## You don’t think about taxation the right way: capital gains edition

Assume 50% income tax, 10% capital gains tax, and that a man (let’s call him Mitt) earns $1m in Years 1 and 2.

Scenario 1: Mitt spends all his post-tax income. His effective tax rate in Year 1+Year 2 is 50%.

Scenario 2: Mitt saves all his post-tax income from year 1, and it doubles in value. In years 1+2, Mitt’s earned income is $2m, unearned income $500k. He pays $1m in income tax and $50,000 in capital gains tax. His effective tax rate in Year 1 + Year 2 is 1.05/2.5 = 42%. But his effective tax rate in year 2 is 0.55/2 = 28%. Quoting the effective tax rate for the year in which capital gains are realised understates his overall effective tax rate, but does appear to generate the result that is overall tax burden is lower than someone without investment income.

However, this is not the right way to calculate the total ‘burden’ of the tax on Mitt. Steven Landsburg thinks about it a bit differently, as per usual, and arrives at a different result (emphasis his)

To understand Mitt Romney’s tax burden, you have to compare him to his doppelganger Timm Romney, who lives on a planet with no taxes. In the year (say) 2000, Mitt and Timm both earned (say) a million dollars. Timm invested his million dollars, saw it double over the past decade or so, and cashed out his investment this year, leaving him with two million dollars. Mitt, by contrast, paid 35% tax in 2000, leaving him with $650,000. He invested it, saw it double, and cashed out last year, paying 15% tax on the $650,000 capital gain. That leaves him $1,202,500, which is about 60% of what Timm’s got. In other words, the tax system costs Mitt almost 40% of his income.

By contrast, people on our planet without investment income collect their wages, pay 35% in taxes, and spend what’s left. The tax system costs them 35%, while it costs Mitt almost 40%. In other words,

people with investment income bear a higher tax burden, as a percentage of their income, than anyone else

When I read this quickly on the train this morning, I thought this was misleading and wrote the first couple of lines of this post in an email to myself in order for me to finish it later. But very quickly I realised that Steve’s way is the right way to think about it.

Same assumptions as above

Scenario 1: Mitt spends all his post-tax income in years 1 and 2. Had there been no tax, Mitt’s income would be 2.0 times what it was ($2m rather than $1m).

Scenario 2: As above, Mitt saves all his post-tax income from year 1. Had there been no tax, Mitt’s income would be c.2.1 times what it was ($3m rather than $1.45m).

On this method, Mitt’s effective tax rate in my example above would be 52% rather than 42%. I think this is the right way to think about it, insofar as the total cost of all taxation to you is equal to the benefit you would accrue through the elimination of all taxation.

A few weeks ago, I linked to a Megan McArdle post, where she said

…we think about taxes the wrong way around. Most people think that raising a 5% tax rate to 10% is more noticeable (and painful) than raising a 50% tax rate to 55%. After all, the first represents a doubling of your tax rate; the second is only a 10% increase. But this is exactly the wrong way to think about it. The pain of a tax hike is determined not by how your current tax rate compares to your earlier tax rate, but by how your current disposable income compares to your earlier disposable income. Doubling the tax rate from 5% to 10% decreases your disposable income by about 5.25%. But raising it from 50% to 55% decreases your disposable income by 10%. That’s a much bigger whack.

Our instinct when we think about the burden of taxation is to take the tax we think we actually pay, and divide that by our *pre*-tax income under the existing tax regime. The right way to think about our *total *tax burden is the difference between *post*-tax income under the tax regime and *post*-tax income under a no-tax regime, and the right way to think about the burden of a *marginal tax increase* is the change in your *post-*tax income relative to your current *post-*tax income.

This is very interesting. I understand Megan McArdle’s method. I can’t seem to comprehend Steven Landsburg method yet. Do you know whether these tax estimate methods account for the several increased cost to the society due to the activities that doubled the investment amount? For e.g. if the investment supported the activity that received grant from the taxes collected, how would these tax estimate account for it? Say the impact of that grant was that the investment doubled in 10 years instead of 15 years. How will inflation will factor in? Not sure if I completely misunderstood the basic premise of this article.

Curryus,

The way to see what’s going on with Landsburg’s point is that if you assume Mitt has the same savings rate (i.e. he saves the same percentage of his post-tax income) then an income tax of 35% reduces his savings by 35%, which assuming the same rate of return on investment reduces his pre-tax investment income in year 2 by 35% from what it otherwise would have been. That investment income that Mitt ‘would have earned’ never happened because of the income tax. It’s a cost to Mitt, even though it isn’t tax paid to the government. It just never happened.