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## Statistical Inference in Applied Tax Analysis

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### 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?

- 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

- 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

- 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

- 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

- 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:
- 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

- 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

- 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.

- 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.

- 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.

- 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.

- 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 contemporaneous changes in their economic variables?

Panel issues.

- 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?

- 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 cross-sections, 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.

- 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

- 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

- 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 one-time 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.

Can one be more precise?

- 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.

What happened in 2005?

- A surge in repatriations: went from about $60b/year to $362b in 2005.
- Dharmapala, Foley and Forbes ask what firms did with repatriated funds.
- 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?

- 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:
- 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?

- 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.

- 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?

- 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?

- 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:
- 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.

- 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 country-years, 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.

- 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?

- 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 1980-2008, 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?

- 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 1991-2008 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.

- 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.

- 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.

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