## 2.1    Portugal and the Empresa na Hora Reform

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---

### Background and motivation
- After joining the European Monetary Union in 1999, Portugal entered a prolonged slump with anemic productivity and output growth (Blanchard, 2007).
- Until 2005, Portugal was considered one the least business-friendly countries according to international ranking.
  - Before the reform it took 56-78 days to start a business.
  - An entrepreneur needed to fill in around 20 forms, provided by different public agencies, and complete 11 procedures, for a total cost of e2,000.

### The Empresa na Hora reform (program design and outcomes)
- Part of the SIMPLEX modernization plan designed by UCMA (Unidade de Coordena̧c ̃ao da Modernazi ̧c ̃ao Administrativa).
- Key features:
  - Start a business “on the spot” via a single personal visit to an official Registry.
  - UCMA designed standardized pre-approved documents created on pre-defined firm names.
  - Within an hour, on average, an entrepreneur receives:
    - an official legal person identification card,
    - a Social Security number,
    - and a registration of the enterprise in the Business Registry.
  - Monetary costs shrunk to e360.
  - The law was approved on July 6th, 2005 (Decreto Lei 111/2005).
  - It involved virtually all sectors of economic activity and was intensively advertised by the government.
- Recognitions and rankings:
  - European Commission selected Portugal for the European Enterprise Award in 2006.
  - Portugal moved from averaging around the 113th position (out of 155 countries) in the Doing Business Index to around the 33rd.

### Implementation and rollout
- Implementation was staggered across municipalities due to budget constraints and need to train public servants.
- Initial rollout (post-Decreto Lei approval in July 2005):
  - Six One-Stop Shops opened in four cities: Coimbra, Aveiro, Moita and Barreiro.
  - Out of the 308 municipalities, 99 had a One-Stop Shop by the end of 2008.
- Registration rules and empirical implication:
  - A firm was allowed to register in any One-Stop Shop regardless of the firm’s operating location.
  - Empirical approach assumes firms registered in the same municipality in which they were operating; conversations with public officials indicated One-Stop Shops’ coverage was local.
  - Authors note that if entrepreneurs crossed municipal borders to register, this would, if anything, bias estimates of the expansionary effect downwards.
- Note on name customization:
  - It is possible for an entrepreneur to request a personalized name for the business and have all documents ready within two business days.

### Data sources and sample construction
- Main dataset: Quadros de Pessoal (administrative records on the universe of limited-liability firms with at least one employee in Portugal).
  - Coverage: years 2000-2008; dataset built from a census submitted each year in October.
  - Provides firm-, establishment-, and worker-level information.
  - Variables used: firms’ entry, exit, sector of activity (5-digit level), municipality location, annual nominal sales, employment.
  - Rationale: Empresa na Hora concerned creation of new firms rather than openings of establishments; over 93% of firms in Portugal have only one establishment.
- Supplementary datasets:
  - Instituto dos Registos e Notariado: exact opening date of each One-Stop Shop across the Portuguese municipalities.
  - Instituto Nacional de Estat́ıstica: municipality-level data on total residents and local demographic information.
- Sample construction details:
  - Firms considered to have exited if they stop appearing in the dataset for at least two consecutive years (equivalent to the last-time-appeared definition for more than 97% of cases).
  - Dropped pre-existing firms that change legal form to limited liability company over their life cycle to avoid capturing legal-form changes.
- Final sample characteristics:
  - On average, 125,000 non-financial private corporations per year.
  - Time window allows inclusion of five years preceding the reform and measures impact during the first four years of implementation.
  - Average entry rate: 7.5%.
  - Average exit rate: 9.5%.
  - Firm size distribution:
    - 50% of firms have less than 4 employees.
    - 50% of entrants have less than 2 employees.
- Limitation:
  - Sample ends in 2008 due to a drop in Quadros coverage thereafter; not all reformed municipalities observed for the same number of years after opening.

### Empirical strategy and identification
- Identification exploits staggered opening of One-Stop Shops across municipalities using a generalized difference-in-differences specification with municipality and year fixed effects.
- Baseline regression framework (notation preserved):
  - y_{m,t} = α_m + δ_t + ∑_τ β_τ 1(t−τ=τ_{0,m}) + γ X_{m,t} + ε_{m,t}.
  - α_m and δ_t are municipality and year fixed effects.
  - 1(t−τ=τ_{0,m}) is a municipality-year dummy equal to 1 whenever municipality m is τ years from the opening of its office; β_{−1} normalized to 0.
  - Parallel-trend assumption: unobserved determinants of outcome evolve in parallel over time across municipalities.
- Entry benchmark regression:
  - y_{m,t} = α_m + δ_t + ∑_{τ=−7}^{3} β_τ 1(t−τ=τ_{0,m}) + γ_m 1(Municipality_m = 1) t + ε_{m,t}.
  - Allows for municipality-specific linear trends; standard errors clustered at municipality level.
- Employment analysis:
  - Dependent variable: log of municipality-level employment in a given year normalized over 1,000 residents.
  - Reference period chosen as t−3 (β_{−3} = 0) to display employment response, capturing both actual and expected entry effects.

### Results — Entry
- Opening of One-Stop Shops significantly increased annual firm entry at the municipality level.
- Effect magnitude:
  - Back-of-the-envelope: increase corresponds to an annual rise in local entry between 12% to 40%, corresponding to an average of 25% per year following the reform.
  - Pre-reform entry rate in Treated municipalities is around 8.5%; the reform led to an approximate increase in entry of two percentage points.
- Coefficient precision:
  - Coefficients for t+2 and t+3 are noisier due to fewer treated municipalities contributing; authors emphasize the average increase and positive, significant coefficients over the time span.
- Robustness:
  - Results robust to relaxing municipality-specific trends and allowing decile-specific trends based on pre-period population and service-orientation; coefficients of β_τ do not differ substantially.

### Results — Local employment
- Employment increased significantly in Treated municipalities relative to Control ones.
- Timing and interpretation:
  - Employment started rising two years prior to the reform (t−2 and t−1), interpreted as incumbents’ adjustment in anticipation of expected entry rather than as differential pre-trends.
  - Lags t−7 to t−3 are flat and not statistically different from zero.
- Magnitude:
  - Employment increased by 5% in the year of the reform.
  - Employment then continued growing at an average annual rate of 4.8%.
  - Coefficients interpreted as cumulative percentage increase in municipality-level employment relative to t−3.
- Robustness:
  - Employment dynamics are robust to different trend specifications (reported in Appendix).
- Interpretation caveats:
  - The estimated 4.8% increase is a local effect and represents an upper bound on country-level employment impact because:
    - Estimates refer to the private sector only (exclude government-owned entities).
    - Local effect includes cross-municipality movement of workers.

### Channels — Decomposition by age groups
- Age classes: age 0−5, 6−15, and 15+.
- Empirical finding:
  - Both young firms and older incumbents contribute positively to the rise in local employment.
  - Back-of-the-envelope combining age-group coefficients with average employment shares shows:
    - Around 60% of the overall increase in local employment is due to the response of incumbents older than 5 years old.
    - Entrants and young firms account for the remaining 40%.
  - Firms older than 15 years show a noisier and essentially flat response.

### Channels — Intensive vs Extensive margins by age
- Intensive margin (average firm size y_{m,a,t} = sum employment_i / sum active firms_i):
  - Average size of incumbents increased after the reform.
  - Average size of entrants and young firms remained unchanged.
  - Interpretation: entrants and young firms contributed via the extensive margin (more entrants); incumbents contributed via the intensive margin (more employment per incumbent).
  - Implication: expansion by incumbents indicates the increase in operating firms was not merely formalization of informal firms.
- Extensive margin (exit analysis):
  - Firm-level regression for exit probability Pr(exit_it = 1) with municipality fixed effects.
  - Finding: the exit probability for the average firm remained mostly unaffected by the reform across all age groups.
  - Robust to municipality × 3-digit sector fixed effects and decile-specific trends.

### Channels — Heterogeneous response of incumbents by productivity
- Productivity proxy: revenue labor productivity = nominal sales / employment; ranking using 2004 within age group, 3-digit sector, and municipality.
- Aggregation to municipality-year for top and bottom terciles.
- Empirical findings:
  - Increase in aggregate employment is driven by the most productive firms (top tercile).
  - Bottom tercile’s behavior remained unchanged after the reform.
  - Exit: exiting firms in the top tercile dropped significantly after the reform; exit of the bottom tercile unaffected.
  - Alternative ranking pooling age groups yields weaker but still robust results.

### Sectoral heterogeneity (manufacturing vs services)
- Entry:
  - Entry grew significantly after the reform for the service sector.
  - Entry remained flat for manufacturing.
  - Interpretation: manufacturing decisions less affected by reductions in time and monetary entry costs due to capital intensity; services respond more to local demand changes.
- Employment:
  - Employment increases for the service sector.
  - Employment did not significantly change for manufacturing.
- Average firm size by age and sector:
  - Services: entrants and young firms decreased in average size; incumbents expanded average size.
  - Manufacturing: incumbents mildly expanded average size (evidence suggestive due to small sample and noisy coefficients).
- Robustness: results robust to decile-specific municipality trends based on residents and per-capita value of activity in services.

### Theoretical framework — CES vs Translog demand (summary)
- CES case:
  - Under CES (σ constant), markups constant at σ/(σ−1).
  - Proposition 1 (CES): ∂ln l_i / ∂ln M = −(σ−1−ν)/(σ−1). Implication: response of labor demand is homogeneous across firms; incumbents contract under common calibrations (σ∈[3,7], ν∈[0.5,2]).
  - Proposition 2 (CES): aggregate labor ∂lnL/∂lnM >0 but driven entirely by extensive margin; incumbents shrink homogeneously.
  - Conclusion: CES predictions inconsistent with empirical finding of incumbent expansion and heterogeneous responses.
- Translog demand:
  - Demand features variable elasticities ε_i = 1 + γ/ s_i and markups μ_i = 1 + s_i/γ.
  - Key properties: ε_i increases with M ⇒ markups decrease with M; ε_i decreases with firm productivity a_i (more productive firms face less elastic demand).
  - Propositions under translog:
    - Proposition 3: ∂ln ε_i / ∂ln M >0, ∀i.
    - Proposition 4: heterogeneous impact on firm-level labor; response is increasing in firm productivity: ∂^2 ln l_i / ∂ln M ∂ln a_i >0. Most productive firms expand, least productive contract.
    - Proposition 5: aggregate labor L increases in response to increase in M: ∂lnL/∂lnM >0.
  - Mechanism: competition effect (love-of-variety lowers P and markups) interacts with aggregate demand effect (lower P raises labor supply); more productive firms are relatively insulated and expand.

### Numerical calibration and quantitative results
- Baseline calibration:
  - Productivity distribution: Pareto with scale xm = 2 and shape α = 1.08 (matches pre-reform size dispersion = 0.84).
  - Mass of incumbent firms MI = 1.
  - Markup parameter γ = 1.97 (matches sales dispersion = 1.1).
  - Labor supply elasticity ν = 2.86 (matches average annual rise in employment at municipality level = 4.84%; entry measure changes from 9% to 11.25% consistent with 25% average annual entry increase).
- Baseline numerical outcomes:
  - Firm-level: change in labor demand is increasing in firm productivity; least productive firms cut size, highly productive firms expand.
  - Aggregate decomposition (matching 4.84% annual increase):
    - ∆L - Total = 4.84%
    - ∆L - Entrants = 2.31%  (47.5%)
    - ∆L - Incumbents = 2.54%  (52.5%)
    - Approximately 53% of the increase comes from incumbents (consistent with empirical ~60%).
- Comparative statics:
  - Varying γ:
    - γ= 0.97: ∆L - Total = 7.32%; %∆L - Entrants = 32.3%; %∆L - Incumbents = 67.8%
    - γ= 1.97: ∆L - Total = 4.84%; %∆L - Entrants = 47.7%; %∆L - Incumbents = 52.3%
    - γ= 2.97: ∆L - Total = 4.08%; %∆L - Entrants = 56.1%; %∆L - Incumbents = 43.9%
  - Varying α (productivity dispersion): greater initial dispersion (lower α) strengthens aggregate employment increase for given γ.
  - Varying ν (labor supply elasticity):
    - ν= 1: ∆L - Total = 1.67%; %∆L - Entrants = 134%; %∆L - Incumbents = −34%
    - ν= 2.86: ∆L - Total = 4.84%; %∆L - Entrants = 46.3%; %∆L - Incumbents = 53.7%
  - Interpretation: lower ν weakens firm-level and aggregate employment responses and shifts incidence toward entrants; local employment responses are an upper bound for economy-wide impact because municipal-level ν is higher.

### Key takeaways and policy implications
- Empirical evidence: the Empresa na Hora reform reduced time and monetary entry costs, increased firm entry (average annual increase ~25%), and raised local employment (4.8% annual increase).
- Distributional outcome: the bulk of employment expansion came from incumbents (around 60% empirically; model baseline ~53%), and the expansion was concentrated among the most productive incumbents.
- Model comparison:
  - CES with constant markups predicts homogeneous incumbent contraction and an aggregate increase driven only by entrants—contradicted by the data.
  - Translog demand with variable markups reproduces heterogeneous firm responses and substantial incumbent contribution to aggregate employment gains.
- Policy implication: quantitative models used to evaluate reforms that change the competitive environment or the number of operating firms should incorporate firm heterogeneity and variable markups to capture reallocation and aggregate employment effects.

*Source: wpiea2019276-print-pdf - 2.1 Portugal and the Empresa na Hora Reform; 3.4 Analysis of the Underlying Channels; Appendix A.2.*

### 2.1    Portugal and the Empresa na Hora Reform

### 2.1    Portugal and the Empresa na Hora Reform

### Background and motivation
- After joining the European Monetary Union in 1999, Portugal entered a prolonged slump with anemic productivity and output growth (Blanchard, 2007).
- Until 2005, Portugal was considered one the least business-friendly countries according to international ranking.
  - Before the reform it took 56-78 days to start a business.
  - An entrepreneur needed to fill in around 20 forms, provided by different public agencies, and complete 11 procedures, for a total cost of e2,000.

### The Empresa na Hora reform (program design and outcomes)
- Empresa na Hora was part of the broader SIMPLEX modernization plan designed by UCMA (Unidade de Coordena̧c ̃ao da Modernazi ̧c ̃ao Administrativa).
- Key features:
  - Made it possible to start a business “on the spot” via a single personal visit to an official Registry.
  - UCMA designed standardized pre-approved documents created on pre-defined firm names.
  - Within an hour, on average, an entrepreneur receives:
    - an official legal person identification card,
    - a Social Security number,
    - and a registration of the enterprise in the Business Registry.
  - Monetary costs shrunk to e360.
  - The law was approved on July 6th, 2005 (Decreto Lei 111/2005).
  - It involved virtually all sectors of economic activity and was intensively advertised by the government.
- Recognitions and rankings:
  - European Commission selected Portugal for the European Enterprise Award in 2006.
  - Portugal moved from averaging around the 113th position (out of 155 countries) in the Doing Business Index to around the 33rd.

### Implementation and rollout
- Implementation was staggered across municipalities due to budget constraints and need to train public servants.
- Initial rollout (post-Decreto Lei approval in July 2005):
  - Six One-Stop Shops opened in four cities: Coimbra, Aveiro, Moita and Barreiro.
  - Over the following years the program gradually expanded across the country.
  - Out of the 308 municipalities, 99 had a One-Stop Shop by the end of 2008.
- Registration rules and empirical implication:
  - A firm was allowed to register in any One-Stop Shop regardless of the firm’s operating location.
  - Empirical approach assumes firms registered in the same municipality in which they were operating; conversations with public officials indicated One-Stop Shops’ coverage was local.
  - Authors note that if entrepreneurs crossed municipal borders to register, this would, if anything, bias estimates of the expansionary effect downwards.
- Note on name customization:
  - It is possible for an entrepreneur to request a personalized name for the business and have all documents ready within two business days.

### Data sources and sample construction
- Main dataset: Quadros de Pessoal (administrative records on the universe of limited-liability firms with at least one employee in Portugal).
  - Coverage: years 2000-2008; dataset built from a census submitted each year in October.
  - Provides firm-, establishment-, and worker-level information.
  - Variables used: firms’ entry, exit, sector of activity (5-digit level), municipality location, annual nominal sales, employment.
  - Rationale: Empresa na Hora concerned creation of new firms rather than openings of establishments; over 93% of firms in Portugal have only one establishment.
- Supplementary datasets:
  - Instituto dos Registos e Notariado: exact opening date of each One-Stop Shop across the Portuguese municipalities.
  - Instituto Nacional de Estat́ıstica: municipality-level data on total residents and local demographic information.
- Sample construction details:
  - Firms considered to have exited if they stop appearing in the dataset for at least two consecutive years (equivalent to the last-time-appeared definition for more than 97% of cases).
  - Dropped pre-existing firms that change legal form to limited liability company over their life cycle to avoid capturing legal-form changes.
- Final sample characteristics:
  - On average, 125,000 non-financial private corporations per year.
  - Time window allows inclusion of five years preceding the reform and measures impact during the first four years of implementation.
  - Average entry rate: 7.5%.
  - Average exit rate: 9.5%.
  - Firm size distribution:
    - 50% of firms have less than 4 employees.
    - 50% of entrants have less than 2 employees.
- Limitation:
  - Sample ends in 2008 due to a drop in Quadros coverage thereafter; not all reformed municipalities observed for the same number of years after opening.

### Empirical strategy and identification
- Identification exploits staggered opening of One-Stop Shops across municipalities using a generalized difference-in-differences specification with municipality and year fixed effects.
- Baseline regression framework (notation preserved from source):
  - y_{m,t} = α_m + δ_t + ∑_τ β_τ 1(t−τ=τ_{0,m}) + γ X_{m,t} + ε_{m,t}.
  - α_m and δ_t are municipality and year fixed effects.
  - 1(t−τ=τ_{0,m}) is a municipality-year dummy equal to 1 whenever municipality m is τ years from the opening of its office; β_{−1} normalized to 0.
  - Parallel-trend assumption: unobserved determinants of outcome evolve in parallel over time across municipalities.
- For entry analysis the regression used (benchmark):
  - y_{m,t} = α_m + δ_t + ∑_{τ=−7}^{3} β_τ 1(t−τ=τ_{0,m}) + γ_m 1(Municipality_m = 1) t + ε_{m,t}.
  - Allows for municipality-specific linear trends; standard errors clustered at municipality level.
- For employment analysis:
  - Dependent variable: log of municipality-level employment in a given year normalized over 1,000 residents.
  - Reference period chosen as t−3 (β_{−3} = 0) to transparently display employment response, capturing both actual and expected entry effects.

### Results — Entry
- Opening of One-Stop Shops significantly increased annual firm entry at the municipality level.
- Effect magnitude:
  - Using back-of-the-envelope calculations, the increase corresponds to an annual rise in local entry between 12% to 40%, corresponding to an average of 25% per year following the reform.
  - Pre-reform entry rate in Treated municipalities is around 8.5%; the reform led to an approximate increase in entry of two percentage points.
- Coefficient precision:
  - Coefficients for t+2 and t+3 are noisier due to fewer treated municipalities contributing; authors emphasize the average increase and positive, significant coefficients over the time span.
- Robustness:
  - Results robust to relaxing municipality-specific trends and allowing decile-specific trends based on pre-period population and service-orientation; coefficients of β_τ do not differ substantially.

### Results — Local employment
- Employment increased significantly in Treated municipalities relative to Control ones.
- Timing and interpretation:
  - Employment started rising two years prior to the reform (t−2 and t−1), interpreted as incumbents’ adjustment in anticipation of expected entry rather than as differential pre-trends.
  - Lags t−7 to t−3 are flat and not statistically different from zero.
- Magnitude:
  - Employment increased by 5% in the year of the reform.
  - Employment then continued growing at an average annual rate of 4.8%.
  - Coefficients interpreted as cumulative percentage increase in municipality-level employment relative to t−3.
- Robustness:
  - Employment dynamics are robust to different trend specifications (reported in Appendix).
- Interpretation caveats:
  - The estimated 4.8% increase is a local effect and represents an upper bound on country-level employment impact because:
    - Estimates refer to the private sector only (exclude government-owned entities).
    - Local effect includes cross-municipality movement of workers.

*Source: wpiea2019276-print-pdf - 2.1    Portugal and the Empresa na Hora Reform*

### 3.4    Analysis of the Underlying Channels

### 3.4    Analysis of the Underlying Channels

### Decomposition by Age Groups (3.4.1)
- Firms are classified into three age classes: age 0−5, 6−15, and older than 15 (15+).
- Employment is aggregated by municipality-year for each age group and equation (2) is estimated separately for each age group.
- Identification assumption: firms belonging to any age group in the Treated municipalities would have behaved as the corresponding ones in the Control municipalities absent the reform and absent different trends across municipalities.
- Empirical finding:
  - Both young firms and older incumbents contribute positively to the rise in local employment.
  - Back-of-the-envelope calculation combining age-group regression coefficients with average employment shares in the pre-reform period shows:
    - Around 60% of the overall increase in local employment is due to the response of incumbents older than 5 years old.
    - Entrants and young firms account for the remaining 40%.
- Caveat: firms older than 15 years show a noisier and essentially flat response, largely due to their small and uneven distribution across municipalities.

### Intensive Margin of Adjustment by Age Groups (3.4.2)
- Measure of average firm size by municipality m, age group a, and year t:
  - y_{m,a,t} = (sum_{i∈(m,a,t)} employment_i) / (sum_{i∈(m,a,t)} active firms_i)
- This y_{m,a,t} is used as the dependent variable in regression equation (2).
- Empirical findings:
  - The average size of incumbents increased after the reform.
  - The average size of entrants and young firms remained unchanged.
  - Interpretation:
    - Entrants and young firms contributed to the aggregate rise in employment exclusively via the extensive margin (increase in the number of entrants).
    - Incumbents contributed via the intensive margin (increase in employment per operating incumbent).
- Robustness: result is robust to relaxing municipality-specific trends and allowing for different trends (reference to Figure 14 in the Appendix).
- Implication: expansion by incumbents indicates the increase in operating firms was not merely formalization of previously informal firms; there was an actual increase in the number of operating firms.
- Novelty: expansion of incumbents following increased entry is novel and inconsistent with predictions of current workhorse models of firm dynamics (see Section 4).

### Extensive Margin of Adjustment by Age Groups (Exit Analysis) (3.4.3)
- Exit analysis conducted at the firm level; baseline regression:
  - Pr(exit_it = 1) = α_m + δ_t + sum_{τ=−7}^{τ=3} β_τ 1(t−τ^0,m = τ) + sum_m γ_m 1(Municipality_m = 1)_t + ε_{i,t}. (Equation (3))
- exit_it is an indicator equal to 1 if firm i exits operations in year t.
- By allowing only for the municipality effect, the specification controls for within-municipality variation and allows variation across sectors to remain consistent with municipality-level regressions.
- Empirical finding:
  - The exit probability for the average firm remained mostly unaffected by the reform across all age groups.
- Robustness: result holds when replacing municipality fixed effect with municipality × 3-digit sector fixed effects and when replacing municipality-specific trends with trends by deciles of municipalities (see Panel (b) and Figure 14 in the Appendix).

### Heterogeneous Response of Incumbents (3.4.4)
- Heterogeneity dimension studied: differences in productivity across firms.
- Productivity proxy: revenue labor productivity = nominal sales / employment.
- Firms ranked using 2004 (the year preceding announcement and implementation) revenue labor productivity within each age group (0-5, 6-15, 15+), 3-digit sector, and municipality.
- Aggregation:
  - Total employment and total exit aggregated at the municipality-year level for the first and third terciles.
  - Dependent variables are municipality-level aggregates of employment and exit for each tercile normalized by 1,000 residents.
- Empirical findings (Figure 11 panels (a) and (b)):
  - The increase in aggregate employment is driven by the most productive firms (top tercile).
  - The bottom tercile’s behavior remained unchanged after the reform.
  - Exit behavior: number of exiting firms in the top tercile dropped significantly after the reform; exit behavior of the bottom tercile remained unaffected.
- Robustness:
  - Alternative ranking pooling age groups (ranking within 3-digit sector and municipality) yields weaker but still robust results (reference to Figure 15 in the Appendix).

### Analysis of the Reform by Sector (3.5 summary)
- Sectoral focus: 1-digit classification, concentrating on manufacturing and services.
- Entry:
  - Entry grew significantly after the reform for the service sector.
  - Entry remained flat for manufacturing.
  - Interpretation: manufacturing is capital-intensive (high fixed capital investment), so decisions less affected by reductions in time and monetary entry costs; services respond more to local demand changes induced by the One-Stop Shop.
- Employment:
  - Employment increases for the service sector.
  - Employment did not significantly change for manufacturing.
- Average firm size by age group and sector:
  - In services:
    - Average size of entrants and young firms decreased (consistent with smaller firms being more responsive to reduction in entry costs).
    - Incumbents expanded their average size.
  - In manufacturing:
    - Incumbents mildly expanded average size (evidence considered suggestive due to small sample and noisy coefficients).
- Robustness: results robust to decile-specific municipality trends based on residents and per-capita value of activity in services (see Figure 16).

### Theoretical Framework and CES Case (brief)
- General model: heterogeneous firms, monopolistic competition, demand q_i = D(p_i, M, E, P̃) with elasticity ε(p_i, M, E, P̃) = −D_1 D p_i; marginal cost mc_i = w / a_i; markup μ_i = ε/(ε−1).
- Entrants pay f_e units of the aggregate final good; endogenous mass of entrants M_E determined by expected zero-profit condition: ∫ V(a_i; M, E, P̃) dF(a_i) = f_e P. (Equation (7))
- Aggregate labor supply: L_S = (w / P)^ν, with ν > 0. (Equation (10))
- Under CES demand:
  - q_i = (p_i / P)^{−σ} E / P. (Equation (13))
  - Aggregate price index: P = (∫_{0}^{M} p_i^{1−σ} di)^{1/(1−σ)}.
  - Elasticity σ > 1 is constant and equal across firms; markups are constant at σ/(σ−1).
- Proposition 1 (CES): under CES, the response of labor demand is homogeneous across firms. Moreover,
  - ∂ln l_i / ∂ln M = −(σ−1−ν)/(σ−1). (Equation (14))

*Italic source attribution: Content from "3.4 Analysis of the Underlying Channels" in the provided IMF PDF chapter.*

### Appendix A.2.

### Appendix A.2.

### Ambiguity of labor demand under CES
- The Proposition implies each firm's employment falls if σ−1> ν (i.e., if the demand elasticity for each good i is higher than the elasticity of labor supply); otherwise labor demand of each firm increases.  
- Under common calibrations in the literature (σ∈[3,7] and ν∈[0.5,2]), the reform leads to a decline in the size of all operating firms.
- Despite incumbents contracting, aggregate labor L increases with the mass of operating firms M:
  - Proposition 2: Under CES, ∂lnL/∂lnM >0.
- Mechanisms:
  - Competition effect: increase in M reduces aggregate price level P (love-of-variety), incumbents downsize and all face the same decline in demand regardless of productivity.
  - Aggregate demand effect: lower P raises labor supply and aggregate demand; under standard ν the aggregate demand rise does not offset incumbent downsizing.
- Resulting implication: under CES the aggregate increase in L is driven entirely by the extensive margin (increase in M), inconsistent with heterogeneous incumbent responses observed empirically.

### Translog demand: formulation and properties
- Demand for good i (symmetric translog expenditure):
  - qi = [1/M − γ(ln pi − lnp)] E / pi.  (equation (15) in source)
  - Average price ln p = (1/M ∫0^M ln pi di).  (equation (16))
- Aggregate price index:
  - ln P = 1/(2γM) + E(ln p(a)) − (1/2) γ M V(ln p(a)).  (equation (18))
- Firm pricing and market shares:
  - pi = (1 + si/γ)^(1) (1/ai)  = μi 1/ai  = μi mci.  (equation (19))
  - si = max{0, 1/M − γ[ln pi − ln p]}.  (equation (20))
  - Demand elasticity: εi = 1 + γ/si.  (equation (21))
- Key properties:
  - εi increases with M ⇒ markups decrease with M.
  - εi increases with firm price level ⇒ in equilibrium εi decreases with firm productivity ai (more productive firms face less elastic demand).

### Heterogeneous firm-level labor responses (Propositions under translog)
- Proposition 3: Under translog, ∂ln(εi)/∂lnM >0, ∀i.
- Proposition 4: In the translog framework, the reform has a heterogeneous impact on firm-level labor li; the response is increasing in firm productivity:
  - ∂^2 ln li / ∂lnM ∂ln ai >0.
  - Most productive firms expand employment while least productive firms reduce employment, regardless of parameter specification.
- Proposition 5: Under translog, aggregate labor L increases in response to an increase in M:
  - ∂lnL/∂lnM >0.
- Mechanisms:
  - Competition effect: fall in P via love-of-variety and reduction of markups; incumbents hurt ceteris paribus, but more productive firms face lower demand elasticity and are relatively less hurt.
  - Aggregate demand effect: lower P raises labor supply LS and stimulates aggregate expenditure E, increasing demand for each firm; net effect causes high-productivity incumbents to expand.

### Numerical example: calibration (baseline)
- Productivity distribution: Pareto with scale xm = 2 and shape α = 1.08 (matches pre-reform standard deviation of firm size = 0.84).
- Normalize mass of incumbent firms MI = 1.
- Markup parameter γ = 1.97 (matches sales dispersion = 1.1).
- Labor supply elasticity ν = 2.86 (matches average annual rise in employment at municipality level = 4.84%; entry measure changes from 9% to 11.25% consistent with 25% average annual entry increase).
- Table of baseline calibration (parameters and targets):
  - Mass of incumbent firms MI = 1
  - Productivity scale parameter xm = 2
  - Productivity shape parameter α = 1.08 — Size dispersion = 0.84
  - Markup parameter γ = 1.97 — Sales dispersion = 1.1
  - Labor supply elasticity ν = 2.86 — Local employment response = 4.84%

### Numerical example: baseline results
- Firm-level: change in labor demand is increasing in firm productivity; least productive firms cut size, highly productive firms expand.
- Aggregate decomposition (matching 4.84% annual increase in local employment):
  - ∆L - Total = 4.84%
  - ∆L - Entrants = 2.31%  (47.5%)
  - ∆L - Incumbents = 2.54%  (52.5%)
  - Approximately 53% of the increase comes from incumbents (consistent with empirical ~60% finding).

### Inspecting the mechanism: comparative statics on γ and α
- Role of γ (translog preference parameter):
  - Markup μi = 1 + (1/γ) si.
  - Higher γ implies (i) lower markup levels, (ii) less dispersed markup distribution, (iii) less responsive markups to market-share changes.
  - Net effect in numerical examples: the reform’s effect on aggregate employment is decreasing in γ (the responsiveness channel dominates).
  - Table for different γ:
    - γ= 0.97: ∆L - Total = 7.32%; %∆L - Entrants = 32.3%; %∆L - Incumbents = 67.8%
    - γ= 1.97: ∆L - Total = 4.84%; %∆L - Entrants = 47.7%; %∆L - Incumbents = 52.3%
    - γ= 2.97: ∆L - Total = 4.08%; %∆L - Entrants = 56.1%; %∆L - Incumbents = 43.9%
  - When overall employment effect rises, relative contribution of incumbents rises.
- Role of α (Pareto shape parameter):
  - Greater initial productivity dispersion (lower α) strengthens the overall increase in employment for given γ.
  - Mechanism: stronger reallocation toward high-productivity firms reduces P further and stimulates labor supply; initial misallocation (increasing in 1/α) is corrected more when dispersion is higher.
  - Note: increase in aggregate labor as a function of initial productivity dispersion is stronger for higher γ.

### Assessing economy-wide impact: variation in labor supply elasticity ν
- Local employment response is an upper bound for economy-wide impact because:
  - Municipal-level ν is higher (commuting and omission of government-sector worker movements).
- Comparative statics on ν show lower ν weakens firm-level and aggregate employment responses; relative incidence shifts toward entrants when ν is lower.
- Table for different ν:
  - ν= 1: ∆L - Total = 1.67%; %∆L - Entrants = 134%; %∆L - Incumbents = −34%
  - ν= 2.86: ∆L - Total = 4.84%; %∆L - Entrants = 46.3%; %∆L - Incumbents = 53.7%
- When ν = 0 the contribution of incumbents is negative (fixed labor force reallocates to entrants).

### Key takeaways and implications
- Empirical evidence: reform that reduced entry costs increased firm entry and aggregate employment; bulk of employment expansion came from incumbents, with heterogeneous incumbent responses—most productive incumbents expanded.
- CES models with constant markups predict homogeneous reductions in incumbent employment and are inconsistent with empirical findings.
- Translog demand with variable markups delivers:
  - Heterogeneous firm-level responses (high-productivity incumbents expand).
  - Substantial contribution of incumbents to aggregate employment increases.
- Policy implication: quantitative models used to evaluate reforms that change competitive environment or the number of operating firms should incorporate firm heterogeneity and variable markups to capture reallocation and aggregate employment effects.

*Source: Appendix A.2. (wpiea2019276-print-pdf)*

### References

### wpiea2019276-print-pdf - References

### Major literature and themes cited
- Empirical and theoretical literature on entry, firm dynamics, market deregulation, and macroeconomic effects: Aghion et al. (2005, 2009); Atkeson and Burstein (2008); Blanchard (2007); Blanchard and Giavazzi (2003); Cacciatore et al. (2016a, 2016b, 2016c, 2017); Duval and Furceri (2018); Eggertsson et al. (2014); Feenstra (2003); Hopenhayn (1992); Melitz (2003); among others.
- Focus areas reflected in citations: entry regulation and entrepreneurship, one-stop shop reforms (Empresa na Hora), industry concentration, markups and trade, structural reforms and growth, firm entry/exit and job creation, and translog demand formulations.

### Key empirical statistics and descriptive facts (from tables)
- Table 5: One-Stop Shop Program Implementation
  - Years: 2005, 2006, 2007, 2008, 2009, Total
  - Number of shops: 20, 28, 31, 36, 49, 164
  - Number of counties implementing: 13, 24, 28, 34, 46, 145
  - Number of counties >1 shop: 6, 31, 20, 12
- Table 6: Descriptive statistics on municipality groups (period 2000-2004). Means (standard deviations) and [25th, 75th percentiles]:
  - Entry rate: Treated 8.5% (4.6%) [5.7%, 10.2%]; Never-Treated 9.4% (6.9%) [5.4%, 11.9%]; Early-Treated 7.9% (4%) [5.8%, 8.7%]; Late-Treated 8.8% (5%) [5.6%, 10.8%]
  - Entrants x 1,000 inhab: Treated 0.83 (0.4) [0.56, 1.02]; Never-Treated 0.71 (0.45) [0.4, 0.97]; Early-Treated 0.88 (0.34) [0.64, 1.03]; Late-Treated 0.81 (0.42) [0.54, 1.01]
  - Exit rate: Treated 8.4% (2.8%) [6.8%, 10%]; Never-Treated 7.7% (4.1%) [5.3%, 10%]; Early-Treated 8.5% (2.3%) [7%, 9.7%]; Late-Treated 8.3% (3%) [6.6%, 9.9%]
  - Exit x 1,000 inhab: Treated 0.93 (0.38) [0.67, 1.1]; Never-Treated 0.68 (0.4) [0.38, 0.94]; Early-Treated 1.1 (0.39) [0.8, 1.3]; Late-Treated 0.84 (0.35) [0.6, 1.1]
  - Active firms x 1,000 inhab: Treated 10.67 (3.8) [8.1, 12.9]; Never-Treated 8.32 (3.4) [5.7, 10.4]; Early-Treated 12.21 (3.8) [9.4, 15.1]; Late-Treated 9.8 (3.5) [7.4, 11.7]
  - Employment rate (Census): Treated 47.2% (24%) [34.4%, 59.2%]; Never-Treated 34.1% (21%) [25.8%, 44.3%]; Early-Treated 53.7% (27%) [39.8%, 65.7%]; Late-Treated 43.4% (18%) [30.6%, 54.9%]
  - Residents (mean): Treated 66,896.1 (128,244) [17,852, 74,965]; Never-Treated 18,540,7 (41,762.5) [6,396, 21,135]; Early-Treated 114,213.3 (149,881.3) [44,162, 142,728]; Late-Treated 39,421.6 (56,260.2) [14,241, 52,604]
  - Share of pop aged 65 or more: Treated 19.07% (6.5%) [14.3%, 22.3%]; Never-Treated 22.05% (8.2%) [17.3%, 26.3%]; Early-Treated 16.31% (3.99%) [12.9%, 19.9%]; Late-Treated 20.7% (7.21%) [16.2%, 24.7%]
  - Macro-sector sales shares (means and sd): Agriculture 2.82% (6%); Manufacturing 28.3% (19%); Construction 12.1% (9%); Services 46.66% (19%)
    - Comparable sector shares reported for Never-Treated, Early-Treated, Late-Treated municipalities as well.
- Table 7: Descriptive statistics on non-financial corporations (period 2000-2008)
  - Entry Rate: 7.5%
  - Exit Rate: 9.3%
  - Operating Firms: 125,015
  - Employment Sector Shares: Agriculture 1.63%; Manufacturing 32.6%; Construction 15.13%; Services 50.64%
  - Sales Sector Shares: Agriculture 1.52%; Manufacturing 26.6%; Construction 10.14%; Services 61.74%
  - 2-yr Survival Rate Entrants: 69.7%
  - 4-yr Survival Rate Entrant: 46.6%
  - Size, age, and entrant distributions given (p1, p25, p50, mean, p75, p99 shown as 1 2 4 7.13 8 55 etc. in table formatting)

### Empirical analyses and figures (regression designs and outcomes)
- Common regression specification used across figures (municipality-level aggregates unless stated):
  - y_{m,t} = α_m + δ_t + Σ_{τ=−7}^{3} β_τ 1(t − τ_{0,m} = τ) + Σ_m γ_m 1(Municipality_m = 1) t + ε_{m,t}
  - τ_{0,m} corresponds to the year the One-Stop Shop opened in municipality m.
  - Standard errors clustered at the municipality level. 90% confidence intervals reported.
- Figure-based outcomes summarized by variable:
  - Entry: estimates of β_τ for total entrants per 1,000 residents (Figure 6).
  - Total employment: estimates of β_τ for log(total employment per 1,000 residents) (Figure 7).
  - Employment by age groups (Age 0-5, Age 6-15, Age 15+): municipality-level total employment per 1,000 residents by age group (Figure 8).
  - Average firm size by age groups: average size = Tot. Employment / Tot. Firms for age groups (Figure 9).
  - Exit probability by age groups: firm-level regressions of Pr(exit_it) for age groups, with versions allowing 3-digit sector × municipality fixed effects (Figure 10).
  - Heterogeneous responses by incumbents' productivity terciles: regressions on employment and exit for top and bottom terciles (productivity proxied by sales per employee, ranked within 3-digit sector, municipality, age group) (Figure 11).
  - Sector-specific impacts (Manufacturing vs Services): entry, total employment, average size by age groups, exit probability by age groups (Figure 12).
  - Robustness and heterogeneity explored with decile-specific trends, alternative rankings, and various fixed-effect interactions (Figures 14–16, Appendix).

### Theoretical derivations and main analytical results (Appendix A.2)
- Production and labor demand under CES:
  - l_i = a_i^{σ−1} M^{σ/(1−σ)} [E(a^{σ−1})]^{σ/(1−σ)} Y (equivalently as derived in equations (23)–(30)).
  - Using labor supply normalization w = 1 and L = P^{−ν}, closed-form expressions for Y and L derived: Y = [E(a^{σ−1})]^{1/(σ−1)} M^{1/(σ−1)} L and L = (σ/(σ−1))^{−ν} M^{−ν/(1−σ)} [E(a^{σ−1})]^{−ν/(1−σ)} (equations (28) and (29)).
- Proposition 1 (labor per firm elasticity w.r.t. M):
  - ∂ln l_i / ∂ln M = (1 − σ + ν)/(1 − σ) > 0 if σ < 1 + ν.
  - Cross-derivative ∂^2 ln l_i / ∂ln M ∂ln a_i = 0 ∀ i.
- Proposition 2 (aggregate labor elasticity):
  - ∂ln L / ∂ln M = ν/(σ − 1).
- Translog demand model key identities (derivations from Feenstra (2003) style):
  - Demand level: q_i = [1/M − γ(ln p_i − ln p)] E / p_i (equation (31)).
  - Aggregate price index: ln P = 1/(2 γ M) + E(ln p(a)) − 1/2 γ M V(ln p(a)) (derivation shown).
  - Elasticity and markup: ε_i = 1 + γ / s_i and μ_i = 1 + s_i / γ (via steps in derivation).
- Proposition 3 (elasticity response to M):
  - s_i decreases with M for all i: ∂s_i / ∂ln M < 0 ∀ i (shown via integral constraint ∫ s(a_i) dF(a_i) = 1/M and equations (34)–(37)).
  - Consequently ∂ln ε_i / ∂ln M > 0, ∀ i.
- Proposition 4 (interaction of market size and firm productivity on labor):
  - ∂^2 ln l_i / ∂ln M ∂ln a_i > 0 (equation (40)): larger market size M increases sensitivity of firm labor to firm productivity a_i.
- Proposition 5 (aggregate labor increases after reform):
  - Since ∂s_i / ∂ln M < 0 and p_i = (1 + s_i/γ)^{1} / a_i, ∂ln P / ∂ln M < 0 and with ln L = −ν ln P, aggregate labor L increases after the reform.

*Source: wpiea2019276-print-pdf - References*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019276-print-pdf.pdf_