Tuesday, January 30, 2018

Republican Tax Reform: Part 8–Average vs. Marginal Rates

This is the old conflict in decision-making: accounting is mostly backwards-looking, while economics and finance are mostly forward-looking. How much money did we make versus how much money will we make? Of course, the data we gather about the former is much more accurate than the forecasts we make about the latter.

So, accountants are pretty good at providing average values (from decisions made in the past), and the economic evidence is that people base decisions that they are making right now on marginal values.

It would be nice if we could measure those marginal values used to make decisions in the past, but typically our data isn’t measured that way. We can tease them out with econometrics, but it isn’t that easy (since expectations are ephemeral, yet they may critically affect marginal values).

In the case of taxes, what the government is setting is tax rates that are marginal. Then people make decisions about what to do (which we can observe) and what not to do (which we can’t observe) based on those. Lastly the accountants count up just the former, and provide averages for just that part of the whole picture.

N.B. This is not a knock on accountants or accounting, just one more statement of why social sciences are harder than natural sciences—our elements decide not to do stuff sometimes and theirs’ don’t.

What we need to pay attention to from a macroeconomic policy perspective is the marginal tax rates. This Republican reform reduced them a lot on corporations, and a little bit on individuals. You could also argue that some of the changes (like child care tax credits) changed marginal rates for some as well. So we should expect big changes in how firms behave, and not so big changes in how individuals behave.

But what we will get data on out in the future is average tax rates.

In an earlier post, I used the example of the marginal rate being 10% on your first thousand, and 20% on everything above that. Those are the two marginal rates.

Now, if you have $200 you pay $20, or $800 you pay $80, and the average tax rate is 10%. It’s the same as the marginal rate because those numbers all fall within one bracket.

But if you have income from both brackets, the average rate will fall between the two brackets.† So, if you have $1,100, you pay 10% on the first thousand, 20% for the remaining $100, for a total of $120. Divide that by $1,100 and you get an average rate of 10.91%.

A further complexity is added as income continues to rise: the average tax rate will go up and approach the higher marginal rate in the limit. So, if you have $2,000 you’d pay $300 in taxes (for a 15% rate), and if you have $10,000 you’d pay $1,900 for a 19% average rate.

FWIW: There’s really nothing new in that arithmetic. The average tax rate is a weighted average of marginal tax rates, and this is what weighted averages do as the weights change.

The result is things like Table 1 in the Summary of the Latest Federal Income Tax Data, 2016 Update from The Tax Foundation (yes, you need to click through and look at it). It shows that the top earners average rate was 27%, even though this page from yesterday’s post shows the top marginal rate for that year was 39.6%.

And yes, you do see demagogues noting that such and such a rich person only paid some percentage of their income in taxes even though they’re rich and should qualify for a higher rate. In the future, your response should be something like “Duh … do the math”. Arithmetically, it has to work this way, and we should know better than to complain about it.

Unfortunately, a lot of people want to use the tax system to punish people or behaviors they don’t like (this is called a Pigou tax after the economist that first described it). There’s nothing wrong with that. And the typical response is to raise what we can (those marginal tax rates) to get the average rate to go up.

The message here is that you have to raise those marginal rates quite a lot to get much movement out of the average rate. And the marginal rates are the ones that affect decisions. So what you’re really saying is let’s go straight after the decisions people make to move the needle on this indirectly connected gauge called an average rate.That’s a recipe for really clumsy and ham-handed government policy. <in a sarcastic voice> “Gee … that doesn’t ever happen, does it?”

And, the message is that if you really want to discourage some behavior, the brackets are not that critical, but cranking up the marginal rates very quickly is. Yet, it seems like this is also something that policymakers are disinclined to do. The evidence is the proliferation of rates, exemptions, and deductions at the low end of the tax code to get some people out of paying the tax.‡

† With more than two brackets, it will fall between the bottom one and the top one. But since exemptions and deductions create a 0% bracket, the average rate will just be less than the top marginal rate paid by that person.

‡ An interesting phenomenon in development economics is that poor countries often have ridiculously punishing marginal tax rates. The reason is that they design their rates and brackets to mimic some richer developed country’s, but they scale down the borderlines of those brackets to fit into the amounts of money the locals actually have. So you end up with us defining the rich who are deserving of high marginal rates at something like $200,000, and them setting their threshold at $2,000. Maybe that much does make you rich in a poor country, but what you’re really doing is excessively taxing a local, and undertaxing a potential foreign investor. I first saw this in Klitgaard’s book Tropical Gangsters over 30 years ago, so it’s not a new idea.

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