Concluding Remarks

Over the past 30 years from the early 1970s to the early 2000s, labor supply in Europe was declined by about 30% relative to the US. The decline in labor supply comes from hours worked per worker and employment rates. Europe has witnessed steadily higher labor taxes and more generous government-supplied non-employment benefits than the US. Some studies attributed declining hours worked per worker in Europe relative to the US to higher labor taxes, while other studies accredited high unemployment rates in Europe to more generous non-employment benefits. This paper studies a model that consider labor search within the neoclassical growth framework so as to investigate the effects on labor supply along both intensive and extensive margins in one unified general equilibrium framework. We use the model to envisage and compare the relative effects of increases in labor taxes and more generous

15 Labor supply is decreased by 30.14% when LSE=1 and by 12.74% when LSE=0.5. Moreover, labor supply is decreased by 36.1% when γ=0.235, by 24.12% when γ=0.54 and by 21.21% when γ=0.72.

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non-employment benefits on hours worked per worker and employment rates.

We find that an increase in the labor tax decreases hours worked per worker and employment rates with an overstated adverse effect on hours worked per worker if employment is fixed as is in Prescott (2002, 2004). Moreover, more generous non-employment benefits decrease employment rates and increase hours worked per worker, with an understated adverse effect on employment rates if hours worked per worker are fixed as are in Ljungqvist and Sargent (2007, 2008a). In the baseline parameterization, we find that increases in labor taxes and non-employment benefits together explain about 75% of declining labor supply in Europe relative to the US over the past 3 decades, with the fraction accounted for being increasing in the labor supply elasticity and decreasing in the labor’s contribution in matching.

Finally, our model has a limitation. The labor force is fixed in our model wherein people who are not employed are treated as the non-employed who are entitled to non-employment benefits. In reality, the labor force is variable and people may be out of the labor force. An extension of our research is to compare the effects of labor taxes and unemployment benefits on employment rates and hours worked per worker in a context with an endogenous labor force. In particular, male labor force participation had declined and female labor force participation had risen over the period under study. The aggregate effects may be different between Europe and the US which suggest an alternative mechanism.

Mathematical Appendix

2. The Search Effort Equation The relationship

17 If the worker devoted more effort in searching, it would increase his outside option or reservation wage.

Hence, we suppose MRS_s^e>_0.

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18 We assume that the direct effect dominates in order to ensure the diminishing marginal benefit.

(1 ) (1 ) 0

derived as follows. By substituting (A2a), we rewrite (A3a) and (A4a) as follows.

τ τ ,

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(

)

τ ≡ − τ − − λ >

 ^v _s^v _{s s}−^s _s

s s

E MB MB v MB

MRS MB ,

(

)

≡ − − − >

_{b b}^v _s^v _{s s}−^bs _s

s s

E MB MB v MB

MRS MB ¹⁹

Thus, Loci E and H are both negatively sloping in the (e, l) plane.

Moreover, a standard result is that a higher unit cost of vacancy creation λ0 leads to less vacancies and thus less employment, i.e.

0 0.

λ <

dde Let D L E L E≡  _{e l} −  _{l e} denote the determinant of the Jacobean matrix in (A5a)-(A5b). Straightforward calculation gives

0 0,

λ = − <^Ll

dde D which requires − > −^_^{e }_^e

l l

L E

L E and D>0. Therefore, the two curves have at most one intersection.

19 We assumed that the direct effects of all these derivatives dominated the indirect effects resulted from the changes of searching effort.

Table Appendix

Table 1: Hours and Employment in the EU Relative to the US, 1970-73 and 2000-2003.

Hours worked

per person Employment rate Hours worked per worker 70-73 00-03 diff. 70-73 00-03 diff. 70-73 00-03 diff.

Belgium 92.86 72.5 -20.36 95.44 83.65 -11.79 97.29 86.7 -10.59 France 109.63 74.87 -34.76 103.36 89.52 -13.84 106.07 83.65 -22.42 Germany 132.79 77.42 -55.37 107.91 90.34 -17.57 123.04 85.7 -37.34 EU-11 109.63 81.4 -28.23 101.51 88.91 -12.60

(43.42%) 107.99 91.57 -16.42 (56.58%) United States 100 100 0 100 100 0 100 100 0 Note: 1. The hours worked per person are the total hours worked divided by the number of the population aged 15-64; the employment rate is the number of the employed divided by the number of the population aged 15-64; the hours worked per worker are the total hours worked divided by the number of the employed.

2. All US values are normalized to 100 in 1970-73 and 2000-03. All EU data in 1970-73 and 2000-03 are normalized to the U.S. values in the respective period. EU-11 includes Belgium, Denmark, Finland, France, Germany, Ireland, Italy, Netherlands, Spain, Sweden and the UK. We use the population of a country as the weight of the country in calculating the data for the EU-11.

3. Numbers in parenthesis are the composition of differences in hours worked per person in EU-11 into employment and hours worked per worker.

Sources: Data on total numbers of hours worked and total numbers of the employed are taken from OECD (2010a), whereas data on total numbers of the population aged 15-64 are taken from OECD (2010b).

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Table 2 Benchmark parameter values and calibration

Benchmark Parameters and Observables quarterly

physical capital’s depreciation rate δ 0.0200

time preference rate ρ 0.0100

aggregate consumption-aggregate output ratio c/y 0.6700

capital’s share α 0.3224

job finding rate per job seeker sμ 0.8336

fraction of employment e 0.7500

vacancy-searching worker ratio v/(1-e) 1.0000

coefficient of goods technology A 1.0000

coefficient of the cost of vacancy creation and management λ1 1.0000 fraction of time devote to work of the employed el 0.2500

effective tax rate on labor income τ 0.4000

labor supply elasticity LSE 0.6500

Calibration

fraction of time spend on search of the non-employed s 0.1667

effective job finding rate μ 5.0016

job separation rate ψ 0.2779

vacancy creation ν 0.2500

employee recruitment rate η 0.8336

coefficient of the cost of vacancy creation and management λ0 0.1061

equilibrium wage w 1.4257

unemployment compensation b 0.1516

inverse of intertemporal elasticity of substitution of leisure σ 3.0769 utility weight of leisure for the employed χ1 0.6971 utility weight of leisure for the non-employed χ2 1.6813

labor searcher’s bargaining power β 0.7183

labor searcher’s share in matching technology γ 0.7183

coefficient of matching efficacy m 3.0193

Table 3: Quantitative Results

el e l

Benchmark 0.25000 100% 0.75000 100% 0.33333 100%

τ↑30% 0.21996 -12.02% 0.70841 -5.55% 0.31050 -6.85%

b↑40% 0.23699 -5.20% 0.70302 -6.26% 0.33710 1.13%

τ↑30% and b↑40% 0.19691 -21.23% 0.60953 -18.73% 0.32306 -3.08%

Figure Appendix

Figure 1: Steady state

Figure 2: Long-run effects of higher wage taxes (τ)

Figure 3: Long-run effects of higher non-employment benefits (b) l

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3 Relative Effects of Labor Taxes on Working