10 August 2022
AperTO - Archivio Istituzionale Open Access dell'Università di Torino
Original Citation:
Using a Microeconometric Model of Household Labour Supply to Design Optimal Income Taxes
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DOI:10.1111/sjoe.12015
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1
Using a Microeconometric Model of Household Labour Supply
to Design Optimal Income Taxes*
Rolf Aaberge
°
and Ugo Colombino
#
Abstract
Empirical applications of optimal taxation theory have typically adopted analytical expressions for the optimal
taxes and then imputed numerical values to their parameters by calibration or using previous estimates. We aim
at avoiding the restrictive assumptions and the possible inconsistencies of that approach. By contrast, we
identify optimal taxes by iteratively running a microeconometric model based on 1994 Norwegian data until a
given social welfare function is maximized given the public budget constraint. The optimal rules envisage
monotonically increasing marginal rates (negative on very low incomes) and – compared to the current rule – a
lower average rate, lower marginal rates on low incomes and higher marginal rates on very high incomes.
Keywords: Optimal taxation, Microsimulation, Random Utility Model.
JEL classification: H21, H31, J22.
* We thank Tom Wennemo for skilful programming assistance and a referee for very detailed and
useful comments and suggestions. Ugo Colombino received financial support from the Italian
Ministry of University and Research and the Compagnia di San Paolo. ICER is gratefully
acknowledged for providing financial support and excellent working conditions for Rolf Aaberge.
°Rolf Aaberge, Research Department, Statistics Norway, Oslo, Norway, rolf.aaberge@ssb.no.
#
Ugo Colombino, Department of Economics “Cognetti De Martiis”, University of Torino, Italy,
ugo.colombino@unito.it
2
I. Introduction
This paper presents an empirical analysis of optimal income taxation. The purpose is not new, but the
exercise illustrated here differs in many important ways from previous attempts to empirically
compute optimal taxes. The standard procedure adopted in the literature starts with some version of
the optimal taxation framework originally set up in the seminal paper by Mirrlees (1971). The next
step typically consists of imputing numerical values – either determined by calibration or taken from
previous empirical analysis – to the parameters (e.g. wage elasticities of labour supply) appearing in
the formulas produced by the theory. This literature is surveyed by Tuomala (1990). A recent strand of
research adopts a similar approach to address the inverse optimal taxation problem, i.e. retrieving the
social welfare function that makes optimal a given tax rule (Bourguignon and Spadaro, 2005). There
are two main problems with the optimal taxation literature: 1) The theoretical results become
amenable to an operational interpretation only by adopting rather restrictive assumptions concerning
the preferences, the composition of the population and the structure of the tax rule; 2) The empirical
measures used as counterparts of the theoretical concepts are usually derived from previous estimates
obtained under assumptions different from those used in the theoretical model. As a consequence the
consistency between the theoretical model and the empirical measures is dubious and the significance
of the numerical results remains uncertain. The typical outcome of these exercises envisages a lump-
sum transfer which is progressively taxed away by very high marginal tax rates (MTRs) on lower
incomes (i.e. a negative income tax mechanism). Beyond the “break-even point” (i.e. the income level
where the transfer is completely exhausted), the MTRs are close to constant. Tuomala (2010) suggests,
however, that these results are essentially forced by the restrictive assumptions made upon
preferences, labour supply elasticities and distribution of productivities (or wage rates). Interestingly,
when Tuomala (2010) adopts a more flexible specification of the utility function he finds that the
optimal system is progressive with monotonically increasing MTRs.
3
While most of the studies mentioned above were essentially illustrative numerical exercises,
several recent contributions have attempted to use optimal taxation results in the empirical evaluation
or design of tax-transfer reforms. Diamond (1980, 1998), Revesz (1989) and Saez (2001) make
Mirrlees’s results more easily interpretable by reformulating them in terms of labour (or income)
supply elasticities in order to provide a direct link between theoretical results and empirical measures.
Saez (2002) develops a model amenable to empirical implementation that focuses on the relative
magnitude of the labour supply elasticities at the extensive and intensive margin. Immervoll et al.
(2007) adopt Saez’s (2002) approach to evaluate alternative income support policies in European
countries. Blundell et al. (2009) and Haan and Wrohlich (2010) also use Saez (2002) to evaluate taxes
and transfers for lone mothers in Germany and UK, whereas Kleven et al. (2009) provide results on
the taxation of couples. Although these new contributions are interesting attempts to advance towards
the empirical implementation of theoretical optimal taxation results, they still rely on restrictive
assumptions and suffer from a possible inconsistency between the theoretical model and the empirical
measures used to implement it. For example, the basic version (adopted in the empirical exercises
mentioned above) of the model proposed by Saez (2002) does not account for income effects
1
and
moreover relies on rather restrictive assumptions upon the way the households respond to changes in
the relative attractiveness of the opportunities in the budget set.
2
When it comes to empirical
applications (as in Immervoll et al. (2007), Blundell et al. (2009) and Haan and Wrohlich (2010)), the
parameters of the theoretical models are given numerical values estimated with microeconometric
models that do not adopt the same restrictive assumptions as Saez (2002). Of course, some of those
limitations and potential inconsistencies might be overcome in the future, but analytical solutions of
the optimal income taxation problem will likely never be fully consistent with flexible structural
labour supply models. We follow here a different and possibly complementary approach. We do not
start from theoretical results dictating conditions for optimal tax rules under various assumptions.
1
Income effects can be accounted for, as in Saez (2001), at the cost of notable analytical and computational complications.
2
In Saez (2002) each individual has only three opportunities to choose from: non-participation and two adjacent labour
income brackets.
4
Instead we use a microeconometric model of labour supply in order to identify by simulation the tax
rule that maximizes a social welfare function under the constraints that the households maximize their
own utility and the total net tax revenue remains constant. The microeconometric simulation approach
is common in evaluating tax reforms, but has not been much used in empirical optimal taxation
studies. The closest examples adopting a similar approach are represented by Fortin et al. (1993),
Aaberge and Colombino (2006), Colombino et al. (2010) and Blundell and Shephard (2011).
3
Analytical solutions are still crucial for understanding the “grammar” of the problem and for
suggesting promising directions of reform. By contrast, microeconometric models and computational
solutions allow for the introduction of less restrictive specifications of preferences and opportunity
sets and the evaluation of more complex tax-transfer rules. The estimated model we use here
represents the choices of both couples and singles, it adopts a flexible specification of the preferences,
it accounts for quantity constraints in labour supply choices and it can accommodate a detailed
representation of complex tax-transfer systems. The optimal tax rules turn out to envisage an average
tax rate lower than the current one, a modest lump sum tax (interpretable as a property tax), a negative
tax on low incomes (close to mechanisms such as the Earned Income Tax Credit or the In-Work
Benefit policies) and a progressive MTR profile culminating to a 100 per cent MRT on very high
incomes (about 1.5 per cent of the sample). This scenario contrasts sharply with respect to the results
obtained by the numerical exercises inspired by the seminal contribution of Mirrlees (1971). It is
closer to the picture that typically comes out of empirical applications adopting the theoretical results
of Saez (2002). However, using a flexible microeconometric model as a computational tool, we are
able to explore a larger variety of tax-transfer rules and to perform a more articulated analysis of the
effects of the various rules upon different segments of the population. Obviously, the results of our
computational exercise cannot claim similar generality as the analytical solutions. While the latter
3
Fortin et al. (1993) use a calibrated (not estimated) model with rather restrictive (Stone-Geary) preferences and focus on
alternative income support schemes rather than on the whole tax rule. Aaberge and Colombino (2006) report on preliminary
results of a simpler version of the exercise illustrated in this paper. Colombino et al. (2010) analyse basic income support
mechanisms in some European countries. Blundell and Shephard (2011) identify the optimal design of a specific UK policy
addressed to low income families with children. They do not treat the problem of interpersonal comparability, which,
however, in their case might be less important given the smaller and less heterogeneous target population.
