Is the Gasoline Tax Regressive in the Twenty-First Century? Taking Wealth into Account

Abstract

Poterba (1991a) has much influenced the literature on the distributional effects of carbon pricing. Poterba argues that the incidence of energy/environmental taxes across households is better appreciated if the relative tax burdens are measured against total expenditure, interpreted as a proxy for lifetime income, instead of annual income. This way, however, since the distribution of total expenditure is structurally more uniform, the incidence of energy price increases is always less regressive than when annual income is used. This outcome is often taken to lessen the relevance of equity concerns regarding carbon pricing. Almost twenty-five years after Poterba (1991a), Piketty (2014) revived the idea that wealth is a dimension of economic welfare constituting an increasingly important source of inequality. We show that omitting wealth in measuring ability to pay means underestimating the regressivity of carbon pricing and its inequity towards younger people. Using household-level data and statistical matching, we revisit Poterba's application and compare the distributional incidence of the US gasoline tax for different measures of ability to pay: total expenditure, income and wealth-adjusted income. Regressivity is not a reason to forgo carbon pricing as a cost-effective approach to climate mitigation, but calls for consideration and compensation of the distributional effects.

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Author Author and Author Author
MWP 2016/19
Max Weber Programme
Is the Gasoline Tax Regressive in the Twenty-first
Century?
Jordi J. Teixidó and Stefano F. Verde

European University Institute
Max Weber Programme
Is the Gasoline Tax Regressive in the Twenty-first
Century?
Jordi J. Teixidó and Stefano F. Verde
EUI Working Paper MWP 2016/19

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Abstract
Poterba (1991a) has much influenced the literature on the distributional effects of carbon pricing. The
gist of Poterba’s study is that the distributional incidence of energy/environmental taxes across
households is better appreciated if the relative tax burdens are measured against total expenditure
instead of annual income. Interpreted as a proxy for lifetime income, total expenditure is more stable
over time. As a result, the incidence of energy price increases is less regressive than when annual
income is used. This outcome is often taken to lessen the relevance of equity concerns regarding
carbon pricing. Almost twenty-five years after Poterba (1991a), Piketty (2014) revived the idea that
wealth is a dimension of economic welfare constituting an increasingly important source of inequality.
We show that omitting wealth in measuring ability to pay means underestimating the regressivity of
carbon pricing and its inequity towards younger people. Using household-level data and statistical
matching, we revisit Poterba’s application and compare the distributional incidence of the US federal
gasoline tax for different measures of ability to pay: total expenditure, income and wealth-adjusted
income.
Keywords
Gasoline tax, Carbon pricing, Wealth, Distributional effects, Inequality.
Jordi J. Teixidó
Max Weber Fellow, 2015-2016
Stefano F. Verde
Florence School of Regulation – Climate, RSCAS

1. Introduction
The idea of taxing fossil fuels in proportion to their carbon content goes back as far as the 1970s,
when the threat of anthropogenic climate change started to be recognized
1
. In 1990, Finland was the
first country to introduce a carbon tax, followed shortly after by the Netherlands, Sweden and
Norway. Today carbon pricing, whether in the form of carbon taxes or cap-and-trade systems, is in
force in several countries, but overall is far from being sufficiently diffuse or deep to significantly
improve the prospects of climate change. Global greenhouse gas (GHG) emissions have been rising
steadily since the industrial revolution and will continue to do so unless counteracting policies are
ramped up. In this respect, a change of gear is at last in prospect. An intensification of mitigation
policies around the world should materialize under the framework recently set out by the Paris
Agreement
2
. Accordingly, in the next few years carbon pricing is expected to become more
widespread and deeper than it is currently.
Most economists favour carbon pricing in that it is a cost-effective approach to reducing GHG
emissions (Baumol and Oates, 1971). Nevertheless, carbon pricing in the real world is not popular or
easy to implement. For carbon pricing to be politically sustainable, its side effects need to be
effectively managed
3
. By raising the cost of energy, unilateral carbon pricing can be detrimental to the
international competitiveness of domestic energy-intensive firms. At the same time, inasmuch as
energy goods are a necessity in households’ consumption
4
, carbon pricing tends to affect the poor
more than the wealthy in relative terms. That is, it tends to be regressive. The revenues generated by
carbon pricing, be they the yield of a carbon tax or of the auctions of emission allowances under a
cap-and-trade system, could be used to at least partially offset these undesirable effects. Though this is
easier said than done
5
, the deeper the level of carbon pricing, the more critical it is that both the
competitiveness and distributional issues are properly addressed.
This paper offers a new perspective and new empirical evidence on the distributional incidence
of gasoline taxes and, by extension, of carbon pricing across households. Specifically, it fills a gap in
the literature by considering wealth as a dimension of economic welfare additional to income. This
innovation provides us with a more accurate representation of reality, in which the wealth owned by a
person, or a household, contributes to her ability to pay (taxes). In this sense, ignoring wealth is an
omission that alters the portrait of distributional effects, as wealth is both more concentrated than
1
See, for example, the early contributions of Nordhaus (1977a, 1977b), among the first proponents of carbon
taxation.
2
The Paris Agreement is the international agreement, under the United Nations Framework Convention on
Climate Change, dealing with climate mitigation, adaptation and finance, starting in the year 2020.
3
Moreover, a growing literature deals with the public’s cognitive difficulties and worldviews that hinder its
adoption. Drews and van den Bergh (2015) provide a comprehensive literature review on the determinants of
public support for climate policies.
4
In the developed economies, the income elasticity of energy demand is typically smaller than 1.
5
Earmarking is somewhat infrequent and unpopular among economists, as it generally means foregoing
alternative more efficient uses of the revenues.

income and imperfectly correlated with income. This issue appears to be increasingly relevant in light
of Thomas Piketty’s warning, in his Capital in the twenty-first century (Piketty, 2014), that wealth
concentrations have been rising and may well continue to rise unless corrective policies are
undertaken.
While taking wealth into account is generally desirable for the completeness of any equity
assessment, it is particularly opportune in relation to carbon pricing. This is the case for different
reasons. First, carbon pricing without a redistributive mechanism linked to it effectively amounts to
financing a public good, namely climate stability, through regressive taxation. Consequently, it often
encounters strong resistance motivated by equity concerns. Second, the need to reduce GHG
emissions and the related commitment of the Paris Agreement, suggest that carbon pricing will
become deeper in the near future. Third, following James Poterba’s work in this field (1989, 1991a,
1991b), a significant proportion of the literature concludes by playing down the relevance of the
distributional effects of carbon pricing. This outcome stems from specific methodological choices,
notably that of considering (expected) lifetime ability to pay instead of (observable) current ability to
pay.
Using household-level data from the 2012 round of the US Consumer Expenditure Survey (CE)
and from the 2013 Survey of Consumer Finances (SCF), we revisit Poterba’s 1991 seminal paper “Is
the gasoline tax regressive?” (Poterba, 1991a). Poterba’s analysis is extended, empirically, by
imputing observed wealth in the SCF to households in the CE and, theoretically, by considering
wealth as one dimension of economic welfare and, hence, as a complementary measure of ability to
pay. Based on annual gasoline expenditure, we estimate the economic burden of the federal gasoline
tax ($0.184/gallon) relative to three alternative measures of ability to pay: a) annual total expenditure,
as a proxy for lifetime income (Poterba’s approach), b) annual income and c) annual wealth-adjusted
income, which is annual income augmented with a wealth annuity. The analysis of the results consists
in the comparison of the three measurements of the relative tax burdens, first, across the respective
distributions of ability to pay measures and, then, across the distribution of the head of household’s
age. The correlation between wealth and age, due to the first accumulating over time, indeed implies
that the distributional incidence of carbon pricing across age groups changes depending on whether
wealth is considered. Considerations about intergenerational equity are relevant to climate policy
given the difference between the young and the elderly in both the responsibilities for causing climate
change and the related costs faced in prospect.
The rest of the paper is organized as follows. Section 2 reviews the relevant literature. Section 3
explains why wealth should be considered in this context. Section 4 derives and compares the
distributional incidence of the US federal gasoline tax according to alternative measures of ability to
pay. Section 5 concludes.

2. Literature review
The connections between gasoline taxation and carbon pricing are such that our analysis while dealing
with the former can also be relevant to the latter. Focusing on gasoline taxes simplifies the analysis in
terms of data, methodology and assumptions, while being sufficient to identify the role of wealth in
the equity assessment of any policies affecting energy prices.
Aside from the substitution between motor fuels with different carbon content (principally
gasoline and auto diesel), studying the economic effects of gasoline taxes is effectively equivalent to
studying the effects of carbon pricing in the road transportation sector. A second connection between
gasoline taxes and carbon pricing concerns the relative degree of regressivity. Price increases in motor
fuels are typically less regressive than price increases in home fuels (principally electricity and natural
gas), as the demand for the first is more income elastic than that for the second (e.g., Barker and
Köhler, 1998; Tiezzi, 2005; Callan et al., 2009; Ekins et al., 2011; Hassett et al., 2012; Kosonen,
2014; Flues and Thomas, 2015; Verde and Pazienza, 2016). As a result, gasoline taxes are usually less
regressive than carbon pricing when this is operating in other sectors of the economy, notably
electricity generation and the residential sector.
The following literature review focuses on the methodological aspects most relevant to our
analysis. It first covers the empirical studies on gasoline taxes and, subsequently, those on carbon
pricing.
2.1 The distributional incidence of gasoline taxes
The empirical literature on the distributional incidence of gasoline taxes largely uses household
survey data to estimate tax burdens or welfare effects across income levels or socio-demographic
characteristics. The frameworks used are either static or allow for demand response to price changes,
often within demand system models estimated under separable utility assumptions. In the applications
to developed economies, gasoline taxes are found to be regressive to varying degrees or
approximately proportional, in this case often with middle-income households bearing the heaviest
burdens
6
. Importantly, however, the results are not independent from the choices made concerning the
methodology. As noted by Sterner (2012a), at least two types of choice can affect the distributional
outcome significantly. One concerns the inclusion or exclusion of the households that do not own any
vehicles. Since most of these households are at the bottom of the income distribution, their inclusion
(exclusion) in the calculations results in a less (more) regressive outcome. The second choice
concerns the variable measuring the ability to pay or, rather, the time horizon over which the ability to
pay is valued. This is typically the present or, in an ex-ante perspective, a person’s lifetime. The
longer the time horizon, the less variable is the distribution of economic welfare, due to both earnings
patterns over time and income mobility, so gasoline taxes are less regressive over a lifetime. For a
6
In developing economies, gasoline taxes are generally progressive (Sterner, 2012a).

number of countries, Sterner (2012b) contrasts the different distributional incidence of the same
gasoline taxes obtained using the current ability to pay approach and the lifetime approach.
The present paper deals with the implications of the second choice above. In addressing this
question, we are not the first to take a critical stance: Chernick and Reschovsky (1992, 1997, 2000)
were the first, but also the last as far as we are aware. They brought arguments and evidence that
fundamentally question James Poterba’s lifetime approach to estimating the distributional incidence
of gasoline taxes (Poterba, 1991a) and carbon taxes (Poterba, 1991b). Poterba’s approach, which leads
to the conclusion that these taxes are not regressive over a lifetime, consists in the use of current total
expenditure as a proxy for lifetime income and, therefore, as a measure of lifetime ability to pay.
Chernick and Reschovsky point out that this approach, which emanates from Milton Friedman’s
permanent income theory of consumption (Friedman, 1957) and the companion life-cycle model of
saving (Ando and Modigliani, 1963), rests on a set of very strong assumptions, namely: a) income
mobility is very high; b) gasoline consumption decisions are made on the basis of lifetime income;
and c) total consumption is a constant fraction of lifetime income. Using longitudinal data, they test
Poterba’s results by deriving the incidence of the US gasoline tax over an 11-year period, finding that
the gasoline tax burdens are in fact only slightly less regressive than annual burdens. The authors
emphasize that the main reason for the similarity of annual and intermediate-run burdens is the limited
degree of income mobility.
In spite of Chernick and Reschovsky’s analysis and findings, many subsequent studies assess
the distributional incidence of gasoline taxes and carbon taxes using Poterba’s lifetime approach.
Only few take the lifetime perspective while applying more sophisticated approaches than Poterba’s,
including notably Fullerton and Rogers (1993) and Bull et al. (1994). Both the frequent lack of
income data (or of sufficiently good quality income data) in household surveys and its computational
simplicity, may at least partly explain the fortune of Poterba’s approach as reflected in the number of
its followers.
2.2 The distributional incidence of carbon pricing
The literature on the distributional effects of carbon pricing is methodologically more diverse than
that on gasoline taxes. This is the case because carbon pricing can cover an area of the economy that
is broader than the transportation sector. Accordingly, economy-wide models are often used: usually
either computable general equilibrium (CGE) models or macroeconometric models (occasionally
combined with microsimulation models). The advantage of using these models for distributional
analysis is that secondary and general equilibrium effects are taken into account. The CGE literature,
in particular, stresses the capability of these models to capture the distributional effects of carbon
pricing occurring through both the uses side of income, i.e. consumption and savings, as well as the
sources side of income, i.e. the returns to labour, capital and the other primary factors. The
distributional incidence of carbon pricing is thus given by the sum of the effects unfolding over the

two sides of income, which in turn depend on the use of the revenues generated by carbon pricing
(“revenue recycling”) and the (related) impact on the economy. Over time, progressive sources-of-
income effects may partially or even entirely offset the regressive uses-of-income effects typically
captured by partial equilibrium models. Rausch et al. (2011) and Dissou and Siddiqui (2015) illustrate
this type of CGE result.
The CGE literature also stresses the efficiency-equity trade-off between alternative uses of the
revenues generated by carbon pricing. Namely, the redistributive options tackle the regressive
distributional effects, but not the efficiency loss of the economy due to carbon pricing. Vice versa,
through the reduction of distortionary taxes, typically on labour or capital, the efficiency revenue
recycling options tackle the economy’s efficiency loss, but not the distributional effects. This trade-off
relates to our analysis in that underestimating regressivity makes efficiency-enhancing tax cuts unduly
more attractive relative to the redistributive alternatives.
3. Why considering wealth
In official statistics, annual income is the standard measure of ability to pay used to determine the
degree of tax progressivity or regressivity. However, we have just seen that alternative measures of
ability to pay are considered in the empirical literature. Notably, estimated lifetime income measuring
lifetime ability to pay is often used to determine the lifetime distributional incidence of gasoline taxes
or carbon pricing. Fullerton and Rogers (1991), who are among the most prominent proponents of the
lifetime perspective, argue that policymakers should be concerned with “short run equity” as well as
“long run equity”: “the fairness of a tax should be evaluated both on how current taxes reflect current
ability to pay and on how lifetime taxes reflect lifetime ability to pay”.
The central argument of the present paper is that considering wealth as a complementary
measure of ability to pay constitutes an improvement on the use of sole annual income and, all the
more so, of lifetime income. In contrast with Fullerton and Rogers’ point above, short run equity and
long run equity are not equivalent or equally relevant. The two concepts fundamentally differ in that
the first is observable while the second can only be predicted. As far as equity judgments are
concerned, realised outcomes matter, while predicted outcomes do not matter as much. Second, the
lifetime perspective necessarily rests on a set of assumptions which affect the reliability of the results.
Nonetheless, the lifetime results are often presented as lessening the relevance of equity concerns
regarding carbon pricing (e.g., Hassett et al., 2009; Sterner, 2012a, 2012b; Kosonen, 2014; Mathur
and Morris, 2014; Parry, 2015; Williams, 2016). This takes us a step away from the reality of the
equity problem. There is in fact greater urgency for the measurement of ability to pay to be extended
“in perimeter”, by considering wealth, rather than in time, as with the lifetime perspective. The
present section elaborates on these points.

3.1 Ex post equity versus ex ante equity (or short run equity versus long run equity)
The lifetime perspective in evaluating the distributional incidence of gasoline taxes and carbon
pricing, and of all taxes in general, implies that interpersonal comparisons are based on expected
lifetime ability to pay as opposed to observed current ability to pay. Yet, because expectations may
obviously not be what occurs, people normally make equity judgments based on observed welfare
differentials. For the same reason, welfare programs are calibrated based on observed welfare
differentials, not expected ones. As Warren (1980) points out, expectations are central to the
economic theory concerned with the making of rational choices ex ante; but fairness in taxation
should depend – and indeed does depend, in the real world – on outcomes, not expectations.
We thus find the lifetime studies of interest for the analytical insights that they offer, but not as
much for the utility of the related policy implications. By contrast, considering wealth in measuring
current ability to pay is an innovation that provides us with a better representation of reality. This is
because wealth is a dimension of economic welfare (see below) and people internalize observed
wealth differentials (just like income or consumption differentials) in making equity judgments.
Nevertheless, as it stands, the literature on the distributional incidence of gasoline taxes and carbon
pricing ignores wealth altogether.
3.2 Wealth as a dimension of economic welfare
Which, among income, consumption and wealth, should be targeted by direct taxation is a question
long debated by economists. The matter is complex because it relates to philosophical views as well
as both economic and practical considerations. Related to this question, there now seems to be general
agreement that income, consumption and wealth capture different dimensions of a person’s economic
welfare. The Commission on the Measurement of Economic Performance and Social Progress, a.k.a.
the Stiglitz-Sen-Fitoussi (SSF) Commission, recommended in its final report that income,
consumption and wealth be considered together to measure economic welfare and, therefore, to
measure ability to pay (Stiglitz et al., 2009). In the same document, the use of the three indicators is
explained as follows:
“Income flows are an important gauge for the standard of living, but in the end it is consumption and
consumption possibilities over time that matter. The time dimension brings in wealth. A low-income
household with above-average wealth is better off than a low income household without wealth. The
existence of wealth is also one reason why income and consumption are not necessarily equal: for a
given income, consumption can be raised by running down assets or by increasing debt, and
consumption can be reduced by saving and adding to assets. For this reason, wealth is an important
indicator of the sustainability of actual consumption.”

About forty-years before the SFF Commission, Weisbrod and Hansen (1968) were the first to
study the implications of considering wealth (or net worth) as a store of potential consumption and,
therefore, of economic welfare. The authors devised a method whereby income and wealth are
combined into a single indicator of economic welfare. They then explored the implications of using
the income-wealth indicator (“wealth-adjusted income”, as we call it below) for the assessment of
economic inequality, including tax progressivity and regressivity, and for the prediction of
consumption behaviour. The key element of the authors’ analysis is the imperfect correlation between
income and wealth, which means that households’ welfare ranking is different depending on whether
income or the income-wealth indicator is used. Weisbrod and Hansen’s income-wealth indicator was
refined and integrated in the Levy Institute Measure of Economic Well-being (LIMEW) (Wolff et al.,
2007), from which our application below borrows some methodological aspects.
3.3 Wealth inequality and carbon pricing: “the elephant in the room”
It is a well-known fact that the distribution of income and the distribution of wealth differ
significantly, the latter being more concentrated than the former. In Capital in the twenty-first century,
Piketty (2014) examines the evolution of the two distributions, primarily in Europe and in the US,
since before the nineteenth century. While wealth concentrations are much lower today than at the
peak, in the years preceding World War I, one of Piketty’s main conclusions is that very high wealth
concentrations may characterise the economy of the twenty-first century. The last four decades have
indeed seen a positive trend in wealth concentrations over time, especially in the US, which may well
continue if certain conditions persist. In this context, taking wealth into account – to evaluate people’s
welfare and to address distributional issues – is all the more desirable. Yet, to date annual income
remains the only measure used for such purposes.
The utility of considering wealth is general, in the sense that it would benefit any type of
assessment concerning economic equity. However, we deem it to be particularly relevant for
appreciating and, thereby, for dealing with the opposition to carbon pricing motivated by equity
concerns. First, one needs to recall that the ultimate purpose of carbon pricing is to maintain a stable
climate, which is a (global) public good. Second, everyone supports public goods as long as their cost
is shared in a way that is perceived as fair. Indeed, it is difficult to imagine that no opposition would
arise to a public good being financed through regressive taxation. Though never clearly
acknowledged, as far as we are aware, carbon pricing without a redistributive mechanism linked to it
effectively corresponds to this type of setting
7
. Considering wealth in evaluating economic welfare is
therefore all the more desirable in relation to carbon pricing. Adapting a figurative expression, if
wealth is the elephant in the room that somehow goes unnoticed, carbon pricing as a public good
problem makes the room smaller: so the elephant is even bigger in relative terms.
7
The provision of public goods is usually financed through the general tax system, which in the modern fiscal
state is not regressive.

4. The distributional incidence of the US gasoline tax
In the US, three tax layers apply to the consumption of gasoline and auto diesel, namely, federal taxes,
State taxes and local taxes. The federal tax rate on gasoline is currently 0.184 $/gallon and has not
changed since 2006. The federal tax rate on auto diesel is 0.244 $/gallon. State and local taxes can
differ significantly across the country and, as compared with the federal taxes, are more frequently
subject to revisions. In recent years, growing concerns related to declining fiscal revenues and high
CO
2
emissions meant that the option of raising gasoline taxes has received increasing consideration in
the public policy debate. However, raising gasoline taxes is still anything but a popular measure, all
the more so in an economy heavily dependent on private transportation.
Using data referring to the year 2012, we derive the distributional incidence of the US federal
gasoline tax across households. The purpose of the analysis is to show the implications of using
different ability to pay measures for the resulting distributional incidence. Bringing in wealth as a
measure of ability to pay complementary to income is our contribution to the literature, which results
in a more accurate rendering of the distributional incidence. The first part of this section is devoted to
a) the data work for imputing wealth to the households in our sample and b) the assumptions made for
determining wealth-adjusted income. The second part deals with the differences in distribution
between the alternative ability to pay measures. The third part examines the respective differences in
distributional incidence both across welfare levels and the head of household’s age.
4.1 Data
Our analysis is based on household-level data from the 2012 round of the US Consumption
Expenditure Survey (CE). Our sample consists of 2,179 households, those for whom annual
expenditure could be derived
8
. Developed by the Bureau of Labor Statistics (BLS), the CE is the most
comprehensive data source on US households’ consumption choices, including information on
expenditure, income and socio-demographics
9
. The CE serves well the purpose of our study, as is the
case for most of the closely related US literature.
Crucially, however, the CE does not contain information (or, rather, not sufficiently accurate
information) on households’ wealth. To overcome this limitation, we use statistical matching (aka
data fusion) whereby household-level information on wealth is imported from the US Survey of
Consumer Finances (SCF) into our CE sample. After performing the statistical matching, we follow
Wolff et al. (2005, 2007) and Wolff and Zacharias (2009) in developing an indicator of economic
well-being which aptly combines households’ income and wealth. This indicator, measuring what is
hereafter referred to as wealth-adjusted income, allows us to assess the distributional incidence of the
gasoline tax taking the wealth dimension of a household’s ability to pay into account. The three
8
In the 2012 round of the CE, this is the number of households with four quarterly interviews.
9
The BLS uses the CE to periodically revise the expenditure weights of the Consumer Price Index.

measures of ability to pay, namely income, total expenditure and wealth-adjusted income, are flow
variables directly comparable to one another.
4.1.1 Statistical matching
The purpose of statistical matching is to obtain joint information on the not jointly observed variables
(D’Orazio et al., 2006). The most common setting is that of two surveys drawn from the same
population and sharing a set of common variables, X, typically socio-demographic variables, but not
other variables, Y and Z, whose relationship is of interest. In practice, we use statistical matching to
assign specific households’ observed wealth in the SCF sample to the households in our CE sample.
The imputation of wealth is based on the relationships between the common variables (X) and both
wealth (Y) and gasoline expenditure (Z). The resulting fused dataset is the initial CE sample (which
includes information on gasoline expenditure) augmented with imputed wealth.
After harmonizing the variables shared by the two surveys, only those with similar empirical
distributions in the two datasets and, also, statistically associated with both wealth and gasoline
expenditure in the donor and recipient datasets, respectively, are selected as matching variables
(D’Orazio et al., 2006). These turn out to be the following: household income, housing tenure, age of
the reference person, her education level, her marital status and her employer type. Propensity score
matching (Rässler, 2002) is then used to assign observed wealth in the SCF to each household in the
CE dataset. Propensity scores are derived based on the matching variables above and the Mahalonobis
distance function is applied to pair households across the two datasets. The resulting fused dataset
satisfactorily meets the standard validity requirements of statistical matching (Rässler, 2002, 2004).
More details on the matching procedure are provided in Section A of the Appendix.
4.1.2 Measuring wealth-adjusted income
Annual income is the sum of labour income (wages and salaries) and property income (interests,
dividends and rents). Wealth is, by contrast, a stock variable, here defined as “net worth”: the current
value of all marketable or fungible assets less the current value of all debts. Following Wolff and
Zacharias (2009), we consider only assets that can be readily converted to cash, and so converted into
potential consumption, without compromising current consumption. Accordingly, consumer durable
goods, future social security benefits and future retirement benefits from defined-benefit private
pensions are not included. To combine wealth and income into a single ability to pay measure, wealth
as just defined needs to be converted into a flow variable. It is converted into a stream of constant
annual payments (annuities) covering the expected remaining life of the head of household or of the
younger spouse if there is one
10
. Basically, wealth is spread evenly over time such that its stock is
10
Together with age, we take into account gender differences in life expectancy. Life expectancy estimates are
taken from Arias (2015).

exhausted at the end of the given expected lifetime. Wealth-adjusted income is then the sum of annual
income and a single wealth annuity.
The wealth annuities have two main components corresponding to home and non-home assets.
The first component is an imputed rent for owner-occupied housing. The second is derived based on a
weighted average of historical rates of return on different types of assets. Table 1 shows summary
statistics of households’ (imputed) assets and liabilities per adult equivalent
11
in the fused dataset
12
.
Table 1 – Net worth (per adult equivalent) and its composition.
Mean Std. Dev. Min Max Mean share
of Net worth Ownership
rates
a
Net worth 217,293 413,973 -242,446 3,446,505 100% 100%
Assets
Owner-occupied housing 108,533 151,996 0 2,500,000 50% 70%
Real estate and business 49,184 203,522 -78,000 2,894,000 23% 28%
Liquid assets 23,510 59,821 0 815,000 11% 94%
Financial assets 27,502 113,193 0 1,764,000 13% 33%
Retirement assets 54,562 149,937 0 2,123,001 25% 50%
Debts
Mortgage debt 37,897 69,116 0 890,666 17% 44%
Other debt 8,103 19,928 0 450,000 4% 61%
a.: Percentage of households owning the asset.
Housing is a universal need and home ownership frees the owner from the obligation of paying
a rent, leaving an equivalent amount of financial resources for other uses. The rent imputed to the
households owning their home is calculated by multiplying the value of the given dwelling by the US
ratio of (imputed) rent-to-home value for owner-occupied homes. Formally, the imputed rent of
household i is IR
i
= h
i
*(IR/H), where h
i
is the value of the dwelling, while IR and H are the country-
level sums of the imputed rents and values, respectively, of owner-occupied homes
13
. The 2012 US
rent-to-home ratio (IR/H) is 5.7% and, on average, IR
i
makes up 8.9% of wealth-adjusted income
(Table 2).
The non-home component of the wealth annuity is derived by updating and applying the return
rates used by Wolff and Zacharias (2009) (see Table B1, in the Appendix). We use average return
rates calculated over the period 1972-2012
14
. As these rates already include both capital gains and any
11
The new OECD equivalence scale is used, in which the head of household weighs 1, all other household
members aged over 13 weigh 0.5 each, and those under 14 weigh 0.3 each.
12
Sampling weights are applied in all the calculations presented in this paper (including summary statistics).
13
The 2012 value of IR is taken from the National Income and Product Accounts, Table 7.12, Line 154 (Bureau
of Economic Analysis, 2015). The 2012 value of H is taken from the Federal Reserve’s (2012) Flow of Funds
Accounts.
14
The data on return rates are from the Federal Reserve’s (2012) Flow of Funds Accounts (see Appendix C).

income the assets may generate, property income is subtracted from household annual income to
avoid double counting.
Table 2 – Composition of wealth-adjusted income.
Variable Mean Std. Dev. Median
Income 79.1% 22.8 84.3%
Property income -1.3% 9.8 -0.0%
Wealth annuity 22.1% 21.5 16.4%
Non-home wealth annuity 13.1% 18.0 5.2%
Home-wealth annuity 8.9% 10.5 6.9%
4.2 Differences between the distributions of alternative ability to pay measures
For a household, or an individual, the relative burden of the gasoline tax is given by the tax payment
embedded in her gasoline expenditure relative to her ability to pay. In the literature, the denominator
of this ratio is either annual income or annual total expenditure as a proxy for lifetime income. We
consider wealth as an additional dimension of economic welfare. Since wealth is a stock variable,
while both income and total expenditure are flows, wealth-adjusted income (rather than wealth) is the
third alternative measure of ability to pay directly comparable to the others. The distribution of the
relative tax burden across households is clearly dependent on that of the variable at the denominator:
the more uneven (dispersed) the distribution of the ability to pay measure, the more uneven the
distribution of the relative tax burden too. Moreover, to the extent that the different measures of
ability to pay are imperfectly correlated with one another, the ranking of households by tax burden
will also depend on which measure of ability to pay is used.
4.2.1 Differences in distribution and households’ ranking
With reference to the fused dataset, Table 3 reports descriptive statistics of the sample distributions of
a) annual income, b) annual total expenditure, c) wealth and d) wealth-adjusted income, all of which
are expressed in per adult equivalent terms. While the median of total expenditure is not much smaller
than that of income, the distance widens for the upper parts of the two distributions, as one would
expect. The distribution of wealth exhibits negative values up to around the 10
th
percentile, it becomes
positive and rapidly increases thereafter.
The skewness statistics indicate that the distribution of wealth is the most asymmetric, as being more
positively skewed than those of income and especially of total expenditure. The kurtosis statistics tell
us that the distribution of wealth is also that with the heaviest tails (relative to the rest of the
distribution). We can then deduce that the wealth distribution has a longer right tale. This is reflected
in the higher concentration of wealth as measured by the Gini coefficient and pictured in Figure 1.

Table 3 – Distributions of Net worth and ability to pay measures (per adult equivalent).
Net worth Income Total
expenditure Wealth-adj.
income
1
st
percentile -45,740 1,629 6,538 3,016
5
th
percentile -14,497 7,064 9,739 8,382
10
th
percentile -5,252 10,000 11,636 11,764
25
th
percentile 967 17,680 17,045 22,314
50
th
percentile 57,666 31,481 26,416 42,110
75
th
percentile 241,866 53,199 39,569 77,375
90
th
percentile 617,200 85,833 56,644 134,699
95
th
percentile 1,035,670 110,528 71,688 192,688
99
th
percentile 2,033,803 213,486 111,197 320,233
Mean 217,293 42,392 31,613 61,356
Std. Dev. 413,937 39,594 21,167 62,166
CV 1.91 0.93 0.67 1.01
Kurtosis 18.66 14.16 11.27 11.31
Skewness 3.50 2.74 2.15 2.49
Gini coefficient 0.76 0.44 0.34 0.47
As the Gini indices show, despite wealth being highly concentrated, wealth-adjusted income is
only slightly more concentrated than income. Wolff et al. (2009) explain that there are two reasons for
the small difference, in terms of concentration, between the two variables. First, household income
and wealth are not perfectly correlated, so that there are households with low income but high wealth
and also with high income but low wealth. Second, the annuity payments are limited in size relative to
annual income, the former making up on average 22% of the latter (Table 2). As a result, the inclusion
of wealth annuities in augmented income does not alter the overall distribution of income very much.
In principle, alternative ability to pay measures may have equally shaped distributions but
entirely different ranking of the statistical units, which are households in our case. In general, the
weaker is the correlation between the two variables, the greater is this type of mismatch. Table 4
illustrates the frequency of these changes in households’ ranking when switching from one measure of
ability to pay to another.

Figure 1 – Lorenz curves of ability-to-pay measures.
0
.2
.4
.6
.8
1
L(p)
0 .2 .4 .6 .8 1
Percentiles (p)
equality line Income
Tot. Expenditure Wealth
Wealth adj. income
For each of the five pairs of distributions, the rows indicate the shares of total households falling in
the same quintiles of the two distributions (in which case the quintile change is equal to 0) or in
quintiles that are one to four quintiles apart (in which case the quintile change ranges between -1 and -
4 and between +1 and +4). In the first column, the comparison of income vs total expenditure shows
that only 46% of all households are equally positioned in the two distributions. The negative values (-
1 to -4) correspond to the households that are relatively richer in total expenditure than in income:
they add up to 25% of all households; and vice versa for the positive values (1 to 4). The mismatch is
slightly more frequent in the comparison of total expenditure vs wealth-adjusted income (second
column), while it is clearly less frequent in that of income vs wealth-adjusted income (third column)
15
.
15
The mismatch is much more pronounced in the comparisons of both total expenditure and income vs wealth
(fourth and fifth column, respectively).

Table 4 – Frequency of changes in quintile ranking (%).
Change in
quintile
Income
vs
Tot. exp.
Tot. exp.
vs
Wealth-adj.
income
Income
vs
Wealth-adj.
income
Tot. exp.
vs
Net worth
Income
vs
Net worth
-4 0.5 0.4 0.5 0.9 1.1
-3 2.0 1.7 0.8 4.1 3.7
-2 5.6 5.2 2.1 10.9 9.7
-1 16.7 20.3 10.7 20.3 20.0
0 46.3 45.2 67.2 30.6 32.2
1 23.0 19.6 18.6 17.3 18.9
2 5.2 5.7 0.2 9.7 8.4
3 0.6 1.6 0.1 4.1 4.3
4 0.1 0.4 0.0 2.2 1.6
Total 100.0 100.0 100.0 100.0 100.0
Correlation 0.72 0.66 0.88 0.34 0.42
4.2.2 Differences across age groups
For the simple reason that people accumulate wealth over time, taking wealth into account in
determining ability to pay has a disequalizing effect over households’ age dimension. To examine this
aspect, we have partitioned our sample into seven groups according to the age of the head of
household (Table 5).
Table 5 – Frequency distribution of households by head of household's age.
Age group < 25 25-34 35-44 45-54 55-64 65-74 > 74
Frequency (%)
3.5
13.0
17.2
20.7
20.0
14.4
11.3
The top graph in Figure 2 shows median wealth per adult equivalent by the head of household’s
age group. The pattern of median wealth across age groups is very clear. The wealth owned by the
median household in the top age group, 75-89 years old, is about ten times that of the median
household in the 35-44 year-old group. The difference is even more striking if the comparison is made
with the two youngest groups; or if cumulated wealth over the three oldest groups is compared with
that of the three youngest.

Figure 2 – Wealth and ability to pay measures by head of household’s age group.
0 50 100 150
15-24 25-34 35-44 45-54 55-64 65-74 75-89
thousand US$
head of household's age
Median wealth by HoH's age
0 20 40 60
15-24 25-34 35-44 45-54 55-64 65-74 75-89
thousand US$
head of household's age
Median Income, Tot. expend., Wealth adj. income by HoH's age
income tot. expenditure wealth adj. income
The bottom graph in the same Figure shows the median values of the different ability to pay
measures – income, total expenditure and wealth-adjusted income – by age group. When contrasting
income and total expenditure, the most significant differences between the two are observed for the
45-54 and the 55-64 mid groups. The pattern of wealth-adjusted income is such that the difference of
income or total expenditure tends to widen with the head of household’s age. Thus, while for the
youngest households, whether income, total expenditure or wealth-adjusted income is considered does
not make much of a difference in absolute terms, it does make a difference for the more mature
households. For these households, substantially higher levels of wealth-adjusted income relative to
income or total expenditure mean that their ability to pay is significantly underestimated when using
one of the two latter measures. Moreover, due again to the highly uneven distribution of wealth across
age, ranking effects correlated with age stem from the inclusion of wealth in the measurement of
ability to pay (see Figure C1, in the Appendix).
4.3 The distributional incidence of the gasoline tax by ability to pay measure
We now turn to examining the distributional incidence of the gasoline tax according to the measuring
of ability to pay. We first focus on tax regressivity, which concerns the distributional incidence of the
tax across levels of ability to pay. We then consider the distributional incidence of the gasoline tax
across age groups.

4.3.1 The degree of tax regressivity
For a person or a household, the relative burden of a commodity tax is given by the ratio between the
tax payment implicit in her consumption of the good and her ability to pay. The distribution of these
burdens across levels of ability to pay determines the degree of regressivity, or progressivity, of the
tax. If the tax under study is one already in force, as opposed to a hypothetical new tax or a tax
increase (in these cases allowing for demand response is relevant), its degree of regressivity is very
well proxied by the distribution of the ratio between expenditure on the given good and ability to pay.
The graphs in Figure 3 show median gasoline expenditure as a proportion of the different ability to
pay measures, by decile (of the corresponding variable measuring ability to pay).
Figure 3 – Gasoline expenditure as a share of alternative ability to pay measures.
0 5 10
median share, %
1 2 3 4 5 6 7 8 910
A) Income
income decile
0 5 10
median share, %
1 2 3 4 5 6 7 8 9 10
B) Tot. expend.
tot. expend. decile
0 5 10
median share, %
1 2 3 4 5 6 7 8 9 10
C) Wealth adj. income
wealth adj. income decile
Gasoline expenditure as a share of:
The median burden of the first decile is clearly highest (11.3%) when ability to pay is measured by
income (A graph). The steep decline of the median burden across the income deciles suggests that the
gasoline tax is highly regressive. The same conclusion applies when ability to pay is measured by
wealth-adjusted income (C graph), but a more rigorous assessment will allow us to ascertain which of
the two measures results in a more regressive outcome (see below). By contrast, the distributional
incidence of the gasoline tax appears to be significantly less regressive when ability to pay is
measured by total expenditure (B graph). As in most of the studies that use total expenditure as a

proxy for lifetime income, the gasoline tax is found to be progressive over the lower part of the total
expenditure distribution and then to turn to regressive over the better-off deciles.
To quantify the degree of tax regressivity for the three alternative measures of ability to pay, we
calculate the Suits index (Suits, 1977). To do this, we first derive each household’s tax payment by
dividing gasoline expenditure by the relevant average gasoline price
16, 17
. Analogous to the Gini index
for its geometrical derivation, the Suits index, S, can take any value between +1 and -1, which
correspond to the limiting cases of progressivity (the wealthiest bear the entire tax burden) and
regressivity (the poorest bear the entire tax burden), respectively, and is equal to 0 in the case of
perfect proportionality. Let y be the cumulative share of overall income, or total expenditure or
wealth-adjusted income, and T the cumulative share of overall tax payments,
5000
11
∫
−=−=
100
0
T(y)dy
K
L
S
(1)
where L is the area under the Lorenz curve and K the area under the 45-degree line of proportionality
(
5000
2
100
100 =×
).
We find:
29.0
−
=
I
S
,
15.0
−
=
C
S
and
36.0
−
=
WI
S
, for income (I), total expenditure (C)
and wealth-adjusted income (WI), respectively. The graph in Figure 4 contrasts the three Lorenz
curves.
Figure 4 – Lorenz curve for the US gasoline tax, by ability to pay measure.
16
We use monthly US average tax-inclusive gasoline prices published by the US Energy Information
Administration.
17
Figure C2, in the Appendix, shows the median tax payment as a proportion of the alternative ability to pay
measures, by decile.

Thus, the gasoline tax turns out to be more regressive if ability to pay is measured by wealth-adjusted
income than if the same is measured by income. The difference is substantial, as it represents a 24%
increase in regressivity. What is more, the difference is rather sizable, representing a 140% increase in
regressivity, if the comparison is made with the outcome resulting from using total expenditure in the
lifetime perspective.
4.3.2 The incidence of the tax across age groups
On average, households with a young or an elderly head of household consume less gasoline than
those with a middle-aged head of household (see Figure C3, in the Appendix). At the same time,
households of the latter type tend to exhibit greater ability to pay (Figure 2 above). However, we here
examine how the incidence of the gasoline tax varies across age groups, depending on the measure of
ability to pay alone.
Figure 5 – Tax burdens as shares of alternative ability to pay measures, by head of household’s age.
0 .1 .2 .3 .4
15-24 25-34 35-44 45-54 55-64 65-74 75-89
median share, %
head of household's age
Gasoline tax payments by ability to pay measure and HoH's age
income tot. expenditure wealth adj. income
Figure 5 shows the relative tax burdens across age groups, by measure of ability to pay. The
disequalizing effect of using total expenditure instead of income turns out to be somewhat limited. By
contrast, when using wealth-adjusted income instead of income, (on average) older age groups
systematically bear lower burdens than younger ones. This means that, in relative terms, the burdens
borne by older (younger) households are overestimated (underestimated) if wealth is not considered in
measuring ability to pay.

5. Conclusions
The literature on the distributional incidence of gasoline taxes, as well as of carbon pricing, ignores
wealth as a dimension of economic welfare and, thus, as a component of ability to pay. With reference
to the US gasoline tax, we show that this is an important omission, which results in a significant
underestimation of both the regressivity of the tax and its inequity towards younger people. Taking
wealth into account exacerbates the regressivity outcome because the distribution of wealth is much
more concentrated than that of income, which is the standard measure of current ability to pay, and all
the more so of total expenditure, often used as a proxy for lifetime ability to pay. Taking wealth into
account also reveals that, in relative terms, younger people actually bear greater tax burdens than
those resulting from using income or total expenditure as measures of ability to pay. This is the case
because, on average, older people own more wealth.
These findings are relevant in light of the opposition to gasoline tax increases, or equally to the
introduction or deepening of carbon pricing, motivated by the inequity of energy price increases. To
be sure, to overcome this type of opposition, the distributional effects in question first need to be
properly assessed. It will then be possible to address them through better calibrated redistributive
measures. The relevance of our findings is further reinforced by the fact that a significant part of the
literature draws conclusions pointing right in the opposite direction. Notably, the lifetime perspective
taken by many empirical studies results in somewhat mitigated distributional effects, including, e.g.,
gasoline taxes turning from regressive to proportional. However, the utility of the policy implications
that this type of result bears is questionable on different grounds. First, the lifetime perspective is
flawed in that people make interpersonal welfare comparisons – and hence equity judgments – based
on realised outcomes, not expectations. Welfare programs are indeed calibrated based on observed
welfare differentials, not expected ones. Second, the strong assumptions underlying the lifetime
approach affect the accuracy of the outcomes.
Our analysis ultimately indicates that, by not considering wealth, the existing literature on the
distributional incidence of gasoline taxes and of carbon pricing is biased against the regressivity of
such policies. Greater regressivity than that emerging from this literature may help explain why equity
concerns are such a big issue in this domain. Of course this does not make the cost-effectiveness case
for environmental policies that raise energy prices any less powerful. It does imply, however, that
their distributional effects should not be underestimated and that appropriate redistributive measures
should be foreseen for the same policies to be fair and, thus, ultimately to be politically sustainable.

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Appendix
A. Propensity score matching
Among the statistical matching methods, the literature distinguishes between parametrical and non-
parametrical approaches, both with their advantages and trade-offs. We here apply a mixed method
which takes the best of both worlds: the parsimony of parametric methods and the robustness to
misspecification of non-parametric techniques (D’Orazio et al., 2006). Specifically, we perform a
propensity score matching (PSM) as described in Rässler (2002).
Though originally developed as a method to infer causal effects (Rosenbaum and Rubin, 1983),
the PSM is increasingly being used to integrate pairs of datasets (Eurostat, 2013; Tedeschi and Pisano,
2013; Kaplan and Turner, 2012; Baldini et al., 2015). The PSM procedure consists of two steps. In the
first step, a logit (or probit) model is fitted to a binary variable, D, indicating which of the two
datasets an observation belongs to (e.g., D = 0 if observation i belongs to the donor dataset, D = 1 if i
is from the recipient dataset). A set of selected variables, X, which are common to both datasets, are
used as independent variables:
)...(
110
1
1
]1Pr[
kk
xx
i
e
XDp
βββ
+++−
+
===
(A1)
The propensity score (PS) is the predicted probability of an observation to belong to the recipient
dataset – the CE sample in our case – conditional on X. The second step consists in matching the
observations according to their PS, so that each unit of the recipient dataset is paired to the
observation in the donor dataset exhibiting the closest propensity score according to a chosen distance
function.
In our application, each CE observation is matched with one SCF observation. The wealth
observed on the latter is then imputed to the former. The size of the SCF sample (30,075 observations)
is much larger than that of our CE sample (2,179), which benefits the efficiency of the matching.
However, due to oversampling of wealthy households in the SCF (Kennickell, 2007), we follow
Bostic et al. (2009) in dropping the top income decile in the SCF dataset. This results in the removal
of the top 5% wealth values (268 observations) and 3 observations with negative wealth.
A.1 Selection of the matching variables
The choice of the matching technique, such as the PSM, is only one of the steps required to integrate
two datasets. The quality of the matching results is strongly dependent on the preliminary selection of
the matching variables. These are a subset of the variables common to the two datasets (donor and
recipient) selected based on both a) the similarity of their empirical distributions in the two datasets

and b) the strength of their statistical association with the variables whose relationship is of interest,
which are wealth and gasoline expenditure in our case.
To verify the first requirement, the common variables need to be homogenous across datasets
both in terms of definition and statistical content. Thus, unless they are already identically defined,
they have to be re-coded to ensure that the information they bear is exactly the same. Table A1 lists
the common variables that have been considered as candidate matching variables.
Table A1: Common variables CE-SCF considered for statistical matching
.
Characteristics of Reference
person and Spouse Marital status, Sex reference person, Sex of spouse, age of reference person, age of spouse,
race of the Reference Person, race of spouse, education of Ref. Person, education of
Spouse, ref. Person self-employed, Spouse self-employed.
Economic Characteristics Family Income Before taxes, family Salaries, non-working group of ref. person
(incnonw1_js), non-working group of spouse (incnonw2_js), hours worked in a week by
ref., hours worked in a week by spouse, number autos, food at home, Food away.
House
Home renter (CU tenure)
,
Rent paid
Household Structure Family size, number of members under 18, number of members over 64.
As the two datasets are samples drawn from the same population, the common variables should
be homogenous in their statistical content too. That is, they should exhibit similar marginal and
conditional distributions (Leulescu and Agafitei, 2013). Only variables with sufficiently similar
distributions in the two datasets can be used in the matching algorithm. Different approaches can be
used to assess the degree of similarity between pairs of distributions, the most popular being the
simple inspection of the frequency distributions and the more rigorous calculation of the Hellinger
distance. The Hellinger distance (HD) ranges between 0 and 1, these extreme values corresponding to
perfect similarity and total discrepancy, respectively. In the literature, HD = 0.05 is often taken as
reference threshold. Figure A1 shows the HD results obtained for the CE-SCF common variables,
while also highlighting those eventually selected as matching variables (see below). Tables comparing
marginal and conditional distributions of the same variables across datasets are available from the
authors upon request.

Figure A1. Hellinger Distances for common variables
The second requirement for a matching variable is to be statistically associated with both the
variable of interest in the donor dataset, Y (wealth), and the variable of interest in the recipient
dataset, Z (gasoline expenditure). After separately regressing Y and Z against the common variables,
only those with sufficiently low HD (ideally below the 0.05 standard threshold) and, at the same time,
showing significant explanatory power are selected as matching variables. To get plausible estimates
of the (unobserved) joint distribution of Y and Z, strong explanatory power of the matching variables
X is indeed critical
18
. In our application, the set of selected matching variables (i.e., those used in the
logit model of the PSM) is narrowed down to: household income, housing tenure, age of the reference
person, her education level, her marital status and her employer type.
A.2 Matching results
Once the matching variables have been selected, different matching algorithms can be considered.
The choice of the matching algorithm is based on the quality of the resulting matching. This is usually
18
If the matching variables have strong statistical association both with Y and Z, the fundamental assumption of
conditional independence between Y and Z (conditional on X) is easier to hold. If so, inference concerning the
actually unobserved association is valid (Rässler, 2004).

assessed by three increasingly demanding criteria concerning the similarity between the distribution
of the observed target variable (here, wealth) in the donor dataset and that of its imputed counterpart
in the fused dataset. With reference to the target variable and the matching variables, the three criteria
concern the preservation of i) the marginal and conditional distributions, ii) the correlation structure,
and iii) the joint distribution (Rässler, 2004). In our application, while different matching methods
perform similarly in terms of wealth’s marginal and conditional distributions, the Mahalanobis metric
(Leuven and Sianesi, 2003) outperform with respect to the other two more stringent criteria. Overall,
the quality of the matching is deemed satisfactory.
(i) Marginal and conditional distributions
The HD between observed wealth in the SCF dataset and imputed wealth in the fused dataset is equal
to 0.05, indicating only a small discrepancy. Table A2 contrasts the respective marginal distributions.
The similarity between the two distributions is also illustrated with the Q-Q plot and the histogram in
Figure A2 (top and bottom graph, respectively).
Table A2. Comparison of wealth distribution between CE and SCF after matching
wealth cutoff SCF Obs. (%) CE Obs. (%) mean diff. Diff/SCF(%)
-366360- -58,418 1,209 5.10% -59,147 74 3.40% 729 -1%
-18550- -8,800 1,195 5.10% -8,965 92 4.20% 166 -2%
-2420- -406 1,184 5.00% -313 102 4.70% -93 23%
330- 1,979 1,203 5.10% 2,159 83 3.80% -180 -9%
3810- 5,733 1,185 5.00% 5,480 95 4.40% 253 4%
8100- 10,276 1,199 5.10% 10,234 89 4.10% 42 0%
13260- 17,165 1,182 5.00% 17,174 97 4.50% -9 0%
21800- 28,447 1,186 5.00% 28,109 111 5.10% 338 1%
35790- 45,522 1,164 4.90% 45,822 119 5.50% -300 -1%
56900- 68,947 1,178 5.00% 69,256 111 5.10% -309 0%
82110- 97,772 1,156 4.90% 98,056 129 5.90% -284 0%
115140- 136,502 1,149 4.90% 135,499 135 6.20% 1,003 1%
159900- 185,634 1,162 4.90% 186,981 126 5.80% -1,347 -1%
213600- 246,228 1,163 4.90% 248,734 120 5.50% -2,507 -1%
282400- 331,172 1,166 5.00% 331,306 122 5.60% -134 0%
387900- 450,216 1,167 5.00% 459,489 117 5.40% -9,273 -2%
530800- 632,371 1,168 5.00% 629,761 120 5.50% 2,610 0%
735250- 886,546 1,169 5.00% 876,751 117 5.40% 9,794 1%
1063300- 1,361,926 1,163 4.90% 1,364,345 123 5.60% -2,420 0%
1780000- 2,537,842 1,189 5.10% 2,596,898 97 4.50% -59,056 -2%
Total 23,537 100% 2,179 100%
Skewness 2.7 2.72 -0.02 -1%
Kurtosis 10.71 11.12 -0.41 -4%
Gini 0.75 0.72 0.03 4%
Theil (0) 1.52 1.33 0.19 13%
Theil (1) 0.91 0.84 0.07 8%

Figure A2. Wealth distribution in SCF and CE
0 1000000 2000000 3000000 4000000
Wealth CEX
0 1000000 2000000 3000000 4000000
Wealth SCF
sample means
0
5
10
15
20
25
30
35
40
Percent
0 1000000 2000000 3000000 4000000
Wealth
SCF observed wealth CE imputed wealth
Figure A3 contrasts the conditional distributions of observed wealth and imputed wealth in the
donor dataset and in the fused dataset, respectively, against some matching variables. The conditional
distributions in the first dataset are generally well preserved in the second.

Figure A3. Conditional distribution of Wealth before and after fusion.
0 500000 1.0e+06
Owned Rented
0 500000 1.0e+06
Married Widowed Divorced Separated Never married
0 500000 1.0e+06
Working Retired Other
0 500000 1.0e+06
Non White White
0 500000 1.0e+06
16- 25- 29- 32- 35- 37- 40- 43- 45- 48- 50- 52- 54- 57- 59- 62- 64- 68- 73- 79-
0 500000 1.0e+06
No school 8th grade 12th grade HS gradeSome Colle.Ass. Deg.B ach. Deg. Postgrad.
mean of wealth (SCF) mean of wealth (CE)
Moreover, Table A3 contrasts the composition of observed wealth and that of imputed wealth.
Again, the main distributional characteristics are maintained after the matching. Thus, the relative
importance of the different wealth components (as well as the respective ownership rates) is similar in
the donor and in the fused dataset.
Table A3. Wealth components in imputed CE and observed SCF
Variable Mean Std. Dev. Ownership rates
CE SCF CE SCF CE SCF
Net Worth
217,293
100%
236,089
100%
413,974
473,921
100%
100%
Assets
Owner-occup. house 108,533 50% 140,820 60% 151,996
200,514 68% 61%
Real estate and
business 49,185 23% 50,803 22% 203,522
207,561 27% 30%
Liquid assets 23,511 11% 25,785 11% 59,821
72,965 93% 92%
Financial assets 27,502 13% 33,095 14% 113,194
147,581 33% 32%
Retirement assets 54,563 25% 61,781 26% 149,937
167,384 50% 48%
Debts
Mortgage debt - 37,897
-17% - 61,870 -26% 69,117
11,398 42% 41%
Other debt - 8,104
-4% - 14,325
-6% 19,929
28,702
60% 63%
Note: values with sampling weights . a. Ownership rates refer to the percentage of households that actually own the given asset.

(ii) Correlation structure
The second, more demanding assessment criterion concerns the preservation, after the matching, of
the correlation structure of wealth and the matching variables. Accordingly, Table A4 contrasts the
relevant correlation matrices in the donor dataset (observed wealth) and in the fused dataset (imputed
wealth). No major differences are observed.
Table A4. Correlation structure between common variables in both SCF and CEX after fusion
Ln
(netw.) Ln (F.
Income) Sq.
Income
Self.
Empl.
Ref House
tenure Age
ref.
sq.
age
ref. No
school Some
Coll Bach.
D. Post. marit.
ln(networth) 1.00
ln(Family Income Before taxes) 0.59 1.00
Squared Family Income Before taxes 0.35 0.58 1.00
Self employed Ref. -0.10 0.18 -0.01 1.00
House tenure -0.58 -0.32 -0.17 0.11 1.00
Age Ref. Person 0.32 -0.02 -0.01 -0.46 -0.32 1.00
Squared Age Ref. Person 0.29 -0.07 -0.04 -0.48 -0.29 0.98 1.00
No school -0.03 -0.05 -0.02 0.01 0.02 0.01 0.01 1.00
Some College -0.08 -0.10 -0.09 0.01 0.08 -0.05 -0.04 -0.02 1.00
Bach. Degree 0.22 0.22 0.13 0.04 -0.10 -0.03 -0.04 -0.02 -0.23 1.00
Postgrad. 0.29 0.33 0.26 0.04 -0.12 0.02 0.00 -0.02 -0.19 -0.21 1.00
marital st. separated -0.15 -0.13 -0.04 0.01 0.12 -0.05 -0.06 -0.01 0.03 -0.04 -0.06 1.00
Ln
(netw.) Ln (F.
Income) Sq.
Income
Self.
Empl.
Ref House
tenure Age
ref.
sq.
age
ref. No
school Some
Coll Bach.
D. Post. marit.
ln(networth) 1.00
ln(Family Income Before taxes) 0.46 1.00
Squared Family Income Before taxes 0.33 0.56 1.00
Self employed Ref. -0.03 0.36 0.14 1.00
House tenure -0.54 -0.24 -0.16 0.04 1.00
Age Ref. Person 0.23 -0.20 -0.07 -0.54 -0.20 1.00
Squared Age Ref. Person 0.20 -0.23 -0.10 -0.56 -0.17 0.99 1.00
No school -0.08 -0.05 -0.02 -0.04 0.04 0.04 0.04 1.00
Some College -0.03 -0.03 -0.06 0.02 0.07 -0.04 -0.04 -0.02 1.00
Bach. Degree 0.19 0.21 0.16 0.13 -0.10 -0.10 -0.11 -0.03 -0.23 1.00
Postgrad. 0.26 0.23 0.23 0.04 -0.07 0.04 0.03 -0.02 -0.18 -0.19 1.00
marital st. separated -0.12 -0.09 -0.04 0.02 0.06 -0.04 -0.04 -0.01 0.01 -0.04 -0.03 1.00
(iii) Joint distribution
Finally, the similarity of the joint distributions of wealth and the matching variables is assessed by
regressing observed wealth and imputed wealth, in the respective datasets, against the matching
variables. The statistical significance of the difference between the two sets of coefficients is then
evaluated by means of a Hausman test. Table A5 shows the estimated coefficients of the two wealth

functions as well as the outcome of the Hausman test. With reference to the latter, both at the .01 and
.05 significance level, we fail to reject the null hypothesis that the coefficients are not systematically
different. This result further validates the reliability of the matching performed.
Table A5. Hausman test on wealth function between observed and fused wealth.
Dep. Variable: ln(Wealth)
(b)
(B)
(b
-
B)
Fused (CE) Observed (SCF) Difference S.E.
Family Income Before taxes 0.000022 0.000021 0.000001 0.000001
Squared Family Income Before taxes 0.000000 0.000000 0.000000 0.000000
Self employed Ref. -0.198223 -0.162168 -0.036055 0.081554
House tenure -1.842897 -1.721890 -0.121007 0.081784
Age Ref. Person 0.016197 0.023399 -0.007203 0.011739
Squared Age Ref. Person 0.000106 0.000054 0.000052 0.000106
No school -1.943236 -0.259389 -1.683847 0.615699
Some College 0.436587 0.380951 0.055636 0.089805
Bach. Degree 0.744419 0.828986 -0.084567 0.089676
Postgrad. 1.010688 0.901698 0.108991 0.107256
marital st. separated -0.755710 -0.532961 -0.222750 0.250013
chi2(8) = (b-B)'[(V_b-V_B)^(-1)](b-B) 14.390
Prob>chi2 0.072
Notes: Ho: difference in coefficients not systematic.
B. Rates of return on different assets
Table B1 . Long term average rates of return (non-home wealth)
Asset return rate *
Assets
Real estate and business 2.54
Liquid assets 0.61
Financial assets 3.03
Retirement assets 2.79
Debts
Mortgage debt -3.81
Other debt -3.81
Notes: Deflated values. These return rates consist in an updated
version of those in Wolff and Zacharias (2009).

C. More results
Figure C1 – Changes in quintile ranking by head of household’s age group.
-1.5
-1
-.5
0
.5
1
15-24 25-34 35-44 45-54 55-64 65-74 75-89
mean quintile change
head of household's age
Income vs Tot. expend.
-1.5
-1
-.5
0
.5
1
15-24 25-34 35-44 45-54 55-64 65-74 75-89
mean quintile change
head of household's age
Income vs Wealth
-1.5
-1
-.5
0
.5
1
15-24 25-34 35-44 45-54 55-64 65-74 75-89
mean quintile change
head of household's age
Tot. expend. vs Wealth
-1.5
-1
-.5
0
.5
1
15-24 25-34 35-44 45-54 55-64 65-74 75-89
mean quintile change
head of household's age
Tot. expend. vs Wealth adj. income
Figure C2 – Gasoline tax payments as a share of alternative ability to pay measures.
0 .1 .2 .3 .4
median share, %
1 2 3 4 5 6 7 8 910
A) Income
income decile
0 .1 .2 .3 .4
median share, %
1 2 3 4 5 6 7 8 9 10
B) Tot. expend.
tot. expend. decile
0 .1 .2 .3 .4
median share, %
1 2 3 4 5 6 7 8 910
C) Wealth adj. income
wealth adj. income decile
Gasoline tax payments as a share of:

Figure C3 – Annual gasoline expenditure per adult equivalent by head of household’s age group.
0 500 1,000 1,500 2,000
15-24 25-34 35-44 45-54 55-64 65-74 75-89
US$
Median gasoline expenditure per adult equivalent by HoH's age