Means-Testing, Overlapping Social Programs, and Marginal Tax Rates

THIS HAS BEEN UPDATED NOW, SO DISREGARD THE VERSION THAT WAS AVAILABLE FOR 4 HOURS ON FRIDAY MORNING.

Here’s a primer on how marginal tax rates work, and how they interact with means-testing.

First off, we describe taxes as either marginal or lump-sum. Marginal rates are set as a percentage of something else, like income taxes. Lump-sum taxes are set as a set fee that’s (more or less) constant, like the cost of fishing licenses.

Politicians like marginal rates because it’s a lot easier to collect a lot of money if you’re just skimming a percentage off the top. For perspective, our households total annual federal income taxes are in the range of the value of a new car; can you imagine having the cash around to buy a car in one lump-sum each April 15? It’s not gonna’ happen.

Economically, the thing is, marginal taxes distort people’s decisions, making them do things they wouldn’t otherwise. Lump-sum taxes do that sometimes, but not always, and definitely on a smaller scale … mostly because they’re simple binary choices that are over and done with right away.

In practice, marginal tax rates look like this. Suppose you pay a flat tax of 10% of your income:

Gross Income	Taxes Paid	Net Income	Effective Tax Rate
0.00	0.00	0.00	0%
1.00	0.10	0.90	10%
10.00	1.00	9.00	10%

Easy, right?

You can already start to see a very simple aspect of how marginal tax rates are distortionary. Even though everyone pays the same marginal tax rate, their effective tax rates are different: choose not to work, and your choosing a different tax incidence.

We complicate things by adding steps to our flat tax rates. We could smoothly adjust tax rates, but we usually don’t. Instead we say the rate is 10% on your first $10, and 20% on anything above that. Like so:

Gross Income	Taxes Paid	Net Income	Effective Tax Rate
0.00	0.00	0.00	0.0%
1.00	0.10	0.90	10.0%
9.00	0.90	8.10	10.0%
10.00	1.00	9.00	10.0%
11.00	1.20	9.80	10.9%

This is still pretty easy. The distortion which economists worry about is more complex now: adding the step has made the effective tax rates change unevenly.

There’s one important thing to notice about the system in that second table: the highest marginal rate exceeds the effective tax rate. The reason for this is that the effective tax rate is a form of weighted average.

Now let’s suppose we add a social program, whereby everyone gets a guaranteed income of $1, say by a lump-sum tax credit. Now the table looks like this:

Gross Income	Net Tax/Subsidy Paid	Net Income	Effective Tax Rate
0.00	0.00 - 1.00 = -1.00	1.00	-infinity
1.00	0.10 - 1.00 = -0.90	1.90	-90.0%
9.00	0.90 - 1.00 = -0.10	9.10	-1.1%
10.00	1.00 – 1.00 =  0.00	10.00	0.0%
11.00	1.20 – 1.00 =  0.20	10.80	1.8%

Not so easy now, right?

What is really interesting though, is that this implies that once we have a single marginal tax rate that’s distortionary … it makes the new system of two overlapping tax rates distortionary, even if one of the taxes is lump-sum.

Digression: If you’re confused right now, join the club. But, it’s important that as an economics student that you work through this and get it right. Being befuddled by the math has a name: functional innumeracy. It’s like functional illiteracy, except with math. Personally, I think a lot of our problems with means-testing come about because most politicians, bureaucrats, the media that covers their actions … and voters … are functionally innumerate

Now consider what happens if we add means-testing. What is that exactly? It basically means that some social program has steps that make it progressive. Everyone thinks these are a good thing (and to a certain extent they are): less welfare for those that are richer.

Except this really screws up our effective tax rates. Consider a 50% reduction in that $1 subsidy that kicks in at a $5 income:

Gross Income	Net Tax/Subsidy Paid	Net Income	Effective Tax Rate
0.00	0.00 - 1.00 = -1.00	1.00	-infinity
1.00	0.10 - 1.00 = -0.90	1.90	-90.0%
9.00	0.90 - 0.50 =  0.40	8.60	4.4%
10.00	1.00 – 0.50 =  0.50	9.50	5.0%
11.00	1.20 – 0.50 =  0.70	10.30	6.4%

Again, it’s a pain to work out the arithmetic. What’s important is that each step we bring in from a single program increases the number of steps and complexity we observe in the final effective rate.

Now, here’s what governments do: they keep adding new programs, each with their own means-testing steps. And sometimes the situation gets complicated enough that weird stuff starts to happen. Consider this table; now I have a third program that pays out $1 to everyone with income under $9.50, and nothing to everyone else:

Gross Income	Net Tax/Subsidy Paid	Net Income	Effective Tax Rate
0.00	0.00 - 2.00 = -2.00	2.00	-infinity
1.00	0.10 - 2.00 = -1.90	2.90	-190.0%
9.00	0.90 - 1.50 = -0.60	9.60	-6.7%
10.00	1.00 – 0.50 =  0.50	9.50	5.0%
11.00	1.20 – 0.50 =  0.70	10.30	6.4%

The key result comes from the steps that are set independently: we now have the bizarre situation where a pay cut can lead to higher net income.

How do we get into this mess? Roughly it’s because Democrats propose new social programs to attract votes (because everyone forgets about the last time the introduced a new program). Republicans find it’s politically unpopular to oppose those programs too strongly. So instead, they choose to do something stupid, and impose means testing. And the Democrats go along with this because 1) they get their program, and 2) they look conciliatory and tough at the same time. The end result is multiple overlapping programs with steps in different positions.

Casey Mulligan has made the argument that the ARRA (aka “the stimulus package”) put 4 million people in the position of paying a tax in excess of 100% on marginal income. In short, they take home more money if they don’t work. Here’s a chart from his testimony before Congress:

The bar indicates that, prior to the passage of ARRA, most of the benefit to working for this group of people was offset by taxes and lost benefits. The response of Congress to the weak economy was then to tack on more benefits, with enough means-testing to make it unbeneficial for some to work.

What are those programs? Looking at the chart, most of them stayed the same. But, they increased the Earned Income Tax Credit, they created a new program called FAC (basically, extended unemployment benefits), added another new one called SCAP (basically, new and improved food stamps), and introduced a subsidy to help offset the costs of the existing COBRA program (that allows the recently unemployed to keep their health insurance with their old employer for a couple of years).

All of those sound good, and they probably are. They are certainly good-hearted. But combined together, what they’ve done is created a Frankenstein monster: a whole that doesn’t behave as we’d like, cobbled together from parts without enough introspection.

What can we do about this? Step one would be to get rid of this green-eyeshade, bean counting, approach to government finance. We need more gatekeeping on ideas before they become law, and less penny-pinching on the back end. Step two would be to get rid of the idea of progressive steps: not only do we need flat taxes, but we need flat benefits too. In that light, substitution of a guaranteed income program for existing overlapping programs would be a good thing. But, if you check the proposals, substitution doesn’t happen, supplementation does. And that doesn’t solve this problem at all.