Evaluating the Move to a Linear Tax System in Germany and Other European Countries

Abstract

This paper proposes a comparison of the results of tax policy analysis obtained on the basis of unitary and collective representations of the household. We first generate labour supplies consistent with the collective rationality, by use of a model calibrated on microdata as described in Vermeulen et al. [Collective Models of Household Labor Supply with Nonconvex Budget Sets and Nonparticipation: A Calibration Approach (2006)]. A unitary model is then estimated on these collective data and unitary and collective responses to a tax reform are compared. We focus on the introduction of linear taxation in Germany. The exercise is replicated for other European countries and other topical reforms. Distortions due to the use of a unitary model turn out to be important in predicting labour supply adjustments, in the design of tax revenue neutral reforms, and in predicting a reform’s welfare implications.

Appendices

Appendix A: Detailed description of the German tax-benefit system

Germany has a personal income tax system administered at the federal level and regulated by the Personal Income Law (Einkommensteuergesetz). The German tax system is characterized by a comprehensive tax that covers labour earnings as well as income from other sources, such as capital investment or housing rents, and by joint taxation for married couples. For our exercise we use a simplified form of the 1998 German tax-benefit system. ⁹ Gross income is the sum of income from different sources: income from employment, capital investment, rental and leasing and maintenance payments received from an ex-partner. Gross taxable income is equal to gross income minus income-related expenses. The standard deductions are listed in Table A.1.

Table A.1 Simplified tax-benefit system for household taxation, Germany 1998 singles (married couples)

The function applied to the tax base is smoothly progressive. In 1998 the top rate applied was 53% for yearly earnings in excess of DM 120,041. ¹⁰ Earnings below the basic personal allowance of DM 12,365 are tax free. The tax schedule used is the same for singles and for couples. However for couples, the ‘Ehegattensplitting’ method (marital splitting) is used: the tax rate is applied to half of the joint taxable income, and the outcome is doubled in order to obtain the total income tax liability of the spouses. Tax rate progressivity and marital splitting lead to a relative advantage for married couples if spouses have unequal incomes.

Parents can opt for either a child benefit (DM 220 for the first and the second child, DM 300 for the third and DM 350 from the fourth child on) or a child allowance, that is a lump-sum deduction of DM 6,912 for each child up to age 27, if still in education or doing military or civil service. Due to the progressive tax scheme the child benefit is less, and the tax deduction is more, favorable for high-income households.

Social benefits are means-tested and depend on the number of people in the household. ¹¹ As a simplification, we assume that the maximum social benefit (including housing benefit and special payments) a person can receive is DM 1,000 a month and DM 700 for the partner. ¹² In addition there are age-dependent supplementary payments for children. The amount of the transfer is decreasing in the level of earned income (‘anrechnungsfreies Erwerbseinkommen’). In addition, social benefits are related to the geographical location, since they are paid by the local governments and housing benefits depend on the average rent of the locality. We distinguish only between East- and West Germany, and approximate that social benefits are 10% lower in the East. The difference between East- and West Germany stems from the lower costs of living in the East as a substantial fraction of the social benefit is the housing benefit. Finally, social benefit payments depend on the wealth situation of the household, and child benefits are deducted from social benefit payments.

As a graphical illustration of the tax-benefit system described above, Fig. 5 depicts a typical situation for a couple with two children. The husband has an hourly wage rate of 25 euro, the wife earns 18 euro per hour. The household does not have any capital inflows or income from rental or leasing. It is therefore eligible for means-tested social benefits at low labour income. The parents receive child benefit for both children. From a yearly gross income of just above 80,000 euro they will opt for child allowance instead, as the tax relief exceeds the lump-sum benefit payment. Figure 5 also reveals the nonconvexity of the resulting budget constraint when labour earnings are high enough for social benefit payments to cease.

Fig. 5

The 1998 German tax-benefit system. Situation of a couple with two children. The wife and the husband earn respectively 18 and 25 euro per hour. They potentially receive means tested social benefit

Appendix B: Sample description

Table B.1 shows descriptive statistics for singles and for couples with various sociodemographic characteristics. On average, women have a lower schooling and vocational education level than men. For example 15% of the husbands in the sample have a polytechnic or university degree, but only 8% of the wives. More than half of the couples live with 1 child at most. Only few households receive housing or social benefits. Most couples have capital income.

Table B.1 Descriptive statistics on the selected samples

Appendix C: Concavity condition of the unitary utility function

The utility function is

$$\begin{aligned} U\left(c,l^{f},l^{m}\right)= \beta_{c}\ln (c-\bar{c})+\beta _{f}\ln (l^{f}-\bar{l}^{f})+\beta _{m}\ln (l^{m}-\bar{l}^{m})\\ +\delta \ln (l^{f}-\bar{l}^{f})\ln (l_{m}-\bar{l}^{m}) \end{aligned}$$

We assume that all the differences $c-\bar{c},l^{f}-\bar{l}^{f}, l_{m}-\bar{l}^{m}$ are strictly positive, as well as the coefficients β _c ,β _f and β _m . Since the gradient of U is

$$\partial U=\left[ \begin{array}{l} \frac{\beta _{c}}{c-\bar{c}}\\ \frac{1}{l^{f}-\bar{l}^{f}}\left[\beta_{f}+\delta\ln\left(l_{m}-\bar{l}^{m}\right)\right]\\ \frac{1}{l_{m}-\bar{l}^{m}}\left[\beta_{m}+\delta\ln\left(l^{f}-\bar{l}^{f}\right)\right]\\ \end{array} \right],$$

a sufficient condition for U to be increasing in its arguments is

$$\delta>\min\left\{-\frac{\beta _{f}}{\ln\left(l_{m}-\bar{l} ^{m}\right)},-\frac{\beta_{m}}{\ln\left(l^{f}-\bar{l}^{f}\right)} \right\}.$$

(C.1)

We assume that this condition is satisfied. The hessian of U is

$$ \partial^{2}U=\left[ \begin{array}{lll} -\frac{\beta_{c}}{\left(c-\bar{c}\right)^{2}}; 0\\ 0 -\frac{\beta _{f}+\delta\ln\left(l_{m}-\bar{l}^{m}\right)} {\left( l^{f}-\bar{l}^{f}\right)^{2}} \frac{\delta}{\left( l^{f}- \bar{l}^{f}\right) \left( l_{m}-\bar{l}^{m}\right)}\\ \frac{\delta}{\left( l^{f}-\bar{l}^{f}\right) \left( l^{m}- \bar{l}^{m}\right)} -\frac{\beta _{m}+\delta \ln \left( l^{f}- \bar{l}^{f}\right)}{\left( l^{m}-\bar{l}^{m}\right)^{2}}\\ \end{array} \right].$$

(C.2)

Calling A the second diagonal block, concavity of U is then equivalent with A negative, thus, given condition 5, with A>0. Thus the concavity condition is

$$\left[\beta_{f}+\delta\ln\left(l^{m}-\bar{l}^{m}\right)\right] \left[\beta _{m}+\delta\ln\left(l^{f}-\bar{l}^{f}\right)\right] >\delta^{2}.$$

(C.3)