## 3. Bivariate Relations between Labor Market Policies and Efficiency

## Source details

**Canonical URL:** [3. Bivariate Relations between Labor Market Policies and Efficiency](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0992.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0992.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0992.pdf.json)

---

### Introduction and paper scope
- Focus: the role of the size of the public sector on level of national income and labor supply, building on Prescott (2002).
- Two-part approach:
  - General equilibrium cross-country quasi-accounting framework (Prescott-based) to trace size-of-government effects on the level of national income and compare predictions to a broad contemporaneous sample.
  - Partial-equilibrium specifications (including search/friction models) to explore mechanisms where government spending can raise efficiency.
- Context: longstanding per-capita income gap between the U.S. and Western Europe; competing explanations include measurement issues, labor market institutions, tastes, and size of government.

### The basic model and accounting framework
- Representative-agent utility (sum over working-age population):
  - U = Σ_{t=0}^{∞} β^{t} [log(c_{it}) + α log(T - h_{it})] (Equation (1)).
- Parameters/assumptions explicitly used:
  - Time endowment: T>0.
  - Discount factor: β ∈ (0,1).
  - Leisure preference parameter: α = 1.54.
  - Capital share (1 - θ) calibrated: 0.3 (“We calibrate the capital share at 0.3”).
  - Long-run technological growth γ = 2 percent (US 20th-century average).
- Production: CRS Cobb-Douglas with country-specific A and inputs K and aggregate hours H = h * N; resource constraint given in Equation (2).
- Log-level decomposition of per-working-age output (Equation (3)): log y = t*γ + log A + (1-θ) log k + log h.
- Empirical accounting (Table 1): labor factor explains the bulk of lower incomes in Europe over the last decade; euro-zone members often associated with depressed labor supply; U.K.’s underperformance linked to productivity rather than labor supply.

### Modeling government and the tax wedge
- Government decomposed into spending and revenues; tax bases considered: consumption taxes, labor income taxes, capital taxes.
- Base-case household budget constraint given in Equation (4).
- Intratemporal labor-leisure first-order condition (Equation (5)) introduces the tax wedge as the term in square brackets.
- Labor share from CRS production: share of labor income out of output = 1 - θ (Equation (6)).
- Effective marginal labor tax rate definition (Equation (8)):
  - τ ≡ τ_{h} + (1 - τ_{h}) τ_{c} + τ_{k} + τ_{i} (the text defines an effective marginal labor tax rate τ; see Equation (8) in source).
- Prescott’s adjustment for marginal vs. average personal income tax rates: multiplier 1.6 on average-to-marginal conversion (“Prescott (2002) assigns a multiplier of 1.6”).
- Closed-form expression for hours worked as a function of the intra-temporal tax wedge, labor share, preferences, and consumption share (Equation (9)): h = function of τ, θ, α, and c/y.

### Quantitative calibration and welfare experiments
- Parameter values used explicitly:
  - α = 1.54.
  - Capital share = 0.3.
  - Long-run growth γ = 2 percent.
  - Prescott marginal tax multiplier = 1.6.
- Hours worked measure: annual hours worked in the business sector divided by 52 and multiplied by the employment rate of the population aged 15–64.
- Predicted versus actual time series: Figures 1a–1n report predicted versus actual weekly hours worked, marginal effective tax rate series, and consumption/output ratios for 1970–2001.
- Two thought experiments using the welfare measure from Appendix II:
  - (i) Cut marginal tax rate by five percentage points (with offsetting spending cuts).
  - (ii) Adopt U.S. taxation levels (with offsetting spending changes).
- Example numerical welfare statement:
  - “For example, had Belgium between 1990–99 cut marginal income tax rates by five percentage points, it would have reaped a welfare gain equivalent to 7⅓ percent of aggregate consumption (or of 21 percent if it had adopted US tax levels).”
- General finding: these tax-policy counterfactuals imply potentially large steady-state welfare gains for many countries (country-by-country percent-of-consumption gains reported in Table 2).

### Fit of the Prescott-style model and extensions
- Model fit diagnostics:
  - General coefficient of determination R^2s computed (Table 3) comparing predicted and actual hours worked over 1970–99.
  - Main outcomes:
    - Excellent explanation for France and Germany; important explanatory power for Belgium and Japan.
    - Poor fit (often negative R^2) for a number of countries: U.K., Denmark, Sweden, Switzerland, and the U.S.
  - Allowing country variation in consumption/output ratios improves fit for some countries; the marginal contribution of the tax wedge improves fit especially for core euro-zone economies (France, Germany, Netherlands) and Spain and Denmark.
- Alternative utility curvature (Appendix III):
  - Generalized utility (Equation (16)) adds curvature (γ parameter) and leads to alternative hours relation (Equation (17)) involving the capital stock.
  - Calibration with this extension does not substantially change welfare-simulated gains; it improves fit for the Netherlands and Japan (positive R^2s) but does not materially alter main conclusions.

### Introducing labor market frictions and search
- Motivation: basic model underpredicts labor supply in several high-tax countries (Nordic countries excluding Norway, Switzerland, U.K.), suggesting household’s effective tax burden implied by labor supply is often smaller than measured marginal tax rates.
- Search-friction specification:
  - Modified utility reflecting search/unemployment (Equation (18)): U = log c + α log(T - h - u) (paper writes eqn (18) as )1 log()log(),( u h T c h c u − − + α — preserve the structure as in source).
  - Marginal static labor supply condition with unemployment u (Equation (19)): h = function of τ, θ, α, c/y, and (1 - u) terms.
- Empirical implementation uses long-term unemployment as proxy for search/friction costs; Table 4 reports goodness-of-fit for 1990–99:
  - Including unemployment as a friction variable improves model fit notably in countries previously underpredicted (Nordic countries, U.K.).
- Search-and-matching model (Appendix IV) introduces vacancy cost k and match productivity w:
  - Calibration across countries (1990–99) yields clustering (Figure 2):
    - Sweden and Denmark: lower vacancy costs, high match productivity.
    - Germany, Netherlands, Norway: lower vacancy costs but relatively low match productivity.
    - Other countries: relatively high vacancy costs and middle-of-the-range productivities.

### Bivariate and multivariate evidence on policies and efficiency
- Policy variables considered (OECD measures and EPL indexes):
  - ALMP = Active Labor Market Policies (expenditure as share of GDP).
  - PLMP = Passive Labor Market Policies (expenditure as share of GDP).
  - EPL = Employment Protection Legislation index.
- Bivariate scatter observations (Figure 3):
  - ALMP and PLMP show some positive relation with higher match productivity.
  - Relation between ALMP and vacancy cost is weak; EPL correlations with productivity and vacancy cost are weak.
- Multivariate OLS regression results (Table 5; t-statistics in parentheses; significance indicated by *, **, *** at 10, 5, 1 percent):
  - Column (1) — dependent variable: match productivity w
    - Constant = 0.58*** (t = 7.084).
    - ALMP coefficient = 0.19** (t = 2.391).
    - PLMP coefficient = 0.15*** (t = 3.758).
    - R squared = 0.80; observations = 14.
  - Column (2) — dependent variable: vacancy cost k
    - Constant = 3,656 (t = 1.339).
    - ALMP coefficient = -4,495* (t = -1.731).
    - EPL coefficient = 1,758* (t = 1.576).
    - PLMP coefficient = 3,067** (t = 2.243).
    - R squared = 0.25; observations = 14.
  - Column (3) — dependent variable: overall inefficiency k/w
    - Constant = 8,979*** (t = 2.891).
    - ALMP coefficient = -8,167** (t = -2.765).
    - EPL coefficient = 2,817** (t = 2.220).
    - PLMP coefficient = 1,745 (t = 1.122).
    - R squared = 0.34; observations = 14.
  - Column (4) — dependent variable: excess hours (Prescott model prediction error in hours per week)
    - Constant = -0.78 (t = -0.445).
    - ALMP coefficient = 4.06** (t = 2.418).
    - EPL coefficient = -2.21** (t = -3.065).
    - PLMP coefficient = 0.65 (t = 0.731).
    - R squared = 0.53; observations = 14.
- Authors’ interpretation:
  - Match productivity is significantly boosted by both ALMP and PLMP in about equal measure.
  - ALMP lowers vacancy cost, but PLMP can offset that effect; EPL raises vacancy cost and the k/w ratio (labor market inefficiencies).
  - Overall, ALMP improves productivity and reduces frictions; PLMP raises productivity but can raise vacancy costs; EPL tends to worsen inefficiency.
  - Column (4) confirms ALMP is associated with higher actual labor supply relative to Prescott predictions; EPL reduces excess labor supply.

### Policy implications and conclusions
- The blanket claim that size of government alone explains European vs. U.S. labor supply is not supported across the broader sample; however:
  - Size of government plays a significant role in explaining lower labor supply in core euro-zone countries and implies potentially large welfare costs.
- Efficiency-enhancing uses of tax revenue receive support in the data, but actual governments’ spending often does not align with what would be needed to fully enhance efficiency.
- PLMP (direct income support) is not found superior to ALMP on efficiency grounds; PLMP are widespread despite efficiency trade-offs.
- Policies that do not directly increase government size (e.g., EPL) can nevertheless impart significant costs by protecting insider rents and reducing labor market flexibility.
- Distributional considerations matter: the form of income support and employment protection affects redistribution and preservation of insider rents; further work should address redistribution explicitly.
- Broader empirical consistency:
  - Tax-distortion argument best applies to core euro-zone countries.
  - Some European countries (Nordic) appear to implement policies that keep labor markets functioning with fewer frictions (e.g., low vacancy costs and higher match productivity), consistent with “flexicurity” arrangements discussed in the paper.

### Appendix highlights (I–IV)
- Appendix I: labor supply is constant over time along balanced growth path (A.11).
- Appendix II: welfare-equivalent consumption measure accounts explicitly for leisure; welfare improvement equation (A2.1) provided.
- Appendix III: introducing risk aversion and capital; key results include h decreasing in capital tax K τ and (K/AH) decreasing in γ; intra-temporal condition (A3.10).
- Appendix IV: calibrating labor market search frictions:
  - Model equations (A4.1)–(A4.6) specify production per matched worker, wage split, choice of hours, matching rates, value functions, free entry, and steady state.
  - Calibration assumptions: one period = one year; r = 0.048 and s = 0.3.
  - France benchmark: normalized θ = 1, w = 1, computed FRA k ≈ 11,438 (as presented).
  - Table A4.1. Calibrated parameter values (Theta(j), w(j), k(j)) — selected entries preserved exactly:
    - Belgium: 1.001, 1.08, 11,922
    - Denmark: 2.79, 1.62, 10,259
    - Finland: 0.84, 1.22, 16,246
    - France: 1.00, 1.00, 11,438
    - Germany: 2.43, 0.91, 6,256
    - Italy: 1.07, 0.95, 11,334
    - Japan: 15.54, 0.66, 2,283
    - Netherlands: 4.09, 0.91, 5,139
    - Norway: 5.98, 0.84, 3,449
    - Spain: 0.48, 0.81, 15,799
    - Sweden: 3.51, 1.20, 7,274
    - UK: 2.12, 0.83, 7,351
    - Canada: 1.37, 0.81, 8,542
    - Switzerland: 15.76, 0.64, 1,793
    - USA: 4.09, 0.71, 4,885
    - Greece: 1.41, 0.72, 7,973

*Source: IMF Working Paper _wp0992, Section 3: “Bivariate Relations between Labor Market Policies and Efficiency.”*

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

### _wp0992 - References..............................................................................................................

### Tables
- 1. GDP Level Accounting relative to the U.S............................................................................6
- 2. Incremental Welfare Improvement for Different Tax Policies............................................27
- 3. Goodness of Fit over the Period 1970–99............................................................................29
- 4. Goodness of Fit of the Friction Model.................................................................................32
- 5. OLS Regression of Labor Market Efficiency Indicators and Policies.................................36

### Figures
- 1. Key Parameters of the Baseline Model by Country, 1970–2001.........................................11
- 2. Calibrated Vacancy Cost and Match Productivity (1990–99) .............................................34

*Source: _wp0992 - References.............................................................................................................. (PDF filename: _wp0992 - References..............................................................................................................)*

### 3. Bivariate Relations between Labor Market Policies and Efficiency ...................................36

### _wp0992 - 3. Bivariate Relations between Labor Market Policies and Efficiency ...................................36

### Introduction and paper scope
- Focus: the role of the size of the public sector on level of national income and labor supply, building on Prescott (2002).
- Two-part approach:
  - General equilibrium cross-country quasi-accounting framework (Prescott-based) to trace size-of-government effects on the level of national income and compare predictions to a broad contemporaneous sample.
  - Partial-equilibrium specifications (including search/friction models) to explore mechanisms where government spending can raise efficiency.
- Context: longstanding per-capita income gap between the U.S. and Western Europe; competing explanations include measurement issues, labor market institutions, tastes, and size of government.

### The basic model and accounting framework
- Representative-agent utility (sum over working-age population):
  - U = Σ_{t=0}^{∞} β^{t} [log(c_{it}) + α log(T - h_{it})] (Equation (1))
  - Parameters/assumptions explicitly used in the paper:
    - Time endowment: T>0.
    - Discount factor: β ∈ (0,1).
    - Leisure preference parameter: α = 1.54.
    - Capital share (1 - θ) calibrated: 0.3 (paper states “We calibrate the capital share at 0.3”).
    - Long-run technological growth assumed exogenous and set at the US 20th-century average of 2 percent (γ = 2 percent).
- Production: CRS Cobb-Douglas with country-specific A (productivity) and inputs K and aggregate hours H = h * N; resource constraint given in Equation (2).
- Log-level decomposition of per-working-age output (Equation (3)): log y = t*γ + log A + (1-θ) log k + log h.
- Empirical accounting (Table 1): labor factor explains the bulk of lower incomes in Europe over the last decade; euro-zone members often associated with depressed labor supply; U.K.’s underperformance linked to productivity rather than labor supply.

### Modeling government and the tax wedge
- Government decomposed into spending and revenues; tax bases considered: consumption taxes, labor income taxes, capital taxes.
- Base-case household budget constraint given in Equation (4).
- Intratemporal labor-leisure first-order condition (Equation (5)) introduces the tax wedge as the term in square brackets.
- Labor share (from CRS production): share of labor income out of output = 1 - θ (Equation (6)).
- Effective marginal labor tax rate definition (Equation (8)):
  - τ ≡ τ_{h} + (1 - τ_{h}) τ_{c} + τ_{k} + τ_{i} (the text defines τ in Equation (8) as c + ch τ? — the document defines an effective marginal labor tax rate τ; see Equation (8) in source).
- Prescott’s adjustment for marginal vs. average personal income tax rates: multiplier 1.6 on average-to-marginal conversion (text: “Prescott (2002) assigns a multiplier of 1.6”).
- Closed-form expression for hours worked as a function of the intra-temporal tax wedge, labor share, preferences, and consumption share (Equation (9)):
  - h = function of τ, θ, α, and c/y (Equation (9) in source).

### Quantitative calibration and welfare experiments
- Parameter values used explicitly in the paper:
  - α = 1.54.
  - Capital share = 0.3.
  - Long-run growth γ set to 2 percent.
  - Prescott marginal tax multiplier = 1.6.
- Prediction approach:
  - Hours worked measure: annual hours worked in the business sector divided by 52 and multiplied by the employment rate of the population aged 15–64.
  - Figures 1a–1n: predicted versus actual weekly hours worked, marginal effective tax rate series, and consumption/output ratios for a broad sample of countries (1970–2001).
- Two thought experiments reported using the welfare measure from Appendix II:
  - (i) Cut marginal tax rate by five percentage points (with offsetting spending cuts).
  - (ii) Adopt U.S. taxation levels (with offsetting spending changes).
- Example numerical welfare statement in the text:
  - “For example, had Belgium between 1990–99 cut marginal income tax rates by five percentage points, it would have reaped a welfare gain equivalent to 7⅓ percent of aggregate consumption (or of 21 percent if it had adopted US tax levels).”
- General finding: these tax-policy counterfactuals imply potentially large steady-state welfare gains for many countries (Table 2 presents the country-by-country percent-of-consumption gains; the example for Belgium is reported verbatim above).

### Fit of the Prescott-style model and extensions
- Model fit diagnostics:
  - Authors compute general coefficient of determination R^2s (Table 3) comparing predicted and actual hours worked over 1970–99.
  - Main outcomes:
    - The model provides an excellent explanation for France and Germany, important explanatory power for Belgium and Japan.
    - Poor fit (often negative R^2) for a number of countries, notably the U.K., Denmark, Sweden, Switzerland, and the U.S.
  - Allowing country variation in consumption/output ratios improves fit for some countries; the marginal contribution of the tax wedge improves fit especially for core euro-zone economies (France, Germany, Netherlands) and Spain and Denmark.
- Alternative utility curvature (Appendix III):
  - Generalized utility (Equation (16)) adds curvature (γ parameter) and leads to an alternative hours relation (Equation (17)) involving the capital stock.
  - Calibration with this extension does not substantially change welfare-simulated gains; it improves fit for the Netherlands and Japan (positive R^2s) but does not materially alter the main conclusions.

### Introducing labor market frictions and search
- Motivation: basic model underpredicts labor supply in several high-tax countries (Nordic countries excluding Norway, Switzerland, U.K.), suggesting that the household’s effective tax burden implied by labor supply is often smaller than measured marginal tax rates.
- Search-friction specification:
  - Modified utility reflecting search/unemployment (Equation (18)): U = log c + α log(T - h - u) (paper writes eqn (18) as )1 log()log(),( u h T c h c u − − + α — preserve the structure as in source).
  - Marginal static labor supply condition with unemployment u (Equation (19)):
    - h = function of τ, θ, α, c/y, and (1 - u) terms (Equation (19) in source).
- Empirical implementation focuses on long-term unemployment as proxy for search/friction costs; Table 4 reports goodness-of-fit for 1990–99:
  - Including unemployment as a friction variable improves model fit notably in countries previously underpredicted (Nordic countries, U.K.).
- Search-and-matching model (Appendix IV) introduces:
  - Vacancy cost k (friction parameter) and match productivity j (productivity of an employed worker).
  - Calibration across countries (1990–99) yields a scatter of calibrated vacancy costs (vertical axis) and match productivities (horizontal axis) — Figure 2 shows clustering:
    - Sweden and Denmark: lower vacancy costs, high match productivity.
    - Germany, Netherlands, Norway: lower vacancy costs but relatively low match productivity (possible alternative explanation for low labor supply).
    - Other countries: relatively high vacancy costs and middle-of-the-range productivities.

### Bivariate and multivariate evidence on policies and efficiency
- Policy variables considered (OECD measures and EPL indexes):
  - ALMP = Active Labor Market Policies (expenditure as share of GDP).
  - PLMP = Passive Labor Market Policies (expenditure as share of GDP; e.g., unemployment insurance).
  - EPL = Employment Protection Legislation index.
- Bivariate scatter observations (Figure 3):
  - ALMP and PLMP show some positive relation with higher match productivity.
  - Relation between ALMP and vacancy cost is weak; EPL correlations with productivity and vacancy cost are weak.
- Multivariate OLS regression results (Table 5; t-statistics in parentheses; significance indicated by *, **, *** at 10, 5, 1 percent):
  - Column (1) (dependent variable: match productivity w):
    - Constant = 0.58*** (t = 7.084).
    - ALMP coefficient = 0.19** (t = 2.391).
    - PLMP coefficient = 0.15*** (t = 3.758).
    - R squared = 0.80; observations = 14.
  - Column (2) (dependent variable: vacancy cost k):
    - Constant = 3,656 (t = 1.339).
    - ALMP coefficient = -4,495* (t = -1.731).
    - EPL coefficient = 1,758* (t = 1.576).
    - PLMP coefficient = 3,067** (t = 2.243).
    - R squared = 0.25; observations = 14.
  - Column (3) (dependent variable: overall inefficiency k/w):
    - Constant = 8,979*** (t = 2.891).
    - ALMP coefficient = -8,167** (t = -2.765).
    - EPL coefficient = 2,817** (t = 2.220).
    - PLMP coefficient = 1,745 (t = 1.122).
    - R squared = 0.34; observations = 14.
  - Column (4) (dependent variable: excess hours (excess H), i.e., Prescott model prediction error in hours per week):
    - Constant = -0.78 (t = -0.445).
    - ALMP coefficient = 4.06** (t = 2.418).
    - EPL coefficient = -2.21** (t = -3.065).
    - PLMP coefficient = 0.65 (t = 0.731).
    - R squared = 0.53; observations = 14.
- Interpretation of regression evidence (authors’ summary):
  - Match productivity is significantly boosted by both ALMP and PLMP in about equal measure.
  - ALMP also lower vacancy cost, but PLMP can offset that effect; EPL imparts significant labor market inefficiencies (raises vacancy cost and the k/w ratio).
  - Overall, ALMP improves both productivity and reduces frictions; PLMP raises productivity but can raise vacancy costs; EPL tends to worsen inefficiency.
  - Column (4) confirms ALMP is associated with higher actual labor supply relative to Prescott predictions; EPL reduces excess labor supply.

### Policy implications and conclusions
- The simple blanket claim that size of government alone explains European vs. U.S. labor supply is not supported across the broader sample; however:
  - Size of government plays a significant role in explaining lower labor supply in core euro-zone countries and implies potentially large welfare costs.
- Efficiency-enhancing uses of tax revenue receive support in the data, but:
  - Actual governments’ spending often does not align with what would be needed to fully enhance efficiency.
  - PLMP (direct income support) is not found to be superior to ALMP on efficiency grounds; PLMP are widespread despite efficiency trade-offs.
  - Policies that do not directly increase government size (e.g., EPL) can nevertheless impart significant costs by protecting insider rents and reducing labor market flexibility.
- Distributional considerations matter:
  - The form of income support and employment protection affects distribution and the preservation of insider rents; further work should address redistribution explicitly.
- Broader empirical consistency:
  - Tax-distortion argument best applies to core euro-zone countries.
  - Some European countries (Nordic) appear to implement policies that keep labor markets functioning with fewer frictions (e.g., low vacancy costs and higher match productivity), consistent with “flexicurity” arrangements discussed in the paper.

*Source: IMF Working Paper _wp0992, Section 3: “Bivariate Relations between Labor Market Policies and Efficiency.”*

### References

### _wp0992 - References

### References
- Alesina, Alberto, Edward Glaeser, and Bruce Sacerdote, 2005, “Work and Leisure in the U.S. and Europe: Why so Different?” NBER Macroeconomics Annual 2005, Vol. 20, pp. 1–64.
- Bartelsman, Eric, 2004, Macroeconomic Productivity and Regulation, mimeo, (Free University of Amsterdam).
- Bell, Gerwin, 2004, “Recent Productivity Trends in the Netherlands,” in: Kingdom of the Netherlands: Selected Issues, IMF Country Report No. 04/301 (Washington: International Monetary Fund).
- Blanchard, Olivier, 2005, “The Economic Future of Europe,” Journal of Economic Perspectives, Vol. 18, pp. 3–26.
- Disney, Richard, 2004, “Are Contributions to Public Pension Programmes a Tax on Employment?” Economic Policy, July, pp. 267–311.
- Fang, Lei and Richard Rogerson, 2007, “Product Market Regulation and Market Work: A Benchmark Analysis,” NBER Working Paper No. 12891, (Cambridge: National Bureau of Economic Research).
- Hall, Robert E., 1997, “Macroeconomic Fluctuations and the Allocation of Time,” Journal of Labor Economics, Vol. 15, No. 1, pp. 223–50.
- Kennan, John, 1988, “An Econometric Analysis of Fluctuations in Aggregate Labor Supply and Demand,” Econometrica, Vol. 56, March, pp. 317–34.
- Knappe, Eckhard, 1980, Einkommensverteilung in der Demokratie, Haufe Verlag, (Freiburg).
- Ljungqvist, Lars, 2005, Comment on “Work and Leisure in the US, Why so Different?” mimeo, Stockholm School of Economics, July, NBER Macroeconomics Annual 2005.
- Mendoza, Enrique, Assaf Razin, and Linda Tesar, 1994, “Effective Tax Rates in Macroeconomics: Cross Country Estimates of Tax Rates On Consumption and Income,” Journal of Monetary Economics, Vol. 34, December, pp. 297–323.
- Mulligan, Casey B., 1998, “Pecuniary Incentives to Work in the United States During World War II,” Journal of Political Economy, Vol. 106, No. 5, pp. 1033–77.
- Mulligan, Casey B., 2002, “A Century of Labor-Leisure Distortions,” NBER Working Paper No.8774, (Cambridge: National Bureau of Economic Research).
- Prescott, Edward C., 2002, “Prosperity and Depression, American Economic Review,” Papers and Proceedings, May, pp. 1–15.
- Prescott, Edward 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.
- Rogerson, Richard, 2005, Discussion of “Work and Leisure in the U.S. and Europe, Why so Different?” NBER Macroeconomics Annual 2005.
- Sapir, Andre, 2006, “Globalization and the Reform of European Social Models,” Journal of Common Market Studies.

*References continued into appendices below.*

### Appendix I. Labor Supply in Balanced Growth Models — Key results and equations
- Utility function (A1.1): )1log()log(LC−+α
- Production function (A1.2): θθ− = 1 )(LAKY
- Intramarginal (first-order) condition for labor supply (A1.3): θ θ α ))(1( 1 L K A L c − = −
- Resource constraint (A1.4): θθ− =+ 1 LAKKC &
- Dividing resource constraint by K yields (A1.5): θ− =+ 1 )( K L A K K K C &
- Along balanced growth path, K K & is constant at g, and (A1.6): g K K C C == & &
- Let X = 1 − L. From (A1.3) obtain (A1.7): )( L L K K A A X X C C && & & & & −+ = − θ
- Rewritten as (A1.8): )( L L K K A A X X K K && & && −+ = − θ
- From (A1.5) (A1.9): 0))(1(=−−+ K K L L A A && &
θ
- (A1.8) and (A1.9) imply (A1.10): L L X X && =
- Since X + L = 1, (A1.11): L L X X && == 0
- Conclusion: labor supply is constant over time along the balanced growth path (A.11).

### Appendix II. Analysis of Welfare Effects of Different Government Size — Measure construction
- Define c(t) and h(t) as consumption and hours worked associated with tax rate t.
- For t0 > t1 > 0, welfare improvement in consumption equivalent denoted x is given by (A2.1):
  )]0(100log[)]0(log[)]1(100log[)]1)(1(log[thtcthxtc−+=−+−αα
- Note: measure is consumption-equivalent but explicitly accounts for positive partial welfare effect from variations in leisure.

### Appendix III. Introducing Risk Aversion and Capital — Framework and implications
- Production function (A3.1): θθ− = 1 )(AHKY
- Resource constraint (A3.2): θθ δ − • =++ 1 )(AHKKKC
- Along balanced growth path (A3.3): K K C C A A g ••• === where g>0 and H is constant.
- Household utility (A3.4): dt HNC eHCU ttt t γ γα ρ − − − = − − ∫ 1 ])([),(
  - Prescott’s (2002) specification occurs when γ goes to 1.
- Budget constraint (A3.5): tttktthtttc TKrHwKKC+−−+−=+++ •))(1()1()1(δττδτ
- Euler equation (A3.6): γ ρ δ τ − − − == • ))(1( tK r C C g
- Factor market marginal product of capital (A3.7): θ θ θ θ − − = ∂ ∂ = 11 )(])([ K AH AHK K r
- Rewritten Euler equation (A3.8): γ ρ δ θ τ θ − − − == − • ])()[1( 1 K AH g C C K
- Observation: rise in γ (more risk averse) decreases (K/AH).
- Intra-temporal (labor supply) condition (A3.9): c th tt t w HN C τ τα + − = −1 )1(
- With h = H/N, intra-temporal condition (A3.10): th tt c t w NC h )1( /)1( 1 τ α τ − + = −
- Factor market equilibrium wage (A3.11): θ θ θ θ ))(1(])([ 1 AH K AAHK H w − = ∂ ∂ =
- From resource constraint (A3.12): ))(()( AH K g AH K AH C δ θ + − =
- Hence (A3.13): θ θ θ δ )/)(1( ] /)(()/[( AHK AHK g AHKH w C − + − =
  - C/w is decreasing in (K/AH).
- Plugging into 1 − h yields (A3.14):
  ]))((1[ 11 1 1 1 θ δ θ α τ τ − + − − − + = − AH K g h h c t
- Implications:
  - h is decreasing in capital tax K τ.
  - (K/AH) is decreasing in γ; thus rise in γ decreases hours worked h through (K/AH).

### Appendix IV. Calibrating Labor Market Search Frictions for European Countries — Model, calibration, and results
A. Model — structure and equations
- Production per matched worker-firm: 2 w h per period, h = hours worked, w = labor productivity parameter.
- Wage determination: flow output 2wh split equally between worker and firm.
- Choice of hours in employment: maximize (A4.1): )log()1(hTwh−+−ατ where τ = wage income tax rate, T = time endowment.
- First order condition for optimal hours (A4.2): w Th )1(τ α − − =
- Matching technology: each unemployed worker contacts a vacancy at rate 5.0 μ θ, with θ ≡ v/u (vacancy-unemployment ratio); each vacancy contacts a job-seeker at rate 5.0− μ θ.
- Value of unemployment (A4.3): ][ 5.0 UW zr U − + = μ θ
- Value of employment (A4.4): )()log()1(WU shTwhrW − + − + − = α τ
- Free entry condition (A4.5): sr wh k + = − 5.0 μ θ which equates vacancy cost k with expected value of a filled job; each filled job receives profit wh per period.
- Steady state accounting (A4.6): 5.0 μ θ + = s s u which implies flow into unemployment (1 − u) s equals flow out 5.0 μ θ u.
- Definition of equilibrium: set {u, h, W, U, θ} satisfying (A4.2), (A4.3), (A4.4), (A4.5), (A4.6).

B. Calibration procedure — assumptions and steps
- Assumptions:
  - α, s, and μ constant across countries.
  - k and w differ across countries.
- Parameter choices:
  - One period = one year.
  - r = 0.048 and s = 0.3 (048.0 and 3.0 presented as =) 
- Step 1 (France benchmark):
  - Use (A4.6) and observed u to obtain μ; normalize θ for France to unity.
  - Use (A4.5) and observed h to obtain k; normalize w for France to 1.
  - Use (A4.2) to pick α.
- Step 2 (other countries j):
  - Compute θ(j) via (A4.6) assuming μ and s constant.
  - Compute w(j) via (A4.2) assuming T and α constant.
  - Compute k(j) via (A4.5) assuming r, s, μ constant.

C. Calibration results — benchmark France and methodology
- For France (benchmark):
  - = × − = − = 111.0 )11.01(3.0)1( 5.0 θ μ u us 2.43  (expression as given)
  - Normalized θ for France = unity.
  - 1319)5217.2952100(1)642.01()()1( = × − × × × − = − − = h T w τα  (expression as given)
    - Assumed hourly wage for France normalized to unity and yearly time endowment = 100*52 hours.
  - Using (A4.5), France vacancy cost FRA k:
    - 65.10578 3.0048.0 5217.291 1427.2)( 5.0 = + × × × × = + × = − sr wh FRA k μ θ  (expression as given)
  - For France set: 1)(,1)(,10579)( === FRA FRA w FRA k θ

- For other countries:
  - θ(j) computed as: 2 ] )( ] (1 [ [ )( μ θ j u jus j − =
  - w(j) from (A4.2): )]()[(1] )( jh T j jw − − = τ α
  - k(j) from (A4.5): sr j h j w j j k + × = − )()( ] )[ )( 5.0 θ μ

- Table A4.1. Summary of Calibrated Parameter Values (as presented)
  - Columns: Theta(j), w(j), k(j) (labeled Vacancy to unemployment ratio, Productivity/hourly wage, Vacancy cost)
  - Belgium: 1.001, 1.08, 11,922
  - Denmark: 2.79, 1.62, 10,259
  - Finland: 0.84, 1.22, 16,246
  - France: 1.00, 1.00, 11,438
  - Germany: 2.43, 0.91, 6,256
  - Italy: 1.07, 0.95, 11,334
  - Japan: 15.54, 0.66, 2,283
  - Netherlands: 4.09, 0.91, 5,139
  - Norway: 5.98, 0.84, 3,449
  - Spain: 0.48, 0.81, 15,799
  - Sweden: 3.51, 1.20, 7,274
  - UK: 2.12, 0.83, 7,351
  - Canada: 1.37, 0.81, 8,542
  - Switzerland: 15.76, 0.64, 1,793
  - USA: 4.09, 0.71, 4,885
  - Greece: 1.41, 0.72, 7,973
- Calibrated parameters: Source: Authors’ calculations.

*Source: _wp0992 - References (PDF chapter/section).*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2009/_wp0992.pdf_