## wpiea2019087

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### Context and objective
- Mexico has experienced low productivity growth in recent decades.
- Slow technology diffusion is unlikely the main explanation given large foreign investment inflows following trade-opening structural reforms since the 1990s.
- Complementary explanation explored: within-firm growth—individual firms may not invest enough, depressing firm growth and preventing exploitation of economies of scale.
- Research question: what distinguishes the small minority of Mexican firms that grow substantially from the majority that stagnate?

### Data and approach
- Data: five waves of the Mexican Economic Census from 1993 to 2013, linked longitudinally using firm identifiers constructed by Busso and others (2018) and expanded by INEGI staff.
- Measure: firm life cycle growth = cumulative growth rate in a firm’s number of employees from one Census wave to the next.
- Age groups: 0-4 years, 5-9 years, 10-14 years, 15-19 years, 20-24 years.
- Sample restrictions:
  - Include only firms observable since birth.
  - Include only firms observable continuously since birth across relevant waves.
  - Drop firms with birth years differing by more than 4 years across waves.
- Final sample counts by birth wave:
  - 25,653 firms born in the 1993 wave.
  - 56,188 firms born in the 1998 wave.
  - 139,475 firms born in the 2003 wave.
  - 524,854 firms born in the 2008 wave.
- Sector exclusions: financial services, utilities, real estate, professional / technical services, management of shell companies, health and education, arts and culture.
- Additional cleaning: exclude entities with negative or zero reported value added, capital, sales or labor input; omit industries with fewer than 10 firms; remove 1 percent tails of output wedges, capital wedges, and total factor productivity.

### Stylized facts: size, growth and heterogeneity
- State-level cross-sectional elasticity estimates:
  - Elasticity of firm size with respect to non-oil GDP per capita (all firms, controlling for industry composition): 0.21; correlation coefficient slightly below 0.4.
  - Elasticity for manufacturing firms (controlling for industry composition): 0.41; correlation coefficient slightly above 0.4.
  - Elasticity without controlling for industry composition (all firms): 0.16.
  - Elasticity for manufacturing firms without controlling for industry composition: 0.54.
- Average firm life cycle growth:
  - Manufacturing firms grow to around 1.5 times their initial size on average until age 15-19 before stagnating.
  - For the economy as a whole, firms expand to about 1.4 times their initial size by age 15-19.
  - The average Mexican firm stagnates in size after some 15-19 years.
- Distributional heterogeneity:
  - Median firm effectively stagnates at initial size by age 20-24.
  - 90th percentile of firms grows by less than a factor of three by age 20-24.
  - 99th percentile of firms grows to some five times its initial size (eight times for manufacturing firms).
  - By comparison, U.S. manufacturing firms grow to some 4-6 times their initial size by age 20-24.
- Value-added weighted averages:
  - Value-added weighted average cumulative growth reaches more than four by age 20-24 for all firms, and around six for manufacturing firms.

### Econometric baseline decomposition (specification and key coefficients)
- Baseline regression: cumulative growth Qf,t regressed on age-group dummies, state-industry-year fixed effects αs,i,t, control variables Cf,t and variables of interest Xf,t; standard errors clustered at state-industry level.
- Key coefficients and findings:
  - Initial size (log): coefficient -0.380*** (Regression 1); other specs show -0.391***.
  - Multi Establishments (dummy): coefficients around 0.58-0.70 (e.g., 0.580*** Regression 1; 0.669*** Regression 2; 0.698*** Regression 4).
  - Social Security Share (share of social security contributions as % of salary payments): coefficient 0.024*** (Regression 2); implies a fully formal firm has, on average across age groups, about 47 percent higher cumulative growth than a fully informal firm (Regression 2 interpretation).
  - Labor Paid Ratio (share of salaried employees): coefficient 0.469*** (Regression 3); implies about 38 percent higher cumulative growth for a fully formal firm per Regression 3 discussion.
  - Concentration (Herfindahl index): positive coefficient 0.150** in one spec (Regression 4) but becomes negative and significant when dropping outliers, indicating generally negative link between market concentration and life cycle growth after outlier removal; concentration values generally lie between zero and 0.15 for most industries.
  - Geographic remoteness (logs):
    - Distance to next major city (population ≥ 500,000): coefficient -0.004*** (Regression 5).
    - Distance to US border (log): coefficient -0.006** (Regression 6).
    - Distance to Mexico City (log): coefficient -0.011** (Regression 7).
  - Financial Access (dummy for having a bank account): coefficient 0.426*** (Regression 8); robust to using access to bank credit as alternative.

### Predicted conditional life cycles (interactions and magnitudes)
- Specification with age-group interactions (Equation 3) used to predict conditional life cycles.
- Predicted effects (holding other factors at means):
  - The average formal firm would grow some 70 percentage points more over the full life cycle than the average informal firm.
  - A firm that is both formal and has financial access would see a cumulative growth rate of some 140 percentage points more than an informal firm without a bank account.
  - A formal firm with a bank account and multiple establishments would grow to 3-4 times its initial size over its full life cycle.

### Manufacturing vs. services differences
- Interactions with a manufacturing dummy show:
  - Age-group interactions with manufacturing are positive and highly significant: manufacturing firms have somewhat stronger life cycle growth.
  - Most interactions of variables of interest with manufacturing dummy are not significant, implying variables matter similarly across sectors.
  - Exception: multi-establishment dummy interaction with manufacturing is highly significant and positive.
- Representative coefficients from Table 3:
  - Age Group 5-9 level term 0.329*** with interaction 0.071*** (Regression 1).
  - Financial Access level term 0.326*** with interaction 0.132*** (Regression 2).
  - Multi Establishments level term 0.572*** with interaction 0.667** (Regression 1) and 1.098** interaction (Regression 2).

### Descriptive decomposition of top and bottom industries
- Top-performing 3-digit industries after 15-19 years:
  - Manufacturing: manufacture of communication and transport equipment (including cars and car parts).
  - Services: largely transport services.
- Bottom-performing industries: retail trade services, which tend to include many micro and informal firms.
- Cohort effects: firms in the 1993 cohort experienced somewhat stronger life cycle growth than later cohorts (1998, 2003).

### Policy implications and recommendations
- Priority structural reforms to support firm growth and reduce misallocation:
  - Reduce informality.
  - Combat undue use of market power in concentrated industries.
  - Strengthen access to financial services.
  - Target infrastructure investments to better connect remote regions to major population centers.
- Policy emphasis on enabling firms to become formal, obtain financial access, and expand into multi-establishment structures could materially increase the share of firms that grow to 3-4 times their initial size.

### Robustness and alternative specifications
- Lagged-regressor specifications (all regressors lagged by five years / one wave) show robustness:
  - Variables subject to endogeneity remain highly significant with expected coefficients.
  - Table C observations: 845,879; 803,585; 745,527; 708,305; 515,495; 489,720.
  - Table C R-squared values: 0.159; 0.164; 0.164; 0.165; 0.144; 0.155.
- Alternative fixed-effect specifications leave results qualitatively unchanged:
  - Table D observations: 1,422,093; 1,088,177; 1,645,378; 1,249,606; 1,615,140; 1,184,486.
  - Table D R-squared values: 0.197; 0.203; 0.184; 0.190; 0.560; 0.697.
  - Some variables drop out as fixed effects absorb variation (e.g., concentration, geographical variables, multi-establishment and initial size with firm fixed effects).

### Key descriptive statistics (sample overview)
- Initital Size: Mean 3.6; Median 2; Std. Dev. 28.9; 5th pctile 1; 95th pctile 7.
- Multi Establishments: Mean 0.02; Median 0; Std. Dev. 0.14; 5th pctile 0; 95th pctile 0.
- Social Security Share: Mean 1.28; Median 0; Std. Dev. 4.59; 5th pctile 0; 95th pctile 12.8.
- Labor Paid Ratio: Mean 0.19; Median 0; Std. Dev. 0.34; 5th pctile 0; 95th pctile 1.
- Concentration: Mean 0.075; Median 0.06; Std. Dev. 0.03; 5th pctile 0.05; 95th pctile 0.16.
- Distance Large City: Mean 77.4; Median 48.5; Std. Dev. 85.6; 5th pctile 110; 95th pctile 250.6.
- Distance US Border: Mean 721.5; Median 746.5; Std. Dev. 251.5; 5th pctile 206.3; 95th pctile 1097.
- Distance Mexico City: Mean 429.3; Median 307.6; Std. Dev. 446.3; 5th pctile 9.1; 95th pctile 1298.2.
- Financial Access: Mean 0.03; Median 0; Std. Dev. 0.16; 5th pctile 0; 95th pctile 1.

### Conclusions and directions for future research
- Main conclusions:
  - Individual firms under-invest, depressing firm growth and preventing exploitation of economies of scale.
  - Formal status, multiple establishments, financial access, participation in diversified industries, and location in population centers are associated with sizable life cycle growth.
  - A firm that is both formal and has financial access is predicted to see a cumulative growth rate of some 140 percentage points more than an informal firm without financial access.
  - Formal firms with financial access and multiple establishments are predicted to grow to 3-4 times their initial size over their life cycles.
- Future research:
  - More detailed study of differences in the distribution of life cycle growth across cohorts and age groups.
  - More explicit examination of the role of market power in driving life cycle growth.

*Source: IMF Working Paper (content unit wpiea2019087, PDF chapter/section).*

### INTRODUCTION __________________________________________________________________ 3

### wpiea2019087 - INTRODUCTION __________________________________________________________________ 3

### Context and objective
- Mexico has experienced low productivity growth in recent decades (Levy and Rodrik, 2017).
- Slow technology diffusion is unlikely the main explanation given large foreign investment inflows following trade-opening structural reforms since the 1990s.
- Complementary explanation explored: within-firm growth—individual firms may not invest enough, depressing firm growth and preventing exploitation of economies of scale.
- Research question: what distinguishes the small minority of Mexican firms that grow substantially from the majority that stagnate?

### Data and approach
- Firm life cycle growth is calculated using five waves of the Mexican Economic Census from 1993 to 2013.
- Longitudinal firm identifiers constructed by Busso and others (2018) and expanded by INEGI staff are used to track establishments over time.
- Focus is on the growth of individual establishments (referred to as "firm growth" for simplicity); in Mexico, establishment and firm-level growth are identical in most cases because very few firms have more than one establishment.

### Stylized facts established
- Firm size is positively correlated with state-level per capita incomes, complementing cross-country results and highlighting the link between firm growth and economic development (Bento and Restuccia, 2018).
- A small minority of Mexican firms grows at rates similar to the average U.S. firm.
  - The vast majority of Mexican firms stagnate at about age 15-19, consistent with Hsieh and Klenow (2014).
  - Some firms grow continuously to several times their initial size by age 20-24.
- Similar evidence found in other contexts: Eslava and Haltiwanger (2017) document that only a small proportion of Colombian firms grow at rates similar to the average U.S. firm.

### Decomposition strategy and headline findings
- Firm life cycle growth is decomposed into contributions of individual firm characteristics using a simple regression framework.
- Key firm characteristics associated with sizeable growth rates:
  - financial access,
  - multiple establishments,
  - formality,
  - membership in diversified industries,
  - location in population centers.
- Regression-based prediction: a firm that is both formal and has financial access would grow substantially (as implied by the regressions presented).

*Source: INTRODUCTION (pages excerpt) from wpiea2019087*

### 2.4 times its initial size. Formal firms with financial access and multiple establishments, in

### wpiea2019087 - 2.4 times its initial size. Formal firms with financial access and multiple establishments, in

### Contributions and main conclusions
- Formal firms with financial access and multiple establishments are predicted to grow to 3-4 times their initial size over their life cycles, an order of magnitude similar to that of the average U.S. firm (Hsieh and Klenow, 2014).
- A very small share of firms (“superstar” firms) grow continually at high rates and tend to be very large firms in industries that form part of the North American supply chain.
- The paper provides evidence that distortions that misallocate resources between more and less productive firms also depress investment by individual firms (Hsieh and Klenow, 2014; Bento and Restuccia, 2017).
- Using data perfectly comparable across Mexican states increases credibility of estimates linking firm size and development; prior estimates include an elasticity of establishment size with respect to GDP per capita of around 0.3 (Bento and Restuccia, 2017; Bento and Restuccia, 2018).

### Data and methodology
- Data: five waves of the Mexican Economic Census from 1993 to 2013, linked longitudinally using an algorithm that constructs firm identifiers (Busso and others, 2018, expanded by INEGI staff).
- Firm life cycle growth measure: cumulative growth rate in a firm’s number of employees from one Census wave to the next.
- Age groups used: 0-4 years, 5-9 years, 10-14 years, 15-19 years, 20-24 years.
- Sample restrictions:
  - Include only firms observable since birth (exclude firms older than 0-4 years in 1993).
  - Include only firms observable continuously since birth across relevant waves.
  - Drop firms with birth years differing by more than 4 years across waves.
- Final sample counts by birth wave: 25,653 firms born in the 1993 wave, 56,188 firms born in the 1998 wave, 139,475 firms born in the 2003 wave and 524,854 firms born in the 2008 wave.
- Sector exclusions: financial services, utilities, real estate, professional / technical services, management of shell companies, health and education, arts and culture; remaining sectors include manufacturing, retail and wholesale trade, transportation and warehousing, accommodation and food services, information and other services.
- Additional data cleaning: exclude entities with negative or zero reported value added, capital, sales or labor input; omit industries with fewer than 10 firms; remove 1 percent tails of output wedges, capital wedges, and total factor productivity.

### Stylized facts: size, growth and heterogeneity
- State-level cross-sectional elasticity estimates:
  - Estimated elasticity of firm size with respect to non-oil GDP per capita (all firms, controlling for industry composition): 0.21; correlation coefficient slightly below 0.4.
  - Elasticity for manufacturing firms (controlling for industry composition): 0.41; correlation coefficient slightly above 0.4.
  - Elasticity without controlling for industry composition (all firms): 0.16.
  - Elasticity for manufacturing firms without controlling for industry composition: 0.54.
- Average firm life cycle growth:
  - Manufacturing firms grow to around 1.5 times their initial size on average until age 15-19 before stagnating.
  - For the economy as a whole, firms expand to about 1.4 times their initial size by age 15-19.
  - The average Mexican firm stagnates in size after some 15-19 years.
- Distributional heterogeneity:
  - Median firm effectively stagnates at initial size by age 20-24.
  - 90th percentile of firms grows by less than a factor of three by age 20-24.
  - 99th percentile of firms grows to some five times its initial size (eight times for manufacturing firms).
  - By comparison, U.S. manufacturing firms grow to some 4-6 times their initial size by age 20-24 (Hsieh and Klenow, 2014).
- Value-added weighted averages:
  - Value-added weighted average cumulative growth reaches more than four by age 20-24 for all firms, and around six for manufacturing firms — indicating a small number of very large firms drive much of aggregate growth.

### Descriptive decomposition of top and bottom industries
- Top-performing 3-digit industries after 15-19 years include:
  - Among manufacturing: manufacture of communication and transport equipment (including cars and car parts).
  - Among services: largely transport services.
- Bottom-performing industries include retail trade services, which tend to include many micro and informal firms.
- Cohort effects:
  - Firms in the 1993 cohort (born prior to NAFTA) experienced somewhat stronger life cycle growth than later cohorts (1998, 2003), possibly reflecting different exposure to trade shocks and crises.

### Econometric baseline decomposition (specification and key coefficients)
- Baseline regression specification (Equation 2): cumulative growth 푄푓,푡 regressed on age-group dummies, state-industry-year fixed effects 훼푠,푖,푡, control variables 퐶푓,푡 and variables of interest 푋푓,푡; standard errors clustered at state-industry level.
- Control variables:
  - Initial size (log): large negative and stable coefficient; firms that start larger are less likely to double in size (coefficient reported as -0.380*** in Table 1, Regression 1; other specifications show similar negative coefficients, e.g., -0.391***).
  - Multi Establishments (dummy): positive and robust coefficient around 0.58-0.70 in baseline Table 1 regressions (e.g., 0.580*** in Regression 1; 0.669*** in Regression 2; 0.698*** in Regression 4).
- Informality measures:
  - Social Security Share (share of social security contributions as % of salary payments): Regression 2 in Table 1 coefficient 0.024***; implies a fully formal firm has, on average across age groups, about 47 percent higher cumulative growth than a fully informal firm (Regression 2 interpretation).
  - Labor Paid Ratio (share of salaried employees): Regression 3 coefficient 0.469***; implies about 38 percent higher cumulative growth for a fully formal firm per Regression 3 discussion.
  - Note: a fully formal firm in Mexico should pay around 16 percent of its workers’ salaries in social security contributions.
- Market concentration:
  - Concentration (Herfindahl index based on 20 largest firms in each 6-digit industry-state-wave): Regression 4 in Table 1 shows a positive coefficient 0.150** in one specification, but becomes negative and significant when dropping outliers (Table 2), indicating a generally negative link between market concentration and life cycle growth after outlier removal; concentration values generally lie between zero and 0.15 for most industries.
- Geographic remoteness (all reported in logs in regressions):
  - Distance to next major city (population ≥ 500,000): coefficient -0.004*** in Table 1, Regression 5.
  - Distance to US border (log): coefficient -0.006** in Table 1, Regression 6.
  - Distance to Mexico City (log): coefficient -0.011** in Table 1, Regression 7.
  - Coefficients generally negative and significant, but magnitudes described as not necessarily economically large given variables take values generally between 0 and 10 and fixed effects capture between-state variation.
- Financial access:
  - Financial Access (dummy for having a bank account): Regression 8 in Table 1 coefficient 0.426***; significant despite reduced observations because variable available only in latest two Census waves.
  - Using access to bank credit as alternative control does not materially change results.

### Predicted conditional life cycles (interactions and magnitudes)
- Specification with age-group interactions (Equation 3) used to predict conditional life cycles for combinations of key variables.
- Key predicted effects (holding other factors at means):
  - The average formal firm would grow some 70 percentage points more over the full life cycle than the average informal firm.
  - A firm that is both formal and has financial access would see a cumulative growth rate of some 140 percentage points more than an informal firm without a bank account.
  - A formal firm with a bank account and multiple establishments would grow to 3-4 times its initial size over its full life cycle — broadly similar to the growth of the average U.S. firm (Hsieh and Klenow, 2014).

### Manufacturing vs. services differences (Equation 4)
- Interactions of regressors with a manufacturing dummy indicate:
  - Age-group interactions with manufacturing carry positive and highly significant coefficients: manufacturing firms on average have somewhat stronger life cycle growth.
  - Most interactions of variables of interest with manufacturing dummy are not significant, implying variables (informality, financial access, remoteness, concentration, multi-establishment) matter similarly for manufacturing and services.
  - Exception: multi-establishment dummy interaction with manufacturing is highly significant and positive, implying advantages of multiple-establishment structures are particularly significant for manufacturing firms.
- Representative coefficients from Table 3:
  - Age Group 5-9 level term 0.329*** with interaction 0.071*** (Regression 1).
  - Financial Access level term 0.326*** with interaction 0.132*** (Regression 2).
  - Multi Establishments level term 0.572*** with interaction 0.667** (Regression 1) and 1.098** interaction (Regression 2).

### Policy implications and recommendations
- Push ahead with structural reforms in priority areas to support firm growth and reduce misallocation:
  - Reduce informality (given formal firms grow substantially faster).
  - Combat undue use of market power in concentrated industries (market concentration is associated with weaker life cycle growth once outliers are removed).
  - Strengthen access to financial services (financial access is associated with higher life cycle growth).
  - Target infrastructure investments to better connect remote regions to major population centers (geographic remoteness is negatively associated with growth).
- Policy emphasis on enabling firms to become formal, obtain financial access, and expand into multi-establishment structures could materially increase the share of firms that grow to 3-4 times their initial size.

*Italicized source: IMF Working Paper (content unit wpiea2019087, PDF chapter/section).*

### CONCLUSION

### CONCLUSION

### Stylized facts motivating the analysis
- Firm size is positively correlated with state-level per capita incomes.
- A small minority of Mexican firms grow at rates similar to the average U.S. firm, while most peers stagnate at less than two times their initial size.

### Main analytical findings
- Individual firms under-invest, depressing firm growth and preventing firms from taking sufficient advantage of economies of scale.
- Decomposition of life cycle growth using a regressions framework identifies a set of firm-level features associated with sizable life cycle growth:
  - Formal status (vs. informal)
  - Multiple establishments
  - Financial access (bank account)
  - Participation in diversified industries
  - Location in population centers
- Quantitative magnitudes from regressions:
  - A firm that is both formal and has financial access is predicted to see a cumulative growth rate of some 140 percentage points more than an informal firm without financial access.
  - Formal firms with financial access and multiple establishments are predicted to grow to 3-4 times their initial size over their life cycles, by an order of magnitude similar to that of the average U.S. firm.
- The identified firm-level distortions align with distortions previously linked to resource misallocation (e.g., Misch and Saborowski, 2018) and with the theoretical proposition that such distortions depress investment by individual firms (Hsieh and Klenow, 2014; Bento and Restuccia, 2017).

### Policy implications and recommendations
- Continued emphasis on structural reforms to address firm-level distortions, including:
  - Reduce tax evasion.
  - Limit the use of market power in concentrated industries.
  - Strengthen access to financial services.
  - Targeted infrastructure investments to better connect remote regions to major population centers, supporting firm growth.

### Robustness of results
- Lagged-regressor specifications (all regressors lagged by five years / one wave) show findings are remarkably robust:
  - Variables likely subject to endogeneity (informality, multi-establishment, financial access) remain highly significant with expected coefficients.
  - Table C observations: 845,879; 803,585; 745,527; 708,305; 515,495; 489,720.
  - Table C R-squared values: 0.159; 0.164; 0.164; 0.165; 0.144; 0.155.
- Alternative fixed-effect specifications (state-sector-year at 6-digit level, municipality fixed effects, firm fixed effects) leave results qualitatively unchanged:
  - Many explanatory variables remain statistically significant with relatively small coefficient variations.
  - Some variables drop out as fixed effects absorb variation (e.g., concentration indicator, geographical variables, multi-establishment and initial size when firm fixed effects are included).
  - Table D observations: 1,422,093; 1,088,177; 1,645,378; 1,249,606; 1,615,140; 1,184,486.
  - Table D R-squared values: 0.197; 0.203; 0.184; 0.190; 0.560; 0.697.

### Key descriptive statistics (sample overview)
- Initital Size: Mean 3.6; Median 2; Std. Dev. 28.9; 5th pctile 1; 95th pctile 7.
- Multi Establishments: Mean 0.02; Median 0; Std. Dev. 0.14; 5th pctile 0; 95th pctile 0.
- Social Security Share: Mean 1.28; Median 0; Std. Dev. 4.59; 5th pctile 0; 95th pctile 12.8.
- Labor Paid Ratio: Mean 0.19; Median 0; Std. Dev. 0.34; 5th pctile 0; 95th pctile 1.
- Concentration: Mean 0.075; Median 0.06; Std. Dev. 0.03; 5th pctile 0.05; 95th pctile 0.16.
- Distance Large City: Mean 77.4; Median 48.5; Std. Dev. 85.6; 5th pctile 110; 95th pctile 250.6.
- Distance US Border: Mean 721.5; Median 746.5; Std. Dev. 251.5; 5th pctile 206.3; 95th pctile 1097.
- Distance Mexico City: Mean 429.3; Median 307.6; Std. Dev. 446.3; 5th pctile 9.1; 95th pctile 1298.2.
- Financial Access: Mean 0.03; Median 0; Std. Dev. 0.16; 5th pctile 0; 95th pctile 1.

### Directions for future research
- More detailed study of differences in the distribution of life cycle growth across cohorts and age groups.
- More explicit examination of the role of market power in driving life cycle growth.

*Source: CONCLUSION, wpiea2019087 - CONCLUSION*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019087.pdf_