the wage and are mandatory for fully formal salaried employees.
  - Non-compliance fines: in the range of 20-350 daily minimum wages per non-registered worker.
  - Limited net benefits from IMSS membership; features include:
    - Non-contributory social insurance system providing free benefits (including health and retirement)
    - Bundled social security benefits with minimum contribution requirements (e.g., minimum requirement of ten contributing years to obtain retirement benefits through IMSS)
  - Levy (2018) estimates an implicit tax on salaried contracts of 12 percent when considering benefits and costs of social security systems.
- Severance / dismissal costs:
  - Implicit cost from severance pay regulations estimated at around 3.2 percent of wages (Heckman and Pages (2004)).
  - 2017 and 2019 labor reforms have limited firing costs and aimed to facilitate dispute resolution.
- Taxation and withholding:
  - State payroll taxes between 2 to 3 percent of wages apply only to salaried workers.
  - Federal income taxes apply to all workers at formal firms, but firms are only required to withhold income taxes for formal salaried workers—leading to widespread evasion by non-salaried workers.
  - Non-salaried workers pay about one-fourth of the expected contributions based on aggregate estimates.
  - Levy (2018) reports tax collections from salaried workers account for 2.5 percent of GDP while tax collections from non-salaried employment account for 0.1 percent.
- Entry costs and administrative burdens for formal firm creation:
  - Steps include authorization for company name, incorporation through a notary, filing with Public Registry of Commerce, obtaining tax registry numbers, registering at IMSS, notifying local government, registering with National Business Information Registry, and paying associated fees.
  - Mexico ranks 94th out of 190 economies in costs and procedural burdens of starting a business (Doing Business (2019)); cost of starting a business is estimated at 17 percent of income per capita.
- Regimes and enforcement:
  - Small Contributor Regime (Repeco) absorbs 93 percent of firms, 52 percent of labor, and 25 percent of capital of the economy (Levy, 2018).
  - Imperfect persecution/enforcement of tax evasion and regulatory violations favors small informal firms with lower probability of penalties.
- Minimum wages: relatively low in Mexico but are expected to double in the next five years.

---

### 4    Modeling approach (overview)
- Builds on Ulyssea (2018): heterogeneous firms choose to be formal or informal (extensive margin); formal firms choose numbers of formal and informal workers to hire (intensive margin).
- Firms face regulatory and idiosyncratic barriers that distort input and formality choices, producing misallocation of inputs across firms and lowering aggregate productivity.
- Simplifying assumption used: workers are homogeneous and indifferent between being informal and formal.

*Source: IMF working paper content provided (sections 2.1–4).*

### 4.1    Heterogeneous firms

### 4.1 Heterogeneous firms

### Model setup and production
- Two sectors: formal and informal. Firms in both sectors produce a homogeneous good (price normalized to one) with the production function: y_i = θ_i l_i^α, where θ_i is idiosyncratic productivity, l_i is labor input, and α < 1.
- Firms face decreasing returns to scale parameterized by α.

### Distortions and profit functions
- Informal firms face:
  - Regulatory distortions increasing in firm size: r_I(l_i).
  - Idiosyncratic distortions: τ_Ii.
  - Overhead costs of operation: c_I (scale with the real wage: c_I = w^γ_I).
- Informal firm profit function:
  - π_Ii = max_{l_i} θ_i l_i^α − (1 + τ_Ii) r_I(l_i) w l_i − c_I
  - r_I(l_i) = (1 + l_i / b_I)
- Formal firms face:
  - Regulatory distortions r_F(l_i) (increasing in number of informal workers hired).
  - Idiosyncratic distortions τ_Fi.
  - Overhead costs c_F (scale with the real wage: c_F = w^γ_F).
  - A constant wedge when hiring formal workers: τ_w (motivated by payroll taxes and social security contributions versus benefits from non-contributory programs).
- Formal firm profit function:
  - π_Fi = max_{l_i} θ_i l_i^α − (1 + τ_Fi) r_F(l_i) w l_i − c_F
  - r_F(l_i) =
    - (1 + l_i / b_F) if l_i < l̃
    - [l_i (1 + l̃ / b_F) + (1 + τ_w) (l_i − l̃)] / l_i if l_i ≥ l̃
  - Threshold l̃ above which formal firms exclusively hire formal workers: l̃ = τ_w^2 / (2 b_F).
- Share of informal workers in formal firms is increasing in firm size (since below l̃ formal firms may hire informal workers).

### Exit and firm value
- Firms face constant exit probabilities each period: δ_I for informal, δ_F for formal.
- In steady state with constant aggregate prices, firm value functions:
  - V_S(θ_i, τ_Si) = max{0, π_S(θ_i, τ_Si, w) / δ_S}, for S = I, F.

### Hiring regimes and marginal revenue productivity (MRP)
- Informal firms: MRP_Ii = y_i / l_i = (1/α) (1 + τ_Ii) (1 + 2 l_i / b_I) w.
- Formal firms:
  - For firms hiring only informal workers (l_i < l̃): MRP_Fi = (1/α) (1 + τ_Fi) (1 + 2 l_i / b_F) w.
  - For firms hiring formal workers (l_i > l̃): MRP_Fi = (1/α) (1 + τ_Fi) (1 + τ_w) w.
- Dispersion in revenue productivity (TFPR) arises from idiosyncratic distortions and regulatory distortions; regulatory distortions create a positive correlation between marginal products and productivity.

---

### Entry
- Continuum of entrepreneurs of mass M enter each period. Entrepreneurs do not know θ_i or τ_Ii and τ_Fi before entry but observe a noisy signal ν_i of productivity.
- Entry options after observing ν_i:
  - Enter informal sector paying entry cost E_I.
  - Enter formal sector paying entry cost E_F.
  - Not enter.
- After entry, entrepreneurs observe θ_i and τ_Si and exit if π_Si < 0; if π_Si ≥ 0 they become incumbents. Decision to be informal/formal is fixed upon entry.
- Pre-entry value function:
  - V_0(ν, w) = E[V_S(θ, τ_S, w) | ν], S = I, F.
- Parametric assumptions for estimation:
  - θ_i = ν_i · ε_i.
  - ν_i drawn from a Pareto distribution with scale ν_0 and shape ξ.
  - ε_i log-normal: ln(ε_i) ~ N(0, σ^2).
  - ln(1 + τ_Ii) ~ N(0, σ_I^2).
  - ln(1 + τ_Fi) ~ N(ln(1 + ̄τ_F), σ_F^2).
- Note: Entry costs are in units of output.

---

### Equilibrium conditions
- Representative household with utility U(C) = C, cannot save, inelastically supplies labor L̄.
- Stationary equilibrium: aggregate prices and distributions constant.
- Revenues from distortions are assumed rebated to the household; total consumption = wL + Π + T, where wL is aggregate labor income, Π is aggregate profits minus entry costs, and T is aggregate revenues from distortions.
- Aggregate output Y minus aggregate consumption C equals aggregate entry costs and overhead costs.
- Stationary equilibrium conditions:
  - Labor market clears: L_I + L_F = L̄.
  - Firms maximize expected profits subject to budget constraints.
  - Free entry condition holds in both sectors.
  - Sector sizes remain constant (mass of entrants equals mass of incumbents times exit rate).

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### Aggregate productivity and misallocation
- Aggregate production analyzed via TFP ≡ Y / L̄ (focus on Y due to sensitivity of consumption to rebate assumption).
- Model captures misallocation following Hsieh and Klenow (2009): dispersion in distortions generates dispersion in marginal products and lowers aggregate TFP.
- TFPR dispersion is driven by both idiosyncratic distortions and regulatory distortions that vary with firm size.

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### Estimation: calibration and SMM
- Calibrated parameters (first step):
  - τ_w is set equal to .348, computed as sum of: estimated net tax from contributory programs (.12), net payroll tax on salaried employment (.01), benefits from non-contributory programs (.162), and net tax from evasion of income taxes (.056).
  - δ_F chosen to match exit rate of formal firms in Mexican Census between 2008 and 2013.
  - γ_F chosen so overhead costs for formal firms equal half the monthly wage.
  - ν_0 set so size of an informal firm with no distortion and θ = ν_0 equals 1.
- Parameters estimated in second step (12 parameters): {b_F, b_I, δ_I, γ_I, ξ, E_F, E_I, α, σ, ̄τ_F, σ_I, σ_F}.
- Estimation method: Simulated Method of Moments (SMM), targeting 16 data moments from the 2013 Mexican Census of Manufactures informative on extensive and intensive margins of informality and misallocation:
  - Share of informal workers out of all workers.
  - Share of formal firms out of: all firms, firms with less than 5 workers, firms with 6-10 workers, firms with 11-50 workers.
  - Share of workers that are informal within formal firms with 1-5 workers.
  - Share of informal firms with less than 5 workers and with less than 10 workers.
  - Share of formal firms with: less than 5 workers, 6-10 workers, 11–20 workers, 21–50 workers, more than 50 workers.
  - Difference in median value-added per worker between formal firms and informal firms.
  - 90-10 ratio of value-added per worker for formal firms and for informal firms (TFPR dispersion).
- Identification insights:
  - ̄τ_F identified from value-added per worker gap between formal and informal firms.
  - σ_F and σ_I (variance of post-entry distortion shocks) determine dispersion in value-added per worker within sectors.
  - b_I and b_F (costs of informality parameters) affect dispersion but are insufficient alone to match data.
  - ξ (Pareto shape), σ (variance of post-entry productivity shocks), and α determined by firm size distributions.
  - Strong decreasing returns to scale (low α) estimated to prevent excessive overlap of firm size distributions given large dispersion in post-entry shocks.
  - E_F influences left tail of formal firm size distribution; E_F estimated to be high to match low share of formal firms with fewer than five workers.
  - Relative entry costs (E_I vs E_F) determined by relative shares of informal and formal firms.
  - δ_I governs disadvantage of entering informal sector conditional on entry costs.
  - γ_I (overhead costs in informal sector) affects post-entry survival and left tail of informal size distribution.
  - b_I determines how the share of informal firms decreases with firm size; b_F determines how share of informal workers within formal firms varies with firm size.

*Source: wpiea2019257-print-pdf - 4.1 Heterogeneous firms*

### 5.2    Parameter estimates & model fit

### 5.2    Parameter estimates & model fit

### Parameter estimates (Table 5)
- Calibrated Parameters
  - τw: Regulatory tax wedge in formal sector = 0.35
  - δF: Exit rate in formal sector = 0.08
  - ν0: Location parameter of Pareto distribution = 1,188
  - γF: Overhead costs in the formal sector = 0.45
- Estimated Parameters
  - bF: Cost parameter of informal workers for formal firms = 2.35
  - bI: Cost parameter of informal workers for informal firms = 4.58
  - δI: Exit rate for informal firms = 0.27
  - γI: Overhead costs in informal sector = 0.19
  - ξ: Shape parameter of Pareto distribution = 1.57
  - EF: Entry costs in formal sector = 93,193
  - EI: Entry costs in informal sector = 8
  - α: Decreasing returns to scale = 0.32
  - σ: Post-entry productivity shock variance = 0.27
  - ̄τF: Average distortion in formal sector = 1.01
  - σI: Post-entry distortion shock in informal sector = 1.30
  - σF: Post-entry distortion shock in formal sector = 0.99

### Model fit (Table 6) — targeted moments vs model moments
- Aggregates and shares
  - Share of informal workers out of total workers: Data = 56.5% ; Model = 55.4%
  - Share of firms that are informal: Data = 89.0% ; Model = 92.8%
- Extensive informality margin (share of firms)
  - Informal firms with ≤5 workers: Data = 94.0% ; Model = 95.8%
  - Informal firms with 6-10 workers: Data = 57.0% ; Model = 83.0%
  - Informal firms with 11-50 workers: Data = 35.0% ; Model = 47.9%
- Intensive informality margin (share of workers)
  - Informal workers within formal firms of size 1-5: Data = 21.0% ; Model = 23.3%
- Size distribution of informal firms (share of informal)
  - Informal firms with ≤2 workers: Data = 79.0% ; Model = 76.3%
  - Informal firms with ≤5 workers: Data = 96.0% ; Model = 92.7%
- Size distribution of formal firms (share of formal)
  - Formal firms with ≤5 workers: Data = 52.0% ; Model = 52.0%
  - Formal firms with 6-10 workers: Data = 21.0% ; Model = 17.9%
  - Formal firms with 11-20 workers: Data = 13.0% ; Model = 13.5%
  - Formal firms with 21-50 workers: Data = 8.0% ; Model = 10.1%
  - Formal firms with >50 workers: Data = 6.0% ; Model = 6.5%
- Productivity distribution
  - Median value-added per worker in formal vs informal: Data = 1.05 ; Model = 0.99
  - 90-10 ratio of value-added per worker within informal: Data = 3.49 ; Model = 2.36
  - 90-10 ratio of value-added per worker within formal: Data = 2.64 ; Model = 2.11

### Fit assessment and interpretation
- Overall model performance
  - "Our model does a good job of matching most of the targeted moments, in particular those related to the size distribution of firms in both the formal and informal sectors."
  - The model understates dispersion of productivity within formal and informal sectors despite large variation in idiosyncratic distortions and labor distortions τw.
- Sources of misallocation and dispersion
  - Labor distortions account for a small share of overall misallocation; most variation stems from idiosyncratic distortions (subsidies or taxes).
  - Gains from large subsidies in the informal sector are mitigated by regulatory costs of informality bI, limiting the ability to match large productivity dispersion among informal firms.
  - Some observed dispersion likely reflects transitory factors and mismeasurement not captured by the model.

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### Policy experiments and counterfactuals (summary of Sections 6 and Tables 7–8)
- Counterfactuals considered
  - Reduce τw from 0.35 to 0.23 (removing net tax from contributory programs)
  - Set τw = 0 (remove formal sector regulatory wedge entirely)
  - Reduce formal sector entry costs by 2/3
  - Eliminate formalization entry costs (set formal entry cost = informal entry cost)
  - Reduce dispersion in informal-sector wedges σI to the level observed in the formal sector (holding average informal distortion unchanged)
- Key targets examined: aggregate TFP (proportionate to aggregate output), informal shares (output, employment, firms), and dispersion in value-added per worker.

- Aggregate effects from policy experiments (Table 7)
  - Aggregate TFP: Baseline = 1.00 ; No contributory programs = 1.01 ; No labor wedges = 1.02 ; 2/3 reduction in entry costs = 1.08 ; No entry costs = 1.29 ; Reduced dispersion in inf. wedges = 1.04
  - Informal Share of Firms: Baseline = 92.8% ; No contributory programs = 92.2% ; No labor wedges = 90.9% ; 2/3 reduction in entry costs = 76.6% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 92.2%
  - Informal Share of Employment: Baseline = 55.4% ; No contributory programs = 51.6% ; No labor wedges = 43.7% ; 2/3 reduction in entry costs = 45.5% ; No entry costs = 19.3% ; Reduced dispersion in inf. wedges = 46.6%
  - Informal Share of Output: Baseline = 36.5% ; No contributory programs = 35.0% ; No labor wedges = 31.8% ; 2/3 reduction in entry costs = 24.3% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 35.0%
  - VA/Worker Dispersion (aggregate): Baseline = 88.1% ; No contributory programs = 86.6% ; No labor wedges = 84.0% ; 2/3 reduction in entry costs = 88.8% ; No entry costs = 78.6% ; Reduced dispersion in inf. wedges = 78.0%
  - VA/Worker Dispersion in Informal Sector: Baseline = 81.6% ; No contributory programs = 81.9% ; No labor wedges = 82.7% ; 2/3 reduction in entry costs = 81.9% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 57.0%
  - VA/Worker Dispersion in Formal Sector: Baseline = 78.9% ; No contributory programs = 79.0% ; No labor wedges = 79.0% ; 2/3 reduction in entry costs = 79.8% ; No entry costs = 78.6% ; Reduced dispersion in inf. wedges = 79.0%
  - Tax Revenues (share of output): Baseline = 15.6% ; No contributory programs = 16.9% ; No labor wedges = 19.7% ; 2/3 reduction in entry costs = 19.1% ; No entry costs = 28.2% ; Reduced dispersion in inf. wedges = 18.7%

- Selected model moments under counterfactuals (Table 8 highlights)
  - Share of informal workers: Baseline = 55.4% ; No contributory programs = 51.6% ; No labor wedges = 43.7% ; 2/3 reduction in entry costs = 45.5% ; No entry costs = 19.3% ; Reduced dispersion in inf. wedges = 46.6%
  - Share of firms that are informal: Baseline = 92.8% ; No contributory programs = 92.2% ; No labor wedges = 90.9% ; 2/3 reduction in entry costs = 76.6% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 92.2%
  - Extensive margin — Informal firms with ≤5 workers: Baseline = 95.8% ; No contributory programs = 95.6% ; No labor wedges = 94.9% ; 2/3 reduction in entry costs = 79.6% ; No entry costs = 0.0% ; Reduced dispersion in inf. wedges = 95.8%
  - Intensive margin — Informal workers within formal firms of size 1-5: Baseline = 23.3% ; No contributory programs = 15.3% ; No labor wedges = 0.0% ; 2/3 reduction in entry costs = 30.0% ; No entry costs = 39.7% ; Reduced dispersion in inf. wedges = 22.9%
  - Size distribution of formal firms (examples)
    - Formal firms with ≤5 workers: Baseline = 52.0% ; No contributory programs = 50.8% ; No labor wedges = 50.7% ; 2/3 reduction in entry costs = 79.1% ; No entry costs = 96.8% ; Reduced dispersion in inf. wedges = 50.1%
    - Formal firms with >50 workers: Baseline = 6.5% ; No contributory programs = 6.9% ; No labor wedges = 7.6% ; 2/3 reduction in entry costs = 1.8% ; No entry costs = 0.2% ; Reduced dispersion in inf. wedges = 7.5%
  - Productivity distribution (selected)
    - Median value-added per worker in formal vs informal: Baseline = 0.99 ; No contributory programs = 0.93 ; No labor wedges = 0.73 ; 2/3 reduction in entry costs = 1.07 ; No entry costs = 0.00 ; Reduced dispersion in inf. wedges = 1.02
    - 90-10 ratio of value-added per worker within informal: Baseline = 2.36 ; No contributory programs = 2.37 ; No labor wedges = 2.41 ; 2/3 reduction in entry costs = 2.38 ; No entry costs = 0.00 ; Reduced dispersion in inf. wedges = 1.55
    - 90-10 ratio of value-added per worker within formal: Baseline = 2.11 ; No contributory programs = 2.12 ; No labor wedges = 2.10 ; 2/3 reduction in entry costs = 2.06 ; No entry costs = 1.89 ; Reduced dispersion in inf. wedges = 2.10

### Main policy findings and interpretation
- Reducing the formal sector regulatory wedge (τw)
  - Removing τw entirely would decrease informal employment share from 55 to 44 percent and informal output share from 37 to 32 percent, while fiscal revenues (interpreting τw as a tax) would increase from 16 to 20 percent.
  - In this counterfactual, the intensive margin of informality disappears (formal firms would not hire informal workers).
  - Aggregate productivity increases modestly by 2 percent when removing the wedge entirely.
  - Reason: reducing the labor wedge changes contracting decisions (intensive margin) but does not systematically reallocate inputs from less productive to more productive firms; hence limited effects on misallocation and aggregate TFP.
  - Distributional effect: larger formal firms benefit most; small informal firms face increased competition.
- Reducing entry costs by 2/3
  - Aggregate productivity increases by 8 percent.
  - Informal firms share falls from 93 to 77 percent.
  - Informal employment share falls by 10 percentage points.
  - Formal share of output rises from 80 to 97 percent.
  - Mechanism: affects extensive margin (formalization), reallocating firms into the less misallocated formal sector and boosting formal output share.
- Eliminating formalization entry costs
  - All firms choose to be formal.
  - Aggregate productivity increases by 29 percent.
  - Informal employment share falls by 36 percentage points to 19 percent.
  - Formal firms still hire many informal workers, so some informal employment remains.
  - Small formal firms gain most due to entry cost composition; newly formalized firms experience large gains while unproductive informal firms lose from competition.
- Reducing dispersion in informal-sector wedges σI to formal-sector level
  - Leads to significant formalization along the intensive margin; informal employment reduces from 47 percent in the relevant comparison.
  - Extensive margin formalization is smaller because lower distortions make informal sector more attractive to some firms.
  - Aggregate productivity increases by 4 percent due to reduced misallocation in informal sector.
  - Gains are widespread among formal and informal firms.

### Policy implications emphasized in conclusion
- Both intensive and extensive margins of informality matter quantitatively in Mexico.
- Reducing labor costs induced by payroll taxes and contributory social security systems could substantially increase formal employment but yield only moderate aggregate productivity gains.
- Reducing formalization (entry) costs can lead to larger aggregate productivity gains by affecting the extensive margin and increasing the number of formal firms.
- Much misallocation is attributed to idiosyncratic distortions (some possibly from heterogeneous enforcement), whose causes remain unidentified and warrant further research.
- Authorities should focus on reducing formalization costs and addressing structural shortcomings that prevent the development of larger productive firms regardless of formality status.

*Source: wpiea2019257-print-pdf — Section 5.2 (Parameter estimates & model fit), with related results from Sections 6–7 and Tables 5–8.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019257-print-pdf.pdf_