## 2. Log Employment Probabilities by Firm Size

## Source details

**Canonical URL:** [2. Log Employment Probabilities by Firm Size](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06251.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06251.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06251.pdf.json)

---

### Introduction
- Context and motivation
  - Since the 1970s hours of work declined in Europe relative to the United States and Japan; today the average American works approximately 400 hours more per year than the average European.
  - The paper evaluates the welfare and labor-market consequences of coordinated reductions in the workweek, focusing on France’s sequence of laws culminating in the 35-hours mandate.
- French policy timing and intent
  - Law enacted in 1998 mandated a reduction of the workweek to 35 hours in large firms by 2000 and in small firms by 2002.
  - Official purpose: increase employment during high unemployment (11.5 percent in 1998) via work sharing while protecting monthly earnings for minimum wage workers (SMIC).

### Institutional background and prior evidence
- Sequence of reforms
  - 1982: workweek from 40 to 39 hours.
  - 1998 (Aubry I) and 2000 (Aubry II): detailed provisions; differential transition and overtime treatment for small firms.
- Policy supports and protections
  - Rebates on firms’ social security contributions (declining with monthly income, largest for minimum wage earners).
  - Guarantee that monthly earnings of workers receiving the minimum wage should stay constant.
- Selected prior empirical findings referenced
  - Crépon, Leclair, and Roux (2005): total factor productivity decreased by 3.7% from 1997 to 2000 in firms that reduced the workweek relative to those that did not; employment increased by 9.9% in firms that adopted 35-hours.
  - Crépon and Kramarz (2002): for 1982 reduction from 40 to 39 hours, increased probability of transition from employment to unemployment between 2.3 and 3.9 percentage points.
  - Hunt (1998, 1999) (Germany): reductions in hours decreased employment over 1984–94.

### Theory: one-sector and two-sector frameworks (guiding empirical expectations)
- One-sector model (supply and demand implications)
  - Utility separable in consumption and leisure with potential complementarities in leisure: individual utility U = U(c, H_i, H_hat) where H_hat denotes others’ hours.
  - Positive strategic complementarities in leisure (0 < V12) can generate:
    - Multiple equilibria when 11 2 12 ''VUwV−≥+ (strong complementarities).
    - A coordinated reduction in hours may be socially preferable if positive spillovers in leisure (0 < V2).
  - Demand-side effects:
    - Fixed output and inability to contract overtime: reduction in standard hours can raise employment.
    - If firms can adjust output and face fixed employment costs a, reduction in hours raises per-hour labor cost and can reduce output and employment; capital substitution possible.
- Two-sector extension (large firms covered; small firms uncovered)
  - If hours and workers are perfect substitutes and output fixed, employment in covered sector increases proportionally to hours reduction.
  - With positive leisure complementarities: workers prefer covered sector; wages in large firms may fall relative to small firms (compensating differential).
  - Without complementarities: workers in large firms may be constrained, respond by moving to uncovered sector or taking second jobs; wages in large firms may increase relative to small firms.

### Data and identification strategy
- Data
  - French Labor Force Survey (Enquête Emploi), 1993–2000; matched firm-size data from SIRENE.
  - Last panel 1998–2000 is used to classify treatment (large firms) and control (small firms) before law approval (June 1998); before period 1993–1998; after period 1999–2000.
- Treatment definition(s)
  - Primary: firms with fewer than 20 employees = “small”; firms with 20–49 employees classified as “large” (cutoff at 49 to increase homogeneity).
  - Alternative control: workers already working 35 hours or less before the law.
- Empirical specifications
  - Difference-in-differences (DD) baseline: E[y_it] = α_i + γ_t + β X_i0 + δ_treat * post1999 * 100 + ... (equation (6)).
  - Controls include gender, marital status, interactions, number of children <6, age and age-squared, tenure, region dummies, education.
  - Robustness: allow firm-size specific business cycle interaction by including GDP growth and interaction (equation (7)).
- Sample restrictions
  - Employees aged 15 to 64 with positive net monthly income; self-employed excluded.

### Results — empirical findings (A–E)

A. Hours distribution and wages
- Distributional changes
  - In 1999 most employees were working 39 hours; after the law the proportion working 35 hours increased, led by large firms.
  - By 2002: more than 45 percent of employees in large firms and almost 35 percent of employees in small firms worked on a 35-hour basis (Table 2).
- Regression findings
  - DD estimators for hours worked in large firms relative to small firms are significant and negative, but the implied reduction in reported hours is small: around 20 to 30 minutes compared with the legal reduction of 4 hours (reporting and overtime accounting issues noted).
  - Hourly wages increased in large firms relative to small firms for workers at and above the minimum wage; monthly incomes increased slightly for minimum-wage workers and did not change for workers above minimum wage.
  - Interpretation caveat: wage rigidities and union effects may limit full wage adjustment.

B. Dual-job holdings
- Triple-difference (DDD) results (equation (8)) show:
  - The law increased dual job holdings by 3.3 percentage points (Table 4).
  - Effect robust to controls including firm-size specific business cycle effects.

C. Transitions from large to small firms
- Transition probability effects
  - Comparing employees in large firms working more than 35 hours (treatment) to those working 35 hours or less (control): law increased transitions from large to small firms by about 1.2 percentage points (Table 5).
  - Individuals who moved from large to small firms after the law worked more hours than those who stayed in large firms (Table 6), consistent with moves motivated by desire to work more hours.

D. Employment transitions and net employment implications
- Employment → Unemployment
  - For employees working more than 35 hours in base year: transitions from employment to unemployment in large firms versus small firms increased between 1.3 and 1.7 percentage points after 1999 (Table 7).
- Unemployment → Employment
  - Multinomial logit results (Table 8): after 1999 there was an increase in the probability of moving from unemployment to employment, and the increase was significantly larger in large firms than in small firms (p-value for equality of coefficients on unemployed*post1999 = 0.01).
  - Workers unemployed for less than a year are more likely to find a job and, after the law, more likely to find it in a large firm than a small firm.
- Net employment by firm size
  - Multinomial logit comparing employment status over time (Table 9) shows post1999 increases in probability of being employed (relative to unemployed) both in large and in small firms:
    - log[P(large)/P(unemployed)] coefficient on Post1999 = 0.084***.
    - log[P(small)/P(unemployed)] coefficient on Post1999 = 0.068***.
    - p-value for equality of coefficients on Post1999 = 0.487 (fail to reject equality).
  - Figure 2: log odds of employment by firm size move essentially in parallel between 1993 and 2000.
  - Interpretation: despite increased flows into and out of large firms, evidence suggests the law did not raise aggregate employment by March 2000.

E. Satisfaction with hours of work (subjective well-being)
- Eurobarometer comparison (1996 vs 2001)
  - Ordered probit results (Table 10):
    - Year 2001 coefficient = -0.125***.
    - France dummy = -0.179***.
    - Year2001*France interaction = 0.017 (not significant).
  - Conclusion: no significant improvement in French workers’ satisfaction with hours of work in 2001 relative to 1996 compared with other EU countries.

### Key quantitative findings and magnitudes
- Unemployment rate in France in 1998: 11.5 percent.
- Crépon, Leclair, and Roux (2005): total factor productivity decreased by 3.7% from 1997 to 2000 in firms that reduced the workweek relative to those that did not; employment increased by 9.9% in firms who adopted the 35-hours schedule.
- Reported reduction in usual hours per worker implied by survey results: around 20 to 30 minutes (compared with legal reduction of 4 hours).
- Dual job holdings: law increased dual job holdings by 3.3 percentage points (Table 4).
- Transitions from large to small firms: increased by about 1.2 percentage points (Table 5).
- Transitions from employment to unemployment in large firms relative to small firms: increased between 1.3 and 1.7 percentage points after 1999 (Table 7).
- Unemployed baseline log odds (Table 8): Unemployed coefficient for log[P(large)/P(unemployed)] = -2.664***; Unemployed*post1999 = 1.767***; p-value for equality of unemployed*post1999 coefficients across outcomes = 0.01.
- Employment log-odds post1999 (Table 9): Post1999 coefficients 0.084*** (large) and 0.068*** (small); p-value for equality = 0.487.
- Satisfaction regressions (Table 10): Year 2001 = -0.125***; France = -0.179***; Year2001*France = 0.017.

### Synthesis of interpretation and policy-relevant implications
- Behavior and welfare signals
  - A significant fraction of workers in large firms changed behavior to circumvent constrained hours: increased dual-job holding, moves from large to small firms, and higher hourly wages in large firms (consistent with compensation demands).
  - Subjective satisfaction with hours did not improve for French workers relative to other Europeans.
- Labor-market composition and turnover
  - Evidence indicates increased job turnover and reallocation: increases in both inflows (unemployment → employment, especially into large firms) and outflows (employment → unemployment; large → small firms).
  - Patterns are consistent with both supply-side responses (workers constrained by hours) and demand-side responses (firms adjusting workforce due to higher per-hour costs), and data cannot fully disentangle these mechanisms.
- Aggregate employment effect
  - No clear evidence the 35-hours mandate increased aggregate employment by March 2000; employment increases occurred but were not larger in large firms relative to small firms.
- Welfare assessment
  - The reduction in working hours did not operate clearly as a beneficial coordination mechanism for the workforce at large; the empirical evaluation is partial and based on revealed preferences, but overall assessment in the paper is negative: the law failed to raise aggregate employment and increased job turnover; a significant share of the workforce appears constrained by the policy.

*Source: IMF Working Paper, section "2. Log Employment Probabilities by Firm Size" (extracted from the supplied PDF content).*

### References..............................................................................................................

### References

### Tables (Inventory)
- 1.     Summary     Statistics...........................................................................................................16
- 2.     Distribution of Usual Weekly Hours ...............................................................................16
- 3.     Hours, Wages, and Monthly Income ...............................................................................17
- 4.     Dual Job Holdings............................................................................................................18
- 5.     Transitions from Large to Small Firms............................................................................18
- 6.     Usual Weekly Hours for Workers Who Move from Large to Small Firms.....................19
- 7.     Transitions from Employment to Unemployment ...........................................................19
- 8.     Transitions     from     Unemployment to Employment ...........................................................20
- 9.     Employment .....................................................................................................................21
- 10.   Satisfaction with Hours of Work .....................................................................................22

### Figures (Inventory)
- 1.     Annual Hours Worked per Person Employed..................................................................23

*Source: _wp06251 - References..............................................................................................................*

### 2.     Log Employment Probabilities by Firm Size...................................................................23

### 2.     Log Employment Probabilities by Firm Size

### Introduction
- Context and motivation
  - Since the 1970s hours of work declined in Europe relative to the United States and Japan; today the average American works approximately 400 hours more per year than the average European.
  - The paper evaluates the welfare and labor-market consequences of coordinated reductions in the workweek, focusing on France’s sequence of laws culminating in the 35-hours mandate.
- French policy timing and intent
  - Law enacted in 1998 mandated a reduction of the workweek to 35 hours in large firms by 2000 and in small firms by 2002.
  - Official purpose: increase employment during high unemployment (11.5 percent in 1998) via work sharing while protecting monthly earnings for minimum wage workers (SMIC).

### Institutional background and prior evidence
- Sequence of reforms
  - 1982: workweek from 40 to 39 hours.
  - 1998 (Aubry I) and 2000 (Aubry II): detailed provisions; differential transition and overtime treatment for small firms.
- Policy supports and protections
  - Rebates on firms’ social security contributions (declining with monthly income, largest for minimum wage earners).
  - Guarantee that monthly earnings of workers receiving the minimum wage should stay constant.
- Selected prior empirical findings referenced
  - Crépon, Leclair, and Roux (2005): total factor productivity decreased by 3.7% from 1997 to 2000 in firms that reduced the workweek relative to those that did not; employment increased by 9.9% in firms that adopted 35-hours.
  - Crépon and Kramarz (2002): for 1982 reduction from 40 to 39 hours, increased probability of transition from employment to unemployment between 2.3 and 3.9 percentage points.
  - Hunt (1998, 1999) (Germany): reductions in hours decreased employment over 1984–94.

### Theory: one-sector and two-sector frameworks (guiding empirical expectations)
- One-sector model (supply and demand implications)
  - Utility separable in consumption and leisure with potential complementarities in leisure: individual utility U = U(c, H_i, H_hat) where H_hat denotes others’ hours.
  - Positive strategic complementarities in leisure (0 < V12) can generate:
    - Multiple equilibria when 11 2 12 ''VUwV−≥+ (strong complementarities).
    - A coordinated reduction in hours may be socially preferable if positive spillovers in leisure (0 < V2).
  - Demand-side effects:
    - Fixed output and inability to contract overtime: reduction in standard hours can raise employment.
    - If firms can adjust output and face fixed employment costs a, reduction in hours raises per-hour labor cost and can reduce output and employment; capital substitution possible.
- Two-sector extension (large firms covered; small firms uncovered)
  - If hours and workers are perfect substitutes and output fixed, employment in covered sector increases proportionally to hours reduction.
  - With positive leisure complementarities: workers prefer covered sector; wages in large firms may fall relative to small firms (compensating differential).
  - Without complementarities: workers in large firms may be constrained, respond by moving to uncovered sector or taking second jobs; wages in large firms may increase relative to small firms.

### Data and identification strategy
- Data
  - French Labor Force Survey (Enquête Emploi), 1993–2000; matched firm-size data from SIRENE.
  - Last panel 1998–2000 is used to classify treatment (large firms) and control (small firms) before law approval (June 1998); before period 1993–1998; after period 1999–2000.
- Treatment definition(s)
  - Primary: firms with fewer than 20 employees = “small”; firms with 20–49 employees classified as “large” (cutoff at 49 to increase homogeneity).
  - Alternative control: workers already working 35 hours or less before the law.
- Empirical specifications
  - Difference-in-differences (DD) baseline: E[y_it] = α_i + γ_t + β X_i0 + δ_treat * post1999 * 100 + ... (equation (6)).
  - Controls include gender, marital status, interactions, number of children <6, age and age-squared, tenure, region dummies, education.
  - Robustness: allow firm-size specific business cycle interaction by including GDP growth and interaction (equation (7)).
- Sample restrictions
  - Employees aged 15 to 64 with positive net monthly income; self-employed excluded.

### Results — empirical findings (A–E)

A. Hours distribution and wages
- Distributional changes
  - In 1999 most employees were working 39 hours; after the law the proportion working 35 hours increased, led by large firms.
  - By 2002: more than 45 percent of employees in large firms and almost 35 percent of employees in small firms worked on a 35-hour basis (Table 2).
- Regression findings
  - DD estimators for hours worked in large firms relative to small firms are significant and negative, but the implied reduction in reported hours is small: around 20 to 30 minutes compared with the legal reduction of 4 hours (reporting and overtime accounting issues noted).
  - Hourly wages increased in large firms relative to small firms for workers at and above the minimum wage; monthly incomes increased slightly for minimum-wage workers and did not change for workers above minimum wage.
  - Interpretation caveat: wage rigidities and union effects may limit full wage adjustment.

B. Dual-job holdings
- Triple-difference (DDD) results (equation (8)) show:
  - The law increased dual job holdings by 3.3 percentage points (Table 4).
  - Effect robust to controls including firm-size specific business cycle effects.

C. Transitions from large to small firms
- Transition probability effects
  - Comparing employees in large firms working more than 35 hours (treatment) to those working 35 hours or less (control): law increased transitions from large to small firms by about 1.2 percentage points (Table 5).
  - Individuals who moved from large to small firms after the law worked more hours than those who stayed in large firms (Table 6), consistent with moves motivated by desire to work more hours.

D. Employment transitions and net employment implications
- Employment → Unemployment
  - For employees working more than 35 hours in base year: transitions from employment to unemployment in large firms versus small firms increased between 1.3 and 1.7 percentage points after 1999 (Table 7).
- Unemployment → Employment
  - Multinomial logit results (Table 8): after 1999 there was an increase in the probability of moving from unemployment to employment, and the increase was significantly larger in large firms than in small firms (p-value for equality of coefficients on unemployed*post1999 = 0.01).
  - Workers unemployed for less than a year are more likely to find a job and, after the law, more likely to find it in a large firm than a small firm.
- Net employment by firm size
  - Multinomial logit comparing employment status over time (Table 9) shows post1999 increases in probability of being employed (relative to unemployed) both in large and in small firms:
    - log[P(large)/P(unemployed)] coefficient on Post1999 = 0.084***.
    - log[P(small)/P(unemployed)] coefficient on Post1999 = 0.068***.
    - p-value for equality of coefficients on Post1999 = 0.487 (fail to reject equality).
  - Figure 2: log odds of employment by firm size move essentially in parallel between 1993 and 2000.
  - Interpretation: despite increased flows into and out of large firms, evidence suggests the law did not raise aggregate employment by March 2000.

E. Satisfaction with hours of work (subjective well-being)
- Eurobarometer comparison (1996 vs 2001)
  - Ordered probit results (Table 10):
    - Year 2001 coefficient = -0.125***.
    - France dummy = -0.179***.
    - Year2001*France interaction = 0.017 (not significant).
  - Conclusion: no significant improvement in French workers’ satisfaction with hours of work in 2001 relative to 1996 compared with other EU countries.

### Key quantitative findings and magnitudes (preserved exactly)
- Unemployment rate in France in 1998: 11.5 percent.
- Crépon, Leclair, and Roux (2005): total factor productivity decreased by 3.7% from 1997 to 2000 in firms that reduced the workweek relative to those that did not; employment increased by 9.9% in firms who adopted the 35-hours schedule.
- Reported reduction in usual hours per worker implied by survey results: around 20 to 30 minutes (compared with legal reduction of 4 hours).
- Dual job holdings: law increased dual job holdings by 3.3 percentage points (Table 4).
- Transitions from large to small firms: increased by about 1.2 percentage points (Table 5).
- Transitions from employment to unemployment in large firms relative to small firms: increased between 1.3 and 1.7 percentage points after 1999 (Table 7).
- Unemployed baseline log odds (Table 8): Unemployed coefficient for log[P(large)/P(unemployed)] = -2.664***; Unemployed*post1999 = 1.767***; p-value for equality of unemployed*post1999 coefficients across outcomes = 0.01.
- Employment log-odds post1999 (Table 9): Post1999 coefficients 0.084*** (large) and 0.068*** (small); p-value for equality = 0.487.
- Satisfaction regressions (Table 10): Year 2001 = -0.125***; France = -0.179***; Year2001*France = 0.017.

### Synthesis of interpretation and policy-relevant implications
- Behavior and welfare signals
  - A significant fraction of workers in large firms changed behavior to circumvent constrained hours: increased dual-job holding, moves from large to small firms, and higher hourly wages in large firms (consistent with compensation demands).
  - Subjective satisfaction with hours did not improve for French workers relative to other Europeans.
- Labor-market composition and turnover
  - Evidence indicates increased job turnover and reallocation: increases in both inflows (unemployment → employment, especially into large firms) and outflows (employment → unemployment; large → small firms).
  - Patterns are consistent with both supply-side responses (workers constrained by hours) and demand-side responses (firms adjusting workforce due to higher per-hour costs), and data cannot fully disentangle these mechanisms.
- Aggregate employment effect
  - No clear evidence the 35-hours mandate increased aggregate employment by March 2000; employment increases occurred but were not larger in large firms relative to small firms.
- Welfare assessment
  - The reduction in working hours did not operate clearly as a beneficial coordination mechanism for the workforce at large; the empirical evaluation is partial and based on revealed preferences, but overall assessment in the paper is negative: the law failed to raise aggregate employment and increased job turnover; a significant share of the workforce appears constrained by the policy.

*Source: IMF Working Paper, section "2. Log Employment Probabilities by Firm Size" (extracted from the supplied PDF content)._

### REFERENCES

### _wp06251 - REFERENCES

### Employment protection, labor market regulations, and reforms
- Acemoglu, D., and J. Angrist, 2001, “Consequences of Employment Protection? The Case of the Americans with Disabilities Act,” Journal of Political Economy, Vol. 109, No. 5, pp. 915–57.
- Kugler, A., and G. Pica, 2005, “Effects of Employment Protection on Worker and Job Flows: Evidence from the 1990 Italian Reform,” Discussion Paper, Bonn: Institute for the Study of Labor (IZA), No. 1743.
- Prescott, E.C., 2004, “Why Do Americans Work So Much More Than Europeans?” Federal Reserve Bank of Minneapolis Quarterly Review, Vol. 28, No. 1, pp. 2–13.

### Work-sharing, hours reduction, and employment effects
- Crépon, B., and F. Kramarz, 2002, “Employed 40 Hours or Not Employed 39: Lessons from the 1982 Mandatory Reduction of the Workweek,” Journal of Political Economy, Vol. 110, No. 6, pp. 1355–89.
- Crépon, B., M. Leclair, and S. Roux, 2005, “RTT, Productivité et Emploi: Nouvelles Estimations sur Donnees d’Enterprises,” Économie et Statistique, Paris: INSEE, No. 376-77, June, pp. 55-89.
- Freeman, R., 1998, “Work-Sharing to Full Employment: Serious Option or Populist Fallacy?” in Generating Jobs: How to Increase Demand for Less-Skilled Workers, ed. by R. Freeman and P. Gottschalk, New York: Russell Sage Foundation, pp. 195–222.
- Hunt, J., 1998, “Hours Reductions As Work-Sharing,” Brookings Papers on Economic Activity, No. 1, pp. 339–81.
- Hunt, J., 1999, “Has Work-Sharing Worked in Germany?” The Quarterly Journal of Economics, Vol. 114, No. 1, pp. 117–48.

### Comparative work and leisure, productivity, and macro perspectives
- Alesina, A., E. Glaeser, and B. Sacerdote, 2005, “Work and Leisure in the U.S. and Europe: Why So Different?” NBER Macroeconomics Annual, Vol. 20, Issue 1, pp. 1–64.
- Blanchard, O., 2004, “The Economic Future of Europe,” Journal of Economic Perspectives, Vol. 18, No. 4, pp. 3–26.
- Cooper, R., and A. John, 1988, “Coordinating Coordination Failures in Keynesian Models,” The Quarterly Journal of Economics, Vol. 103, No. 3, August, pp. 441–63.

### Well-being and subjective measures related to work
- Diener, E., and E. Suh, 1999, “National Differences in Subjective Well-Being,” in Well-Being: the Foundations of Hedonic Psychology, ed. by D. Kahneman, E. Diener and N. Schwarz, New York: Russell Sage Foundation, pp. 434–50.

*Source: _wp06251 - REFERENCES*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2006/_wp06251.pdf_