Saturday, January 26, 2013

The Varying Meanings of "Fair Share"

I had what may be a bit of an epiphany this morning about why I can never understand the arguments that the President and others make for the "rich" paying "their fair share."

When I hear those words, I always think of their fair share of the federal tax burden of the country.  Because I think of it that way, I tend to look at tax distribution tables as a way to think about the question of fairness.  Because of changes in income distribution, I don't look at the distribution directly but rather I look at the change in total effective tax rates over time.

Here are two views of the comparison between 1979 (the first time CBO did the analysis) and 2013 (post the ATRA).





















So we can look at this two ways, either in terms of the change in effective tax rate in percentages or percentage points.  In percentage points, effective Federal tax rates have declined by 6.1 points at the bottom of the income distribution and 0.6 points at the top of the income distribution.

In percentage terms, the comparison is directionally the same but an even larger order of magnitude.  Yet, despite these numbers, many maintain that the "rich" aren't really paying their fair share.  So my thought this morning was that maybe those who make this claim are not referring to fair share of the total tax burden but instead to fair share of their income, regardless of how much others are paying.

This seems a rather odd way of discussing fair share but it's the only one that makes any sense in light of the underlying data.  Now if only they would let us in on what the magical fair share of income is....beyond "higher" I mean.

Thursday, January 24, 2013

On the meaning of spending "cuts"

Have a look at this framing of future spending from the TaxVox blog at the Tax Policy Center.

Ryan’s promise to balance the budget in a decade with no tax increases implies cuts in federal spending unseen since the U.S. disarmed after World War II. Most lawmakers are horrified that the automatic spending cuts now scheduled for March would cut military spending by 9.4 percent and domestic spending by about 8 percent. (And note this so-called sequester would exempt Social Security and Medicaid as well as Medicare benefits from any cuts).

So I got to wondering about the nature of this "cut."  And I wanted to go back to the earlier post I had done on balancing the budget.  If you recall, I ended that post asserting that we would be running a deficit of about 1.2% of GDP assuming:

1.  We grew spending at the rate of growth of inflation plus relevant population

2.  We asked government (ex-transfer payments) to improve efficiency by 10% over a decade.

3.  We eliminated spending on the wars and brought "automatic stabilizers" back to their non-recession levels of spending.

So I wanted to revisit the draconian cuts argument.  In point of fact, the tax increases passed at the beginning of this year account for an improvement in the picture of about 0.4% of GDP so that would take our 1.2% of GDP deficit down below 1%.  So, if we did nothing more than have government grow "base" spending at the rate of inflation plus population, we'd get the deficit down under 1% of GDP by 2022 and on a trend to balance within a few additional years.

I'd also point out that the statement from the TPC is factually incorrect.  Let's say we reduced spending from current levels (22.8% of GDP in FY2012) down to the 19% that will be collected in taxes under current law by 2022.  That's a reduction of 3.8% as a percent of GDP over a decade.  From 1990 to 2000, spending as a percentage of GDP fell by 3.7%.  From 1991 to 2001, it was pretty much the same.  The comparison to WWII is highly inapt.  From 1944 to 1954, spending fell by more than 20% of GDP.  What the Ryan budget would set us up for is something like the 1990s and nothing like the period 1945 to 1955.  You'd think the folks at TPC would know better.

Is Paul Ryan the Only Keynesian Left?

I found this post at the always good TaxVox blog interesting.  It lays out the positions of the parties on reducing the deficit.  It contrasts the position of Paul Ryan (who wants to balance the budget within 10 years) with Democrats who seem to be focused on a stable debt to GDP ratio.

The Goal Line. But Democrats and Republicans don’t even agree on the goal line in this game. While Ryan wants balance in a decade, Democrats are not thinking about balancing the budget at all. Their aim: Stabilize the debt so it does not grow faster than the economy. This would set the ratio of debt to Gross Domestic Product at about 73 percent.

To return to the question I asked before.  How does Keynesian thinking allow for "stable debt to GDP" to be a target over a 10 year period of time?  Is it A) that economic cycles are now 20+ years long and therefore we are running deficits during the down side of the cycle to be offset by surpluses in the good side of the cycle or B) that liberals have surrendered the ghost of Keynes and the through cycle target is now a deficit to GDP ratio of 4 to 6% (the nominal through cycle GDP growth rate)?

It certainly looks like the latter.  So perhaps Paul Ryan is the only Keynesian left.  Wouldn't that be an interesting turn of events?

Friday, January 18, 2013

How the Mighty Have Fallen

Well, it's official.  Keysianism has jumped the shark.  I think it's worth reviewing the bidding here.

If we go back to the original theory of Keynes, yes there was deficit spending but it was supposed to be largely offset by running surpluses during good times.  Thus, through the entirety of an economic cycle, the debt was supposed to remain roughly flat.  In other words, under the original theory, while there would be deficits in any given year, there wouldn't be much debt accumulated over time.  In other words, the target deficit on average through an economic cycle was zero.

Several years ago, the terrain began to shift and budget theorists and politicians began to talk about the notion of "primary balance."  This notion is simple, namely that the budget is in balance with the exception of debt service.  What this means is that the budget deficit is equal to or lower than interest on the debt.  Since interest payments currently run about 1.5% of GDP, the notion of primary balance would imply running deficits under this level.  Note, this notion abandons a balance through cycle and proposed continued perpetual deficits, but small ones.

More recently, we've abandoned that notion as too restrictive and now begun to argue that deficits are fine as long as they don't grow the debt to GDP ratio.  Now this is even a higher standard of how much deficit is good since GDP generally grows faster than the 1.5% that current debt service accounts for.  This latter standard is the standard that is commonly in use among more liberal economists today such as Paul Krugman or the CBPP.

But until recently, I thought primary balance was a through cycle view just like the original Keynesian view.  But, based on this piece by Dr. Krugman today, I'm beginning to understand my error.  Krugman writes

Recently the nonpartisan Center on Budget and Policy Priorities took Congressional Budget Office projections for the next decade and updated them to take account of two major deficit-reduction actions: the spending cuts agreed to in 2011, amounting to almost $1.5 trillion over the next decade; and the roughly $600 billion in tax increases on the affluent agreed to at the beginning of this year. What the center finds is a budget outlook that, as I said, isn’t great but isn’t terrible: It projects that the ratio of debt to G.D.P., the standard measure of America’s debt position, will be only modestly higher in 2022 than it is now.
The center calls for another $1.4 trillion in deficit reduction, which would completely stabilize the debt ratio; President Obama has called for roughly the same amount. Even without such actions, however, the budget outlook for the next 10 years doesn’t look at all alarming.
So in the view of Paul Krugman and the CBPP, it's OK to do nearly nothing because the debt to GDP ratio (proclaimed the standard measure of the US debt position) will not increase very much between now and 2022.

But let's take a look at what the CBO expects from the economy over the 10 year period...in short rapid growth, full employment and low inflation for about 8 of the 10 years.  So the new standard is that slowly growing the debt to GDP ratio in an era of full employment is OK.

We've gone from saying we should run a surplus (Keynes) in good economic times to saying that it's OK to run a deficit of 3 or 4% of GDP, a rate that has rarely been seen outside of wars (Krugman).  My how the mighty Keynes has fallen.  One almost wonders whether he'd recognize himself in his newest incarnation.


Almost but Not Quite

Well, House Republicans are getting closer.  They've figured out that they need to pass a debt ceiling increase but they haven't figured out how to do it yet.

When you compare their approach to what I've suggested, you'll see two key deficiencies in their proposal.

1.  There's no principal behind the budget increase.  Validating the principal of raising the debt ceiling to cover committed funds is important and something that is clearly missed in the three month extension.

2.  Pushing the Senate to pass a budget resolution is a good idea but the enforcement mechanism (withholding pay) does nothing to ensure future debt ceiling increases proceed apace.  Rather tying future increases to the deficits in the budget resolution ensures a long-term solution to the problem as well as a short term one.

Congress is losing the opportunity to reform the way we design and execute the debt ceiling.  This is an opportunity that should not be lost.

Saturday, January 12, 2013

A Potential Solution to the Debt Ceiling

I'd like to take one argument that I have heard a lot of folks, particularly on the left make, and use that to make an argument about how we might manage the debt ceiling.  First the argument and what I think is wrong with it.  You can find a simple version of it here.  Trying to ignore some of the invective, the crux of the argument is:

Obama has said he will not negotiate over the debt ceiling increase.  Good…I hope he sticks to that, because the debt ceiling shouldn’t be something that ever needs to be negotiated.  It shouldn’t even need authorization by Congress, it should simply be required that the U.S. Treasury have the capability to always pay the bills that Congress has already authorized.  The “trillion-dollar platinum coin” issue has been making the rounds as an option for Obama to bypass Congress if the GOP continues to play with economic disaster by making the debt-ceiling a political football. 

Now, the part of this statement is true is that Congress has already authorized spending that will push us above the debt ceiling but, in point of fact, it hasn't authorized very much, probably less than $300 billion.

1.  The Senate has not proposed and Congress has not passed a budget in more than 3 years.  Thus, there is no agreed upon spending blueprint for FY2013.

2.  The government is currently being run via a series of continuing resolutions.  The latest CR expires in March of 2013

3.  Assuming Secretary Geitner was correct that we hit the current ceiling on 12/31/12, this means that Congress has agreed to run the government for about 3 months post the passing of the ceiling.  Leaving aside timing effects, this means that the government would have about 1/4 of the annual deficit of say $1.1 trillion or about $275 billion to cover.

So yes, the government has agreed to spend $275 billion above the debt ceiling but not more than that.  Thus, the argument made by so many only justifies raising the debt ceiling by $275 billion.

However, there's the germ of a solution in the overall point.  I'd propose that Congress do the following.

1.  Immediately raise the debt ceiling by $275 billion dollars in what is called a "clean increase" of the debt ceiling.

2.  Attach an increase in the debt ceiling of whatever amount is required to the CR that much be passed prior to March 27.  In my view, I would increase the debt ceiling by 110% of the projected deficit created.

3.  Require that a debt ceiling increase be attached to each house's budget and that budget resolutions were the only way to raise the debt ceiling.  Thus, when each house passed its budget it would also be passing an increase to the debt ceiling and budget bills would be required to be passed, else the debt ceiling could not be increased.

4.  Finally, require a "true up" process at the end of every year.  That is, the ceiling could be adjusted for variance from projected costs and revenues but "only" for technical projections.  This could be done during the following year's budget process.

The consequence?  Well, the House, Senate and White House would have to agree on a budget (in order to increase the debt ceiling) and that increase would already be baked into law.  We might have to do some true ups when the economy tanks or thrives but, over time, those should cancel each other out.

Of course Congress would hate this because they'd have to pass a budget and they'd have to raise the debt ceiling showing how much debt they were adding every year.  But wouldn't this be much better approach to it than the current mess?

Tuesday, January 1, 2013

The (Not Quite) Worst Deal Imaginable

Well, I can say this for the current fiscal cliff deal.  It is not quite the worst deal imaginable but it does come close.  Here are some immediate and top of mind reactions.  I reserve the right to change some of these as more of the details come out but for now I think I can stick with...

  1. It's mostly a "small" tax increase bill.  The net tax increase is being reported at about $600 billion  over 10 years.  That averages $60 billion a year against deficits that look like they are going to be in the $1 trillion plus range for the foreseeable future off of this baseline.  So we should prepare for our fifth straight year of deficit spending greater than a trillion dollars and 7% of GDP.
  2. It gives away some of the benefit of "tax reform" before we've even gotten to tax reform.  It's hard to find exact estimates but the PEP and Pease changes probably raise about $100 billion or so in the 10 year window.  That's $100 billion of the $800 billion or so that has been discussed in "tax reform" discussions.
  3. It makes a future "grand bargain" much, much harder.  The notion of a "grand bargain," that is tax increases for spending cuts was always a decent idea in the context of Washington but it would appear that idea is all but dead.  There's just not much one can do on tax increases now without increasing taxes on the middle class and thus the math of a grand bargain is simply not going to work.
  4. It smells like a spending increase relative to the baseline.  The only report I've seen says "net" spending reductions are $15 billion.  But Congress includes reduction in debt service as a spending reduction and likely is using current policy as the baseline.  Thus, the debt service change (probably $60 to $90 billion of the $600 total) is probably counted as a spending cut meaning that spending, ex-debt service, most likely increased.
So is there anything good about the bill?  I can only come up with two things.  First, the reported permanent indexing of the AMT to inflation is a really good thing.  Assuming that stays in, it's a positive change from our perpetual patching process.  Second, the continuation of UI benefits is, from my perspective, also a good thing.  We can debate the merits of the UI system but putting some money in the pockets of people who have been employed is a good thing until we figure out a better unemployment system.  Sure it costs $30 billion but we could easily make that up somewhere else if we really wanted to.

And that's pretty much all she wrote.  Can kicking continues and looks like it's going to continue on pace for the foreseeable future.  There will be a lot of griping on both sides but in my view, Washington is simply incapable of dealing with the debt problem we have.  This latest event simply sheds more light on their (and our) dysfunction.

Saturday, December 22, 2012

How to be Irresponsible

It's a bit rare that I cross post here but this post from Christopher Demuth is worth reading in its entirety.

In a nutshell, it exposes the loss of focus of both Keynesianism and supply side economics.  Both have been subverted by the political process into a force for moving consumption to today and costs to the future.  In effect, we have a political process that competes for how to be irresponsible as opposed to whether to be.

Which brings me to the current fiscal cliff debate, the perfect incarnation of the how to be irresponsible discussion.  On one side, we have the Democratic party which is asserting that tax increases on 2% of households and (small) unspecified future spending changes will be sufficient to avert the fiscal crisis we face.

On the other side we have the Republican party which is asserting that future unspecified (but larger) spending reductions are sufficient to address the crisis.  I mean, look at these plans in context.  Over the next decade, we plan to spend about $45 trillion and tax about $35 to $40 trillion.  And our tax and spending plans amount to a change of $2 trillion or so in total, a 2.5% change from the most unbalanced place we've ever been.  And that's DC's version of difficult choices.

And that's the debate...a debate about how to be irresponsible...about which irresponsible ideology will prevail.  Unfortunately, regardless of the outcome of the debate, the future is the same.  We run up debt until we can't anymore.  At that point, some combination of future taxpayers and asset holders get well and thoroughly screwed.

Monday, September 24, 2012

The Meaning of Words

It's one thing when false information is presented in opinion pieces, but when it's presented in news pieces, that's a horse of a different color.  For instance, we have this from Reuters by way of yahoo news.

WASHINGTON (Reuters) - U.S. Republican presidential candidate Mitt Romney said he thinks it is "fair" that he pays a lower tax rate on his investment income of $20 million last year than someone who made $50,000 annually.

Now, I strongly suspect that most readers would read this as asserting that the average taxpayer who makes $50,000 pays a higher federal tax rate than does Mitt Romney.  But of course, this isn't true.  Courtesy of the TPC, we can see that taxpayers in the $40,000 to $50,000 range average 12.1% in total federal taxes (excluding imputed corporate taxes) while taxpayers in the $50,000 to $75,000 range average 14.5%.  Asserting that people earning $50,000 pay more than Romney simply flies in the face of the numbers.

Or maybe the authors meant to argue there is some taxpayer who makes $50,000 who pays a higher rate than Romney.  This latter statement is almost certainly true but not, I think, a reasonable inference from the quoted paragraph.

Sunday, September 23, 2012

Applying FICA tax to Mitt Romney

On another site on which I am a frequent participant, I was asked about the implications of applying the FICA tax to capital income.  It seems an interesting exercise so I did the calculations which I will repeat here.

Starting with the IRS SOI data from 2009 (the most recent year currently available), we can gather up the additional income that was reported and would be subject to a potential FICA tax on investment income.  This income totals to about $443 billion in 2009.  Were we to subject that income to the full employee side tax rate of 7.7% (6.2% for SS and 1.5% for Medicare), we'd get total taxes raised of about $34 billion.

Comparing this to total FICA taxes in 2009 of $890 billion according to the CBO suggests that applying FICA taxes to investment income would increase FICA tax receipts by a bit less than 4%.

But what of its affect on governor Romney?  Well, it would have raise his effective tax rate by 7.7 percentage points up to 21.8 percent.  So we can conclude that it would have made people feel better about governor Romney's taxes (maybe) but made little difference otherwise.

Well Worth the Read

This speech from Richard Fisher at the Dallas Fed is well worth reading in its entirety.  It speaks to both the current monetary situation and, at least in my view, the limitations of macroeconomic modeling.

It's worth remembering that a model is only good in the area in which there are historical observations.  We are no longer in that area.

Saturday, September 22, 2012

Why Romney's Tax Rate is Lower Than Yours (Maybe)

So now that Mitt Romney has released another tax return, we're going to get a rehash of stories on the fact that Mitt Romney's tax rate is lower than the average American's.  But let's take a look at whether this is true; and, to the degree it is, why it's true.

To start, we'll use the TPC estimates of 2011 tax rates.  Now Mitt Romney's tax rate was reported to be 14.1%.  So how does that compare?  Well, first we have to choose what to compare it to. One approach would be to compare Romney's rate to the sum of the income and payroll tax rates.  It's clear that neither the corporate tax nor the estate tax can be discerned from Romney's tax return.  It's also true that Romney's FICA tax is unknowable from his return but we can assume that Romney's FICA tax is pretty close to zero as a percentage of his income.

So if we look at income plus payroll taxes by income group, we find that middle income taxpayers (the middle quintile of earners) have a lower tax rate than Romney (12.1% vs 14.1%) and the second quintile has a slightly higher rate (16.0% versus 14.1%).

So what accounts for the difference?  Well, many people have claimed that the difference is driven by "preferential rates on capital gains."  But this just doesn't seem to be true.  Taxation on capital gains is different from ordinary income in two ways.  One, it's taxed at a flat 15% and two, there is no FICA tax on capital income.  So let's pull these two things apart.

To look at the effect of the rate differential, let's just look at the effective federal income tax rate.  By this measure, Romney's effective tax rate is higher than every group of taxpayers below the 96th percentile, hardly lower than most Americans.

So what's accounting for the difference is the fact that FICA taxes aren't applied to capital gains and (for most of them) are capped at an income threshold.  But these two things have been true of FICA taxes for as long as they have existed.  So, in effect, the root cause of all of this is the fact that FICA taxes don't apply to capital income.  Nobody has proposed changing this and it has always been this way.

Just thought it worth pointing out.

Friday, September 14, 2012

False Unequivalence

So I'm normally a fan of Derek Thompson over at The Atlantic.  I quite often disagree with him but I think he's normally pretty good.  But here he's pretty awful.

Let's review.  He takes Governor Romney rightly to task for saying that "middle class" should be defined as having less than $250,000 in annual income.  But here's what you can find on the White House website.

Unless the House of Representatives takes action before January 1, 2013, taxes will go up on 114 million middle-class families. Nearly everyone in Washington agrees that’s a bad idea. That’s why President Obama is calling for -- and the Senate has already passed--  legislation that will keep the middle class from paying thousands of extra dollars next year.

So the President will reduce taxes on 114 million middle class families.  As it turns out, according to the census, there are only 118 million households in the US and 79 million family households.  So the most charitable view of the WH website is that the President has the same definition of "middle class" as does Governor Romney.  Of course, a less charitable view, which is what Derek applies to Governor Romney, would suggest that the President thinks he can reduce taxes for 130 percent of all family households in the United States.

There's no reason to defend Romney's statement as it's wrong.  But, at best, it's no more wrong that what's up on the WH website.  Either way, the selective outrage here is really crazy.

Saturday, August 25, 2012

A Long Reply to Peter Orzag

Well, I don't get to post in the Washington Post but I do want to reply to Mr. Orzag's most recent column there.  Warning to all, this is going to be a long post as his is a long column with quite a lot of misrepresentations.

First, federal Medicaid spending is currently forecast to double by 2040, from 2 percent of gross domestic product to 4 percent. Under Ryan’s budget, it is projected to be cut in half over that period. This dramatic turnaround will supposedly occur by turning Medicaid over to the states through block grants. Anyone want to bet that will work? If states can’t find huge efficiencies in Medicaid, expect them to pressure the federal government to avoid the fanciful reductions in federal support assumed in the Ryan budget.

It's kind of interesting really.  This is nothing more than an argument that Mr. Orzag believes that Medicaid cannot survive on 3% per year increases in funding (which is what is in the Ryan budget) from the current baseline.  Mr. Orzag is entitled to his opinion and he may prove to be right but this hardly proves anything.  As I've written elsewhere, assuming the end to our slow growth period, as all forecasters have and assuming 1% annual efficiency in Medicaid spending, 3% growth in Medicaid is not a bad forecast over the next decade.  In the longer run, it may be worse but this is hardly the ridiculous assumption that Mr. Orzag assumes it to be.

Second, the Wisconsin congressman has specified $4.5 trillion in tax cuts, counting on massive rollbacks of tax breaks — such as the mortgage interest deduction — to pay for them. But he offers no details as to how to achieve such reductions, and most serious tax analysts don’t think such changes are politically feasible.

Let's assume this is true.  Mr. Ryan and Mr. Romney have specific two objectives, rolling back rates 20% and cutting deductions to offset.  My Orzag is making the assumption that the first objective will trump the second if they are in conflict.  He has no way of knowing this is true and, the projections in the Ryan budget actually appear to assume the first trumps the second sine the revenue line is revenue neutral to the current policy baseline.  Again, Mr. Orzag is offering no proof just the least charitable read he can offer.

Third, Ryan assumes that other spending, including nondefense discretionary spending, will fall from more than 12 percent of GDP last year to less than 5 percentby 2040. Again, he provides scant details on how to get there. 

This one is actually a bit funny.  Mr Orzag may want to read the President's budget at some point.  It assumes that total discretionary spending will fall to 5.0% of GDP by 2022.  The notion that Mr. Ryan might go from 5 percent to below 5% by 2040 doesn't really seem all that difficult to imagine.  You'd think as a past member of the Obama administration, Mr. Orzag might be aware of this fact.

Ryan says he would cut tax rates for all families, but that doesn’t mean the middle class would be any better off. Even after the Bush tax cuts, Ryan’s reductions would amount toabout $1,000 a year for families with annual incomes between $50,000 and $75,000— compared with a cut of more than $250,000 a year for those with incomes above $1 million.

This one is fun with numbers.  According to the TPC, the average family with an income of between $50,000 and $75,000 pays 5.7 percent of their income in federal income taxes (which is what is being changed here).  We'll charitably call that about $3500 per year.  This family is receiving a tax reduction of about one third, using Mr. Orzag's own estimate (which comes from the partisan CBPP).  The family with over $1,000,000 on average pays an average of about $600,000 in federal income taxes and receives about the same 1/3 reduction.  Thus, the gap in the amount saved is caused not by the unfair change in the tax code but by the gap in their current tax contributions.  As an aside, the tax rate changes in the Ryan plan do nothing to tax distribution.  It's simple math.

Furthermore, unlike the proposal from the nonpartisan Domenici-Rivlin deficit-reduction commission, the Ryan budget does not include any provisions to create jobs immediately. With unemployment above 8 percent, we should couple any long-term deficit reduction with additional support for the economy today. That would help the middle class more than promises of a tax cut that will probably turn out to be a mirage.

Oh dear.  So the Ryan plan is like the bipartisan Bowles Simpson plan in that it doesn't include immediate stimulus.  It is interesting that Mr. Orzag wouldn't mention the Bowles Simpson plan which his boss created.  With the deficit above $1 trillion already, perhaps Mr. Orzag should explain why the next trillion of deficits will do more than the first trillion. I'd also be curious if Mr Orzag would support all of Domenici Rivlin which, quite interestingly calls the same approach to Medicare as in the Wyden-Ryan plan (the current incarnation of Ryan's approach to Medicare).

“Both administrative costs (including profits) and payment rates to providers are higher for private plans than for Medicare,”the report said. That effect, according to the CBO, would outweigh any savings achieved by people choosing less costly health care.

But this assumption from the CBO is achieved by assuming that Medicare can continue to cost shift onto private insurance in perpetuity (which of course it cannot) and Mr Orzag also fails to mention that the plan would save the government a ton of money which the CBO concludes in the same report he cites.

Suffice it to say this piece which appears under the title "Five Myths About Paul Ryan's Budget" should probably be titled "5 Reasons Peter Orzag Has a Difference of Opinion with Paul Ryan."  To classify something as a myth typically requires demonstrating it is not true.  Mr. Orzag falls a long way short of that bar.

Sunday, August 19, 2012

Horizontal Equity

Given the various incarnations of tax reform on the table, particularly from the Republicans in the Presidential debate, we are going to see a lot of discussion on the issue of tax equity.  Unfortunately, nearly all of this discussion is going to focus on the notion of vertical equity, that is, the equity between people of different incomes.

In some ways, a far more important discussion on the tax side is to be had around the notion of horizontal equity.  Oddly though, there is almost no published data on the topic of horizontal equity.  There are numerous papers on the topic as a conceptual matter but very little in the way of data.

But to illustrate the problem, we can look at the following table from the Tax Policy Center which shows the distribution of households who have zero or negative Federal income tax liability.  What this will show you is a reasonable number (thousands) of people with zero income tax liability who have high levels of income.  This fact is (in part) a result of lack of horizontal equity in the tax code.

There are literally hundreds of drivers of a lack of horizontal equity (mortgage interest deduction, child care credit, alimony income, etc.).  Each of these drivers is designed to fulfill some overriding policy objective that tax writers think they have; however, taken collectively they drive a large amount of horizontal inequity.

And horizontal inequity has effects that seep over into the discussion of vertical equity.  Remember the famous discussion about Warren Buffett versus his assistant.  Leaving aside the fact that Mr. Buffett did the tax calculation incorrectly, it is still a comparison driven by horizontal equity more than vertical equity.  People in Mr. Buffett's income class do in fact pay higher average effective federal taxes than people in his secretary's income class.  It is horizontal equity (and his faulty calculations) that drives this anecdote.

Which brings us to the debate over tax reform.  A smart campaign would push tax reform on the basis of horizontal equity.  Such a campaign would have a whole lot of ammunition to use.  The fact that neither side wants to talk about it is only an example of how much politicians like to be able to use the tax code to try to influence all of us to exhibit the "right" behaviors.