Dual income tax reform in Germany: A microsimulation approach

My base data set is drawn from the 2005 wave of the German Socio-Economic Panel (GSOEP). I merge some retrospective data from the 2006 wave, such that the base data set refers to 2005, the same fiscal year the German Council of Economic Experts reform proposal refers to.

Choice alternatives are generated using GMOD, a tax-benefit microsimulation model for Germany developed by the author. GMOD calculates personal income taxes, social security contributions and benefits. It allows for the standard benefits and tax concessions such as housing benefits and child-benefits, allowances for child-raising, child-raising leave and maternity as well as assistance for education or vocational training. Furthermore, it accounts for tax abatements for dependent children and for the education of dependent children, for child-care, tax credits for single parents, maintenance payments and income-splitting for married couples.

A dual income tax differentiates between capital and labor income and taxes these differently. So I have to derive two tax bases, one for capital income, and one for other sources of household income, called “labor income”.

Currently, GMOD calculates seven sources of income, because the current German Income Tax Law (Einkommensteuergesetz, EStG) levies one tax schedule on the sum of income from the following exhaustive list of seven sources of income: (1) income from agriculture and forestry (§ 13 EStG), (2) income from trade or business (§ 15 EStG), (3) income from independent personal services (§ 18 EStG), (4) income from dependent personal services, i.e. wages, salaries and retirement benefits of civil servants (§ 19 EStG), (5) income from investment of capital (§ 20 EStG), (6) income from rentals and royalties (§ 21 EStG), and (7) other income designated in § 22 EStG, e.g. notational return on investment of a pension from statutory pensions insurance. Gross earnings from all of these sources are calculated by GMOD based on information available in my base data set described above, on the German income tax law and on income tax directives. Net income from the first three sources is calculated on the accrual basis and called “profit-based income”. Net income from the other four sources is defined as the excess of total receipts over income-related expenses.

According to the German Income Tax Law (EStG-E) as proposed by the SVR2008, there will be four categories of income (see § 2 EStG-E): (1) income from business activities (§ 13, § 15 and § 18 EStG-E), (2) income from employment (§ 19 EStG-E), (3) capital income (§ 20, § 21, and § 22 EStG-E), and (4) derived income (§ 23 EStG-E).

To map the traditional seven sources of income to the new categories capital and labor income I proceed as follows: (1) Income from business activities corresponds to traditional “profit based income”. (2) Income from employment corresponds to the traditional income from dependent personal services. (3) Income from capital assets is derived from traditional income from capital investments (§ 20 EStG) and income from rentals and royalties (§ 21 EStG). (4) Derived income corresponds to traditional “other income” designated in § 22 EStG. In my base data set, I do not have information on income from private sale transactions mentioned in § 22 EStG-E, so I have to ignore it. I assume that the cash method of accounting is used with respect to income from business activities. Thus, taxpayers report their revenues when received and their expenses when paid.

The labor income tax base includes wages, salaries (including the employers’ calculatory salaries) and civil pensions. The capital income tax base includes business profits, dividends, capital gains, interest and rental income. Taxable labor income and taxable capital income are obtained by subtracting personal allowances and other deductions from the respective tax base. The savings allowance of 750 Euro for the income from capital investments (§ 20 Section 4 EStG) will be abolished.

The decomposition of profit-based income in a capital and a labor share is the crux of the DIT. The calculatory salary, i.e. the labor income of the self-employed, is hard for an individual to measure and even harder for tax authorities to verify. I use the following trick: First, I estimate a Mincer-type wage function based on observable characteristics on the sub-sample of wage earners. In my data I observe determinants of wages for all individuals. Therefore, I am able to predict the calculatory salary for all self-employed individuals. Finally, I derive their capital income as the residual. (See Wagenhals & Buck, 2009, for details about this decomposition approach.) In my view, this approach improves upon the procedure of using an arbitrary sharing rule (see e.g. Gottfried and Witczak, 2009). In any case, due to data constraints, I did not have the option to compute calculatory salaries for the self-employed as residual profits.

The dual income tax combines a progressive tax schedule for labor income with a flat tax rate on capital income.

I assume that labor income is taxed according to the current income tax schedule (§ 32 a EStG), and that capital income is taxed with a rate of 25 percent (including the solidarity surcharge). To avoid legal concerns and a potential deterioration with respect to the current legal position I follow the German Council of Economic Experts (2008, pp. 108–110).

Figure 1

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§ 32 a EStG-E defines the DIT income tax function: Let v denote taxable income in Euro (rounded down to the next Euro) according to § 2 Section 5 Clause 1 EStG-E, and let K denote capital income in the sense of § 2 Section 3 Clause 2 EStG-E (also rounded down to the next Euro). Then the personal income tax T amounts to

where

(x, y, z are also rounded down to the next Euro). The symbol t denotes the solidarity surcharge (i.e. currently t = 0.055).

Figure 1 shows marginal tax rates, i.e. the tax rates that apply to the last Euro of the tax base. It compares the current marginal tax schedule (based on § 32 a EStG) with the DIT schedule for taxpayers with fixed taxable capital incomes of different amounts. The solid line shows the current tax rates (T 2005). Under a dual tax regime this line refers to taxpayers without any capital income. For taxpayers with capital income a so-called stretched tax scale is applied. This means that the taxation of capital income is incorporated in the tax schedule in terms of a proportional zone. The length of this variable proportional band depends on the amount of taxable capital income. The return component of income is taxed proportionally while any profits beyond those are taxed progressively as labor income. As examples, I use marginal tax rates for capital incomes of 10,000, 20,000 and 30,000 Euro.

I represent any individual’s choice set by a six-state labor supply regime and approximate actual hours per week h^a by hours levels h ∈ H := {0,10,20,30,40,50} applying the following rounding rule

For all elements h in the choice set H I use GMOD to calculate household net incomes as

where w denotes the gross wage rate, μ is income from sources other than employment and T(·) is the tax-benefit function conditional on a vector of observed characteristics x. I assume that preferences can be represented by a utility function U and that individuals act as if to maximize utility

subject to the budget constraint

where $\overline{h}$ denotes total time endowment.

To obtain random utilities (needed for estimation and simulation), I add state-specific random errors e(h) to utilities for all states h ∈ H. This gives random utilities

If the state-specific random errors are i.i.d. Type I extreme value distributed, then the probability P of working h^j hours is

For the specification of the utility function, I follow the tradition started by Keane and Moffit (1998) and choose a flexible form quadratic direct utility function. Written in terms of individual consumption c = c(h) and leisure $l:=\overline{h}-h$ I obtain

where α_cc, α_ll, α_cl, β_c and β_l denote unknown parameters. I assume that preferences vary through taste-shifters on income and leisure coefficients:

where γ_c0, g_c, γ_l0 and g_l denote unknown coefficients and x is a (row) vector of individual characteristics² and following van Soest (1995) dummy variables for part-time categories in order to capture the disutility of inflexible arrangements in the utility functions.

I deal with unobserved wage rates by estimating the expected market wage rates conditional on observed characteristics using Heckman’s two-step approach: I first estimate a reduced form participation equation, get the Mill’s rate and use it in a Mincer-type wage equation to correct for sample selection bias. I account for wage rate prediction errors by integrating out the disturbance term of the wage equation in the likelihood as suggested by van Soest (1995).

Estimation of the unknown preference parameters is based on a mixed logit model proposed by McFadden and Train (2000). Under mild regularity conditions, it can approximate the choice probabilities of any discrete choice model derived from random utility maximization as closely as desired. Under the assumption that the income coefficients are normally distributed and all other coefficients are fixed I proceed by maximum simulated likelihood.

For married or cohabiting couples I allow for joint decision making. Each partner may account for the decision of the other partner when deciding on hours worked. I assume that each household member selects one of six regimes: non-participation or one of five employment states ℏ ∊ H = {0,10,20,30,40,50} (the elements denoting hours per week). Thus, the choice set for couples is H × H. Actual individual working hours observed in the data are rounded (as above) to fit the elements in this set.

I assume that preferences of a couple may be represented by a flexible quadratic utility function

Here $\begin{array}{l}\begin{array}{ccc}& & \\ & & \\ & & \end{array}\\ l_m:=\overline{h}-h_m,l_f:=\overline{h}-h_f;l\end{array}$ denotes leisure and h hours worked of male ( m ) or female ( f ) persons, while c denotes their joint net income. The α and β coefficients are unknown population parameters. The sign of α_fm indicates whether male and female leisure are substitutes or complements. Similar to the case of single persons, some preference parameters depend on personal, household and other characteristics. Supplementing representative household utility I add stochastic terms accounting for state specific errors (needed for estimation and simulation) and finally derive the probability of choosing any consumption-leisure combination in the set of feasible household decisions. Estimation proceeds via mixed logit and simulation by calibration⁴ as described above. I derive household gross earnings assuming state invariant male and female gross wage rates, and calculate the corresponding state specific net household income for each hours combination in the choice set H × H using GMOD and my base data set described above.

A more comprehensive version of this report, available only in German, includes an elaborate tax amending bill of the income tax law proposed (EStG-E). (See Sachverständigenrat zur Begutachtung der gesamtwirtschaftlichen Entwicklung, Max- Planck-Institut für Geistiges Eigentum, Wettbewerbs- Und Steuerrecht, Zentrum für Europäische Wirtschaftsforschung, 2006).

Individual characteristics embedded are age and age squared, place of residence in East Germany (yes=1, no=0), nursing case in the family (yes=1, no=0), citizenship (not German = 1, German=0), high education, i.e. degree from universities or from universities of applied sciences (yes=1, no=0), low education, i.e. no vocational qualification attained (yes=1, no=0), handicapped person (yes=1, no=0), number of children under 6, and number of children between 6 and 16.

See Kreedy and Kalb (2005) for a very detailed explanation of labor supply transition matrices.

“Individual” calibration now refers to calibration based on the estimated preference functions of the couples.

The data used in this publication were made available by the German Socio-Economic Panel Study (GSOEP) at the German Institute for Economic Research (DIW), Berlin.

The author is greatly indebted to Gijs Dekkers, Ulrich Scheurle and two anonymous referees for valuable comments.

1. Version of Record published: August 31, 2011 (version 1)

© 2011, Wagenhals

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