The assignment of the tax to a recipient

(3.50)

Similarly, when the inequality in (3.48) is fulfilled and the individual gives his or her tax to the state, , the resulting corner solution is:

(3.51)

(3.52)

In both cases religious and secular voluntary giving are lower than in the benchmark.

It should also be noted that when only one of the two sets of conditions in (3.47) and (3.48) is fulfilled, the taxpayer has the possibility to assign his or her tax to the other institution and avoid the corner solution. However, as will be shown in the next section, choosing the regular over the corner solution is not always the optimal decision. If both sets of conditions are fulfilled, one of the two corner solutions outlined above must be chosen.

3.5.2 The assignment of the tax to a recipient

The second step of the decision process is the selection of the recipient of the tax. The individual chooses the alternative that offers the highest utility. In order to calculate the utility level, I insert the optimal amounts of consumption and religious and secular giving that were calculated in the previous step into the utility function (3.35). I start again with the regular solution (no binding restriction) and go on to examine each of the possible corner solutions in turn.

3.5.2.1 No binding restrictions

If none of the restrictions concerning and is binding, the utility of the taxpayer is

(3.53)

with

(3.54)

Contrasting this utility level with the benchmark utility (3.14), the factor in the first summand of (3.53) is added. Utility strictly grows in . If either equals one, the factor disappears and the same amount of utility from charitable giving and secular consumption as in the benchmark can be reached.

In order to decide about , the individual compares the utility level for and . The two utility levels differ only in the factors and , respectively. From examining (3.53) it is clear that ( ) is chosen if . In other words, the individual chooses the alternative that best fits his or her own preferences. If and are equal, the individual is indifferent between the choice options.

Parameters determining the marginal utility of the commodities, and , do not play a role in the regular solution because by assumption distortions in the amount given are only caused by the perceived lack of fitting captured in and , not by the amount of taxes paid (which are below the amount the individual would give in the benchmark).

The individual chooses the alternative which is closest to the benchmark solution in terms of charitable contributions made and total utility, given the fitting parameters and . The chosen alternative is the one which minimizes total charitable contributions. This can easily be seen when comparing (3.41) and (3.44).

3.5.2.2 One binding restriction

If only restriction (3.47) concerning the Cobb-Douglas parameter with respect to religious giving, , is binding and the individual decides to attribute his or her tax to the church,

, the resulting level of utility is

(3.55)

Since both religious and secular non-tax giving are distorted in comparison to the benchmark, the individual arrives at a utility from charitable giving and secular consumption that is lower than in the benchmark case. If the individual instead decides to attribute his or her taxes to the state, the utility level of the regular solution (3.53) with is achieved.

In order to determine the assignment choice of the individual, one has to compare the utility from giving to the church in (3.55) to the utility from giving to the state in (3.53).

In order to choose the secular alternative, the following inequality must be fulfilled:

(3.56)

There are feasible values for and for which this inequality and the conditions for a corner solution in (3.47) are fulfilled and others for which they are not. In other words, both the corner solution and the regular solution can be optimal. In general, a low value of , i.e. a low accordance between the use of funds by the church and the individual’s preferences will induce the individual to assign his or her money to the state. In a similar fashion, a high value of will also make it more likely that the state is chosen as the receiver of the taxes. The marginal utility of secular giving, which manifests itself in , is of no importance.⁴⁵ In contrast, the marginal utility of giving to religion, , does matter. The lower , the more likely it is that the individual chooses the state. The income has no influence on the decision.

The total amount of giving is

(3.57) In contrast to the regular solution above, the chosen alternative is not necessarily the one that implies the lower amount of total giving.

Now I turn to the case where restriction (3.48) on , the marginal utility of secular giving, is binding and the individual decides to attribute his or her taxes to the state, . The resulting utility is

(3.58)

In order to see whether the individual chooses the corner or the regular solution, this utility level must be compared to utility in the unrestricted case (3.53) with . The resulting

condition for the individual to choose the religious community as the receiver of the assignment tax is

(3.59)

The total amount of giving is

(3.60) One can easily see that the condition for choosing one of the alternatives and the total amount of giving for the case with are symmetric to the solution discussed above for

, i.e. is replaced by and is replaced by . Under these premises the same discussion as in the case above applies.

3.5.2.3 Two binding restrictions

If the inequalities in (3.47) and (3.48) are both fulfilled for the individual, i.e. he or she always ends up in a corner solution independent of who receives the tax, the two possible outcomes are the two restriction cases discussed in the previous section. Whether the individual attributes the tax to the church or the state can be determined by equating

and . The result is

(3.61) Which of the two alternatives is chosen depends on both the marginal utilities of the two types of giving, and , and the individual’s opinion about the use of revenues by church and state, and . If , the church (the state) will receive the tax if . A decrease in will ceteris paribus increase the chances that the church (the state) receives the funds.

One could say that a high marginal utility of religious (secular) giving can be counteracted in the giving decision by the state’s (the church’s) use of funds for purposes that the individual highly agrees with.

Total giving in the case where both restrictions are binding is

(3.62)

This amount is higher than what the individual gives in the benchmark case without the tax, . However, the purpose that is supported by the tax receives a higher amount of money than in the benchmark, while the other cause receives less. As an example, imagine that an individual decides to attribute his or her tax to the church without making any additional voluntary contributions to the church. Total religious contributions equal , which is higher than the benchmark contribution level, . However, total contributions to secular causes amount to , which is less than benchmark contributions .

It should also be noted that choosing the alternative that provides the highest utility for the individual is not equivalent to minimizing total charitable contributions and that the total giving is independent from the fitting parameters of the two alternatives.

Several conclusions can be drawn from the discussion of the tax assignment system. First, if the government chooses a tax rate that is sufficiently high, it is possible to increase the overall amount of voluntary contributions. Nevertheless, the government should be aware that if the majority of citizens choose one of the two alternatives – say, the church – the church might end up with more donations than in the benchmark case, while secular purposes might receive even less than the benchmark amount.

Second, low fitting of the use of revenues with the preferences of individuals can also be used to increase the total amount of charitable contributions. Thus, religious organizations and the state can direct their tax revenues to causes that they consider important while expecting that each taxpayer makes some additional voluntary contributions to the causes that matter most to him or her. However, if only the church or the state lowers the fitting with individuals’

preferences, while the other institution does not, the institution with the higher fitting parameter will receive the bulk of the tax revenues. In other words, the tax assignment system encourages competition between church and state for tax revenues. Such competition is centered on the fitting parameters and (see Meuthen, 1993: 195 and sources therein).

3.5.3 The church membership decision

The decision about church membership is straightforward. The utility of membership is

decision on giving and the membership choice, just as in the voluntary giving system.

Therefore all individuals with a non-negative utility from membership are church members:

(3.63)

3.6 Discussion

3.6.1 Summary of results for religious and secular contributions The first set of research questions that this chapter tries to answer is:

Does the institutional framework affect decisions on religious and secular charitable giving?

Which are the variables that influence the decision on the amount given and the division of contributions between religious and secular beneficiaries?

The results show that the existence of taxes – church taxes and assignment taxes – can, but need not always, bias the amount of voluntary contributions and the distribution to different causes. Further, the results suggest that taxes – should they have an influence on voluntary contributions – tend to reduce the purely voluntary contributions, but increase total giving, i.e.

taxes and additional voluntary giving taken together. Two channels are identified through which church and assignment taxes can increase total giving. First, the compulsory tax amount can be higher than what the individual gives in the benchmark case, i.e. in the absence of a tax system. Second, the individual might agree with the amount of taxes he or she has to pay, but not with how these taxes are used. If the taxpayer has the impression that the causes which are most important to him or her do not benefit enough, he or she might decide to make some additional voluntary contributions.

In the voluntary giving system, the amount given by an individual positively depends on his or her income and the marginal utility of giving to each of the two types of organizations, captured by and . Since purely voluntary contributions represent the case without any institutional provisions that restrict individuals in their giving choices, I use this system as a benchmark against which I compare the church tax and the tax assignment system.

I find that in the tax systems, some additional variables affect the amount given and how giving is divided between religious and secular causes. First, the use of taxes by the organizations which receive them, captured by and ; and second, the tax rate .

In both tax systems, the benchmark outcome concerning the amount and distribution of contributions can be reached. Some preconditions need to be fulfilled. In the church tax system, one possibility is that the individual disaffiliates from the church and decides freely whether and how much to give. But even as a church member, the benchmark outcome can be reached if the individual fully agrees with the use of funds by the church, . In addition,

exceed the amount that would be giving voluntarily, . In that case, the individual completely substitutes his or her own voluntary giving for the church tax and makes additional non-tax contributions until his or her preferred level of giving is reached. Although the amount given and the distribution between religious and secular charities is the same as for non-members, the individual will prefer the membership alternative if his or her benefits from church membership, , are positive.

In the tax assignment system the benchmark solution can also be achieved if at least one of the fitting parameters is one, and/or . In addition, the tax rate must not exceed the Cobb-Douglas parameter which refers to the type of giving where the fitting is complete: if ( ) then it must be true that ( ) is greater than or equal to . The tax would then be assigned to the organization that is perceived as acting in concordance with own preferences, and additional giving is distributed such that the benchmark solution without a tax system in place is reached.

In the church tax system, giving is distorted in comparison to the voluntary giving system when the individual is a church member and church taxes are too high from the individual’s point of view, , and/or the fitting with respect to the church is not perfect, . In all these cases, total giving is higher than without the tax system in place. However, when obligatory contributions are too high or not used in accordance with preferences, additional voluntary giving is cut for both religious and secular purposes. Furthermore, the results show that in the regular solution total giving negatively depends on the fitting parameter with respect to the church, . In the corner solution, individuals do not make any voluntary contributions to the church. Their secular contributions depend on the amount of taxes they have to pay, but not on how these are used by the church.⁴⁶

46 The results reveal some similarities, but also some differences with Borgloh (2012) who develops the only theoretical model of church taxes and voluntary giving in Germany that I am aware of. Both models find that church taxes lead to a reduction in charitable contributions. This is not surprising because in both cases church taxes and charitable contributions are modeled as substitutes. However, in Borgloh (2012) the crowding-out is complete, while in my model it is not when because in that case the two types of giving are not perfect substitutes. Borgloh also distinguishes between what I call in my paper “regular” and “corner solutions”, i.e.

cases when the church member does or does not make additional religious contributions. In Borgloh’s paper the distinction is simply between individuals who donate and who do not donate because she models only one type of donation. Both models assert in their findings that a higher church tax (in my own model: church tax rate) increases the probability that individuals are in the corner solution. However, Borgloh also describes a solution where non-members do not make any charitable contributions. Such a state is impossible in my own model because in the utility function which I use the first euro of giving has infinite utility, while Borgloh assumes that the marginal utility of the first euro of giving is finite. If the marginal utility of the first euro of giving is lower than the marginal utility of the last euro of consumption, Borgloh’s model predicts non-giving non-members.

The additional findings from my own model, which cannot be deducted from Borgloh (2012), are grounded in the fact that in my model church taxes and charitable giving are not perfect substitutes: first, church taxes and

In the tax assignment system, the benchmark is not achieved when the organization that receives the tax (the state or the church) does not act completely in accordance with the preferences of the individual and/or if the tax is higher than what would be optimal for the individual. When tax rates are sufficiently low, such that the tax amount is less than what the individual gives voluntarily, the individual chooses the alternative with the better fitting.

However, when tax rates are high, the option with the best fitting might not be the one that maximizes individual utility. Imagine that the fitting parameter with respect to the church is high, but the person hardly receives any utility from religious giving, i.e. is very low. In such cases the individual might decide to attribute his or her taxes to the state, even though the state uses only a fraction of its revenues on the causes that are important to the individual.

In addition, the individual will make a voluntary charitable contribution to a secular cause that is in line with his or her preferences and a (small) religious contribution. The decision who receives the tax is completely independent from the income of the taxpayer.

In both tax systems the field of charitable activity that eventually receives the tax has higher revenues than in the benchmark case, while the other type of organization loses revenues.

While in the church tax system it is clear that churches profit and secular organizations lose revenues, it is a priori unclear which organizations profit and which lose with the tax assignment system in place.