## _wp1517

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---

### I. Introduction — scope and main conclusions
- Study sample: 24 upper-middle-income countries (UMICs), 1995–2011.
- Two primary contributions:
  - Examines public employment impact on labor market outcomes in developing countries.
  - Explicitly examines the role of rents in the public sector and the substitutability of public production in transmission channels.
- Main empirical conclusions:
  - Results do not support the hypothesis that creation of public jobs reduces unemployment.
  - Some evidence that creation of public-sector jobs destroys private-sector jobs.
  - Magnitude of impact on private employment increases with:
    - degree of substitutability between public and private production;
    - size of job compensation (rents) in the public sector.
- Policy implication highlighted: reforms that reduce rents and the size of public employment may improve labor market performance; policymakers should avoid using public employment as a tool for reducing unemployment in the medium-to long-run.

### II. Theoretical framework and mechanisms (model summary)
- Structure and key assumptions:
  - Representative private-sector firm with decreasing returns to labor; public sector produces goods consumed by all individuals.
  - Private-sector workers represented by a trade union; unemployment needed to stabilize wages.
  - Unemployed search either for a public or a private job, but not both simultaneously.
  - Wage in private sector equals marginal product of labor; government sets public employment and negotiates public wage with public-sector trade union.
- Key analytical implications (equations referenced in source: A7–A15):
  - Expected returns to searching for public-sector jobs increase with number of public jobs and public wage; share of labor force affiliated with public sector increases with public jobs and public wages relative to private wages (equation A8).
  - Creation of one public job reduces unemployment only if the crowding-out of private employment is less than one; crowding-out increases with relative public-sector rents (equation A10).
  - If public jobs produce non-substitutable goods, private productivity and wages increase; if public jobs produce substitutable goods, the relative price of private goods decreases, negatively influencing private wages and participation.
  - Public-sector expansion reduces aggregate unemployment only when λ = wg/wp < 1; crowding-out amplified when λ > 1.
  - Government creates public jobs until marginal utility of public good equals marginal social cost; marginal cost increases with λ (A15).

### III. Methodology and data
- Sample and data sources:
  - 24 UMICs, period 1995–2011.
  - Data from Key Indicators of the Labor Market (KILM), LABORSTA (ILO), country statistical offices, and other agencies.
- Definitions and processing:
  - Public employment defined narrowly (excludes employment by state-owned enterprises).
  - Time-averaging: macroeconomic variables averaged over three-year periods to remove cyclical fluctuations.
- Instruments (to address endogeneity of public employment):
  - Urbanization rate.
  - Population density.
  - Exposure to international trade (trade openness).
  - Five World Economic Forum indices: cooperation in labor-employer relations; flexibility of wage determination; rigidity of employment; hiring and firing practices; redundancy costs.
- Data limitations:
  - Sample size constrained by data availability.
  - Unemployment excludes discouraged workers.
  - Three-year averaging may not fully remove transitory shocks; lack of five-year averages due to data limitations.
  - GDP per capita growth included in simultaneous-equation regression to control for lower private-sector labor demand during weak economic activity.

### IV. Empirical stylized facts and key statistics
- Public employment share and dynamics:
  - Share of public employment in total employment averages 13 percent across sample for 1995–2011.
  - In 60 percent of countries the share increased over time.
  - In 2011, public employment share ranged from 4.7 percent (Kazakhstan) to 33.4 percent (Namibia).
  - Country dynamics: Mexico and Costa Rica stable; Belarus, Chile, Malaysia, Peru, Thailand steadily increasing (1995–2008); Jordan, Kazakhstan, Turkey steadily decreasing; remaining countries exhibited large swings.
- Volatility (standard deviation, 1995–2010):
  - Average unemployment volatility: 2.7.
  - Average public employment volatility: 0.9.
  - Highest unemployment volatility: Albania (5.8), South Africa (5.3), Mauritius (4.6).
  - Lowest unemployment volatility: Mexico, Thailand, Belarus.
  - Highest public employment volatility: Ukraine (6.5); other high: South Africa and Jordan.
  - Lowest public employment volatility: Mexico and Panama.
- Correlation patterns:
  - Half of countries show positive correlation between public employment and unemployment; half show negative correlation.
  - Statistically significant positive correlation in six of 12 countries: Brazil, Colombia, Malaysia, Mauritius, Panama, Ukraine.
  - Statistically significant negative correlation in five of 12 countries: Albania, Belarus, Peru, Turkey, Uruguay.
  - Cross-country (average) relationship: negative but statistically insignificant correlation between public employment and unemployment.

### V. Econometric evidence and robustness
- Estimation approaches:
  - Fixed effects, GLS, OLS, two-stage least squares (TSLS), and three-stage least squares (3SLS) to address endogeneity and joint determination of public employment, private employment, and unemployment.
- Key econometric findings:
  - Public employment statistically significant at least at the 10 percent level for fixed effect and GLS methods, indicating importance in explaining unemployment alongside institutional variables.
  - Public employment statistically significant at the 5 percent level and has a negative impact on private employment only in the OLS regression (Table 3).
- Simultaneous-equations / 3SLS (country-specific effects specification):
  - Public employment impact on unemployment: coefficient = 0.299, standard error = 0.11, statistically significant (***).
    - Interpretation provided in source: creation of 100 public jobs adds about 20 unemployed workers, with 95 percent confidence interval of [10, 40].
  - Public employment impact on private employment (country-specific effects): coefficient = -0.15 (not statistically significant in that specification).
- Simultaneous-equations / 3SLS (institutional-variables specification):
  - Public employment impact on private employment: coefficient ≈ -0.706 (negative and statistically significant).
    - Interpretation provided in source: creation of 100 public jobs destroys 70 private jobs on average, with confidence interval [-137, -5].
  - Comparative benchmarks cited in source: Boeri, Nicoletti, and Scarpetta (2000) estimate destruction of 30 private jobs per 100 public jobs; Algan, Cahuc, and Zylberberg (2002) and Behar and Mok (2013) estimate 150 and 100 respectively.
- Instrument strength and tests:
  - Trade openness consistently significant (at least at the 10 percent level) in all 3SLS specifications: trade openness positively associated with public employment.
  - Productivity (Wagner’s law) increases public employment but effect not statistically significant.
  - Population density and urbanization show mixed significance.
  - First-stage F statistics of TSLS regressions are about 2, suggesting instruments are not very strong.
  - J test of over-identifying restriction failed to reject null that coefficients on instruments are zero (per source).

### VI. Heterogeneity: rents and substitutability (split-sample 3SLS highlights)
- General result: crowding-out of private employment by public employment is larger where public-sector rents are higher and where public production is more substitutable for private production.
- Selected split-sample coefficients (public employment effect; standard errors in parentheses as in source):
  - Unemployment regressions (selected):
    - High Wage Premium: public employment = 0.464* (0.28)
    - High Corruption: public employment = 0.219** (0.10)
    - High Public Goods Substitutability (Defense): public employment = 0.334*** (0.09)
    - High Public Goods Substitutability (Health): public employment = 0.321 (0.35)
  - Private employment regressions (selected):
    - High Wage Premium: public employment = -1.451** (0.69)
    - High Corruption: public employment = -0.192 (0.36)
    - High Public Goods Substitutability (Defense): public employment = -1.125*** (0.30)
    - High Public Goods Substitutability (Health): public employment = -1.882** (0.82)
- Empirical appendix (3SLS estimates, Table A2.I) snapshot (coefficients and standard errors preserved from source):
  - Unemployment regression example coefficients:
    - Public employment: 0.314 (0.28); 0.169* (0.10); 0.268*** (0.09); 0.253 (0.35)
    - Productivity: -2.484** (1.21); -2.642*** (0.94); -4.671*** (0.91); -2.789* (1.62)
    - R-squared reported: 0.935; 0.940; 0.968; 0.924
    - Number of observations reported: 835; 448; 60
  - Private employment regression example coefficients:
    - Public employment: -2.009*** (0.48); -0.0615 (0.36); -1.125*** (0.30); -2.694*** (0.81)
    - R-squared reported: 0.345; 0.867; 0.430; 0.946
    - Number of observations reported: 805; 345; 56
  - Significance markers in table: *** p<0.01, ** p<0.05, * p<0.1
  - Footnote preserved: p-value from a test that the interaction coefficient on higher rent in the public sector and higher substitutability of public production in a full-sample specification is equal to zero.

### VII. Mechanisms, caveats, and theoretical interpretation
- Mechanisms emphasized in source:
  - Higher public-sector rents increase expected returns to public-sector job search, attracting workers to public sector at the cost of private sector, increasing wage pressure and decreasing private employment.
  - If public production substitutes private production, increased public employment exerts competitive pressure, lowering relative price of private goods, negatively influencing wages and private participation.
  - Public job creation may increase labor taxes, reducing private hiring.
  - Public-sector rents can influence schooling decisions and create skill mismatch.
- Participation and feedbacks:
  - Public employment crowds out private jobs, which can increase private-sector marginal productivity and wages and thereby attract more workers into labor market, partially offsetting crowding-out.
- Statistical and interpretive caveats:
  - Instruments are weak (first-stage F ≈ 2); some specification sensitivity in results.
  - Three-year averaging may not remove all transitory shocks.
  - Study analyzes medium-term effects; does not capture short-run nominal rigidities or demand movements.
  - Results do not provide an assessment for the optimal level or size of public employment in MICs; country-specific features matter (trade exposure, education, country size, urbanization, natural resources).

### VIII. Policy implications and conclusions (preserved phrasing and emphasis)
- Short-run vs. medium/long-run:
  - Short-run employment programs may yield temporary gains, but medium- to long-run creation of public jobs does not reduce unemployment and can increase unemployment in some specifications.
- Core policy recommendations:
  - Reforms aimed at reducing public-sector rents and the size of public employment may improve labor market performance.
  - Policymakers should avoid relying on public employment creation as a medium-to long-run tool to reduce unemployment.
  - Avoid large, well-paid public job creation in areas producing goods highly substitutable with private sector output, as this amplifies adverse labor-market outcomes.
  - Align public-sector wages with private-sector wages and ensure public sector provides complementary (not substitutable) goods to improve outcomes.
- Interpretation guidance:
  - Results should be interpreted with caution and tailored to country-specific circumstances when determining optimal public employment levels.

*Source: International Labor Organization, country authorities, and IMF staff calculations (content as provided in the supplied PDF excerpt).*

### References ________________________________________________________________22

### _wp1517 - References ________________________________________________________________22

### I. Introduction
- Policymakers sometimes view expansion of public employment as a tool to reduce high unemployment; public employment accounts for an important share of total employment in many upper-middle-income countries (UMICs).
- In many UMICs, a relatively large size of government coexists with persistently high unemployment.
- This study analyzes the impact of public employment on labor market performance for 24 UMICs.
- Two contributions:
  - Examines public employment impact on labor market outcomes in developing countries.
  - Explicitly examines the role of rents in the public sector and the substitutability of public production in transmission channels.
- Focus on primary UMICs because:
  - (i) economic conditions and relations differ compared to low-income countries (LIC);
  - (ii) these countries managed to achieve a certain level of development regardless of different initial conditions;
  - (iii) data for public and private sector employment and wages are very limited for LICs.
- Main study conclusions highlighted:
  - Results do not support the hypothesis that creation of public jobs reduces unemployment.
  - Some evidence that creation of public-sector jobs destroys private-sector jobs.
  - Magnitude of impact on private employment varies by model specification and increases with:
    - degree of substitutability between public and private production;
    - size of job compensation (rents) in the public sector.
  - Channels through which public employment affects private employment:
    - (i) higher public-sector rents increase expected returns to public-sector job search, attracting workers to public sector at cost of private sector, increasing wage pressure and decreasing private employment;
    - (ii) if public production is substitutable for private production, increased public employment exerts competitive pressure, lowering relative price of private goods, negatively influencing wages and private-sector participation.
  - Policy implication: reforms that reduce rents and the size of public employment may improve labor market performance; policymakers should avoid using public employment as a tool for reducing unemployment in the medium-to long-run.

### II. Literature Review
- Prior literature concentrated on labor market institutions to explain cross-country unemployment differences.
- Key findings from related studies:
  - Temporary public employment programs can increase wage pressure in the private sector, reducing private employment (Holmlund and Linden, 1993; Calmfors and Lang, 1995).
  - Public-sector expansion increases equilibrium unemployment if unions are relatively more powerful in the public sector than in the private sector (Holmlund, 1997).
  - Positive shocks to government goods purchases increase private output and private employment; positive shocks to government employment have the opposite effects (Finn, 1998).
  - Empirical evidence of crowding-out effects:
    - Demekas and Kontolemis (2000) for Greece; Malley and Moutos (2001) for Germany, Japan, and the United States: strong crowding-out.
    - Edin and Holmlund (1997): public employment decreases unemployment in the short run, no significant long-run effect.
    - Boeri, Nicoletti, and Scarpetta (2000): one public job crowds out 0.3 private jobs.
    - Algan, Cahuc, and Zylberberg (2002): one public job crowds out 1.5 private jobs and increases the number of unemployed by 0.3.
    - Behar and Mok (2013): full crowding-out effects in a large cross-section including developing and advanced countries.
  - Feldmann (2009): large share of government consumption in total consumption and large share of transfers and subsidies in GDP increase unemployment in developing countries.

### III. Theoretical Framework and Mechanisms
- Theoretical model (details in Appendix A) assumptions and structure:
  - Representative private-sector firm produces goods with decreasing returns to labor.
  - Public sector produces goods consumed by all individuals.
  - Private-sector workers are represented by a trade union bargaining with the firm; unemployment needed to stabilize wages.
  - Unemployed search either for a public or a private job, but not both simultaneously.
  - Firms manage employment; wage equals marginal product of labor; private unemployment rate determined by intersection of vertical wage curve and increasing labor demand curve.
  - Benevolent government sets public employment and negotiates public-sector wage with a public-sector trade union, maximizing social value minus cost.
- Key theoretical implications:
  - Expected returns to searching for public-sector jobs increase with number of public jobs and public wage; share of labor force affiliated with public sector increases with public jobs and public wages relative to private wages (equation A8).
  - Public job creation attracts workers into public sector at cost of private sector if relative public-private wage is constant (equation A9).
  - Creation of one public job reduces unemployment only if the crowding-out of private employment is less than one; crowding-out increases with relative public-sector rents (equation A10).
  - Substitutability between public and private production affects participation:
    - If public jobs produce non-substitutable goods (justice, police), private productivity and wages increase, positively influencing participation.
    - If public jobs produce substitutable goods, relative price of private goods decreases, negatively influencing private wages and participation.
- Model focus: role of rents in the public sector and degree of substitutability; does not incorporate distortionary tax financing effects; analyzes medium-term effects and does not capture short-run nominal rigidities or demand movements.

### IV. Methodology and Data
- Empirical analysis sample: 24 upper-middle-income countries in 1995–2011.
- Data sources: Key Indicators of the Labor Market (KILM) and LABORSTA databases from the International Labor Organization (ILO), country statistical offices, and other agencies.
- Public employment definition: narrow—does not include employment by state-owned enterprises.
- Time-averaging: averaged time-dependent macroeconomic variables over three-year periods to remove cyclical fluctuations.
- Instrumental variables for public employment to address joint determination with unemployment:
  - Urbanization rate (measure of economic development and public infrastructure/spending/employment growth per “Wagner’s law”).
  - Population density (captures fixed cost of providing government services).
  - Exposure to international trade (higher foreign exposure may reduce or increase public sector size).
  - Five World Economic Forum indices capturing wage-setting and labor-employer features: index of cooperation in labor-employer relations; flexibility of wage determination; rigidity of employment; hiring and firing practices; redundancy costs.
- Data notes and limitations:
  - Sample size subject to data availability.
  - Unemployment data exclude discouraged workers.
  - In some countries, public employment may include temporary public workers; their share is very small.
  - Three-year averaging may not fully remove transitory shocks; lack of five-year averages due to data limitations.
  - GDP per capita growth included in simultaneous equation regression to control for lower private-sector labor demand during weak economic activity.

### V. Empirical Stylized Facts and Key Statistics
- Cross-country heterogeneity in public employment:
  - Share of public employment in total employment averages 13 percent across sample for 1995–2011.
  - In 60 percent of countries the share increased over time (Table 1).
  - In 2011, public employment share in total employment ranged from 4.7 percent in Kazakhstan to 33.4 percent in Namibia.
- Dynamics of public employment across countries:
  - In two countries (Mexico, Costa Rica) public employment as a share of working-age population was stable over time.
  - In five countries (Belarus, Chile, Malaysia, Peru, Thailand) the share increased steadily in 1995–2008.
  - In three countries (Jordan, Kazakhstan, Turkey) share decreased steadily over time.
  - Remaining countries exhibited large swings in the share of public employment.

### VI. Main Findings and Policy Implications
- Empirical results confirm public employment plays a significant role in medium-to long-term labor market performance.
- Main empirical findings:
  - Creation of public jobs does not reduce unemployment (results do not support unemployment-reducing hypothesis).
  - Evidence that public-sector job creation destroys private-sector jobs (crowding-out).
  - Impact on private employment increases with:
    - degree of substitutability between public and private production;
    - size of job compensation (public rents).
- Policy recommendations:
  - Reforms aimed at reducing public-sector rents and the size of public employment may improve labor market performance.
  - Policymakers should avoid relying on public employment creation as a medium-to long-run tool to reduce unemployment.

*Source: _wp1517 - References ________________________________________________________________22*

### 20.      In many countries, policymakers respond to a high level of unemployment by

### _wp1517 - 20.      In many countries, policymakers respond to a high level of unemployment by

### Key empirical findings
- Half of the countries in the sample have positive correlation between public employment and unemployment rate, while the remaining half have negative correlation.
- Correlations that are statistically significant:
  - Positive correlation: six out of 12 countries (Brazil, Colombia, Malaysia, Mauritius, Panama, and Ukraine).
  - Negative correlation: five out of 12 countries (Albania, Belarus, Peru, Turkey, and Uruguay).
- Cross-country (average) relationship: a negative, though statistically insignificant, correlation between public employment and unemployment (Figure 1).
- Volatility (standard deviation, 1995–2010):
  - Average unemployment volatility: 2.7.
  - Average public employment volatility: 0.9.
  - Countries with highest unemployment volatility: Albania (5.8), South Africa (5.3), Mauritius (4.6).
  - Countries with lowest unemployment volatility: Mexico, Thailand, Belarus.
  - Highest public employment volatility: Ukraine (6.5); other high: South Africa and Jordan.
  - Lowest public employment volatility: Mexico and Panama.

### Econometric evidence and robustness
- Labor market institutions explain part of cross-country unemployment differences; however, many institutional variables become insignificant under GLS.
- The only institutional variable consistently significant across specifications is hiring and firing practice (more flexible practice associated with lower unemployment).
- Public employment effects:
  - Public employment is statistically significant at least at the 10 percent level for fixed effect and GLS methods, indicating public employment is an important factor in explaining unemployment in addition to institutional variables.
  - Public employment is statistically significant at the 5 percent level and has a negative impact on private employment only in the OLS regression (Table 3).
  - Endogeneity concern: public employment, private employment, and unemployment are jointly determined; two-stage least squares and three-stage least squares (3SLS) used to address endogeneity.
- Simultaneous-equations / 3SLS results (country-specific effects specification):
  - Public employment impact on unemployment: coefficient = 0.299, standard error = 0.11, statistically significant (***).
    - Interpretation: creation of 100 public jobs adds about 20 unemployed workers, with 95 percent confidence interval of [10, 40].
  - Public employment impact on private employment (country-specific effects): coefficient = -0.15 (not statistically significant in that specification).
- Simultaneous-equations / 3SLS results (institutional-variables specification):
  - Public employment impact on private employment: coefficient ≈ -0.706 (negative and statistically significant in specification with labor market institutions).
    - Interpretation: creation of 100 public jobs destroys 70 private jobs on average, with confidence interval [-137, -5].
  - Comparison to other studies: Boeri, Nicoletti, and Scarpetta (2000) estimate destruction of 30 private jobs per 100 public jobs; Algan, Cahuc, and Zylberberg (2002) and Behar and Mok (2013) estimate 150 and 100 respectively.

### Heterogeneity: rents and substitutability matter
- Instruments and determinants of public employment:
  - Trade openness is consistently significant (at least at the 10 percent level) in all 3SLS specifications: trade openness positively associated with public employment.
  - Productivity (Wagner’s law) increases public employment but effect not statistically significant.
  - Population density and urbanization show mixed significance depending on specification.
- Split-sample 3SLS (Table 5) — effects by public-sector rent and substitutability:
  - Unemployment rate regressions (selected coefficients):
    - High Wage Premium: public employment = 0.464* (0.28)
    - High Corruption: public employment = 0.219** (0.10)
    - High Public Goods Substitutability (Defense): public employment = 0.334*** (0.09)
    - High Public Goods Substitutability (Health): public employment = 0.321 (0.35)
  - Private employment regressions (selected coefficients):
    - High Wage Premium: public employment = -1.451** (0.69)
    - High Corruption: public employment = -0.192 (0.36)
    - High Public Goods Substitutability (Defense): public employment = -1.125*** (0.30)
    - High Public Goods Substitutability (Health): public employment = -1.882** (0.82)
  - Implication: public employment destroys more private jobs in countries with higher public-sector rents and when public production is highly substitutable with private production.
- Statistical caveats:
  - Instruments used (urbanization rate, population density, trade openness) individually significant in first-stage, but F statistics of the first stage of TSLS regressions are about 2, suggesting instruments are not very strong.
  - J test of over-identifying restriction failed to reject null that coefficients on instruments are zero.

### Mechanisms and theoretical interpretation
- Possible channels for public employment increasing unemployment or destroying private jobs:
  - Public job creation may increase labor taxes, reducing private hiring.
  - Competitive pressure from public producers on output and wages can crowd out private producers.
  - Attractive public-sector rents (wage premium, job security, working conditions, power) draw workers into public sector, influencing schooling decisions and fostering skill mismatch.
- Theoretical determinants of public employment in the model:
  - Public employment is linked to productivity, labor market institutions, and valuation of public goods; valuation of public goods approximated by urbanization rate, population density, and trade openness.

### Policy implications and conclusions
- Short-run vs. medium/long-run:
  - Policymakers often use public employment programs to address high unemployment; short-run gains may exist, but medium- to long-run effects can increase unemployment.
- Main empirical conclusions:
  - No evidence that public employment reduces unemployment in the medium to long-run; some evidence suggests public jobs may increase unemployment (though this is not robust across specifications).
  - Robust evidence that public employment can destroy private sector jobs, especially where public-sector rents are higher relative to private-sector rents and public production substitutes private production.
- Policy recommendations:
  - Reforms to reduce public-sector rents and the size of the public sector can improve labor market performance and reduce distortionary impacts of public employment.
  - Avoid large, well-paid public job creation in areas producing goods highly substitutable with private sector output, as this amplifies adverse labor-market outcomes.

*Italic: Source: International Labor Organization, country authorities, and IMF staff calculations (content as provided in the supplied PDF excerpt).*

### 33.      However, our results should be interpreted with caution. They do not provide an

### _wp1517 - 33.      However, our results should be interpreted with caution. They do not provide an

### Interpretation and policy implications
- Results do not provide an assessment for the optimal level or size of public employment in MICs.
- Policymakers should take into account country-specific features when determining optimal public employment: exposure to international trade, the level of education, the size of the country, the degree of urbanization, and access to natural resources.
- Results underscore the need for:
  - aligning public-sector wages with those of the private sector, and
  - the public sector providing complementary goods to the private sector,
  to improve labor market outcomes in these countries.

### Theoretical model — labor market setup
- Population and participation:
  - Working-age population normalized to 1.
  - N ≤ 1 denotes labor market participation.
- Sectors and production:
  - Private sector: representative firm produces output using labor only; private employment denoted Lp.
  - Public sector: Lg jobs, each producing a unit of a good.
- Preferences and utilities:
  - Individual with income w has utility w + H(Lg), with H’(•) > 0, H”(•) < 0.
  - Unemployed workers have no income and derive utility only from public goods produced by the public sector.
- Search and indifference:
  - Unemployed U = N - Lp - Lg can search for public or private jobs; in equilibrium unemployed workers are indifferent between the two choices under rational expectations.

### Trade union and bargaining framework
- Private-sector trade union maximizes total utility of Np workers who belong to private sector.
- Expected utility of an unemployed worker in the private sector:
  - Zp = upH(Lg) + (1 - up)[wp + H(Lg)] = H(Lg) + (1 - up)wp (A1)
  - where wp is private wage and up = (Np - Lp)/Np is private-sector unemployment rate.
- Trade union objective:
  - Vp = Lp[wp + H(Lg)] + Max(Np - Lp, 0) Zp (A2)
- Right-to-manage Nash bargaining (relative bargaining power of workers stated but symbol omitted in source) with disagreement payoffs NpZp for union and zero for firm yields conditions (A3) and (A4) and an interior solution with Lp < Np.
- Cobb–Douglas technology implication:
  - Unemployment rate independent of labor-force size; depends only on private wage markup.
- Private-sector unemployment not directly influenced by public employment except through allocation of Np and Ng; private wage wp = AF’[Np(1 - up)] influenced by public sector size through Np.

### Public sector search and relative wage parameter λ
- Job-finding probability in public sector = Lg / Ng.
- Expected utility of worker searching for public-sector job given public wage wg.
- Public wage assumed proportional: wg = λ wp, where λ > 0 measures relative public-sector wages to private-sector wages.
- Equilibrium indifference: Zp = Zg ≡ Z (A7).
- Consequences:
  - Number of workers in public sector increases with number of public jobs and increases more strongly when λ is large (higher public wages).
  - λ(1 - ug) = 1 - up implies unemployment rate is higher in public sector than private sector iff λ > 1 (i.e., wg > wp).
  - Private jobs are necessarily crowded out by public jobs; crowding-out stronger when λ is larger.
  - Aggregate unemployment: public-sector expansion decreases aggregate unemployment iff λ = wg/wp < 1.

### Participation effects and feedbacks
- Participation endogeneity:
  - Let individuals enjoy different out-of-labor-market utility levels; distribution denoted (symbol omitted in source).
  - Participation attractive when out-of-labor-market utility plus H(Lg) is lower than Z from (A7).
  - Participation rate F[z - H(Lg)] increases with public employment (A11).
- Mechanism:
  - Public employment crowds out private jobs, increasing marginal productivity and wages in private sector, attracting more workers into labor market.
  - Higher participation increases private employment and reduces the crowding-out effect of public jobs on private sector.
- Other channels:
  - Public jobs may affect out-of-labor-market welfare by producing goods valuable in that state and influence private-sector productivity.

### Government choice of public employment and bargaining in public sector
- Benevolent government maximizes social value of public good H(Lg) minus cost wgLg; public employment financed lump-sum for simplicity.
- Public labor demand condition derived (symbolic condition in source).
- Participation exogenous assumed for simplicity (N = 1) in this section.
- Public-sector trade union objective analogous to private-sector union (A12).
- Nash program for public-sector wages with relative bargaining power (symbol omitted in source) yields condition (A13) with interior solution.
- Combining (A13), (A4), and arbitrage (A7) implies relative wages determined by wage markups depending on labor demand elasticity and bargaining power parameters (A14).
- Empirical point: labor demand elasticity empirically similar across sectors; trade union density usually higher in public sector, leading to higher rents in public sector.
- Government creates public jobs until marginal utility of public good equals marginal social cost; marginal cost increases with λ = wg/wp, so higher public-sector wages induce government to create fewer public jobs (A15).

### Empirical appendix — Three-Stage Least Squares (3SLS) estimates (Table A2.I)
- Specification: Public Employment Impact on Unemployment and Private Employment based on the size of public rent and substitutability of public production, with labor market institutions instead of country-specific effects.
- Panel headings in table: High Wage Premium, High Corruption, High Public Goods Substitutability (Spending on Defense), High Public Goods Substitutability (Spending on Health).
- Unemployment rate regressions — coefficients (standard errors in parentheses):
  - Public employment: 0.314 (0.28); 0.169* (0.10); 0.268*** (0.09); 0.253 (0.35)
  - Productivity: -2.484** (1.21); -2.642*** (0.94); -4.671*** (0.91); -2.789* (1.62)
  - Cooperation in labor-employer relations: 2.351** (1.04); 3.197*** (1.00); 2.087*** (0.57); 5.612*** (0.69)
  - Flexibility of wage determination: -2.588*** (0.98); -1.255* (0.68); -3.000*** (0.41); 3.173 (3.34)
  - Rigidity of employment: 0.0432** (0.02); -0.0271 (0.02); -0.025 (0.03); -0.132 (0.11)
  - Hiring and firing practices: 2.902*** (1.00); 0.353 (0.76); 0.858 (0.98); -9.298*** (1.61)
  - Redundancy costs: 3.70E-05 (0.02); 0.0828*** (0.02); 0.209*** (0.01); 0.147*** (0.05)
  - Time effects: Yes* (all columns)
  - p-value of the interaction coefficient: 1; 0.687; 0.733; 0.713; 0.83 (as presented in table)
  - R-squared: 0.935; 0.940; 0.968; 0.924
  - Number of observations: 835; 448; 60
- Private employment regressions — coefficients (standard errors in parentheses):
  - Public employment: -2.009*** (0.48); -0.0615 (0.36); -1.125*** (0.30); -2.694*** (0.81)
  - Productivity: 9.85 (9.00); 6.168* (3.62); 10.11 (6.29); 1.588 (4.11)
  - Cooperation in labor-employer relations: 8.06*** (2.81); -16.56*** (3.77); -5.381 (4.16); 6.203*** (1.61)
  - Flexibility of wage determination: -6.369* (3.36); 25.67*** (2.57); -3.413 (2.85); 38.95*** (7.72)
  - Rigidity of employment: 0.00184 (0.11); 0.0231 (0.09); 0.243 (0.17); -1.127*** (0.25)
  - Hiring and firing practices: 6.294* (3.63); -1.814 (2.87); 4.03*** (4.03); -18.98*** (3.70)
  - Redundancy costs: 0.0834* (0.05); 0.0789 (0.06); 0.134** (0.06); -0.523*** (0.12)
  - Time effects: Yes* (all columns)
  - p-value of the interaction coefficient: 1; 0.004***; 0.003***; 0.000***; 0.000*** (as presented in table)
  - R-squared: 0.345; 0.867; 0.430; 0.946
  - Number of observations: 805; 345; 56
- Notes:
  - Standard errors in parentheses.
  - Footnote: "1 this is the p-value from a test that the interaction coefficient on higher rent in the public sector and higher substitutability of public prudaction in a full-sample specifications is equal to zero"
  - Significance markers: *** p<0.01, ** p<0.05, * p<0.1

### Key analytical conclusions (model and empirical)
- The model implies private jobs are crowded out by public jobs; crowding-out effect amplified when public wages exceed private wages (λ > 1).
- Public-sector expansion reduces aggregate unemployment only when public wages are lower than private wages (λ < 1).
- Participation responses to public employment tend to soften the crowding-out effect by increasing private employment through higher private-sector wages.
- Higher relative public wages (higher λ) reduce the government's optimal level of public jobs because marginal cost of public good rises with λ.
- Empirical 3SLS results indicate heterogeneous impacts of public employment on unemployment and private employment depending on institutional contexts (wage premium, corruption, substitutability of public goods), with many coefficients statistically significant at conventional levels.

*Source: Extracted content from IMF working paper chapter/appendix as provided.*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1517.pdf_