Marginal Cost of Public Funds: from the theory to the empirical application for
the evaluation of the efficiency of the tax-benefit systems
Francesco Figaria, Luca Gandulliab, Emanuela Lezzia,b
a
University of Insubria, b University of Genova
Abstract
The measurement of efficiency of the tax-benefit systems is often limited to proxies as individual work
incentive indicators or labour supply elasticities. In our work, we estimate the Marginal Cost of Public Funds
(MCF) as an overall indicator of efficiency of tax-benefit systems and reforms. The marginal cost of public
funds is the marginal welfare cost for the government of raising revenue by distortionary taxes popolarised in
the theoretical optimal taxation literature. The novelty of our work is the calculation of the MCF indicator fully
based on empirical micro data representative of the population. This indicator combines both changes in labour
force participation (extensive elasticities) and hour-of-work labour supply elasticities depending on working
(intensive elasticities) with the incentives embodied in the tax benefit system at the intensive (effective
marginal tax rates) and extensive margin (participation tax rates). Our results, related to the Italian case,
show first the importance of taking into account the heterogeneity of the population with the second earners,
usually women (both single or in couple), facing a more inefficient system compared to the first
earner. Second, our micro-data based indicator shows the potential bias of MCF indicators based on stylised
and hypothetical measures of work incentives, as usually adopted in the theoretical optimal taxation literature,
given that the variations due to the assumptions related to elasticities and effective tax rates explain a large
part of the indicator itself.
Keywords: Marginal welfare cost, labour supply, tax-benefit system, microsimulation
JEL classification: H21, H41, H20
Pag. 1 a 32
1. Introduction
Economists have long been concerned with finding the optimal level of government spending. The
classic formulation of the problem was given by Samuelson (1954) who assumed that the government
is financed entirely by lump-sum taxes and not by distortionary taxes. In early theoretical
contributions, Stiglitz and Dasgupta (1971) and Atkinson and Stern (1974) demonstrated that the
Samuelson rule for the optimal provision of public goods needs to be modified to account for tax
distortions (Ballard and Fullerton, 1992). Even before Samuelson’s paper, Pigou (1947) pointed out that
public expenditure is usually financed through non neutral taxes that causing distortions in the
allocation of resources impose “indirect damage on the taxpayers … over and above the loss they
suffer in actual money payment”. Harberger (1964) provided formulas to measure the “excess
burden” caused by distortionary taxes instead of lum-sum taxes. In this perspective, the most
prominent calculations of marginal welfare cost of raising revenue by distortionary taxes are those of
Browning (1976 and 1987) for taxes on labor income in the United States. Browning labelled the
welfare cost of taxation as the “marginal cost of public funds” (MCF), defined as the direct tax burden
plus the marginal welfare cost produced in raising the tax revenue. The literature that followed the
contribution by Browning debates the relative merits of many different measures of excess burden of
taxation and of the additional excess burden per marginal dollar of revenue (see for instance Auerbach
and Rosen, 1980). However, much of this literature is fragmented because authors have used different
measures for MCF, based on different assumptions about the nature of government spending, the type
of tax used to finance the government expenditure and labour market behaviour (Dahlby, 2008;
Hansson, 1984).
Notwithstanding such enhancements in the literature, in the empirical evaluation of taxbenefit systems and their reforms the measurement of efficiency is very much limited to proxies as
static individual work incentive indicators (Jara and Tumino 2013) or labour supply elasticities
(Bargain et al. 2014). The substantial theoretical literature on the concept of the marginal cost of
public funds has not been followed by enhancements of its empirical measurement. However, the
marginal cost of public funds has recently attracted a great deal of interest from policy makers who
have begun to think of it as a practical tool for measuring the efficiency costs of a given tax instrument
or tax reform due to the associated indirect distortionary effects in addition the direct effect of the tax
increase. Although different empirical approaches have been proposed they do not take fully into
account the heterogeneity of the population of interest.
The aim of this paper is to fill this gap by implementing a marginal cost of public funds
indicator fully based on empirical micro data representative of the Italian national population and
Pag. 2 a 32
taking into account the details of the tax-benefit system by using EUROMOD, the EU-wide fiscal
microsimulation model (Sutherland and Figari, 2013). In order to do so, we make use of the analytical
measure of the marginal cost of public funds derived by Kleven and Kreiner (2006) who assume a
range of stylised and hypothetical values for the parameters involved in the calculation of the marginal
cost of public funds. In order to take into account the heterogeneity in household characteristics and
budget constraints, we exploit fiscal microsimulation techniques (Figari et al. 2015) which apply
detailed tax-benefit policy rules to a representative sample of households, using survey or register
information on household characteristics and market income as input. The first-order impact of taxbenefit policies on household incomes allow us to consider the entire distribution of the work
incentive indicators at intensive (Effective Marginal Tax Rates) and extensive margin (Participation
Tax Rates). Moreover, static calculations of the effect of tax-benefit policies represent the key
ingredient of the behavioural model used to derive labour supply elasticities.
We test the sensitivity of our micro-data based indicator with respect to those based on stylised
and hypothetical measures of work incentives and the lack of robustness of the marginal cost of public
funds that we observe when stylised parameters values are used suggests the importance of focusing
on micro-data evidence.
The remainder of the paper is structured as follows. Section 2 presents the theoretical framework
adopted for our measure of the marginal cost of public funds reviewing the main concepts and
applications found in the literature. We specify our empirical implementation in Section 3 and we
present our results in Section 4. Section 5 discusses the main policy implications and concludes.
2. The Marginal Cost of Public Funds
The marginal cost of public funds (MCF) quantifies the welfare loss incurred by society in raising an
extra euro of revenue to finance government spending. It is an indicator widely used in the public
economics literature for the evaluation of public spending programs requiring the transfer of resources
from the private to the public sector (Dahlby, 2008). Specifically, the marginal cost of public funds
measures the efficiency loss which occurs when financing public spending programs. An expenditure
program will be efficient only if its benefits are at least as large as the direct cost and the welfare cost
of the funds. Welfare costs (or excess burdens) occur because of the distortion that taxes introduce in
the allocation of resources. Taxes on labour income, for example, distort the labour supply decisions
of workers. The efficiency loss depends on the behavioural responses of economic agents which affect
the total supply in the economy and hence the tax bases. A MCF of, for example, 1.25 means that
marginal government spending must generate a marginal benefit of at least 1.25 in order to
Pag. 3 a 32
compensate for both the tax increase and the associated indirect distortionary effect (Hansson, 1984).
Typically, the MCF is greater than one that is 1+α where α represents the efficiency loss (or cost of
the distortion). This means that for raising an additional euro of tax revenue, at the existing rate, the
society pays an efficiency cost of α while the total cost for the economy is 1+ α. Therefore, the higher
the MCF the larger the cost of the distortion compared to the tax revenue gains (Barrios et al, 2015).
Many formulas for the MCF have been proposed in the public finance literature. Usher (1984)
and Wildasin (1984) derive a formula for a proportional income tax where all individuals have the
same labour supply elasticities. Wildasin (1984) suggests a formula for the MCF for a “digressive”
income tax and a proportional income tax (assuming that all the marginal tax rates are increased in
the same proportion). Browning (1987) and Mayshar (1991) propose a formula for a single-person
framework, and Dhalby (1998) shows how Browning and Mayshar’s formulas are special cases of
his generalised one.
Various approaches have been used to estimate the MCF at macro or aggregate level. By using
the CGE modelling, researchers provide estimates for the MCF for taxes in the US (Ballard et al.,
1985), in Sweden (Hansson and Stuart, 1985), in Finland (Dixon et al., 2012), in African countries
(Auriol and Warlters, 2012) and in the EU countries (Barrios et al, 2013). Dahlby and Farede (2012)
use econometric estimations to derive the MCF of Canadian provinces for corporate income tax,
personal income tax and sales tax. Stuart (1984), Ballard (1990), and Ballard and Fullerton (1992)
applied an approach based on computer simulation techniques.
Although most of these studies has focused on the effect of taxation on labour supply, it is
difficult to compare their findings because these contributions are based on different assumptions
about the nature of government spending, the type of tax of interest, and the labour market behaviour.
This literature follows a common approach which considers labour supply responses only along the
intensive margin, i.e. changes in hours of work for those already working and not along the extensive
margin – the margin of entry and exit from the labour market. However, the empirical labour market
literature shows that changes in labour force participation is primarily responsible for the observed
variation in the labour supply (Heckman, 1993; Blundell and MaCurdy, 1999).
Consistently with this empirical literature Kleven and Kreiner (2006) investigate theoretically
the implications of extensive labour supply responses (participation in labour force) for the marginal
cost of public funds. They derive an analytical expression for the MCF that is function of the
observable tax and benefit parameters along with labour supply elasticities on the intensive and
extensive margins of response.
Therefore, the marginal cost of public funds is computed as follows:
Pag. 4 a 32
𝑀𝐶𝐹 =
1
∑𝑙𝑖=1 [1 −
(1)
𝑚𝑖
𝜏𝑖
𝑐
1 − 𝑚𝑖 (Φ𝑖 𝜀𝑖 − 𝜃𝑖 ) − 1 − 𝑚𝑖 𝜂𝑖 ] 𝑠𝑖
where 𝑚𝑖 is the marginal effective tax rate (at the intensive margin for individual i), and 𝜏𝑖 is the
participation tax rate (marginal tax rates at the extensive margin for individual i). Moreover, in this
formula there are two margins of labour supply response: 𝜂𝑖 , the participation elasticity, and 𝜀𝑖 , the
hours elasticity, conditional on already participating. The uncompensated elasticity at the intensive
margin can be decomposed into a compensated elasticity, 𝜀𝑖𝑐 and an income effect 𝜃𝑖 :
𝜀𝑖 = 𝜀𝑖𝑐 − 𝜃𝑖
The term Φ𝑖 in the formula (1) indicates the change in the ratio of marginal over average tax rates at
the margin. Assuming that the MCF is calculated for a proportional tax increase, Φ𝑖 = 1 and
considering the uncompensated elasticity at the intensive margin, the MCF is computed as follow:
𝑀𝐶𝐹 =
1
𝑚
𝜏𝑖
𝑖
∑𝑙𝑖=1 [1 −
𝜀
−
𝑖
1 − 𝑚𝑖
1 − 𝑚𝑖 𝜂𝑖 ] 𝑠𝑖
(2)
The weight 𝑠𝑖 are the earnings shares, equivalent to the tax increase shares of the different income
groups in the total taxes (because of the proportional tax reform case).
This measure does not include into the calculation of the aggregate costs distributional
concerns. That is, it does not consider the implication of a tax reform on social welfare thus focusing
entirely on the efficiency aspect of taxation1. This implies that the social value of an extra unit of
consumption is uniform across all individuals in a society. However, even if distributional concerns
are not addressed explicitly, heterogeneity still matters for the welfare cost of raising government
revenue (Kleven and Kreiner, 2006). There is in fact a high degree of variation and correlation in
earnings, taxes, benefit, and behavioural parameters across the population that is taken into account.
By using stylised and hypothetical values for labour supply elasticities, Kleven and Kreiner, (2006)
find that the MCF rises dramatically once that the heterogeneity in the labour supply response across
different categories of workers is taken into account. Moreover, they show that the estimated effect
1
This is the most common approach in the literature. A measure which includes into the calculation of the aggregate cost
the distributional preferences, the heterogeneity of wages and labour fixed costs is the broader concept of “social marginal
cost of public funds” (SMCF) developed by Dahlby (1998 and 2008). Kleven and Kreiner (2006) also present a more
general theoretical framework to measure SMCF.
Pag. 5 a 32
of taxes varies significantly once that the participation effect is distinguished from the number of
hours of work.
In this paper we make use of the MCF formula proposed by Kleven and Kreiner, (2006) thus
following their analytical and empirical approach in calculating a MCF measures for Italy. In this
respect, we follow Decoster et al. (2015) that is the only attempt to derive the MCF taking fully into
account the heterogeneity of the population although using stylised labour supply elasticities.
3. Empirical implementation for Italy
In order to derive the MCF taking fully into account the heterogeneity of the population and the
budget constraints faced by individuals, we need information on the full distribution of earnings,
marginal effective tax rates, participation tax rates, and intensive and extensive elasticities.
Such information are derived exploiting a microsimulation approach (Figari et al. 2015), in
order to compute static work incentive indicators and to derive the budget set used to estimate a
structural model of labour supply in order to derive intensive and extensive elasticities.
3.1 Microsimulation model, data and sample of interest
This paper uses the Italian component of EUROMOD, the European-wide tax-benefit model.
EUROMOD simulates tax liabilities (direct taxes and social insurance contributions) and cash benefit
entitlements on the basis of the tax-benefit rules in place and information available in the underlying
dataset. The components of the tax-benefit systems which are not simulated due to lack of information
on previous employment and contribution history in the cross-sectional survey data (e.g. contributory
pensions), as well as market incomes, are taken directly from the data (Sutherland and Figari, 2013).
The simulation of the Italian tax-benefit system has been cross-checked with administrative statistics
and tested through a number of other applications (e.g. Dolls et al., 2012; Bargain et al., 2014; Figari
and Fiorio, 2015; Paulus et al. 2016).
The underlying input dataset comes from the Italian component of the 2010 European Union Statistics
on Income and Living Conditions (EU-SILC) made available by ISTAT. The data contains
information on 5,963 households and 47,420 individuals. Monetary values refer to the 2009 as well
as the simulation of the tax-benefit system.
The sample of interest is composed of individuals in couples or single, restricted to those aged
between 18 and 59 years, without any pension and self-employment incomes and not in education.
The same restrictions apply to the partner of individuals in couples. The final sample includes 1,031
single women, 844 single men and 4088 couples. The restriction of the sample to the “labour market
flexible” individuals is common in the literature on behavioural evaluation of tax reforms and is
Pag. 6 a 32
motivated by the aim to exclude individuals whose labour choices are affected by factors that are not
or cannot be controlled for in the labour supply model. Examples of these factors include disability
status, educational choices, early retirement, self-employment and professional activities. Moreover,
it is reasonable to assume that for the women included in the sample, the employment decision and
the number of hours worked per week are the channels through which they respond to tax reforms,
while for self-employed hours of work and employment are not the important margin of response.
Figure 1 shows the overall sample distribution by equivalised disposable income deciles and Figure
2 reports the distribution of the individuals in the equivalised disposable income decile groups. From
Figure 2 we can see that a relative majority of single women (25%) and single men (20%) belong to
the first decile group and a smaller concentration of single men is in the second to sixth decile group.
Individuals in couple are distributed more evenly across the income distribution.
Figure 1. Sample distribution by income Figure 2. Sample distribution by income
deciles
deciles and by group
Note: Individuals are grouped per households deciles based on equivalised disposable income2.
Overall, in our aggregate sample the earnings shares are increasing across income deciles. The eighth
and ninth decile have the 15% of the earnings share each. This means that individuals in the upper
part of the income distribution face a higher tax increase shares among the different income groups
in the total taxes (see Figure 3). Couples have very similar earnings share distributions. Single men
group faces a sudden increase in the earnings shares at the sixth income decile whereas the increase
in the earnings shares is stepwise for the group of single women with a peak at the eighth decile (see
Figure 4).
2
Disposable income is equivalised using the standard OECD equivalence scales, assigning a weight of 1 to the first adult,
0.5 to each subsequent adult and 0.3 to each child aged below 14.
Pag. 7 a 32
Figure 3. Earnings shares by income deciles
Figure 4. Earnings shares by income deciles and by subsample
3.2 Marginal effective tax rates
Marginal effective tax rates (𝑚𝑖 ) measure the incidence of the tax and benefit system on a marginal
increase of earnings. They indicate how much of a marginal increase in earnings is taxed away. They
can be considered as indicator of the financial incentive for individuals to increase their earnings by
increasing the working time or the intensity of work effort.
Pag. 8 a 32
In calculating the marginal effective tax rates we follow the approach developed by Jara and
Tumino (2013). Marginal effective tax rates are computed taking into consideration taxes paid by,
and benefits received by all members of the household. Formally, individual level marginal effective
tax rates are calculated as:
𝑚𝑖 = 1 −
0
1
𝑌𝐻𝐻
−𝑌𝐻𝐻
𝐸𝑖1 −𝐸𝑖0
(3)
where YHH is the household disposable income and Ei is the individual earnings. Therefore, the
numerator measures the change in household disposable income due to the increase in the individual
earnings and the denominator is equal to the increase in earnings itself.
The marginal tax rate for each individual is computed by increasing earnings of the individual
by 3% and measuring the total change in the household taxes and benefits3.
Figure 5 plots the marginal effective tax rates across income deciles for our sample. Low
income earners are more likely to have relatively low marginal tax rates compared to high income
earners. At the bottom of the distribution, marginal effective tax rates are quite low due to the tax
reliefs granted to low earnings individuals but they increase quite rapidly also due to Family
allowance decreasing with family income. The marginal effective tax rate values are monotonically
increasing with a peak of 43 percent at the tenth income decile, as a result of the progressive personal
income tax schedule and the social insurance contributions paid by employees.
Figure 5. Average marginal effective tax rates by income deciles
3
The extra 3% earnings roughly corresponds to an extra working hour per week assuming a full-time employee working
40 hours per week (Jara and Tumino, 2013).
Pag. 9 a 32
If we look at the marginal effective tax rates patterns across our four subsamples (single women,
single men, women in couple, and men in couple), as expected the incidence of the tax-benefit system
on a marginal increase of earnings for singles women is very similar across income deciles to the
incidence for single men (Figure 6). Marginal effective tax rates for men in couple are always higher
relatively to marginal effective tax rates of their female partners which are likely to be second earners
in the couple and hence facing a lower income tax rate. The difference between the distribution of the
marginal effective tax rates for women and men in couple is significant (t-test p-value and MannWhitney tests p-values < 0.05).
Figure 6. Average marginal effective tax rates by income deciles and by subsample
3.3 Participation tax rates
The participation tax rate (𝜏𝑖 ) is a measure of the monetary attractiveness of working as opposed to
not working. To compute the participation tax rate on a given individual, we calculate the difference
between the individual disposable income when the individual is working (𝐶𝑖 𝐼𝑊 ) and the individual
disposable income if the individual were to exit the labour market (𝐶𝑖 𝑂𝑊 ). We then divide this
difference by the gross income from employment (𝑌𝑖 𝐼𝑊 ). Therefore, the individual participation is
calculated as:
τ𝑖 = 1 −
(𝐶𝑖 𝐼𝑊 −𝐶𝑖 𝑂𝑊 )
𝑌𝑖 𝐼𝑊
(4)
Pag. 10 a 32
where superscripts 𝐼𝑊 and 𝑂𝑊 denote the working status in-work and out-of-work respectively, and
𝑌𝑖 𝐼𝑊 is the gross income from employment.
Figure 7 shows the pattern of the participation tax rates across income deciles. For low income
deciles values are around 57-58%. They tend to increase to 59% from the fifth decile to return again
to 57% at the upper income decile. This pattern is consistent with the findings of Immervoll et al.
(2005, 2007).
Figure 7. Average participation tax rates by income deciles
Participation tax rates have been simulated for our four subsamples as well. For single men
values are ranging between 55-56 percent across income deciles as shown in Figure 4. Men in couple
have a slightly higher participation tax rates distribution, ranging between 57-59 percent. Single
women face relatively low participation tax rates at the lower part of the income distribution, then
they are increasing when moving to the upper part of the income distribution. Women in couple
experience participation tax rates up to 60% at the sixth income deciles (see Figure 8).
Pag. 11 a 32
Figure 8. Average participation tax rates by income deciles and by subsample
3.4 Behavioural responses: empirical methodology
In order to calculate the extensive and intensive labour supply elasticities we develop a static
structural discrete choice model of labour supply following a growing literature (e.g. van Soest, 1995;
Blundell et al., 2000). Structural models provide direct estimations of preferences through the
specification of the functional form of the utility function. The assumption behind the discrete choice
models is that utility-maximising individuals choose from a discrete set of alternatives in terms of
working hours to maximise the utility of the household on the basis of ‘preferences’ over hours H and
net income Y. At each point in the choice set corresponds a given budget on the basis of the earnings
of each individual and the tax-benefit system rules simulated by EUROMOD.
Suppose the utility function for a household is given by:
U (𝑌, 𝐻 𝑓 , 𝐻 𝑚 )
(5)
subject to household income:
𝑌 = 𝐸 𝑓 (𝑤 𝑓 , 𝐻 𝑓 ) + 𝐸 𝑚 (𝑤 𝑚 , 𝐻 𝑚 ) + 𝑁 + 𝐵 (𝐸 𝑓 , 𝐸 𝑚 , 𝑁 | 𝑋) − 𝑡 (𝐸 𝑓 , 𝐸 𝑚 , 𝑁 | 𝑋)
where the utility depends on the female 𝐻 𝑓 and male 𝐻 𝑚 hours of work and the household disposable
income Y, given earnings of both partners (𝐸 𝑓 , 𝐸 𝑚 ), other income (N) and benefits B and taxes t
according to individual and household characteristics X, Other individuals living in the household
Pag. 12 a 32
and their behaviour is taken as exogenous as well. Female and male wage rate, 𝑤 𝑓 and 𝑤 𝑚 , are
estimated for all the observations of our sample (workers and non-workers) through a Heckman wage
equation to take into account the selection bias in the observed working conditions. The two-stage
procedure – namely first estimating wage rates and then using them in the labour supply estimations
– is common practice (e.g. Creedy and Kalb, 2005; Bargain et al., 2014)4.
The choice set of each individual is made up of five j = 0, …., J alternatives, which means J = 5 for
singles and J = 5 x 5 for couples, with choices characterised by 0 to 60 hours per week (specifically
we have the following five hours range brackets: 1. (0-9), 2. (10-24), 3. (25-34), 4. (35-44), 5. (4560))5.
The utility function can be decomposed into a deterministic and a stochastic component:
𝑈𝑗 = 𝑉𝑗 + 𝜖𝑗
(6)
for each choice j= 1, …, J, where V is the portion of utility given by the observable characteristics
while the error term 𝜖𝑗 captures the portion from unobservable characteristics6.
At each alternative j, the realisation of the deterministic part of the utility function (i.e. V j) is given
by the following quadratic functional form with fixed costs7 linear in the parameters:
𝑓
𝑓
𝑓
𝑓
𝑉𝑗 = 𝛼𝑌𝑗 + 𝛽𝑌𝑗2 + 𝛾𝐻𝑗 + 𝛿𝐻𝑗𝑚 + 𝜀(𝐻𝑗 )2 + 𝜁(𝐻𝑗𝑚 )2 + 𝜂𝑌𝑗 𝐻𝑗 + 𝜃𝑌𝑗 𝐻𝑗𝑚 + 𝜄𝐻𝑗 𝐻𝑗𝑚
𝑓
−κ 𝑓 (𝐻𝑗 > 0) − κ𝑚 (𝐻𝑗𝑚 > 0)
(7)
where income (Y) and hours of work (𝐻 𝑓 and 𝐻 𝑚 ) enter in both level and square. Observed
heterogeneity, captured by observable characteristics, cannot be identified directly because these
characteristics do not vary across alternatives and would be ruled out in the estimation. It enters
through the linear utility parameters:
𝛼 = 𝛼0 + 𝛼1 ′𝑋
(8)
γ = γ0 + γ1 ′𝑋
(9)
𝛿 = 𝛿0 + 𝛿1 ′𝑋
(10)
4
See Table 1 and 2 in Appendix for estimates of the wage equation.
We checked the sensitivity of our results to alternative definition of the choice set.
6
Error terms are also assumed to represent possible observational errors, optimization errors, or transitory errors.
7
Fixed costs improve the fit of the model estimated as model parameters as in Callan, van Soest, and Walsh (2009) or
Blundell et al (2000). These costs, denoted κ𝑓 and κ𝑚 , are nonzero for positive hour choices and depend on observed
characteristics (for example, the presence of young children).
5
Pag. 13 a 32
allowing marginal utilities of income (Y) and hours of work (𝐻 𝑓 and 𝐻 𝑚 ) to depend on a vector of
family characteristics (X) including polynomial form of age, education level, region, and presence of
children.
Assuming that the error terms is independently and identically distributed across alternatives and
households according to the Extreme Value Type I distribution, the (conditional) probability of
choosing the alternative k is given by the following logit expression (McFadden, 1974)8:
𝑃𝑟𝑘 =
exp(𝑈𝑘 )
∑𝑗 exp(𝑈𝑘 )
𝑘 ∈𝐽
(7)
The parameters, estimated using Maximum simulated Likelihood, are shown in Tables 3, 4 and 5
respectively for couples, single women, and single men in the Appendix.
3.4.1 Labour Supply Elasticities at the Extensive and Intensive Margins
Labour supply elasticities are calculated using the estimated model and predicting the change in
working hours and participation rates following a marginal uniform increase in wage rates of 10% .
The intensive margin elasticity 𝜀𝑖 corresponds to the response in work hours among workers, and the
extensive margin elasticity 𝜂𝑖 to the participation response (measured in percent change in work hour).
The choice an individual faces follows in fact the probability rule Pr(choice=k) = Pr[U(H fk) > U(Hfj)]  k ≠ j, j = 1,…,
J according to which the probability that an individual chooses the alternative k is equal to the probability that the utility
associated with the choice k is larger than the utility associated with any other choice j.
8
Pag. 14 a 32
Figure 9. Extensive and Intensive elasticities by income deciles
Figure 10. Extensive and Intensive elasticities by income deciles and by subsample
Pag. 15 a 32
4. Results
By using the information presented above to compute formula (2) for the whole sample, we get an
aggregate marginal cost of public funds equal to 1.116. This implies that the efficiency costs of raising
an extra unit of government revenue is 0.12 (MCF – 1).
However, from the information presented above, the heterogeneity of the four subsamples emerges
as a striking feature of our data and our approach based on micro data representative of the national
population allow us to take it fully into account. The MCF value computed for each subgroup are in
Table 4.
Table 4. MCF values by gender and status
Female
Male
Single
1.1308
1.0386
Couple
1.1603
1.0556
For women, both single or in couple, the MCF is higher than men: this is mainly due to higher
elasticities values. Women in couple have the highest MCF whereas the lowest cost of distortion of
a tax reform refers to single men. Therefore, specific values for subgroups of MCF suggest that for
the same tax-benefit system women (both single and in couple) face a more inefficient system
compared to men (both single and in couple).
The robustness of the MCF based on stylised parameters
In order to test the impact of individual heterogeneity on the MCF we substitute our labour supply
elasticities with the stylised values used by Kleven and Kreiner (2006) and reported in the Table 3 in
the Appendix. For the intensive elasticity, they assume that it is constant across earnings deciles and
small (0 or 0.1). For the extensive elasticity, based on available evidence, they assume it is higher for
those in the lower part of the income distribution and then decreasing with income, with values
between 0.8 and 0.3 at the bottom of the distribution and zero elasticities at the top. Table 4 in the
Appendix reports the results of the MCF for our aggregate data using the stylized elasticities of the
five scenarios proposed by Kleven and Kreiner (2006).
The use of stylized elasticities make the aggregate MCF measure to vary from 1.111 to 1.344.
However, although we observe a 21% of variation, the MCF obtained with the elasticities derived by
our empirical data (1.116) is yet in the range of the MCF values computed by using the elasticities
Pag. 16 a 32
scenarios (Figure 11). This is not always true when we look at the MCF measures for subgroups. For
men in couple, single men, and women in couple the MCF computed with empirical elasticities is
either higher or lower than the maximum/minimum MCF value calculated by using the elasticities
scenarios. Specifically, when using the stylized elasticities the MCF measure varies of 25-26% for
single women (from 1.133 to 1.423) and for men in couple (from 1.146 to 1.445). The MCF value
varies of 22% for single men (from 1.122 to 1.365) and 17% for women in couple (from 1.083 to
1.270).
Figure 11. Aggregate MCF calculated using different elasticities scenarios
Only for the subgroup of “women in couple” the MCF measure obtained with the elasticities derived
by our empirical data is in the range of the MCF values computed by using the elasticities scenarios
(Figure 12)9. Table 5 in the Appendix shows the MCF values computed by using the elasticities
scenarios for our subgroups. This indicates the importance of taking into account the specificities of
the different sub group of the population and a potential lack of robustness of the MCF indicator
based on stylised values in order to reach policy conclusions.
9
Although we can consider the MCF value for single women obtained with the elasticities derived by our empirical data
(1.131) in the range of the MCF values computed by using the elasticities scenarios as well since the minimum value of
the range is 1.133.
Pag. 17 a 32
Figure 12. MCF by subsamples calculated using different elasticities scenarios
Redistributive effects of a reform on income on the MCF
We apply an increment of the individual income in order to measure the redistributive effects of a
reform on income and the consequent effects on our empirical efficiency measure of the MCF.
Specifically, we increase individual earnings of a constant amount, Euros 80. This structural reform
has been implemented in Italy during the Renzi government. Hence, we proceed with a second stage
of microsimulations, which consider the tax-benefit system and provide a new level of disposable
income. Therefore, we calculate the earnings shares, the marginal effective tax rates, and the
participation tax rates at the aggregate level and by subsamples. In the calculation of the new MCF
values we use the same labour supply elasticities at the intensive and extensive margins because we
assume individual preferences as fixed. Table 5 shows the MCF values post reform at the aggregate
level and by subsamples. Moreover, it shows how the MCF values change when we use the stylized
elasticities of the five scenarios presented by Kleven and Kreiner (2006). At the aggregate level, the
MCF is 1.119, very similar to its pre-reform value. For women the MCF is higher than men. Single
women face a more inefficient system compared to men (both single and in couple). The lower
Pag. 18 a 32
distortion of the tax reform refers to single men whose MCF is 1.040. We find, therefore, the same
pattern of results.
The use of stylized elasticities make the aggregate MCF measure to vary from 1.115 to 1.348. The
MCF obtained with the elasticities derived by our empirical data (1.119) is yet in the range of the
MCF values computed by using the elasticities scenarios. However, for men (both single and in
couple) we observe that MCF measure obtained with the elasticities derived by our empirical data is
not in the range of the MCF values computed by using the elasticities scenarios. Our empirical MCF
values are lower of the minimum MCF values obtained by using stylized elasticities. This implies a
higher accuracy and robustness of the empirical MCF indicator.
Table 5. MCF calculation post reform
Elasticities scenarios
MCF
Aggregate data
Scenario 1
1.1446
Scenario 2
1.1654
Scenario 3
1.1695
Scenario 4
1.1150
Scenario 5
1.3481
Our empirical elasticities
1.1196
Single Women
Scenario 1
1.1759
Scenario 2
1.1998
Scenario 3
1.2137
Scenario 4
1.1416
Scenario 5
1.4336
Our empirical elasticities
1.1339
Single Men
Scenario 1
1.1392
Scenario 2
1.2019
Scenario 3
1.1798
Scenario 4
1.1296
Scenario 5
1.3744
Our empirical elasticities
1.0405
Women in Couple
Scenario 1
1.1181
Scenario 2
1.1247
Pag. 19 a 32
Scenario 3
1.1245
Scenario 4
1.0830
Scenario 5
1.2626
Our empirical elasticities
1.1600
Men in Couple
Scenario 1
1.1801
Scenario 2
1.2116
Scenario 3
1.2283
Scenario 4
1.1544
Scenario 5
1.4651
Our empirical elasticities
1.0583
5. Discussion and conclusion
This paper builds a marginal cost of public funds indicator fully based on empirical micro data
representative of the population. Specifically, in this work the indicator measures the efficiency of
the 2009 Italian tax-benefit system calculated for a sample of nearly six thousands households. By
using EUROMOD, values of marginal effective tax rates, participation tax rates, and earnings shares
have been simulated. Following the Kleven and Kreiner (2006) theoretical framework, the simulated
static results have been combined with intensive and extensive labour supply elasticities in order to
take into consideration both worked hours among workers and labour market participation in the
MCF calculation.
Results show that the aggregate marginal cost of public funds is equal to 1.201, implying an
efficiency costs of raising an extra unit of government revenue of 0.201. The inefficiency of the Italian
2009 tax-benefit system can be better explained by the marginal cost of public funds calculated for
four subsamples (single women, single men, married women, and married men). Higher MCF values
show that a higher costs of distortion of the tax-benefit system for women compared to men. For
example, for married women there is an efficiency cost of 0.16, the highest MCF value among those
of the four subsamples. This welfare loss can be due to the high extensive elasticities that married
women present. Married women face relatively lower values of marginal effective tax rates (at least
at the lower part of the income distribution) compared to men in couple and singles, meaning that a
lower proportion of a marginal increase in their earnings is taxed away. Married women have a high
Pag. 20 a 32
propensity to enter the labour market as indicated by a high participation tax rate compared to the
other three workers subsamples.
Compared to married workers, single women have negative extensive elasticities between the
third and fifth deciles. However, parametric and non-parametric tests show that there is no significant
difference between the distribution of extensive elasticities of single women compared to the
distributions of extensive elasticities of the other subgroups. Single women have lower intensive
elasticities compared to women in couple (t-test and Mann-Whitney tests p-values < 0.05) and this
might explain a lower MCF with respect to the MCF of married women.
A test the sensitivity of our micro-data based indicator with respect to those by Kleven and
Kreiner (2006) based on stylised and hypothetical measures of work incentives was run. The
aggregate marginal cost of public funds can vary of 21%. For single women and men in couple MCF
can vary up to 26%. For single workers and for married women the MCF value calculated using our
empirical elasticities is not even in the range of MCF values obtained by using hypothetical
elasticities. Therefore, the lack of robustness of the marginal cost of public funds that we observe
when stylised parameters values are used suggests the importance of focusing on micro-data
evidence.
Pag. 21 a 32
References
Aaberge, R. and U. Colombino (2014). Labour supply models, in C. O’Donoghue (Ed.), Handbook
of Microsimulation Modelling. Contributions to Economic Analysis Vol. 293, Emerald.
Atkinson, A. B. and N. H. Stern (1974). Pigou, Taxation and Public Goods. Review of Economic
Studies 41, 119-128.
Auerbach, Alan J. and Rosen, Harvey S. (1980), Will the Real Excess Burden Please Stand Up? (or,
Seven Measures in Search of a Concept), National Bureau of Economic Research Working Paper No.
495, Cambridge
Auriol, E. and M. Warlters (2012). The marginal cost of public funds and tax reform in Africa, Journal
of Development Economics, 97(1): 58‐72.
Ballard, C. L. (1990). Marginal Welfare Cost Calculations: Differential Analysis vs. BalancedBudget Analysis. Journal of Public Economics 41, 263-276.
Ballard, C. L. and D. Fullerton (1992). Distortionary Taxes and the Provision of Public Goods.
Journal of Economic Perspectives 6, 117-131.
Ballard, C. L., Shoven, J. B., and J. Whalley (1985). General equilibrium computations of the
marginal welfare costs of taxes in the United States. The American Economic Review 75(1):128‐
138.
Bargain, O., K. Orsini, and A. Peichl (2014). Comparing Labour Supply Elasticities in Europe and
the US: New Results. Journal of Human Resources 49 (3), 723-838.
Barrios, S., Fatica, S., Martínez-López, D., & Mourre, G. (2015).The fiscal effects of work-related
tax expenditures in Europe(No. 1504). Universidade de Vigo, GEN-Governance and Economics
research Network.
Barrios, S., Pycroft, J., & Saveyn, B. (2013). The marginal cost of public funds in the EU: the case
of labour versus green taxes.Fiscal Policy and Growth, 403.
Blundell, R. W. and T. MaCurdy (1999). Labor Supply: A Review of Alternative Approaches, in O.
Ashenfelter and D. Card (eds.), Handbook of Labour Economics vol. 3A. ElsevierScience B.V.:
Amsterdam.
Browning, E. K. (1976). The marginal cost of public funds. The Journal of Political Economy, 283298.
Browning, E. K. (1987). On the Marginal Welfare Cost of Taxation. American Economic Review 77,
11-23.
Dahlby, B. (1998). Progressive taxation and the social marginal cost of public funds. Journal of
Public economics, 67(1), 105-122.
Dahlby, B., (2008), The Marginal Cost of Public Funds. Theory and applications. M.I.T. Press,
Cambridge, Mass.
Pag. 22 a 32
Dahlby, B. and E. Ferede (2012), The effects of tax rate changes on tax bases and the marginal cost
of public funds for Canadian provincial governments, International Tax and Public Finance 19: 844883.
Decoster, A., Perelman, S., Vandelannoote, D., Vanheukelom, T., and Verbist, G. (2015). A bird's
eye view on 20 years of tax-benefit reforms in Belgium, EUROMOD Working Paper Series, EM
10/15, June
Dixon, P., J. Honkatukia and M. Rimmer, (2012), "The Marginal Cost of Funds from Different Taxes
in Finland", GTAP Resource#3877,
https://www.gtap.agecon.purdue.edu/resources/res_display.asp?RecordID=3877.
Figari, F., A. Paulus, and H. Sutherland (2015). Microsimulation and policy analysis. In A. B.
Atkinson and F. Bourguignon (Eds.), Handbook of Income Distribution, Volume 2, Chapter 25, pp.
2141-2221. Elsevier-North Holland.
Hansson, I. and C. Stuart (1985), Tax revenue and the marginal cost of public funds in Sweden,
Journal of Public Economics27(3): 331-353.
Hansson, I. (1985). Marginal cost of public funds for different tax instruments and government
expenditures. In Limits and Problems of Taxation (pp. 17-32). Palgrave Macmillan UK.
Harberger, Arnold C. (1964), The Measurement of Waste”, American Economic Review, 54, 58-76
Heckman, J. J. (1993). What Has Been Learned About Labour Supply in the Past Twenty Years?
American Economic Review Papers and Proceedings 83, 116-121.
Immervoll, H., Kleven, H. J., Kreiner, C. T. and Saez, E. (2005). A micro-level analysis of levels,
distributions and driving factors. Social, Employment and Migration Working Papers 19, OECD.
Immervoll, H., Kleven, H. J., Kreiner, C. T. and Saez, E. (2007). Welfare reform in European
countries: a microsimulation analysis. The Economic Journal, 117: 1–44.
Jara, H. X., & Tumino, A. (2013). Tax-benefit systems, income distribution and work incentives in
the European Union. International Journal of Microsimulation, 6(1), 27-62.
Kleven, H. J., & Kreiner, C. T. (2006). The marginal cost of public funds: Hours of work versus
labour force participation. Journal of Public Economics, 90(10), 1955-1973.
Mayshar, J. (1991). On Measuring the Marginal Cost of Funds Analytically. American Economic
Review 81, 1329-1335.
McFadden, D. (1974) Conditional logit analysis of qualitative choice behaviour in P. Zerembka (ed)
Frontiers in Econometrics. New York: Academic Press.
Pigou, A.C., 1947. A Study in Public Finance, 3rd ed. Macmillan, London.
Saez, E. (2000). Optimal income transfer programs: intensive versus extensive labour supply
responses (No. w7708). National Bureau of Economic Research.
Pag. 23 a 32
Samuelson, P.A., 1954. The pure theory of public expenditure. Review of Economics and Statistics
36(4), 387–389.
Sandmo, A. (1998). Redistribution and the marginal cost of public funds. Journal of Public
economics, 70(3), 365-382.
Stiglitz, J. E. and P. Dasgupta (1971). Differential Taxation, Public Goods and Economic Efficiency.
Review of Economic Studies 38, 151-174.
Stuart, C. (1984). Welfare Costs per Dollar of Additional Tax Revenue in United States. American
Economic Review 74, 352-362
Sutherland, H., & Figari, F. (2013). EUROMOD: the European Union tax-benefit microsimulation
model. International Journal of Microsimulation, 6(1), 4-26.
Usher, D., 1984. An instructive derivation of the expression for the marginal cost of public
funds.Public Finance 39(3) 406–411.
Van Soest, A. (1995) Structural models of family labour supply. A discrete choice approach. The
Journal of Human Resources 30: 63–88.
Wildasin, D.E., 1984. On public good provision with distortionary taxation. Economic Inquiry
32,227–243.
Pag. 24 a 32
APPENDIX
Table 1. Wage Estimation: Women
Coefficient
Robust Standard Error
P-value
Age
0.800
0.4331
0.065
Age square
-0.143
0.1107
0.195
Age cubic
0.010
0.0092
0.282
Education middle
0.304
0.0349
0.000
Education high
0.546
0.0387
0.000
In couple
0.041
0.0250
0.102
-0.010
0.0031
0.002
Number of children
0.016
0.0148
0.259
Number of children 0-2
0.016
0.0368
0.652
Constant
2.938
0.5659
0.000
Age
2.399
0.7928
0.002
Age square
-0.386
0.2053
0.060
Age cubic
0.015
0.0170
0.392
Education middle
0.660
0.0408
0.000
Education high
1.030
0.0614
0.000
In couple
-0.407
0.0484
0.000
Region
-0.095
0.0047
0.000
Children 0-2
-0.268
0.0727
0.000
Children 3-6
-0.289
0.0607
0.000
Children 7-12
-0.245
0.0508
0.000
Children 13-17
-0.123
0.0527
0.019
Children 18+
0.072
0.0592
0.225
Other income
-0.024
0.0086
0.006
Constant
-3.132
0.9772
0.001
Rho
0.019
0.0343
0.573
Sigma
-0.605
0.0543
0.000
Observations
8449
Log wage
Region
Participation
Pag. 25 a 32
Table 2. Wage Estimation: Men
Coefficient
Robust Standard Error
P-value
Age
1.094
0.3259
0.001
Age square
-0.199
0.0868
0.022
Age cubic
0.013
0.0074
0.071
Education middle
0.226
0.0194
0.000
Education high
0.527
0.0294
0.000
In couple
0.025
0.0221
0.259
Region
-0.027
0.0030
0.000
Number of children
0.022
0.0115
0.058
Number of children 0-2
-0.031
0.0315
0.330
Constant
2.722
0.3906
0.000
Age
3.734
0.8368
0.000
Age square
-0.823
0.2275
0.000
Age cubic
0.059
0.0197
0.003
Education middle
0.336
0.0490
0.000
Education high
0.380
0.0821
0.000
In couple
0.396
0.0679
0.000
Region
-0.103
0.0073
0.000
Children 0-2
0.005
0.1018
0.958
Children 3-6
0.085
0.0879
0.336
Children 7-12
0.147
0.0755
0.052
Children 13-17
-0.045
0.0798
0.570
Children 18+
0.102
0.1009
0.312
Other income
-0.015
0.0120
0.221
Constant
-4.095
0.9740
0.000
Rho
0.019
0.0143
0.180
Sigma
-0.628
0.0458
0.000
Observations
7480
Log wage
Participation
Pag. 26 a 32
Table 3. Labour Supply Estimation: Couples
Coefficient
Robust Standard Error
P-value
-0.0002
0.0000
0.009
Income
0.001
0.0007
0.048
Hm
1.032
0.0470
0.000
0.259
0.0335
0.000
0.353
0.1051
0.001
Hm Square
-14.127
0.3560
0.000
Hf Square
-5.667
0.2432
0.000
Hm x Income
-0.001
0.0015
0.554
Hf x Income
0.001
0.0010
0.226
Spouses’ mean Age x Income
-0.000
0.0003
0.125
Spouses’ mean Age square x Income
0.000
0.0000
0.108
Number of children x Income
0.000
0.0000
0.638
Hm x male age
0.063
0.0178
0.000
Hm x male age square
-0.007
0.0020
0.000
Hf x female age
0.065
0.0146
0.000
H x female age square
-0.008
0.0018
0.000
Hm x number of children
0.003
0.0034
0.342
Hf x 1(children 0-2)
0.008
0.0073
0.249
Hf x 1(children 3-6)
-0.012
0.0028
0.000
Hf x 1(children 7-12)
-0.015
0.0027
0.000
H x 1(children 13-17)
-0.009
0.0027
0.001
Hm x 1(region)
-0.023
0.0026
0.000
Hf x 1(region)
-0.035
0.0020
0.000
Fixed cost (FC) for male labour
22.477
0.6189
0.000
FC for male labour x n. of children
0.077
0.1394
0.579
FC for male labour x 1(children 0-2)
0.117
0.1738
0.501
Fixed cost (FC) for female labour
7.294
0.3017
0.000
FC for female labour x n. of children
-0.086
0.0696
0.215
FC for female labour x 1(children 0-2)
0.513
0.2731
0.060
Income Square
Hf
m
H xH
f
f
f
Log-likelihood
Pseudo R2
Observations
-9862.8699
0.2505
4088
Pag. 27 a 32
Table 4. Labour Supply Estimation: Single Women
Coefficient
Robust Standard Error
P-value
Income Square
0.0005
0.0003
0.154
Income
0.0006
0.0017
0.720
Hours
0.399
0.0752
0.000
Hours Square
-6.176
0.4675
0.000
Hours x Income
-0.021
0.0053
0.000
Age x Income
0.000
0.0008
0.904
Age square x Income
0.000
0.0001
0.994
Number of children x Income
-0.000
0.0001
0.000
Hours x age
0.057
0.0346
0.096
Hours x age square
-0.007
0.0043
0.089
Hours x 1(children 0-2)
-0.067
0.0239
0.005
Hours x 1(children 3-6)
-0.016
0.0077
0.041
Hours x 1(region)
-0.033
0.0045
0.000
Fixed cost (FC)
9.590
0.6394
0.000
FC x n. of children
-0.436
0.1999
0.029
FC x 1(children 0-2)
-1.684
0.8574
0.049
Coefficient
Robust Standard Error
P-value
Income Square
-0.0000
0.0006
0.923
Income
-0.0010
0.0018
0.576
Hours
0.9949
0.0964
0.000
Hours Square
-13.0887
0.7986
0.000
Hours x Income
-0.0062
0.0096
0.518
Age x Income
0.0007
0.0009
0.420
Age square x Income
-0.0001
0.0001
0.431
Number of children x Income
0.0000
0.0003
0.939
Hours x age
0.0483
0.0403
0.231
Hours x age square
-0.0066
0.0050
0.188
Log-likelihood
Pseudo R2
Observations
-1433.9093
0.1359
1031
Table 5. Labour Supply Estimation: Single Men
Pag. 28 a 32
Hours x 1(children 0-2)
-0.0183
0.1197
0.878
Hours x 1(children 3-6)
0.0749
0.0982
0.445
Hours x 1(region)
-0.0295
0.0050
0.000
Fixed cost (FC)
20.772
1.2162
0.000
FC x n. of children
-0.8203
0.8613
0.341
FC x 1(children 0-2)
-11.6082
616.374
0.985
Log-likelihood
Pseudo R2
Observations
-963.23904
0.2909
844
Pag. 29 a 32
Table 6. Key variables values for aggregate data by income deciles
Income
Deciles
1
2
3
4
𝑠𝑖
0.042
0.055
0.081
0.079
𝑚𝑖
𝜏𝑖
𝜂𝑖
𝜀𝑖
0.122
0.252
0.272
0.564
0.567
0.568
0.076
0.079
0.063
0.073
5
6
7
8
9
10
0.095
0.097
0.132
0.147
0.150
0.122
0.287
0.330
0.367
0.398
0.414
0.418
0.428
0.576
0.576
0.590
0.585
0.585
0.577
0.577
0.077
0.072
0.061
0.072
0.059
0.102
0.059
0.081
0.071
0.067
0.066
0.064
0.060
0.064
0.061
0.058
Aggregate Data
Table 7. MCF parameters values for subsamples by income deciles
Income
Deciles
1
2
3
4
𝑠𝑖
0.070
0.076
0.059
0.077
𝑚𝑖
𝜏𝑖
𝜂𝑖
𝜀𝑖
0.125
0.314
0.361
0.555
0.551
0.560
0.025
0.008
0.031
0.010
5
6
7
8
9
10
0.122
0.118
0.118
0.148
0.130
0.082
0.373
0.407
0.393
0.419
0.418
0.430
0.458
0.565
0.570
0.567
0.574
0.583
0.575
0.563
-0.027
0.010
-0.053
0.126
0.078
0.506
0.000
0.000
-0.011
-0.012
0.025
0.032
0.030
0.070
0.055
0.049
Single Women
Single Men
𝑠𝑖
0.058
0.043
0.044
0.024
0.091
0.139
0.158
0.131
0.156
0.155
𝑚𝑖
𝜏𝑖
𝜂𝑖
0.130
0.332
0.407
0.402
0.424
0.427
0.427
0.427
0.448
0.451
0.567
0.563
0.573
0.570
0.571
0.570
0.557
0.568
0.555
0.561
0.036
0.033
0.017
0.034
0.050
0.026
0.000
0.019
0.000
0.000
𝜀𝑖
0.022
0.027
0.028
0.028
0.030
0.027
0.033
0.034
0.032
0.035
𝑠𝑖
0.038
0.054
0.085
0.082
0.093
0.092
0.132
0.149
0.152
0.124
𝑚𝑖
𝜏𝑖
𝜂𝑖
0.062
0.099
0.109
0.123
0.184
0.266
0.333
0.373
0.378
0.391
0.543
0.571
0.571
0.591
0.583
0.601
0.594
0.591
0.585
0.587
0.155
0.146
0.137
0.126
0.111
0.114
0.102
0.100
0.107
0.124
𝜀𝑖
0.119
0.127
0.118
0.117
0.116
0.113
0.105
0.106
0.103
0.096
Women in couple
Men in couple
𝑠𝑖
0.038
0.055
0.087
0.084
0.094
0.092
0.131
0.147
0.150
0.122
𝑚𝑖
𝜏𝑖
𝜂𝑖
0.176
0.379
0.414
0.428
0.441
0.449
0.449
0.451
0.448
0.454
0.576
0.570
0.568
0.573
0.576
0.592
0.587
0.585
0.575
0.574
0.044
0.036
0.036
0.033
0.041
0.026
0.013
0.034
0.012
0.038
𝜀𝑖
0.044
0.041
0.039
0.036
0.032
0.031
0.028
0.028
0.027
0.028
Pag. 30 a 32
Table 8. Kleven and Kreiner’s elasticities scenarios
Income
1
deciles
2
3
4
5
6
7
8
9
10
Scenario 1
𝜂𝑖
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
𝜀𝑖
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Scenario 2
𝜂𝑖
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0.0
0.0
𝜀𝑖
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Scenario 3
𝜂𝑖
0.8
0.6
0.4
0.2
0.0
0.0
0.0
0.0
0.0
0.0
𝜀𝑖
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Scenario 4
𝜂𝑖
0.4
0.3
0.2
0.1
0.0
0.0
0.0
0.0
0.0
0.0
𝜀𝑖
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Scenario 5
𝜂𝑖
0.6
0.6
0.4
0.4
0.3
0.3
0.2
0.2
0.0
0.0
𝜀𝑖
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
0.1
Table 9. MCF calculation by using the Kleven and Kreiner’s elasticties scenarios and our
empirical elasticities
Elasticities scenarios
MCF
Scenario 1
1.1459
Scenario 2
1.1617
Scenario 3
1.1660
Scenario 4
1.1113
Scenario 5
1.3447
Our empirical elasticities
1.1161
Pag. 31 a 32
Table 10. MCF calculation by subsamples
Elasticities scenarios
MCF
Single Women
Scenario 1
1.1773
Scenario 2
1.2737
Scenario 3
1.2065
Scenario 4
1.1334
Scenario 5
1.4232
Our empirical elasticities
1.1308
Single Men
Scenario 1
1.1407
Scenario 2
1.2423
Scenario 3
1.1701
Scenario 4
1.1217
Scenario 5
1.3654
Our empirical elasticities
1.0386
Women in Couple
Scenario 1
1.1227
Scenario 2
1.1770
Scenario 3
1.1258
Scenario 4
1.0827
Scenario 5
1.2698
Our empirical elasticities
1.1603
Men in Couple
Scenario 1
1.1767
Scenario 2
1.2932
Scenario 3
1.2177
Scenario 4
1.1463
Scenario 5
1.4454
Our empirical elasticities
1.0556
Pag. 32 a 32