The (Limited) Usefulness of Formal Economic Models

(This post is dedicated to Robert Wegner.)

As a graduate of New York University, I was forced to learn formal models of the economy, which would have horrified me when I was in college and hooked on Austrian economics. However, even though I never would have gone to NYU had I realized what I was getting into, after the fact I was glad that I had done it. There really are benefits of these formal modeling techniques. This isn't to say the benefits outweigh the opportunity costs; obviously graduate students could be doing something else with their time that might be much more valuable in terms of producing good economists. Nonetheless, in this blog post I want to give an example of the power of formal modeling.

The specific issue is whether a consumption or income tax is less distortionary. As usual, we are going to try to compare apples with apples by insisting on revenue neutrality, and we are also not going to worry about issues of privacy.

Following Rothbard, my intuition had always been that an income tax was better (on these limited grounds). I thought, "The government takes a certain amount out of your income, and then you're free to do what you want with it. If you want to invest it, go ahead. If you want to blow it at the racetrack, that's fine too. The government shouldn't be trying to encourage you to save more than your time preferences indicate."

If you ask me now, though, my answer would be the exact opposite. If we make enough assumptions to render the question meaningful, then it is clearly the case that a consumption tax respects people's intertemporal preferences, whereas an income tax penalizes savings. In this sense, then, a consumption tax is Pareto superior; a consumption tax leaves consumers with more utility than an income tax that yields the same (present value) in tax revenues.

In defense of Rothbard and my earlier self, a lot of proponents of consumption taxes aren't clear on this point. They either imply or explicitly claim that their plan "encourages savings and investment" above what would happen in the absence of any taxation, and that is clearly inefficient. (After all, it would be crazy to force everyone to save 99% at gunpoint, even though this would lead to very high GDP growth.)

But as I said, studying a really simple model led me to reverse my earlier position. Under reasonable assumptions, a consumption tax doesn't alter the consumption/savings tradeoff. Yes, people are obviously worse off because their consumption is lower in every period, but they are not hurt by distortions in the intertemporal tradeoffs they face.

Before continuing, let me give the caveat: Of course you can always come up with ways to disprove any sort of "rule" in these types of analyses. E.g. if people had religious views favoring income taxes, then they would obviously be worse off with a switch to consumption taxes. But if we assume people don't care about the tax system itself, that there are equivalent costs of compliance, etc., and just focus on the incentives on individuals' saving rates and preferences for consumption at different points in time, then the consumption tax is clearly superior.

So here's the verbal reasoning: From the individual's POV, the purpose of saving and investing is simply to consume in the future. So really the issue is consumption now versus consumption later. Without any taxes, people refrain from consumption today until the point at which the marginal utility of present consumption is higher than the present utility of the future consumption which that investment would yield.

Slapping on a consumption tax doesn't alter this tradeoff, it simply lowers the level of consumption in every period. Think of it this way: Suppose you were a farmer trying to decide how much corn to eat and how much to plant for next year's harvest. After you made your decision, what if you learned that the cook who makes your meals is a klutz, and so it takes 10% more corn to make a meal than you previously estimated. With this new information, that shouldn't alter how much of your harvest this year you devote to feeding your family, versus how much you plant again. Yes, the amount you set aside to eat right now yields fewer meals, but that is true of the amount you are planting.

In contrast, an income tax does give you an incentive to consume more in the present than you would have without any taxes. It's as if there are locusts that destroy 10% of the crops before you harvest them. Now that you've got the 90% in your possession, you can either eat them or plant them again, when they again will be subject to the locusts. So the technology for converting potential present meals into future meals has changed; now abstaining from one present meal yields a smaller amount of future meals than it did originally. Thus you consume a larger fraction of your harvest, and plant less for next year.

Let me address something that bothered me for a while, even though the above reasoning seemed impeccable. In intermediate micro, professors love to go over indifference curves to show that an income tax is better for the consumer than an excise tax on a particular good. E.g. if there are beer and donuts with their market prices, it is better to take $10 from the consumer and let him spend the remaining $90 however he wants, rather than placing a unit tax on beer (let's say) such that in equilibrium the consumer buys enough of that good to give $10 in tax revenue to the government. The intuition is that not only is the consumer $10 poorer, but under the excise tax beer is made artificially more expensive, and so the individual's options get a double-whammy from the government.

But that's not what's happening here. Specifically, it's not true that you have a "given" amount of income, and then the government let's you spend it on present versus future consumption. If you save and invest, then your future income is higher than it otherwise would be. So that's one difference from the typical intermediate micro demonstration (with a fixed endowment of income that the consumer is allocating between two goods).

The other difference is that with a consumption tax, the government isn't slapping a tax on one possible good, while leaving the other untaxed. Again, the whole purpose of saving is to consume in the future (or to allow your heirs to consume). So there's no distortion, encouraging individuals to save more than they otherwise would (the way there was in an excise tax on beer, which would encourage spending on donuts).

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Now why did I title this blog post the way I did? Because I was only led to the above realizations through working out a very simple model, with two periods and a consumer with utility function U = ln(C1) + ln(C2), and interest rate of 50%, and wage income in each period of $100. I slapped on a 50% income tax and had the consumer optimize, and calculated how much (in PDV in period 1) revenue the government would collect. Then I figured out what rate a consumption tax would have to be in each period to yield the same (PDV in period 1) revenue to the government. In the second approach, the consumer's utility (from the after-tax consumption) is higher than with the after-tax stream of consumption under the first setup. Also, in the consumption tax approach the gross amount of saving is unaffected by the tax; i.e. it is the same whether the consumption tax rate is 0 or positive. This isn't true with the income tax.

Another benefit of using the model: When I first tried to solve for the revenue neutral consumption tax rate, it came out to something like 116%. So I thought I had messed something up, because that was clearly crazy. But then I realized that no, there is nothing illogical (though grossly immoral of course!) about consumption tax rates being higher than 100%. If your wage income is $100, you can, say, save $10, consume $30, and pay $60 in taxes to the government, if the consumption tax rate is 200%. That would be awful, but it's not unsustainable the way a 200% income tax would be.

So the lesson for Austrian purists? I think that formal models allow us to check our intuitions on complex things, such as comparing different tax regimes. Of course you can't rest with the model results; if the results are surprising, you need to figure out whether it's because you made a bogus assumption, or because your intuition is wrong.

I know Rothbard has argued that this is superfluous at best; why translate economics into formal symbols, get a result, and then translate back into English? But the answer here is the same as for why they do this in symbolic logic: Because sometimes the argument is very complex, and you might make a mistake in your reasoning if you try to do it in English.

I never would have come to the understanding that I can now give in purely Austrian terms, had I not known how to create a very crude neoclassical model. I would still think that consumption taxes distort intertemporal decisions vis-a-vis consumer preferences.

One last thing: If I still haven't sold you, consider comparative advantage. If you haven't worked through a ridiculously crude two-good, two-country numerical example, then I submit you probably don't really "see" why free trade makes all countries richer. Sure, that Ricardian model doesn't prove anything, but a simple numerical example illustrates the principles very efficiently. And that's why everybody I've ever seen teach this--including people at Mises University--rely on simple numerical examples.