Transcript Tax Incidence - University of California, Berkeley

Tax Incidence
Also known as, who
bears the burden of
taxation?
What do we get from a first pass at
the data?
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A first (partly naïve) pass indicates that U.S.
federal income tax is paid primarily by the
rich: in 2006 data, the top 20% of income
earners paid 84.2% of the taxes, and the top
1% alone paid 36.7% of the taxes. The
bottom half of income earners paid negative
(!) taxes in total.
This reflects both the progressivity of the tax
system, and the concentration of income in
the United States.
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Total tax burdens: Still a first pass.
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Federal personal income taxes are just part of the federal tax system.
How do we assign burdens of…
– Federal corporate income taxes
– Payroll taxes
– Excise taxes
– Estate and gift taxes
– Other taxes (e.g., tariffs)
The payroll tax is particularly problematic, since subsequent benefits
are tied to tax payments. Not clear whether it should be included.
One way of doing this: assign tax burdens based on arbitrary
assumptions (corporate tax paid by owners of capital, payroll tax paid
by workers, excise taxes paid by consumers, estate tax paid by
decedents). This assignment produces:
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Might anything be wrong here?
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Well yes, because many assumptions – and potentially problematic definitions
– have gone into calculating these tax burdens. For example, who says that
the burden of estate taxes falls only on those who receive, and not those who
give? Or that the corporate tax burden is borne only by owners of capital, and
not by workers or consumers?
The fundamental point is that it is a mistake to attribute tax burdens to those
who remit the taxes, since the burden may lie elsewhere.
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For example, the burden of an excise tax may in part be borne by the seller, in the
form of lower sales prices.
Or if the government increases your tax rate, your wage may rise in part to
compensate you, reflecting that, in the market, providers of services like yours will
demand certain after-tax compensation.
It is natural to forget about the determination of income in thinking about tax burdens,
but it is a mistake to do so, since taxes may well influence relative pretax incomes.
Fortunately, there are undying principles that can – and will – guide our inquiry
into who actually bears tax burdens.
Tax Incidence: Five Principles
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Who cares who pays?
People pay taxes.
Inelasticity is expensive.
Small things can be big.
In general, anything can happen.
Who cares who pays?
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This is the principle that it does not matter – for anything –
whether the seller or the buyer has the formal tax obligation,
and therefore remits the revenue to the government.
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In short, it really does not matter.
Note: this is NOT intuitive. Social Security example: tax is paid
half (7.65%) by employees, half (7.65%) by employers – BUT
THIS DIVISION DOES NOT MATTER, as long as prices are set
by supply and demand.
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Total tax revenue is unaffected either way.
Efficiency is the same either way.
The burden on consumers is the same.
The burden on sellers is the same.
–
Proposed Social Security reforms in 1990 and at other times.
Recent temporary reductions in worker contributions, though not employer
contributions, to social security payroll taxes.
How can we be sure this works?
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Think about there being a “tax jar” at the counter. In one regime, the customer
pays for the good, then puts taxes in the jar. Alternatively, the seller can collect
the tax, then the seller puts the tax in the jar. The difference between the
customer paying the tax, or the seller, is clearly unimportant.
This relies on the idea that prices are determined by supply and demand.
In a competitive market economy, such as that in the United States, this is how
prices are determined.
Occasionally prices are set some other way, perhaps by government regulation
(e.g., as with a fixed minimum wage, or with regulated prices for utilities or
other services), in which case it may well matter who remits the taxes.
And as a practical issue it may well make more sense to have certain parties
remit taxes rather than others, since they can do so at lower cost, or can be
audited with greater ease.
But note that even these administrative considerations are largely about
remittance, not attribution. The social security tax, for example, could be “paid”
75% by employers and 25% by employees without affecting who remits and
who keeps records.
What happens when a tax is imposed?
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If the tax is imposed on buyers, the demand curve shifts DOWN.
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If the tax is imposed on sellers, the supply curve shifts UP. If I wanted
to sell 300 units at a price of $55/unit, I now want to sell 300 units at
$56/unit.
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The demand curve shifts down because if consumers previously wanted 80
units at a price of $20/unit, then, with a $1/unit tax, they will want 80 units
at a price of $19/unit.
This is because the demand curve tells you what people want, not
necessarily what they can get.
Note the implication: the demand curve does NOT shift left, NOR does it
shift to the southwest.
Example: in a competitive market, the supply curve is the marginal cost
curve. Taxes raise the marginal cost of selling a good, thereby raising the
supply curve.
Price per
gallon (P)
The burden of the
(a)
tax is split Price per
gallon (P)
between
A 50 cent tax
consumers and
shifts the effective
Initially,
producers
S1
supply curve.
equilibrium entails
a price of $1.50
$2.00
and a quantity of
C
100 units.
P2 = $1.80
P1 = $1.50
A
(b)
S2
S1
B
Consumer burden = $0.30
P1 = $1.50
A
$0.50
D
Q1 = 100
Quantity in billions
of gallons (Q)
Supplier burden = $0.20
D
Q2 = 90
Quantity in billions
14 (Q)
of gallons
The economic
Price per
(P) tax
burdengallon
of the
is identical to the
previous case.
S
Imagine imposing
the
tax ison
new
TheThe
quantity
demanders
equilibrium
identical
toprice
therather
thanand
suppliers.
is $1.30,
case
when
thethe
tax
quantity
is 90.
was
imposed
on
A the supplier.
Consumer burden
P1 = $1.50
P2 = $1.30
$1.00
Supplier burden
C
B
$0.50
D2
Q2 = 90 Q1 = 100
D1
Quantity in billions
of gallons (Q)
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OK, so it works.
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Principle #1 works because prices are
determined by the intersection of demand
and supply.
It works even if markets are monopolized,
consumers are silly (though they are aware
of taxes), or other problems are present, as
long as there is unconstrained price
determination based on demand and supply.
Principle #2: People pay taxes.
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This principle serves as a reminder that organizations (for
example, corporations or cities) do not themselves ultimately
shoulder the burden of taxation.
Consider the tax on corporate income. The (considerable)
burden of this tax must be borne by one or more of:
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Owners of corporate shares (lower share values, reduced
dividends).
Owners of capital in general (lower rates of return).
Workers (lower wages).
Consumers (higher prices for goods they buy).
Foreigners.
Other people.
When you get right down to it, economics is all about people.
Principle #3: Inelasticity is expensive.
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The burden of a tax is borne by the side of the
market (demand or supply) that is less elastic (i.e.,
less price sensitive).
In an extreme case of perfectly inelastic demand, the
burden of the tax is borne by buyers entirely (and not
at all by sellers).
In the opposite extreme of perfectly elastic demand,
the burden of the tax is borne by sellers entirely.
(Note that consumers do not bear the burden of the
tax even though they wind up reducing their
purchases).
Price per
gallon (P)
D
S2
S1
P2 = $2.00
With perfectly inelastic demand,
consumers bear the full burden.
Consumer burden
P1 = $1.50
$0.50
Q1 = 100
Quantity in billions
of gallons (Q)
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Price per
gallon (P)
S2
S1
$0.50
With perfectly elastic demand,
producers bear the full burden.
D
P1 = $1.50
Supplier burden
$1.00
Q2 = 90
Q1 = 100
Quantity in billions
of gallons (Q)
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Why does it work this way?
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With inelastic demand, the total quantity does not change after
the tax is imposed. Since you have to pay the suppliers a
certain amount to get them to sell you this quantity, there is no
scope for shifting the burden onto sellers. Hence the burden
falls on buyers.
With perfectly elastic demand, the price that consumers face
cannot change, since they will simply purchase other
substitutes, hence consumers do not bear the burden of the
tax.
A similar logic applies to sellers: inelastic supply implies that
sellers bear the tax burden, elastic supply that buyers bear the
tax burden.
Price per
gallon (P)
S
Supply curve does not change
when it shifts up.
P1 = $1.50
Hence the price to consumers
does not change.
D
Q1 = 100
Quantity in billions
of gallons (Q)
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More inelastic supply, smaller
More consumer
elastic supply,
larger
burden.
consumer burden.
(a) Tax on steel producer
(b) Tax on street vendor
P
P
S2
S1
Tax
S2
B
P2
P1
Consumer burden
B
P2
Tax
Consumer burden
A
A
P1
D
Q2 Q1
S1
D
Q
Q2
Q1
Q
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How should one think about these
burdens?
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When the price rises, and it’s something I buy, then I
lose.
Likewise, when the price falls, and it’s something I
sell, then I also lose.
But how much do I lose – can we make that more
precise?
Well, yes: consumers lose consumer surplus, and
sellers lose producer surplus.
The lost consumer plus producer surplus equals the
total tax collected plus the deadweight loss produced
by the tax.
Tax incidence in monopolized markets
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Works roughly the same way as competitive markets, except
that prices are determined by the intersection of MR (marginal
revenue) and MC (marginal cost), rather than demand and MC.
As a general matter, the burden of a tax will be borne partly by
sellers and partly by buyers.
Depending on the details of demand functions, tax burdens
may fall more heavily on sellers in monopoly markets than they
do in the case of competitive markets.
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You get a smaller quantity reaction for a given tax, which in turn
leads to a smaller effect on consumer price.
Reflects that monopoly supply is somewhat less responsive to cost
than supply in competitive markets.
For example, if a monopolist has a horizontal MC curve, then the
price response to the imposition of a tax is less than one-for-one; if
the market were instead competitive, with the same MC curve, the
price response to a tax would instead be one-for-one.
Principle #4: Small things can be big.
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This is the principle that a tax may have a
very small effect on some market price (such
as the price of labor, or the rate of interest),
but nonetheless have a very large effect on
tax burdens.
Take an example: a tax on business activity
in Rhode Island. (Note: Rhode Island is a
very small part of a very large country.)
Business tax in Rhode Island.
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Make the following stylized assumptions:
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Rhode Island is very small (good assumption!)
All output is produced by a combination of labor and capital.
Labor is immobile: people live their whole lives in the states in
which they are born.
The total amount of capital in the United States is fixed, but capital
is freely mobile between states.
Then what happens when we tax businesses in Rhode Island?
The after-tax rate of return to investing in businesses in Rhode
Island CANNOT FALL, since if it did, capital owners would just
invest in California, Florida, New York, or Texas instead.
Hence the owners of Rhode Island businesses DO NOT bear
the burden of the Rhode Island tax.
How does that work?
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In order to keep capital in Rhode Island, it must be the case
that the pre-tax rate of return to investing there rises when the
tax is imposed.
This happens because capital FLEES RHODE ISLAND – and
with less capital, the stuff that is left earns higher rates of
return.
So who bears the burden of the Rhode Island tax? Workers in
Rhode Island! Why?
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Since capital does not bear the burden, workers are what’s left
(and workers can’t leave, by assumption).
With less capital in Rhode Island, labor becomes less productive,
and wages fall to reflect that.
By the way, this is what really happens!
What about the rest of the country?
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The Rhode Island capital goes to California, where it
has the effect of…
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Slightly reducing the rate of return to capital in California
and the rest of the country (greater supply of capital reduces
returns earned by capital), and
Wages rise slightly in California, since labor there is now
more productive due to the added capital.
But…aren’t these effects awfully small? After all,
Rhode Island is tiny compared to California, and any
effect on the rate of return might be to reduce it from
(say) 7% to (say) 6.998%. Yes, except…
Small things can be big!
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The total effect of the Rhode Island tax change on
capital returns in California is the product of the
change in the rate of return and the total amount of
capital in CA. The first is tiny, the second is huge.
Zero times infinity is not necessarily zero.
In this case, it can be shown that a Rhode Island
business tax that raises $100m will…
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Reduce wages in Rhode Island by $100m.
Reduce the return to capital in the whole United States by $100m. (Why?
Because we started by assuming that the total amount of capital in the
United States is fixed. Since U.S. capital is inelastically supplied, capital
bears the whole tax burden – though since the amount of capital in Rhode
Island is NOT fixed, but instead very elastic, that portion of the capital
bears just a tiny tax burden.)
Increase wages in the whole United States by $100m. (This because the
total tax burdens have to sum to $100m.)
Principle #5: In general, anything can
happen.
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What this principle means is that, In General
Equilibrium, Anything Can Happen.
What is general equilibrium? It is the state of all
markets in the economy, not just one at a time. (One
at a time is partial equilibrium.)
Why can anything happen? Because in general
equilibrium, everything affects everything else, and
does so in two ways:
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Through supply.
Through demand.
General equilibrium reasoning.
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In analyzing tax policies (or any other policies) in
general equilibrium, it becomes necessary to trace
the effects that markets have on each other.
Thus, for example, when a tax imposes a burden on
buyers of a good (as would be the case, for
example, if the supply of the good is extremely
elastic), we then ask what happens to their demands
for other goods and services in the economy, and
how their prices are affected.
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There can often be significant spillovers into other markets.
Strictly speaking, it is necessary to find the effects of a tax (or other
government policy) on all the prices and incomes in the economy, though
in practice, we usually just look for the most important effects.
Can odd things happen? Well yes.
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Consider the case of a tax on ground coffee. (This example is
from Vickrey, 1960.) Say that the tax is paid by sellers. This
can have the strange effect of actually reducing (!) the
consumer price of ground coffee (and also reducing the
consumer price of unground coffee beans).
How might that work?
Assume: coffee drinkers can buy either ground or bean coffee
from the store, but ground is more convenient. Only problem is
that the process of grinding coffee in the store is very inefficient,
in that lots of coffee is wasted (falls through cracks in the
machine). This makes ground coffee more expensive, though
it’s still worth it to many consumers who do not like the
messiness of grinding coffee at home. [Assume that
consumers do not waste any coffee when they grind it at home,
since they are so careful when they do so.]
Effect of a tax on ground coffee.
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When the tax is imposed on ground coffee, it raises the price of
ground coffee relative to coffee beans you buy in the store.
Some consumers switch to buying coffee beans instead of the
ground stuff.
This reduces TOTAL coffee that stores buy from coffee
farmers, since the beans entail less wastage than the ground
coffee.
Reduced demand for coffee reduces the prices that stores pay
farmers.
This effect on coffee prices (paid to farmers) may be so great
that the price of ground coffee ACTUALLY FALLS (and the
price of coffee beans falls even more), despite the tax.
The reason: one market affects another.
Who bears burdens of environmental
and other corrective taxes?
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Gasoline is heavily taxed, and gasoline taxes have the potential to
help correct various environmental, health, and traffic congestion
externalities.
Alcohol and tobacco are also heavily taxed. These taxes are imposed
in part to raise revenue, but primarily in order to discourage
consumption of alcohol and tobacco, which are associated with
various social ills, particularly health problems.
One issue that environmentally- and health-friendly tax alternatives
raise is the possibility that their burdens fall disproportionately on lowand medium-income families.
If this is true, then this consideration might erode some of the support
for green taxes and various health-promoting taxes.
Note that, even if this were true, the government would be able to
undo distributional effects by adjusting other taxes (for example, by
reducing income tax burdens on low- and medium-income families, but
that raises other issues, as a result of which this alternative may be
considered not entirely feasible or satisfactory).
Measuring burdens.
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One of the issues in measuring the distribution of tax
burdens in practice is how to think about the
individuals who bear the burdens.
How would we know whether a particular tax
burdens “low income” or “high income” families? We
need to know…
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The incidence of the tax: who bears the burden, and how
much of the burden they bear.
Whether those people are rich or poor, middle income, or
whatever.
Let’s think about the second of these issues.
Over what period of time should family
income be measured?
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There are problems with just looking at one year of income.
First problem: fluctuating incomes.
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Second problem: systematic variation over a lifetime.
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Incomes go up and down because people have good years and
bad years. You could have a bad year and still be generally rich,
or a good year and still be generally poor. (In a typical year, the
American with the lowest income is one of the wealthiest.)
As a practical matter, annual income is a highly imperfect measure
of average lifetime income due to year-to-year fluctuations.
People tend to have low incomes when young, high incomes when
middle aged, and low incomes when retired.
Is a wealthy retiree poor? Annual income (which is low) would say
he or she is poor, but the retiree may have great purchasing
power.
Does it matter how we measure
income?
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Yes. The striking thing is how much it matters.
The Poterba article on the reading list (“Lifetime incidence and
the distributional burden of excise taxes”) looks at the
distributional impact of gasoline, alcohol and tobacco taxes.
In Poterba’s calculations, how one thinks about the
distributional consequences of these alternatives turns on the
lifetime-annual distinction.
This is not surprising, as lifetime incomes exhibit much less
variation than annual incomes: people who are low income may
have higher incomes in other years, and those who have high
incomes in one year may have lower incomes in others.
Poterba presents a table showing the probabilities of transiting
among annual income quintiles between 1971 and 1978:
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Distributional properties of excise
taxes.
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Consider gasoline taxes first. The ratio of gasoline
expenditures to income declines sharply with income (e.g., in
1984, consumers in the lowest income quintile spent 15% of
income on gasoline, whereas those in the highest income
quintile spent only 2.8% of income on gasoline).
If consumers bear the full burden of gasoline taxes, then this
seems to indicate that gasoline taxes are highly regressive, that
the burden falls on low-income families.
Poterba notes, however, that annual income may be a
misleading measure of lifetime resources. For example, some
of the “poor” people in the bottom income quintile are wealthy
retirees who drive their heavy cars around all day.
Poterba proposes using total annual consumption expenditures
as a measure of lifetime income (which is implied by the
permanent income hypothesis). Then looking at the ratio of
current gasoline expenditures to total current consumption
expenditures offers a very different picture:
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A different way of measuring the
distributional of tax burdens.
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Gasoline consumption as a fraction of total
expenditures differs little among total expenditure
(lifetime income) quintiles, other than falling
somewhat for the top quintile.
Similar results appear for alcohol, though the
income/consumption difference is less pronounced
for tobacco.
Note: this makes a big difference! The burden of
excise taxes is almost surely not as heavily
concentrated on low-lifetime-income groups as the
annual consumption/income ratios suggest.
Why does it make such a big
difference?
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Recall that there are two primary reasons why annual income differs
from lifetime resources (as reflected in annual expenditures):
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Poterba offers evidence that the first of these sources , the annual
fluctuations from transitory shocks, is the more important of the two by
looking at how expenditure shares on gasoline, alcohol and tobacco
vary by age.
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Annual income fluctuates due to transitory shocks including unemployment, planned
leave from the labor force for education, care of the elderly or very young, income
from selling long-held capital assets, bonuses, windfalls, and other sources.
Incomes fluctuate over the life cycle, with the young and retirees having lower income
levels.
–
Expenditure shares vary somewhat by age, with those under 25 showing the highest
expenditure shares and those over 75 the lowest.
But these variations are much less pronounced than the expenditure/income ratios in
different quintiles, suggesting that age differences alone probably account for a
relatively small fraction of the variation.
Note, too that expenditure/income varies over the life cycle.
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Lessons from this study.
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In performing tax incidence calculations, it can make
a big difference how one defines income.
By the lifetime resources measure (as reflected in
annual consumption), excise taxes, particularly those
on gasoline and alcohol, do not look nearly so
regressive (falling heavily on those with fewer
resources) as they do by annual income measures.
None of this exactly addresses the issue of who
actually bears the burden of the excise taxes – these
calculations just assume that consumers do, which
they may, but only under certain circumstances.
So who bears the tax burden?
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The bottom line is that the burdens of different taxes
are borne by different groups. (Oh.)
Most – no, all – of the available calculations of tax
burdens are based on simplifying assumptions of
dubious validity. The worst of all is the assumption
that just because someone remits a tax payment
means that they bear the tax burden.
In order to analyze tax burdens it is necessary to
apply the five principles.
Globalization of the economy has the potential to
change tax incidence, particularly if globalization
increases some demand and supply elasticities.
Consumption taxation.
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We have grown accustomed to the notion that
governments tax income, but consumption taxation
is an alternative.
What makes this alternative popular?
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Consumption taxation is generally more efficient than
income taxation, because the deadweight loss of distorting
the saving/investing margin is so large.
Consumption taxation is usually considerably simpler than
income taxation.
Consumption taxes can address externality problems.
Some people believe that fairness dictates that income be
taxed not when earned but when consumed.
Excise taxes can be designed to make users of government
services pay for the services they consume.
The varieties of consumption
taxation.
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Broad-based consumption taxation, such as general
sales taxes or VATs.
(Everybody other than the U.S. has a VAT.)
Excise taxes on specific things.
An income tax that either does not tax the return to
saving (e.g., Roth IRA), or else permits a deduction
for new saving (e.g., traditional IRA).
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This reflects that: Income = Consumption + Saving
Hence: Consumption = Income – Saving.
Why tax specific items with excise
taxes?
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To make users pay for government programs related
to consumption of specific items.
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To discourage the taxed activity, if it generates
externalities.
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Federal tax on bows and arrows, outboard motor fuel,
superfund-type taxes. Air transportation tax.
Taxes on tobacco and alcohol.
Gasoline taxes.
Taxes on tobacco and alcohol.
Taxes on ozone-depleting substances.
Gasoline taxes.
Fact is, the United States makes rather little use of
excise taxes compared to other rich countries.
Federal excise taxes used to
finance related expenditures
Item
Tax rate
Sport fishing equipment
10% of sales price
Electric outboard motors
and sonar devices
Bows and arrows
3% of sales price
Firearms and ammunition
10 or 11% of sales price
11-12.4% of sales price
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Excise tax revenues, as % of
national income, 2002
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Australia
Canada
France
Germany
Japan
United Kingdom
Europe Average
4.5 %
3.2
3.6
3.6
2.1
4.3
4.0
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United States
1.8
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Excise tax revenues as % of total
tax revenues, 2002
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Australia
Canada
France
Germany
Japan
United Kingdom
Europe Average
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United States
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14.3 %
9.5
8.1
10.1
8.2
12.0
9.9
6.9
Other externalities.
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Various bad habits that people have.
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Smoking.
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Accounts for more than 400,000 deaths/year.
Externalities from:
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Large positive externalities from reduced retirement benefits.
Net external cost (47 cents a pack) is small compared to the cost that smokers
impose on themselves ($35 a pack).
Drinking alcohol
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Second-hand smoke.
Reduced workplace productivity.
Causing fires.
Health costs paid by others (out of $75b of annual health costs).
Main external problem is drunk driving ($120b a year in cost).
Also creates problems for drinkers, but these are estimated to be smaller.
Overeating, lack of exercise.
Is there a role for public policy in regulating or taxing unwise individual
behavior? Should we think of that as an externality?
Why tax consumption instead of
income?
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Consumption taxation is much more efficient.
–
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–
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Consumption taxes do not tax returns to saving and investing.
This is where deadweight losses are the largest.
There is a lump-sum component to a switch to consumption taxation.
Consumption taxation is considerably simpler than income taxation.
Certain forms of consumption taxation (e.g., environmental excise
taxes) give the government opportunities to impose Pigouvian taxes
on externality-generating activities.
Some consumption taxes can be used to impose heavier tax burdens
on people who make heavy use of government services.
Many people think that consumption taxation is more fair than income
taxation, since it does not impose a higher tax burden on someone just
because they decide to save their money and consume later.
But one must be comfortable with the distributional consequences of
consumption taxation. One possibility is to combine consumption
taxes with income taxes to achieve the desired distributional result.
But there is a deeper distributional issue associated with the
introduction of consumption taxes. The issue is generational.
What to do about the greedy old
people?
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If the U.S. government were tomorrow to increase
consumption taxes, presumably in place of income
taxes, older generations alive at the time of the
transition would be adversely affected.
The elderly paid income taxes during their working
lives, then would have to pay consumption taxes
later in life. Reducing income taxes along with
increasing consumption taxes will not adequately
compensate them.
The lump sum nature of transiting
to a consumption tax.
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Switching to consumption taxation affords the
government the opportunity to grab some of its
revenue in a lump sum fashion. Some folks will
have already saved, and their saving can be
effectively taxed without affecting their labor supply.
The more revenue the government can get in a
lump-sum fashion, the less it needs to get in a
distortionary fashion with taxes that discourage
income production.
This is part of the reason why consumption taxation
typically looks so good on efficiency grounds.
Probing the efficiency gains.
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Compare two policies: using a broad-based, flat-rate
consumption tax, and using a flat labor income tax.
Neither imposes a tax on the return to saving, so in the long run
they are equivalent.
A consumption tax will, however, look better in any simulation,
because switching to a consumption tax entails hitting any
savings accumulated prior to the transition with a big lump-sum
tax.
The opposite is true of a wage tax, because savers who
anticipated future tax burdens will suddenly not face them if the
government switches to a wage tax.
The burden of the lump-sum tax is not evenly distributed among
members of society: the old bear it disproportionately.
Burdening the elderly.
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Note that switching to a consumption tax
does not produce a Pareto improvement,
since the young benefit at the expense of the
old.
Is it possible to design a consumption taxoriented reform with features to compensate
the elderly? Yes, Auerbach analyzes one,
finding that most of the efficiency gains go
away.
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Generational accounts
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It is possible to keep track of taxes paid by
different age cohorts (and transfers they
receive from the government).
These are known as “generational accounts,”
and were introduced by Alan Auerbach and
Larry Kotlikoff.
There are sobering realities revealed by
these accounts.
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