## Abstract

In this paper, I explore the optimal taxation of singles and couples in an economy with bargaining couples. The government is concerned with the redistribution of income from individuals with high utility to individuals with low utility, recognizing that some individuals live in couple households where resources are unevenly distributed. I analyze how redistributive linear income taxes, which depend on either gender or household composition (or both) impact the distribution of utility within and across households. An interesting implication arising from the interaction between the model elements is that even though between-group lump-sum transfers always favor women, when the bargaining power of men is high, women are subject to a higher tax rate; this in contrast to previous analyses of gender-based taxation. My quantitative analysis demonstrates that the welfare effects of gender-based taxation are sizable and even larger when taxes depend on the composition of the household.

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## Notes

- 1.
Bergstrom (1996) calls this the “harsh words and burnt toast” equilibrium.

- 2.
In contrast, due to the setup of their model, Alesina et al. (2011) only analyze the role of differentiated marginal tax rates.

- 3.
- 4.
In the paper I use the words ‘couple’ or ‘married’ interchangeably. When referring to the members of a couple, I sometimes use the words ‘husband’ and ‘wife’ or ‘spouse.’

- 5.
Keep in mind that

*w*_{ im }≠*w*_{ if }reflects that*i*is an index describing an individual’s*relative*position in the productivity distribution pertaining to his/her gender. - 6.
The matching process has potentially interesting implications for income taxation. Perfect assortative matching seems however a reasonable benchmark. In the quantitative section, I mimic a situation with positive matching by scaling up the wages of all men by a given constant.

- 7.
The primary focus in this paper is on average behavior, hence the exclusion of the extensive margin of labor supply is inessential.

- 8.
As in Apps and Rees (1997), only time enters as an input to the household production. Introducing also consumption goods in the production process would only complicate the analysis with no substance for the results.

- 9.
In order to obtain closed-form expressions for the effects of taxes on the utility of members of couple households, it is necessary to abstract from income effects on labor supply. In the quantitative part of the paper the quasi-linearity assumption is relaxed.

- 10.
If

*z*=1 the market good would be ‘purely private’ and if*z*=2 the good would be ‘purely public.’ This is a reduced-form approach. Manser and Brown (1980) explicitly introduce both private and public market goods. In their model, “love or companionship” amplifies the utility gains from private consumption in a similar fashion. - 11.
- 12.
Notably, Nash-bargaining assumes efficiency. When

*γ*≠1/2, this is referred to as the generalized Nash-bargaining problem which does not satisfy the axiom of symmetry. Concave utility over contracts guarantees that the set of feasible utility possibilities (*U*_{ m },*U*_{ f }) is convex and the Nash-product is quasi-concave. An alternative solution concept is the Kalai–Smorodinski (KS) bargaining solution. While Nash-bargaining requires that the utility possibilities set is convex, KS requires only that it is comprehensive. However, the KS solution does not satisfy ‘independence of irrelevant alternatives’ which is a desirable property of the Nash-bargaining solution. - 13.
I assume the surplus within marriage is sufficiently large so that the participation constraints are satisfied.

- 14.
The introduction of non-income characteristics is an important source of nonlinearity in actual tax-benefit schemes. According to Peichl (2012), a significant fraction of the variation in taxes among EU countries is explained by non-income characteristics.

- 15.
Analogously, a $1 reduction in the income of the family will only reduce the utility of the wife by $(1−

*γ*). - 16.
Recall that the total population size is normalized to 1 and there is an equal mass of men and women in the population.

- 17.
Remember that I am considering the case where utility is quasi-linear in consumption so that there are no income effects on labor supply.

- 18.
The use of statistical operators in this fashion has become a standard way of expressing averages in the linear income tax literature.

- 19.
For instance, assuming quasi-linear utility, Boadway and Pestieau (2006) show in the context of a discrete-type optimal income tax model that the tax system will be more redistributive in the tagged group that has a higher proportion of high-ability persons. In a model with a continuum of types, also assuming quasi-linear utility, Cremer et al. (2010) show that if the skill distribution in one group first-order stochastically dominates the other, tagging calls for redistribution from the former to the latter group.

- 20.
This can be proved by starting from a situation

*G*_{ m }=*G*_{ f }and considering a small increase in*G*_{ f }combined with a small reduction in*G*_{ m }which yields a strict improvement in the social welfare function (assuming no wealth effects on labor supply). - 21.
In the data, the inequality in wages between men and women rises with income.

- 22.
The matching process determines the wage rates in the couple (

*w*_{ im },*w*_{ if }). Because \(w_{im}^{s}=w_{im}\) and \(w_{if}^{s}=w_{if}\), the matching process influences the income distance \(| y_{im}^{s}-y_{if}^{s} |\). - 23.
In contrast, the social marginal utility in Boskin and Sheshinski (1983) arises from the unitary model where the allocation within the household exactly conforms with the weights attached by the social planner.

- 24.
To simplify the exposition, I abstract from the parameter

*χ*in the derivations below. - 25.
That is, \(\frac{1}{\beta}=d\log ( \frac{c_{f}+H}{c_{m}+H} ) / d \log\varPsi _{f} \).

- 26.
The presence of

*Ψ*_{ f }does not mean that the utility of the female enters the utility function of the male, but is simply a requirement of the cooperative solution. - 27.
That this holds also in the presence of income effects is a consequence of the household good and market good being perfect substitutes.

- 28.
It should be noted, however, that cooperative and non-cooperative models will produce the same outcomes when the household production technology is separable and there are no externalities.

- 29.
This assumption serves mainly to sharpen the results. Degrees of ‘caring preferences’ can easily be introduced. In reality, most households probably lie somewhere between the fully cooperative and non-cooperative solution. See Cherchye et al. (2011) for an interesting attempt to estimate the degree of caring inside households.

- 30.
Data has been combined from three sources: ‘Flergenerationsregistret,’ ‘Louise-databasen’ and ‘Lönestrukturstatistiken.’ These statistics cover men and women working in the private and public sector. The original data set includes 1 457 931 wages for women and 1 519 921 wages for men. The gender wage-gap is not constant across ages, hence in reality it might be desirable to make a gender-based tax age-dependent.

- 31.
The wage distributions are approximated using quantiles. The person with the lowest productivity is represented by the 2nd percentile wage rate, the second lowest by the 4th, and so forth up until the 98th percentile. The highest productivity type is associated with the wage rate corresponding to the 99th percentile. This gives a total of 50 taxpayer types. The implied gender wage-gap is around 7 %.

- 32.
These authors note that a substantial literature uses a baseline value of 3 for this coefficient (Hubbard, Skinner, and Zeldes, 1995; Engen, Gale, and Uccello, 1999; Mitchell et al., 1999; Scholz, Seshadri, and Khitatrakun, 2003; and Davis, Kubler, and Willen, 2006). The reader is referred to the references in Einav et al. (2010).

- 33.
The parameter choices are:

*α*^{c}=*α*^{s}=0.6, \(\omega^{c} = \overline{\omega}\), \(\omega^{s} = 0.7\overline{\omega}\), where \(\overline{\omega}=w_{30}/2\) and*w*_{30}is the 30:th percentile of the wage distribution for men. - 34.
Formally, the objective is expressed as \(\sum_{ijk} \pi_{ij}^{k}\rho^{i} V_{ij}^{k}\), where

*ρ*^{i}is the Pareto weight on an individual of type (*i*,*j*,*k*). Note that the same weight*ρ*^{i}applies to all individuals of type*i*, regardless of gender (*j*) and marital status (*k*). - 35.
According to the U.S. Census Bureau, around 57 % of the US population reported in 2000 that they were living with a partner. According to Statistics Sweden there were in Sweden 1 547 000 cohabiting couples (with and without children) and 1 478 000 singles in ages 18–64 in 2009. Hence as a rough estimate I choose

*η*=1/2. - 36.
Note that in the case with divorce-threat points, except in the case where taxes explicitly depend on marriage-status, the demogrant

*G*on couples is always restricted to be the sum of the (single) male and female demogrants. This is because with external threat points, the identity of the individual in the couple receiving the transfer is irrelevant for the intra-household distribution. - 37.
These welfare gains are obtained with the benchmark value

*x*=0.25. I have also performed some sensitivity analysis with respect to the inequality aversion parameter*x*. Higher welfare gains are obtained for a purely utilitarian planner (*x*=0); the welfare gains are 1.59, 1.93 and 2.49 %; lower welfare gains of gender-based taxes are obtained when*x*=1, in this case the welfare gains are 0.32, 1.50 and 2.04 %. In general, the welfare gains of gender-based taxes tend to become smaller as the government becomes relatively more averse to across-household inequality as compared to within-household inequality. - 38.
This reversal of the GBT result also holds true in the model with non-cooperative threat points as

*γ*is increased. - 39.
To understand this, note that when

*γ*=0.5, intra-household inequality is driven by the difference \(y_{im}^{s}-y_{if}^{s}\) which is largest at high income levels. Changing*γ*to 0.75 introduces intra-household inequality equally at each income level. - 40.
Note though that this result depends on the assumption that the bargaining power

*γ*does not affect the benefit each spouse receives from household public goods. - 41.
This can alternatively be interpreted as a rough way of increasing the degree of assortative matching.

- 42.
This reflects that households which are not cooperating cannot reap the benefits of economies of scale in market consumption. However, non-cooperating couples still benefit from the household public good to which they voluntarily contribute. Remember that it is only the threat points which are determined by the inefficient equilibria. The allocation within the couple is still fully efficient.

- 43.
In countries where the effective marginal tax rate contains a social security payroll tax component, if evaluated net of the present actuarial value of future retirement benefits, marginal tax rates are lower for women on average because of their longer life expectancy.

- 44.
Anderberg (2008) surveys the literature and reports that it has found only modest effects of taxes on marriage. Gruber (2004) studies the effect of relaxing divorce law on children’s outcomes and argues convincingly that these effects are more likely to have been obtained through a change in the behavior of families that remain intact rather than through increased incidence of divorce. The current model can be rationalized with an economy where there are people who simply prefer to stay single, are unable to find a spouse (due to high search costs) or simply are unable to cooperate successfully within a couple household. Similarly, couples can be thought of as having made sunk, relationship-specific investments (such as emotional investments) or made joint financial investments in housing.

- 45.
Of course, children might affect the labor supply behavior of couples in many ways, for instance the symmetric home-goods productivity assumption might no longer be as plausible, possibly strengthening the argument for gender-based taxes.

## References

Alesina, A., Ichino, A., & Karabarbounis, L. (2011). Gender-based taxation and the division of family chores.

*American Economic Journal: Economic Policy*,*3*(2), 1–40.Anderberg, D. (2008). Tax credits income support, and couple decisions.

*International Tax and Public Finance*,*15*, 499–526.Apps, P. F., & Rees, R. (1997). Collective labor supply and household production.

*Journal of Political Economy*,*105*(1), 178–190.Apps, P. F., & Rees, R. (2011). Optimal taxation and tax reform for two-earner households.

*CESifo Economic Studies*,*57*, 283–304.Atkinson, A. B., & Stiglitz, J. (1980).

*Lectures in public economics*. New York: McGraw-Hill.Bastani, S., Blomquist, S., & Micheletto, L. (2013). The welfare gains of age-related optimal income taxation.

*International Economic Review*(forthcoming).Bergstrom, T. C. (1996). Economics in a family way.

*Journal of Economic Literature*,*34*(4), 1903–1934.Blomquist, S., & Micheletto, L. (2008). Age-related optimal income taxation.

*Scandinavian Journal of Economics*,*110*(1), 45–71.Blundell, R., & MaCurdy, T. (1999). Labor supply: a review of alternative approaches. In O. Ashenfelter & D. Card (Eds.),

*Handbook of labor economics*, Amsterdam: Elsevier.Blundell, R., & Shephard, A. (2012). Employment, hours of work and the optimal taxation of low income families.

*Review of Economic Studies*,*79*(2), 481–510.Boadway, R., & Pestieau, P. (2006). Tagging and redistributive taxation.

*Annales d’Économie et de Statistique*,*83–84*, 123–147.Boskin, M. J., & Sheshinski, E. (1983). Optimal tax treatment of the family: married couples.

*Journal of Public Economics*,*20*, 281–297.Brett, C. (2007). Optimal nonlinear taxes for families.

*International Tax and Public Finance*,*14*(3), 225–261.Browning, M., Chiappori, P. A., & Lewbel, A. (2004).

*Estimating consumption economies of scale, adult equivalence scales, and household bargaining power*. Working paper 588, Boston College.Cherchye, L., Muynck, T. D., & DeRock, B. (2011).

*Noncooperative household consumption with caring*. Working paper, Tilburg University.Chiappori, P.-A. D. (2009).

*Non-unitary models of household behavior: a survey of the literature*. IZA discussion paper 4603, Institute for the Study of Labor (IZA).Cremer, H., Gahvari, F., & Lozachmeur, J. M. (2010). Tagging and income taxation: theory and an application.

*American Economic Journal: Economic Policy*,*2*(1), 31–50.Einav, L., Finkelstein, A., & Schrimpf, P. (2010). Optimal mandates and the welfare cost of asymmetric information: evidence from the U.K. annuity market.

*Econometrica*,*78*, 1031–1092.Gronau, R. (1977). Leisure, home production and work—the theory of the allocation of time revisited.

*Journal of Political Economy*,*85*, 1099–1123.Gruber, J. (2004). Is making divorce easier bad for children? The long-run implications of unilateral divorce.

*Journal of Labor Economics*,*22*(4), 799–833.Immonen, R., Kanbur, R., Keen, M., & Tuomala, M. (1998). Tagging and taxing: the use of categorical and income information in designing tax/transfer schemes.

*Economica*,*65*, 179–192.Kleven, H. J., Kreiner, C. T., & Saez, E. (2009). The optimal income taxation of couples.

*Econometrica*,*77*(2), 537–560.Lewbel, A., & Pendakur, K. (2008). Estimation of collective household models with Engel curves.

*Journal of Econometrics*,*147*(2), 350–358.Lise, J., & Seitz, S. (2011). Consumption inequality and intra-household allocations.

*Review of Economic Studies*,*78*, 328–355.Lundberg, S. J., & Pollak, R. A. (1993). Separate spheres bargaining and the marriage market.

*Journal of Political Economy*,*101*, 988–1010.Lundberg, S. J., & Pollak, R. A. (1996). Bargaining and distribution in marriage.

*The Journal of Economic Perspectives*,*10*, 139–158.Mankiw, N. G., & Weinzierl, M. (2010). The optimal taxation of height: a case study of utilitarian income redistribution.

*American Economic Journal: Economic Policy*,*2*(1), 155–176.Manser, M., & Brown, M. (1980). Marriage and household decision-making: a bargaining analysis.

*International Economic Review*,*21*, 31–44.McElroy, M. B., & Horney, M. J. (1981). Nash-bargained household decisions: toward a generalization of the theory of demand.

*International Economic Review*,*22*, 333–349.Muthoo, A. (1999).

*Bargaining theory with applications*. Cambridge: Cambridge University Press.Peichl, A. (2012).

*The world is flat: existing tax benefit systems approximate a linear one*. Mimeo.Rosen, H. S. (1977). Is it time to abandon joint filing?

*National Tax Journal*,*30*(4), 423–428.Saez, E. (2001). Using elasticities to derive optimal income tax rates.

*Review of Economic Studies*,*68*, 205–229.Sheshinski, E. (1972). The optimal linear income tax.

*Review of Economic Studies*,*39*, 297–302.Stern, N. H. (1976). On the specification of models of optimum income taxation.

*Journal of Public Economics*,*6*, 123–162.Viard, A. D. (2001). Optimal categorical transfer payments: the welfare economics of limited lump-sum redistribution.

*Journal of Public Economic Theory*,*3*(4), 483–500.Weinzierl, M. C. (2011). The surprising power of age-dependent taxes.

*Review of Economic Studies*,*78*(4), 1490–1518.

## Acknowledgements

I am grateful to Dan Anderberg, Ted Bergstrom, Sören Blomquist, Robin Boadway, John Conley, Vidar Christiansen, Luca Micheletto, Eva Mörk, Katarina Nordblom, Ray Rees, Casey Rothschild, Håkan Selin and Laurent Simula, as well as seminar participants in Uppsala and Oslo, and at the IIPF Conference in Dresden and the NTA Conference in Providence for helpful comments and suggestions. Financial support from Riksbankens Jubileumsfond and the Jan Wallander and Tom Hedelius Foundation is gratefully acknowledged.

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Bastani, S. Gender-based and couple-based taxation.
*Int Tax Public Finance* **20, **653–686 (2013). https://doi.org/10.1007/s10797-013-9285-9

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### Keywords

- Optimal taxation
- Tagging
- Intra-household bargaining

### JEL Classification

- H21
- D13
- J16