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After a brief survey of the empirical findings on income taxation in the US and German economies in Sect. 5.2, you learn about the substantial welfare costs that are associated with the taxation of labor income. In Sect. 5.3, these costs are computed in both partial and general equilibrium. As one result, the deadweight loss of labor income taxation in Germany is found to be twice as high as the one in the US. In Sect. 5.4, the seminal result from optimal taxation that capital income should not be taxed in the long run is derived and discussed critically. Section 5.5 estimates the US Laffer curve and shows that the US government, in contrast to many European governments, can still raise its revenues from labor and capital income taxation by approximately 10% of GDP. In Sect. 5.6, the quantitative effects of higher taxes on economic growth are derived in a Dynamic General Equilibrium (DGE) model and are shown to be substantially higher than those typically found in growth regressions. Finally, we demonstrate that stochastic taxes improve the time series properties of the real business cycle (RBC) model with respect to the volatility of aggregate demand components and the dynamics of labor and wages in Sect. 5.7.
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The two countries were chosen because they are (1) relatively large in size and (2) characterized by substantial differences in their income tax schedules. In addition, these two countries feature prominently in the quantitative analysis of Prescott (
2004) that we reference in the following.
The data are retrieved from the OECD as described in
Appendix 5.2. Tax revenue is defined as the revenues collected from taxes on income and profits, social security contributions, taxes levied on goods and services, payroll taxes, taxes on the ownership and transfer of property, and other taxes.
Spain’s share of government expenditure share in GDP is generally just short of 50% and only amounted to 44% during 2013–2015.
Italy raised its VAT rate by 1 percentage point in both 2011 and 2013.
Take care to distinguish between individual and household income (or wealth). For example, the OECD uses the following conversion system when comparing households with different sizes: a household consisting of one individual is weighted by measure 1.0, while a household with two individuals and no children is weighted by the measure 1.6. Therefore, if the former has an income equal to $100,000 and the latter has a total income of $160,000, both households are reported to have a household income of $100,000.
In 2015, 59% of both US and German households were married couples.
The tax rate is composed of the ordinary income tax rate equal to 42.0% and a surcharge of 5.5% on the taxes, which is called the “Solidaritätszuschlag”. This surcharge was first imposed in 1992 to finance the additional government expenditures resulting from German reunification in 1989. As of this writing, this surcharge remains in effect.
The tax wedge is defined as the deviation from the equilibrium price or quantity as a result of the taxation of a good (or production factor). In the present case, we look at the factor ‘labor’ and its price in the form of the wage.
The contribution rates for pensions and health amounted to 18.7% and 16.85% in 2014, including both the employee’s and employer’s shares. Chapter
6 will focus on the effects of a pension system and optimal social security reform.
Prescott (
2004) applies income tax rates of 59% and 40% for the German and US economies during the period 1993–1996. In particular, he also includes consumption taxes
τ
^{c} in his computations. For this reason, consider the budget constraint (1 +
τ
^{c})
c = (1 −
τ)
wl, where the household consumes its total net income from working
l hours and receiving net wage (1 −
τ)
w. Accordingly, the tax wedge amounts to 1 − (1 −
τ)∕(1 +
τ
^{c}). Since the value added tax in Germany is equal to 19%, while it is 7.5% or less in the US depending on the state, the difference in the tax wedge between these two countries is even larger after accounting for consumption taxes.
An alternative measure to characterize the progressivity of the tax system is presented by the residual elasticity, where the residual is defined as the net income after taxes
Y
^{n} =
Y −
T(
Y ):
$$\displaystyle \begin{aligned}\eta_{Y^n,Y}=\frac{d Y^n}{d Y}\frac{Y}{Y^n}=\frac{1\tau^\prime}{1\bar \tau}.\end{aligned}$$
This measure provides important information to the participants in the wage bargaining process, i.e., employees, unions, and employers.
The figures and the business cycle statistics in Table
5.2 are computed with the help of the GAUSS program
Ch5_data.g.
For this reason, we have also taken the logarithm of the two income tax rates and applied the HP filter with weight
λ = 1600.
Welfare does not need to fall if another distortion is reduced simultaneously, e.g., if an increase in the labor income tax results in a decline in another distorting tax or if the tax revenues are used for welfareimproving government spending.
The legal incidence may affect the economic incidence, for example, in a labor market with a minimum wage. If the minimum wage is defined as the wage that is paid by the employer to the worker, the new equilibrium point depends on who actually pays the taxes.
In the case of a perfectly elastic labor supply, the labor supply curve
l
^{s} is horizontal and a labor income tax rate
τ
^{L} implies a horizontal shift of this curve to
l
^{s}
′. Evidently, the complete economic incidence falls on the producer.
To be consistent with our previous notation, we keep denoting individual labor supply by
l and aggregate labor supply by
L. In the Ramsey model with a representative agent, individual and aggregate labor supply coincided. In the following, we will also introduce compensated labor supply which we will denote by
h.
Remember from microeconomics that the expenditure function specifies the minimum amount of money that is needed to achieve a given level of utility
\(\bar u\).
In the derivation, we use the following property of the expenditure function:
\( \frac {\partial e(w,u)}{\partial w}=h(w,u)\). This result is derived from applying the envelope theorem to the Lagrangian associated with the minimization of expenditures for given level of utility
\(\bar u\):
$$\displaystyle \begin{aligned} {\mathscr{L}} = Y  w h + \mu \left[ u(Y,h)\bar u\right].\end{aligned}$$
Here,
h denotes the compensated (Hicksian) labor supply.
For the derivation of the
DWL, we follow the exposition in Keuschnigg (
2005), pp. 62–64.
Recall that the Marshallian labor supply curve is derived from maximizing utility subject to the budget constraint. Notice that
l
^{0} <
h
^{0} due to the income effect that is considered in the case of
l but not in the case of the compensated labor supply
h.
Chetty, Guren, Manoli, and Weber (
2011) provide a summary review of empirical studies on the labor supply elasticity, including studies on both the
compensated and
Frisch labor supply elasticities.
Since we study the behavior of a representative household, we identify the individual labor supply with the aggregate labor supply and denote both variables by
L
_{t} in the following.
Take care when you compare the general equilibrium effects in Table
5.4 with those resulting from the partial equilibrium analysis reported in Table
5.3. For the partial equilibrium effect, (
5.3) provides an estimation of the average welfare costs from the imposition of a tax, while, in the general equilibrium model, we computed the marginal welfare costs of a onepercentagepoint increase in the tax rate. One can show that the marginal deadweight loss in the partial equilibrium model is equal to
$$\displaystyle \begin{aligned} \frac{dDWL}{dR}=\frac{\frac{\tau^L}{1\tau^L}\eta_{h,w}}{1\frac{\tau^L}{1\tau^L}\eta_{h,w}}.\end{aligned}$$
For example in the German economy with
τ
^{L} = 0.59, the marginal deadweight loss in partial equilibrium, therefore, is equal 56.2% and is close to the general equilibrium effect reported in Table
5.4.
The transition is computed using the method of reverse shooting described in
Appendix 4.1. The method is implemented in the Gauss program
Ch5_welfare_taul.g.
In our computational algorithm, we set the number of transition periods equal to 40, which appears to be sufficient time for the capital stock to converge.
In his analysis, Prescott emphasized that it is important to consider the marginal rather than the average tax rates for consumption, labor, capital, and investment.
If, instead, the explanation for the observed puzzle were that Europeans were lazier than Americans, the parameter
ι in the above utility function should be different for the households in the individual countries.
A similar result is presented by Chakraborty, Holter, and Stepanchuk (
2015), who analyze the effects of both income taxes and the divorce rate in an OLG model. In their crosscountry comparison of the US with 17 EU countries, they find that the lower income tax rates and higher divorce rates in the US explain approximately 45% of the higher labor supply in the US.
Again, we calibrate the utility parameter
ι = 0.3355 (
ι = 0.3256) such that the steadystate labor supply is equal to 30% in case 1 (case 2),
L = 0.30.
For a formal proof, see Chapter 2 in Kocherlakota (
2010).
More formally, a timeconsistent policy is a policy in a multiperiod problem that is optimal in the present period and remains optimal in future time periods. The main reference for the presentation of the timeinconsistency problem is provided by Kydland and Prescott (
1977). Fischer (
1980) presents the problem of timeinconsistent fiscal policy in a twoperiod model. A good textbook illustration of the Fischer model and its implications for optimal tax policy is presented in Chapter 6.2 of Wickens (
2011).
You will be asked to show these results in Problem
5.3.
Notice that income and wealth are not perfectly correlated. Budría Rodriguez, DíazGiménez, and Quadrini (
2002), for example, find that the correlation between labor income and wealth only amounts to 0.27 in the US economy.
Arthur Betz Laffer was a member of Reagan’s Economic Policy Advisory Board (1981–1989) and a 2016 campaign advisor of Donald Trump.
In particular, we neglect income from abroad.
See
Appendix 4.2 for the definition of the Frisch labor supply elasticity.
Notice that, different from the production function (
3.37), we did not introduce
A
_{t} as labor productivity, but as total factor productivity. These two specifications are equivalent for the CobbDouglas production function if the growth of labor productivity
γ is related to
γ
_{A} according to
$$\displaystyle \begin{aligned} 1+\gamma = (1+\gamma_A)^{\frac{1}{1\alpha}}.\end{aligned}$$
The above equation follows from
$$\displaystyle \begin{aligned} Y_t = A_t K_{t}^\alpha L_t^{1\alpha} = K_{t}^\alpha \left( A_t^{\frac{1}{1\alpha}}L_t\right)^{1\alpha}. \end{aligned}$$
In Sect.
3.4 we also showed that, in steady state, output, capital and consumption all grow at the rate
γ so that
\((1+\gamma _A)^{\frac {1}{1\alpha }}\) denotes the stationary growth factor.
We will analyze government debt in greater detail in Chap.
7.
You are asked to derive these equations in Problem
5.4. Notice that the stationary value of the Lagrange multiplier
λ
_{t} is represented by
\(\tilde \lambda _t= \lambda _t \left (\psi ^t\right )^\sigma \).
See also the discussion of these values in Sect.
4.4.5.
Bear in mind that in all tax scenarios that we consider in this subsection, we only compare steady states and neglect transition dynamics.
Trabandt and Uhlig (
2011) also consider 14 EU countries and there ability to generate additional revenues with the help of income taxation. They find that all Scandinavian EU countries Denmark, Finland, and Sweden, and some other European countries, e.g., Austria, Italy, France, and Belgium cannot raise their labor income tax revenues by more than 5% because they are already so close to the peak of the Laffer curve.
Furthermore, labor supply attains a minimum at
τ
^{K} = 73
% and increases for higher capital income tax rates beyond this threshold. For these high capital income tax rates and corresponding low wage rates, the income effect dominates the substitution effect, and lower wages imply higher labor supply.
You are also asked to estimate the Laffer curves for this case in Problem
5.4.
For an overview of these studies, see Chapter 12 of Barro and SalaiMartin (
2003).
Di Sanzo, Bella, and Graziano (
2017) also study the empirical effects of the tax structure on economic growth. In a panel cointegrated VAR analysis, they find that a property tax has the least harmful effects on growth, while they cannot verify a significant difference between the growth effects of the income and the consumption tax when the total tax burden (relative to GDP) exceeds a threshold of 30%.
However, we formulate the model in discrete time to comply with the approach used in the rest of the book. In addition, we consider exogenous labor supply in our model.
For this reason, Irmen and Kuehnel (
2009) suggest considering the growth effects of productive government expenditures in models with Schumpeterian innovation instead of the simple ‘Ak’model.
Alternatively, we could consider an income tax on both labor and capital income.
You are asked to solve this case in Problem
5.5.
You are asked to consider this change in assumptions in Problem
5.8.
The Lagrange multipliers
λ
_{t} and
μ
_{t} are transformed into stationary variables by the division by
\(H_t^{\sigma }\),
\(\tilde \lambda _t=\lambda _t/H_t^{\sigma }\) and
\(\tilde \mu _t = \mu _t/H_t^{\sigma }\).
The calibration and the computation of the steady states are implemented in the Gauss program
Ch5_lucas.g.
Grüner and Heer (
2000) note that this assumption is not innocuous and favors a policy that does not tax capital. As capital income taxes decrease, labor income taxes must increase, and consequently, human capital declines relative to physical capital and output. Therefore, if
G
_{t} is held constant relative to
H
_{t}, government expenditures decline relative to GDP, and we compare economies with different sizes of the government sector. In particular, Grüner and Heer (
2000) derive that the welfaremaximizing flat rate of capital
τ
^{K} increases from 9% to 32% if
G∕
Y is held constant instead. Their result explicitly accounts for transitional dynamics of tax policies where a onceandforall change in
\(\tau ^K_t\) is announced in period
t = 0 and the tax rate
\(\tau ^K_t=\tau ^K\) is held constant during the transition and in steady state.
One reason to restrict the analysis to constant capital income tax rates
\(\tau ^K_t\) is the timeconsistency problem associated with capital income taxation. See also Footnote 33 in this chapter.
Recall that we presented a New Keynesian model that specifies habits and capital adjustment costs in Sect.
4.5.2.
As one of the first articles in this literature, McGrattan (
1994) assumed a VAR process of order 2 in the variables
Z
_{t},
G
_{t},
\(\tau ^K_t\), and
\(\tau ^L_t\). Burnside, Eichenbaum, and Fisher (
2004) even use lags of order 50 and 16 for government consumption and the two tax rates, respectively.
Recall that one basic mechanism in the standard RBC model is the intertemporal substitution of labor. If wages rise, the household increases labor supply in the present period. If the real interest rate increases, the household shifts its working hours from future periods into the present period because the discounted income in future periods from a marginal increase in its labor supply is reduced.
The reader is invited to determine how the response of consumption to higher capital taxes depends on the elasticity of substitution between private and public consumption.
In the RBC literature, many studies have analyzed and attempted to replicate the fact that wages and labor productivity are uncorrelated or even negatively correlated with working hours. One of the early studies is by Burnside, Eichenbaum, and Rebelo (
1993), who introduces labor hoarding into the standard RBC model.
F
_{KK}
K +
F
_{LK}
L = 0 follows from Euler’s theorem and the derivation of
$$\displaystyle \begin{aligned} F(K_t,L_t) = F_{K_t}(K_t,L_t) K_t + F_{L_t}(K_t,L_t) L_t\end{aligned}$$
with respect to
K
_{t}.
According to Table 2 in Prescott (
2004), the tax wedge
\(\frac {\tau ^C+\tau ^L}{1+\tau ^L}\) amounted to 64% in Italy during the period 1993–1996.
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 Title
 Income Taxation
 DOI
 https://doi.org/10.1007/9783030009892_5
 Author:

Burkhard Heer
 Publisher
 Springer International Publishing
 Sequence number
 5
 Chapter number
 5