Policy Analysis

= or or

e E l S e l b b

In the employment function above, l and e exert indirect ambiguous effects via search effort S on the firm’s net marginal benefit of employment. Yet, it is easy to show the direct effects of l and e always dominate these indirect effects. Accordingly, we obtain the following employment function

( ; , , ),τ λ0

− − − −

e E l b=  (24)

which is negatively sloping in the (e, l) plane. See Figure 1 wherein the employment locus is referred to as Locus E (Employment).

Thus, the steady state is determined by the interaction of Loci H and E. By exploring the effects of a higher cost of vacancy creation, it is clear that Locus H needs to be always flatter than Locus E.¹⁰ As Locus H is flatter than Locus E, this implies that the two curves have at most one intersection. See Q0 in Figure 1. The two loci determine steady-state employment (e₀) and hours worked per worker (l₀), and thus labor supply (e0l0).

2.5 Policy Analysis

Although the simplicity of our model confines the breadth of the policies that can be envisaged, two policies of pervasive interest can be studied within our model: a tax on the employed which is proportional to labor income and is used to make a lump-sum

10 A higher cost of vacancy creation λ0 shifts the employment locus down without shifting the hour locus;

should the employment locus be less steep than the hour locus, employment would be increased, not decreased, which is inconsistent.

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transfer; and a benefit to the unemployed which is proportional to labor income as financed by a lump-sum tax. While the former policy has been stressed by Prescott (2002, 2004) in explaining lower hours worked per worker in Europe than the US, the latter policy has been emphasized by Ljungqvist and Sargent (2007, 2008a) in accounting for higher unemployment rates in Europe than the US. We start with the analysis of increases in labor income taxes, followed by increases in non-employment benefits. The comparative-static analysis is delegated in the Appendix. Here, we offer graphical illustrations.

2.5.1 Effects of Labor Taxes

First, we analyze the effects of increases in the labor tax rate (higher τ). Suppose that the initial steady state is at Q0 in Figure 2. Thus, the initial hour worked per worker is l₀, initial employment is e₀, initial unemployment is (1-e₀) and initial labor supply is (e0l0).

When the labor tax rate (τ) is increased, the household’s net marginal cost of working hours increases and thus working hours are decreased; the firm’s net marginal benefit of employment is decreased and thus employment is decreased. Then, Loci H is shifted to Locus H₁ and Locus E is shifted to Locus E₁ in Figure 2. Moreover, with given employment levels, Locus E1 is shifted downward more than that of Locus H1. The reasons are that a higher labor tax rate yields direct effects to decrease working hours in both Loci H and E. However, in Locus H, a higher labor tax rate also generates an offsetting effect via decreasing search effort which reduces the net marginal cost of working hours and thus increases working hours. Hence, Locus H₁ is shifted downward less than Locus E1. The new steady state is at Q1 in Figure 2. As a result, hours worked per worker l1 and employment e1 are lower than their initial levels l0 and e0, respectively.

Accordingly, hours worked per person (e1l1) are lower than the initial level (e0l0).

Note that in Prescott (2002, 2004), there is only an intensive margin (i.e., work hours and leisure hours) and not an extensive margin (i.e., employment and non-employment). The equilibrium condition in Prescott (2002, 2004) may be thought of as involving only Locus H without Locus E, with the initial steady state Q₀ being determined by Locus H and the initial employment level e0 in Figure 2. In this case, a higher labor tax rate (τ) shifts Locus H downward to Locus H1. The new steady state is at Q3. Thus, compared to the case with both intensive and extensive margins, hours worked per worker here are reduced by more to the level l2<l1. Therefore, without an extensive margin in Prescott (2002, 2004), as the adverse effect on employment is not taken into account, the adverse effects on hours worked per worker are overstated. To summarize the results,

Proposition 1 An increase in labor taxes decreases both hours worked per worker and employment. With fixed employment, the adverse effect on hours worked per person is overstated.

2.5.2 Effects of Non-employment Benefits

Next, we analyze the effects of increases in non-employment benefits (higher b).

Suppose that the initial steady state is at Q₀ in Figure 3.

When non-employment benefits are increased, the firm’s net marginal benefit of employment is decreased. With given work hours, employment decreases and thus the Locus E is shifted leftward to Locus E₂ in Figure 3. Moreover, more generous non-employment benefits also decrease search effort which reduces the household’s marginal cost of working hours. With given employment, hours worked per worker

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increase and thus Locus H is shifted upward to Locus H2. The new steady state is at Q2

in Figure 3. As a result, employment is lower but hours worked per worker are higher.

In Ljungqvist and Sargent (2007, 2008a), there is only an extensive margin and not an intensive margin (i.e., fixed working hours). The equilibrium condition in Ljungqvist and Sargent (2007, 2008a) may be interpreted as involving only Locus E without Locus H, with the initial steady state Q0 being determined by Locus E and the initial work-hour level l₀ in Figure 3. In this case, more generous non-employment benefits only shift Loci E downward to Loci E2, and thus the new steady state is at Q3. Compared to the case with both intensive and extensive margins,employment here is reduced by less to the level e₁>e₂. Therefore, without an intensive margin in Ljungqvist and Sargent (2007, 2008a), as the positive effect on hours worked per worker is not taken into account, the adverse effect on employment is understated. To summarize the results,

Proposition 2 An increase in non-employment benefits decreases employment and increases hours worked per worker. With fixed hours worked per worker, the adverse effect on employment is understated.

2.5.3 Quantitative Analysis

We now quantify the effects of increases in labor taxes and non-employment benefits on labor supply. We are particularly interested in understanding the effects on hours worked per worker and employment and thus labor supply in Europe relative to the US over the past 3 decades from the early 1970s to the early 2000s. To this end, we calibrate our model in a steady state to the US economy. We assume that all parameters values in Europe are the same as those in the US except for labor income taxes and

non-employment benefits. Then, we feed in the data of increases in labor income taxes and non-employment benefits in Europe relative to the US in the early 2000s and quantify the effects.

We calibrate parameters and variables at a quarterly frequency. With the annual depreciation rate of capital in the range of 6%-8% and the annual time preference rate of 4%, we follow Ljungqvist and Sargent (2008b) to set the quarterly capital depreciation rate to δ=0.02 and the quarterly time preference rate to ρ=0.01. The data gives the steady-state interest rate at r=0.03. The coefficient of technology is normalized to A=1.

The capital share is about one-third and we follow Prescott (2004) to use the value α=0.3224. With the values of A and α, we compute the effective capital-labor ratio as

11

(_{ρ δ}^α₊ )^−α 33.2622,

= ^A =

q which in turn gives MPL=2.0973 and, via (6), the quarterly capital-output ratio k/y=10.7467 which is consistent with a capital-output ratio of 2.5-3 in annual data.

The fraction of employment in the working-age population is about 75% (cf.

Kydland and Prescott 1991) and thus we set e=0.75. The fraction of time allocated to the market (el) is 25% as pointed out by Prescott (2006). This implies l=0.3333. For the average fraction of time spent to search, we follow Andolfatto (1996) to set s=0.5×l=0.1667. According to Shimer (2005), the monthly job finding rate is 0.45. We go along this rate and translate it into a quarterly value of sμ=1-(1-0.45)³=0.8336, implying μ=5.0016. We employ (13) to compute the quarterly separation rate as a fraction of employment at ψ=(sμ(1-e))/e=0.2779. Moreover, we follow Shimer (2005) by normalizing the steady-state ratio of vacancies to searching workers to one (v/(1-e)=1) which implies the vacancy at v=0.25 in a steady state. Then, we utilize (13) to calibrate η=(sμ(1-e))/v=0.8336.

By setting the consumption-output ratio at c/y=0.67 and normalizing λ1=1, we use

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(17) to calibrate the coefficient of vacancy costs λ0=0.1061. We compute the wage at w=1.4257 from (18). In accordance with Prescott (2004), non-employment benefits are 0.319 times forgone labor income, and hence we calibrate b=0.319×w×l which gives b=0.1516. Based on the data in McDaniel (2007), Rogerson (2008) used the labor taxes in Belgium, France, Germany, Italy, and the Netherlands to represent the tax in Europe.¹¹ We follow this method and calculate the population-weighted average effective tax rate on labor income for these five countries. We find that the average effective tax rate in years 1970-73 is 0.3982 which leads us to set the benchmark labor tax rate to τ=0.4, a rate similar to that of the US as noted in Prescott (2004).

Finally, for the utility function adopted here, the labor supply elasticity is LSE=(1-l)/(σl). The LSE estimated in MaCurdy (1981) ranged from 0.1 to 0.5 for men and is likely higher for women, while Andolfatto (1996) set LSE=1. For present purposes, we choose an intermediate value: LSE=0.65, which implies σ=3.0769. Given this value, (21) is solved for χ1=0.6971 and (19) is solved for χ2=1.6813.¹² We obtain the bargaining share β=0.7183 from (23), which is close to the value of 0.72 used by Shimer (2005). Assuming that Hosios’ rule holds (Hosios, 1990), a search worker’s contribution in matching is pinned down by the labor’s share in the wage bargaining, γ=β. Then, from matching relationships we calibrate m=3.0193. The parameter values, observables and calibrated values are listed in Table 2. Under the benchmark parameter values, we obtain a unique steady state.

Now, we quantify the effects of increases in tax rates and non-employment benefits.

We start by measuring the increase in labor taxes and non-employment benefits in Europe relative to the US in the early 2000s. For labor taxes, based on McDaniel (2007),

11 McDaniel (2007) calculated a series of average tax rates on consumption, investment, labor and capital using national account statistics in 15 OECD countries. The data has been used by Rogerson (2008) and Ohanian et al. (2008).

12 These parameter values indicate that the employed are better off than the non-employed.

we calculate the population-weighted average effective tax rate on labor income in the five European countries under concern in 2000-03 and obtain the tax rate 0.5168. With the data that the effective labor tax rate increased a little bit in the US in the past 30 years,¹³ this indicates an increase of labor tax rates by about 30% in Europe relative to the US from that in 1970-73. Next, based on the data in OECD (1999, Table 2.2), the population-weighted average unemployment payment rate is 69.72% in the five European countries under concern and 50% in the US in the late 1990s. These data suggest that non-employment benefits in Europe are roughly 40% higher than the US.

Given the data, we quantify the effects of increases in the value of τ by 30% and the value of b by 40% from their baselines. In each exercise, the government budget is balanced by adjusting lump-sum taxes or transfers. Quantitative results are illustrated in Table 3.

First, the quantitative effects of increases in the labor income tax are in the first row of Table 3. The results indicate that when the labor income tax rate is increased by 30%, hours worked per worker are decreased from 0.333 to 0.310 which means a drop by 6.85%. The employment rate is decreased from 0.75 to 0.708 which indicates a decrease by 5.55%; thus, the unemployment rate is increased by 5.55%. As a result, labor supply is decreased by 12.02%. Next, the quantitative effects of increases in non-employment benefits are reported in the second row of Table 3. The results suggest that when non-employment benefits are increased by 40%, the employment rate is decreased from 0.75 to 0.703, which is a decrease by 6.26%; thus, the unemployment rate is increased by 6.26%. Hours worked per worker grow slightly from 0.333 to 0.337, which is an increase by 1.13%. As a result, labor supply is decreased by 5.2%.

Our foregoing results indicate that a 30% increase in labor income taxes in Europe

13 Based on the data in McDaniel (2007), the effective labor tax rate (on household income and payroll) in the US increased from 0.1775 in 1970-73 to 0.22475 in 2000-03.

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relative to the US has a large adverse effect on hours worked per worker, which is consistent with the claim made by Prescott (2002, 2004). Yet, there is also a substantial adverse effect on employment rates. Moreover, our results suggest that a 40% increase in non-employment benefits has a large adverse effect on employment which is consistent with the argument made by Ljungqvist and Sargent (2007, 2008a). These quantitative effects imply that a 30% increase in labor income taxes has a more detrimental effect on hours worked per worker but has a less harmful effect on employment than a 40% increase in non-employment benefits.

To see the combined effects of these two adverse labor market institutions, we increase the labor income tax and non-employment benefits at the same time, with the effects shown in the last row of Table 3. The results reveal that the employment rate is decreased from 0.75 to 0.609, which indicates a large drop by 18.73%. Hours worked per worker are decreased from 0.333 to 0.323, which implies a decrease by 3.08%. As a result, these two adverse labor market institutions decrease labor supply by 21.23%.

Compared to the data of a decrease by 28.23% in the EU-11 relative to the US over the past 30 years in Table 1, our quantitative results suggest that higher labor income taxes and more generous non-employment benefits in the EU than the US both can account for about 75% of the declining labor supply in the EU relative to the US over the past 30 years from the early 1970s to the early 2000s.

Finally, we investigate the robustness of the foregoing quantitative results by carrying out two types of sensitivity analysis. First, we vary the LSE by increasing its value to 1 and decreasing its value to 0.5.¹⁴ Next, we envisage whether or not the results are robust when the Hosios’ rule does not hold. In this exercise, we fix the labor’s bargaining share at β=0.7183 and vary the labor’s contribution in matching γ to

14 The value of LSE cannot be smaller than 0.5 as then the calibrated value of χ2 is negative.

take alternative values {0.235, 0.54, 0.72} used by Hall (2005), Hall and Milgrom (2008) and Shimer (2005), respectively. In the first sensitivity analysis, we recalibrate the model and find that all parameter values are the same as those in Table 2 except for the values of σ, χ1, χ2, m and β. In the second sensitivity analysis, we recalibrate the model and find that all parameter values are the same as those in Table 2 except for the value of m. Overall, we find that our foregoing results are robust in that an increase in the labor tax reduces both hours worked per worker and employment rates, and an increase in non-employment benefits lowers employment rates with a small increase in hours worked per worker. The quantitative results indicate that the two adverse labor market institutions explain declining labor supply by more when the labor supply elasticity is larger and the labor’s contribution in search γ is smaller.¹⁵