Statistical Inference in
Applied Tax Analysis
What do we know, and
how do we know it?
How would one forecast the effect
of lower personal income taxes?
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One possibility: compare countries with high and low personal income
taxes.
Even in this case, the challenge is that one needs to know what to look
for. (E.g., if countries with lower personal income taxes tend to have
fewer wars, does it follow that tax cuts promote peace?)
We usually appeal to theory, even at this early juncture, to guide the
investigation. Theory says that higher tax rates might discourage labor
supply and saving, and encourage tax avoidance.
Hence it is natural to consider the correlation between personal tax
rates on things like labor force participation (including retirement
ages), labor hours, saving rates, and tax avoidance.
A difficulty: countries differ in all sorts of dimensions. Is that
necessarily a problem?
Country differences
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It is not necessarily a problem that countries differ in dimensions other
than taxes, but it is certainly a complication.
Formally, what matters is whether the other characteristics along
which countries differ are correlated (positively or negatively) BOTH
with the variable whose effect one studies (tax rates) AND with the
outcome of interest (labor supply).
If not, one is in the clear (sort of).
If yes – and the answer is frequently yes – then there is the potential
for biased estimation and inaccurate inference.
For example, if citizens of wealthy countries want their governments to
provide more (as a fraction of income) than do others, and wealthy
countries have greater labor supply, then high tax rates will be
associated with greater labor supply – even though high tax rates
actually discourage labor supply.
Random assignment
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A common way to think about desirable statistical features of an
investigation is with the analogy to random assignment.
Suppose that tax policy were random (imagine!), or that an investigator
really could randomly assign different tax rates to different places.
Random assignment (largely) takes care of the problem of correlated
omitted variables, and leaves one able to estimate the impact of tax
differences.
One of the beauties of random assignment is that one can estimate
the effect of tax differences even without controlling for other
variables, and get an unbiased estimator of tax effects.
It is still possible to draw the wrong conclusion – an assignment done
randomly may wind up with variables of interest correlated with each
other in a way that generates biased estimates – but this problem
would appear only by chance, and in a large enough and sufficiently
random sample may be unlikely to occur.
Instrumental variables
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A variant of random assignment comes in what is known as
instrumental variables estimation.
Instrumental variables is a two-step procedure in which one first
predicts the value of a variable of interest, and then effectively
uses the predicted value in a subsequent regression analysis.
For example, one might be interested in the impact of country
tax rates on foreign direct investment. One problem is that
country tax rates are correlated with other variables that affect
FDI. Hence simply looking at the relationship between FDI and
country tax rates could lead to inaccurate inferences.
We have a theory that says that smaller countries should have
lower tax rates (and they do). Then one can use country size to
predict tax rates, and look for the correlation between predicted
tax rates and FDI (which is negative).
Issues with instrumental variables
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Instrumental variables is a very useful technique, but it is
fraught with its own problems.
In the tax rate and FDI example, the method relies critically on
two factors:
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Country size is a powerful predictor of country tax rates
Country size does not directly influence FDI in ways that are not captured
by the model.
The first of these is the power of the first stage equation. If this
is not a powerful equation, then the resulting estimates are
biased in the direction of the ordinary least squares estimator.
The second of these is the “exclusion restriction,” reflecting that
the IV procedure effectively assumes that one can use the
country size variable as a pure predictor of tax rates, and that
country size does not independently affect FDI.
External validity
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The problem of correlated omitted variables is really big. But
statistical problems run even deeper than that.
Suppose that there were no issue with omitted variables, and a
study quite correctly found that countries like Bermuda (low tax)
have greater labor supply than countries like France (high tax).
Would it follow that lower U.S. tax rates would increase U.S.
labor supply?
Maybe, maybe not. Any tax effects in Bermuda might reflect
the nature of local industry, or characteristics of the local
population, both of which differ from those in the United States.
External validity: An example
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The problem of external validity is rather obvious. Nevertheless, it arises all the
time, even among professionals.
For example, virtually all statistical studies of tax-motivated income reallocation
use data that compare reported profits in different countries.
Thus, for example, one might investigate the extent to which US multinationals
report more income in low-tax jurisdictions than in high-tax jurisdictions,
attempting (this is hard) to account for how much “should” be reported based
on capital investment and other measures of real activity.
Some have used estimates of these correlations of tax rates and income
reporting to project how much the U.S. loses in tax revenue from firms shifting
reported income out of the US.
Is that a valid procedure? The evidence concerns income reallocation from,
say, Bulgaria to the Bahamas, but the extrapolation concerns income
reallocation from the US to Singapore. The assumption is that tax rate
differences drive income reallocation, and that the same tax rate difference has
the same effect, whether audited by the Bulgarian authorities or the US
authorities.
Time series.
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Instead of comparing countries with differing tax rates, one
might look at what happens when a single country changes
(lowers, say) its tax rate.
Are there any statistical issues there? Oh yeah.
The first issue is that actual tax changes are not generally
random. Countries change their tax rates in response to
changing conditions, and these conditions also affect variables
of interest, so it can be extremely difficult to identify tax effects
separately from other effects.
For example, countries may offer investment tax incentives
during periods when investment is otherwise falling. Bigger tax
benefits might then be correlated in the data with reduced
investment, even though the true behavioral effect of bigger tax
benefits is that they increase investment.
More time series issues.
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There are special statistical issues that arise in estimating
changes over time.
This has to do with the fact that residuals in a time series
estimating equation tend to be correlated with each other in
different time periods.
Often the correlation is positive: if investment rises in one year
it may well rise the following year too.
On the other hand, classic measurement error tends to induce
negative correlation: part of the change in investment (or
anything else) from one year to the next is measurement error,
from which it follows that changes tend to follow each other with
opposite signs, purely as a statistical matter.
Time series information content.
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Correlation over time within a time series raises important
issues about calculating the statistical reliability of an estimate.
On a very practical level this has to do with the standard errors
used to judge the degree of statistical precision.
If changes over time are not entirely independent, then it
follows that there is less variation in independent variables (tax
rates, say) than one might otherwise think.
Since one needs to have lots of variation in order to estimate
behavioral effects with any precision, this can be a big problem.
Panel data estimation.
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Much of the trendy – and influential – statistical work uses
panel data.
Panel data combine elements of cross sections and time series:
these are observations of large numbers of the same actors
over multiple time periods.
For example, one might look at a large sample of countries
from 1970-2005, and ask what happens as their tax rates
change.
A nice feature of panel estimation is that one can implicitly
control for the fact that Costa Rica is different than Germany,
and also control for the fact that 1970 is different than 2005.
One asks: if taxes in Costa Rica went up while those in
Germany went down, how is that correlated with
Panel issues.
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The use of panel data is so appealing that there can be a
tendency to get complacent and sloppy in drawing inferences.
Really, the same issues that arise with cross sections and time
series also arise with panels.
Think about the Costa Rica/Germany 1970-2005 example.
Yes, German tax rates changed over this period, but Germany
itself changed over this period. Indeed, Germany had to raise
taxes to pay for reunification. So it is very hard to get a “pure”
effect of German tax changes from the data.
We say that one does “panel” estimation if one includes fixed
effects for countries (in this example), thereby estimating the
effect of taxation from changes within countries. Without these
fixed effects one does “pooled” estimation.
What should one think, or do?
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There are statistical challenges with almost any method of
estimation.
Most of the challenges reflect, at some level, common sense
intuitions.
It does NOT follow that one cannot learn about the world from
looking at data. Far from it. It’s just that one has to be able to
figure out what one has learned.
One of the big tensions has to do with the information content
of data. Often by far the most information comes from crosssections, but there is the potential for biased inference.
Panel estimation is often more statistically compelling than
cross-section estimation, but relies on changes, for which there
may be much less information.
Example: effects of state taxes.
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U.S. state tax rates differ, and it is interesting and important to
understand the economic impact of these differences.
One can easily construct a panel of state data, and use it to estimate
the effect of state tax changes on business investment, employment,
housing values, other variables.
Here is the problem: states tend to change their tax rates in (rough)
lockstep. CA and NY were high tax states in 1970, and are high tax
states today; NH and TX were low tax then and now. Consequently
there is not much usable tax rate variation in the panel.
There is, however, a lot of usable tax rate variation in the cross
section: compare NY and TX. But that is potentially problematic
because there are other differences.
This is a tradeoff situation. Given that any statistical estimation has
problems, cross sectional evidence may be too readily dismissed.
Personal taxes in Iceland
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There was an interesting personal tax change in Iceland that
illustrates the impact of tax changes on (reported) individual
labor supply.
Iceland in fall 1986 introduced a (surprise, apparently) tax
change that flattened their progressive personal tax rate
structure, prospectively for 1988 and onward.
Significantly, the change modified their administrative regime.
In 1987 and earlier one paid taxes based on the previous year’s
income: 1987 taxes were based on 1986 income. Starting in
1988 one paid taxes based on contemporaneous income.
As a result, nobody paid taxes based on 1987 income: marginal
rates were effectively zero that year. People still had to pay
taxes, but not based on that year’s activity.
Predicted effects
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What should be the impact of the Iceland tax reform?
If taxes influence economic activity (…in Iceland…), then we
should see increased labor supply that year – and the increase
should then disappear thereafter.
The Iceland experiment has the nice feature that it’s not a onetime and forever tax change, for which it would be difficult to
distinguish tax effects from long run trends.
Labor supply effects should be particularly strong in this
instance, because one picks up pure substitution effects (the
impact of a higher after-tax return to working an additional hour)
and not combined with income effects (the effect of greater
taxpayer affluence stemming from a tax cut).
It sure looks like labor supply increased.
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Can one be more precise?
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The aggregate evidence of increased (reported) labor supply is
informative, but it is difficult to distinguish tax effects from other
economic changes at the same time.
One way to identify tax effects is to compare Icelanders whose
taxes were highest in 1986 with those whose taxes were lower.
If the tax change is responsible for the 1987 blip, then the ones
whose taxes were highest should show the greatest
responsiveness to the one-year zero marginal tax rate.
And that appears to be the case for earnings (though not for
hours worked), based on a random sample of 9300 Icelanders
who filed taxes in 1986, 1987, and 1988.
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What happened in 2005?
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A surge in repatriations: went from about $60b/year to $362b
in 2005.
Dharmapala, Foley and Forbes ask what firms did with
repatriated funds.
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The HIA required that the funds be used for permitted
investments: investment, R&D, new employment, certain
acquisitions.
HIA funds could not be used for dividends, share buybacks, or
executive compensation.
DFF report that repatriations were not associated with
greater investment or employment expenses, but with
payouts to shareholders: $1 of repatriations was associated
with $0.91 of share buybacks and $0.08 of dividends.
How do we know what firms would
have done in the absence of HIA?
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One of the problems of inference is that firms that wanted to
do lots of share buybacks in 2005 would normally be
expected to repatriate more from their foreign subs than do
other firms.
DFF use an instrumental variables strategy in which they
predict the likelihood of repatriation in 2005 on the basis of:
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Facing high potential repatriation taxes. This is proxied by a
firm’s average foreign tax rate. Firms with above-median
foreign tax rates are distinguished from those with below
median.
Use of tax haven holding companies. Firms with these holding
companies are predicted to be more likely to repatriate during
the holiday.
The results appear to be sensitive to the use of these
instruments.
What should one conclude?
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It is still not clear exactly what actually happened and why.
The results are very sensitive to how the sample is weighted
(92 cents on the dollar v. 61) and also very sensitive to the
instrumental variables procedure used to predict repatriations
(92 cents on the dollar v. 10).
There is a lot of other evidence, including using PRE reports
from 10-Ks and surveys of executives, that the 92 cents on the
dollar figure is way too high. That has not stopped it from being
widely quoted, however.
Much of the issue seems to be how one extrapolates from the
data, whether one weights observations by size of firm or not,
and then how one extrapolates to the whole sample of U.S.
firms.
Corporate tax rates and bases.
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Paper: “The effect of tax rates and tax bases on corporate tax
revenues: Estimates with new measures of the corporate tax
base,” Laura Kawano (U.S. Treasury) and Joel Slemrod
(Michigan).
National Bureau of Economic Research working paper No.
18440, October 2012.
The paper looks at changes in corporate tax rates and
corporate tax bases in OECD countries from 1984-2004.
The stated point of the paper is to challenge other studies that
find the revenue-maximizing corporate tax rate to be in the low
30s.
But the paper does a lot more than that.
What is the point?
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The paper takes aim at studies reporting that corporate tax revenues
decline as statutory corporate tax rates rise above the low 30s.
The paper notes that it makes little sense to analyze the effect of
statutory tax rate changes without also analyzing the impact of tax bases
(and enforcement).
– Governments often change tax base definitions at the same time that
they change tax rates.
– Even if they did not, the effect of statutory tax rates surely depends
on the prevailing definition of the tax base.
The evidence for OECD countries from 1980-2004:
– In 51% of the country-years with corporate tax rate changes there
were accompanying tax base changes.
– In only 36% of the country-years with no corporate tax changes were
there tax base changes.
How is all this defined?
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Statutory tax rates are easy, but tax base changes are more difficult to
categorize.
The Kawano and Slemrod study is based on careful reading of Annual
Reports of the International Bureau of Fiscal Documentation.
The study categorizes 12 types of tax base changes:
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R&D credits.
Foreign tax credits.
Favorable tax provisions for inbound foreign investment.
Policies that enhance corporate tax enforcement and compliance.
Investment tax credits.
Accelerated depreciation for capital assets.
Other taxes, such as extraordinary profits taxes or corporate net worth taxes.
Loss carry-forward and carry-back rules.
Thin capitalization rules.
CFC legislation.
Other tax base changes.
Empirical patterns, part 1.
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There are frequent corporate tax base changes.
– 433 tax base changes total (there can be more than one
change in a country at one time).
– Most broadened the tax base: 248 of these changes
broadened it (denoted +1), 185 reduced it (denoted -1).
– There was at least one tax base change in 289/725 countryyears, or 41% of the time.
There is no strong association between tax rate changes and the
direction of tax base changes, with perhaps a mild broadening (!)
of the tax base when rates rise.
Countries differ in the extent to which they have changed tax rates
and tax bases, with the United States broadening the tax base a
bit more than others.
Analyzing the effect of tax changes
on tax revenue.
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Statutory corporate tax rates have fallen over time (duh).
Of the 24 OECD countries with complete data, 21 reduced their
statutory tax rates between 1980-2008, and 3 increased their
rates.
Ratios of corporate tax revenues to GDP do not, however, fall
over time (until very recently). Norway is an exception, but that
reflects its rather unusual situation.
At a very crude level, there is no apparent relationship between
corporate tax rates and corporate tax revenues.
What about country differences?
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In a scatterplot there is little apparent relationship
between corporate tax rates and corporate tax
revenues, either in 1980 or in 2008.
When one looks at changes in tax rates from 19802008, more of a positive relationship starts to appear.
A similar pattern appears in the relationship between
changes in corporate tax bases (1980-2004, measured
as the simple sum of the +1 and -1) and changes in
corporate tax revenues over the same period:
broadening the corporate tax base is associated with
greater revenue.
What has been happening to
taxable profits?
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This period has seen very large increases in ratios of taxable
corporate profits to GDP.
The most extreme is Ireland, where total taxable corporate
profits/GDP ratio from 1980-1990 was 2.8%, whereas from 19912008 it was 16.2%.
Taxable profit/GDP more than doubled in 15 out of the 30
countries in the sample, and increased by 50% in 7 others
(though actually decreased in Italy and Japan).
U.S. taxable corporate profits/GDP move with the business cycle,
but has increased by 41.2% over this time span – which is less
than the average OECD country.
Changes in corporate tax bases and
tax rates.
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There is little apparent connection between changes in
corporate tax bases and changes in rates, though most
countries reduced corporate tax rates and expanded
corporate tax bases over this time period.
There is a clearer pattern with respect to a particular tax
base measure, the present value of depreciation
allowances, and tax changes: governments have
reduced depreciation allowances as they have reduced
tax rates.
According to work by Becker and Fuest (International
Tax and Public Finance, 2011, pp. 580-604), this pattern
also holds when one looks at annual changes.
Estimating the effect of changes.
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The study estimates the effect of tax provisions, and their changes, on
corporate tax collections in OECD countries.
Statutory tax rates, and tax rate changes, appear to have little effect on
total tax collections.
Some base changes appear to influence revenues:
– Strengthening thin capitalization rules appears to reduce (!) tax
collections.
– There is some evidence that reducing R&D credits or imposing stiffer
taxes on foreign investors enhances revenues, though only in the
short term.
Mostly the study criticizes previous studies of the relationship between
corporate tax rates and revenues, noting the importance of corporate tax
bases.