Taxing family income: the effects on marriage and how time and resources are shared within households

Main article

In all OECD countries, the central government levies a tax on personal income, with the associated revenues constituting a very significant share of overall government revenue. There is much debate and disagreement among both policy-makers and economists about how incomes should be taxed. This is reflected in important differences in how governments tax personal income in practice. These include top marginal tax rates, how tax rates vary with income, and how the tax system treats individual versus household income. What guidance does economic theory and empirical evidence provide for how incomes should be taxed?

Taxation, labor supply, and marriage

This research is concerned with how personal income taxes and transfers should depend on family income and structure. In some countries, such as the UK, income tax is based purely on an individual’s own personal income, regardless of whether they are married or single. In this case, the income tax liability of an individual does not depend on how much (or how little) any partner earns.

In contrast, some countries, such as the United States, tax individuals based on total family income. For a married couple, this means that both spouses are necessarily subject to the same marginal tax rate. This means that if marginal tax rates are higher for those with higher income (what is known as a progressive tax system), then an individual with a high-earning spouse may face a high (in some cases, top) marginal tax rate on the first unit of income that they earn.

The way that family income is taxed may therefore be expected to have an important influence on labor supply patterns within the household. Moreover, such a joint tax system is not neutral with respect to marriage in the sense that the total tax liability of a household depends on marital status.

A couple pays a ‘marriage penalty’ if the partners pay more income tax as a married couple than they would pay as unmarried individuals. If the reverse is true, then there is said to be a ‘marriage bonus’. Because taxes change the relative desirability of being married (and to whom), the structure of taxes can also have implications for marital patterns.

Optimal design of tax schedules

Following the seminal contribution of Nobel laureate James Mirrlees (Mirrlees, 1971), a large body of theoretical research studies the ‘optimal design’ of tax schedules. In this work, there is an important trade-off between equity and efficiency considerations. The equity (or redistributive) motive means that there is a desire to redistribute income from the rich to the poor. But the ability of the government to achieve this is limited because taxes change people’s incentives to work.

In recent research (Gayle and Shephard, 2019), we study the optimal design of tax schedules in a setting where we recognize that taxes may affect the following important outcomes:

• How much time single and married people devote to work, ‘home production’ activities (such as housework or looking after children) and leisure.
• Who gets married and to whom.
• How resources within the household are shared between family members.

We first present a theory that describes how single and married people allocate their time, and how this varies with the tax system. A married couple must decide who works and how much they work, how much time each person devotes to home production from which both benefit, and how much consumption each person enjoys.

The decisions made by a married couple will depend on the characteristics and preferences of the household, the tax system (which determines how much of the consumption good can be afforded), and the ‘bargaining weight’ within the household. This bargaining weight determines the relative weight that the household places on the preferences (or ‘utility’) of the husband compared with the wife. It follows the ‘collective’ approach to household decision-making introduced by Apps and Rees (1988) and Chiappori (1988, 1992).

Importantly, we allow this bargaining weight to depend on the tax system. This means that within households, taxes have both a direct effect in terms of changing how much people work, and also in terms of changing how the household weights the preferences of the different household members.

Single people decide similarly how to allocate their time. But how does an individual decide whether to get married and to whom? In the economic approach to the family, it is recognized that there are many economic benefits to marriage. These include (but are not limited to) sharing risk, and having access to goods that both members can enjoy equally (in our analysis, this is the home-produced good). So when individuals are making their marital decisions, they are considering the economic value of both being single and different marriage pairings.

An important feature of our analysis is that the economic value of marriage will depend on the bargaining weight, which both varies across different marriage pairings and depends on the tax system. Of course, this is a remarkably unromantic view of marriage, and we therefore allow for individuals to have non-economic taste (or ‘love’) preferences for different types of spouse.

Together, we therefore have individuals making their marriage decisions based on the combined economic and non-economic values. To close the model, it is necessary to ensure that there is ‘market clearing’. In our model, we only consider marriages between men and women, so the relevant criteria is that for each ‘type’ of man and woman, the number of men who want to marry such women is equal to the number of women who want to marry such men.

This is in the spirit of the empirical matching model developed in Choo and Siow (2006). Here we show that we are able to achieve market clearing through the bargaining weight. When a type of man or woman is very desirable in the marriage market, this means that they will tend to have a relatively favorable bargaining weight. Since taxes directly affect the economic value of marriage and being single, taxes can also change the bargaining weight in marriage.

Patterns of US labor supply and marriage

We use the United States as the empirical environment for our study, analyzing data from the American Community Survey and American Time Use Survey. Before we address the question of optimal taxation design, we first estimate our model to obtain parameters that provide the best fit with the data.

We show that we are able to explain patterns of labor supply and marriage both in the United States overall, and across different states (where population characteristics and tax systems differ). We use the model to calculate various labor supply and marriage ‘elasticities’, and show that these are consistent with the findings from the voluminous body of empirical research.

In an exercise similar to that in Blundell and Shephard (2012), we then use our estimated model to explore optimal design problems. In the most general form, we allow the tax authorities simultaneously to choose a tax schedule for single individuals (which depends on their labor income), and a tax schedule for married couples that may depend on the labor income of both family members in a very general way.

Completely independent taxation or fully joint taxation are special cases of our general specification. We adopt a ‘welfarist’ approach where the challenge for the government concerns the choice of these tax schedules so as to maximize some ‘social welfare’ function subject to the government raising some amount of revenue from taxation (to finance schools, roads, healthcare, etc.).

The social welfare function that we consider depends on individual utilities (describing how well-off individuals are) for all individuals in the economy, whether married or single, and we allow for different strengths of redistributive concern.

In choosing taxes, the government recognizes that taxes operate through the following channels:

• First, taxes affect the consumption goods that a household can afford and so directly affect the wellbeing of individuals.
• Second, by changing the returns to work, taxes influence how hard individuals and families wish to work.
• Third, since changes in taxes may have a differential impact on the economic value of being single and of being in different marriage pairings, taxes can affect both the marriage decision and who marries whom.

While the first two points have been studied extensively, the third point is novel to our study. Note that given that we require that the marriage market clears, there will be adjustments in the household bargaining weight as taxes are varied such that taxes affect inequality within the household.

The optimal tax schedule for married couples

The optimal tax schedule for married couples is characterized by ‘negative tax jointness’. This is consistent with a theoretical result in Kleven et al (2009), which does not consider either marriage responses or inequality within households.

Jointness refers to how the marginal tax rate of an individual varies with the earnings of their spouse. In the case of independent taxation, jointness is zero. Similarly, in the case of a progressive fully joint tax system (where the couple is taxed based on combined income), there is positive jointness (as both spouses face the same marginal tax rate).

Negative jointness, obtained here as an empirical result, means that the marginal tax rate of an individual is lower when the earnings of their spouse are higher. This is illustrated in Figure 1, which presents an optimal tax schedule under specific assumptions about the redistributive concerns of the government.

The figure shows how the implied optimal marginal tax rate of an individual depends on an individual’s own earnings and the earnings of their spouse. Conditional on spousal earnings, marginal tax rates are broadly increasing in income. But these marginal tax rates tend to be lower in cases when spousal earnings are higher. This same negative jointness property is robust to a range of assumptions about the strength of redistributive concerns.

While this is a curious result, Immervoll et al (2009) document that the combined tax and transfer system in many European countries is characterized by negative jointness. This emerges as many countries have an independent income tax system, but transfer (or welfare) programs that depend on combined family income. Thus, individuals with a low-earning spouse can face a much higher effective marginal tax rate as they are subject to the withdrawal of the means-tested transfer program. The desirability of negative jointness in Kleven et al (2009) arises because of redistributive concerns, meaning that the government values giving a unit of income more to a poorer family than it does a richer one.

To understand this result, consider a simplified version of their model where earnings can be either high or low. Starting with an independent tax system, the benefit of a transfer from a couple where the husband has low earnings and the wife has high earnings (a low-high couple) to a low-low couple will exceed the cost of an equal-sized transfer from a high-low to high-high couple. By changing taxes in this way, which by design is introducing a small amount of negative tax jointness, social welfare will increase.

While our model departs from the setting in Kleven et al (2009) in important ways, our quantitative analysis suggests that this negative jointness property is somewhat more general.

The importance of negative jointness depends on the economic environment

While we find empirical support for negative tax jointness, it is also important to ask how valuable it is. A natural way to answer this question is to ask how much better the government is able to do by introducing this tax jointness relative to a system with none (independent taxation).

In our main results, we show that this gain is relatively modest, and that it increases as we allow the government to have greater redistributive concerns. This is natural as the argument for negative jointness relies on a redistributive motive.

Indeed, relative to what Figure 1 shows, as redistributive concerns increase, the difference between marginal tax rates as spousal earnings are varied also increases. In addition, we are able to relate the size of the social welfare gain to features of the economy, which helps us to understand situations where allowing for tax jointness may potentially be more or less important.

We explore implications of the difference between men and women’s earnings, often referred to as the ‘gender wage gap’. To understand the relevance of this, note that if men and women were identical in their preferences and earnings ability, then the optimal independent tax system (that is, with zero tax jointness) would also be identical.

But if there are important differences in wages or other characteristics, then the optimal independent tax system would also look very different. If such differential taxation is not possible, then it suggests that there could be an important role for introducing jointness into the tax system.

As a quantitative exercise, we explore the implications of accentuating the difference between spouses by increasing the gender wage gap. As a result of this change, we show that the degree of tax jointness increases, and so too does the associated welfare gain relative to a system of independent taxation. This finding suggests that the gain from tax jointness would have been much larger in the late 1970s (where the gender wage gap was very substantial) than it is today.

We also show that the size of the gender wage gap has important implications for how single individuals are taxed. This is true both because the structure of wages has changed (which is the usual channel) and because taxation provides a useful instrument to address inequality within households.

To understand this last point, note that the bargaining weight in marriage directly depends on how well-off an individual is when single. Thus, if an individual has poor opportunities outside marriage, they will tend to receive a less favorable bargaining weight within marriage. Taxing single individuals more heavily therefore creates a way of reducing the differences between single men and women, which translates into less pronounced differences in the bargaining weight.

The marriage market matters

We explore the importance of the marriage market by considering an alternative environment in which marriage decisions and the bargaining weight within marriage are fixed. We otherwise solve the government’s problem as before, obtaining a system of tax schedules. We then ask how much better the government can do if it explicitly recognizes how taxes affect marriage outcomes.

The answer to this question depends on the set of tax instruments that the government is using. In the case where the tax system is allowed or restricted to be relatively neutral with respect to marriage (for example, independent income taxation) then the cost of neglecting marriage market considerations is somewhat small.

But in cases where the form of the tax system is restricted such that it implies strong non-neutralities (as in completely joint taxation, for example), then the cost of ignoring marriage market responses can become very sizeable.

Gendered taxation can be a useful tax instrument

Prior to Kleven et al (2009), the majority of studies of taxation of couples considered the case of a linearly separable tax system. This means that under such a tax system, the husband and wife are subject to distinct, but constant, marginal tax rates (see for example, Boskin and Sheshinski, 1983).

While there is important variation over time and across countries, a very frequent empirical finding is that the labor supply of women is more responsive to taxes (they have a higher labor supply elasticity) than it is for men.

It then follows that by imposing distinct tax rates by gender (also referred to as ‘tagging’), the government is able to achieve a given level of redistribution at a lower efficiency cost. While this effect is still present in our setting, marriage market considerations also provide a way to address inequality within households.

We find that the bargaining weight typically favors the husband more than the wife. Now, consider the following. Suppose we start from a tax system that does not depend on gender, and that we now tax single men at a high tax rate. This decreases the economic value of being a single man, and so more men would prefer to marry. The only way that this is consistent with our notion of market clearing is if the bargaining weight of women increases. Thus, gendered taxation can affect inequality within households, and we show this effect to be quantitatively important.

Finally, note that while governments do not literally condition taxes by gender in this way, many countries do have transfer programs and tax credits that are only available (or available with greater generosity) to single parents (who are predominantly women).

 

This article summarizes ‘Optimal Taxation, Marriage, Home Production, and Family Labor Supply’ by George‐Levi Gayle and Andrew Shephard, published in Econometrica in 2019.

George-Levi Gayle is at the Washington University in St. Louis. Andrew Shephard is at the University of Pennsylvania.