All Taxes are Distortionary!

So say I put a tax on coffee. Theoretically, it should alter the way I consume coffee. In an Economics (or Intuition) 101 course we learn that I go to Starbucks and now buy tea instead. Fairly straightforward, right?

This is we call a "distortionary effect" of a tax. Basically it changes incentives from what you would have done to what you will do now. And in doing so, it changes the combination/proportions of goods you would have consumed, since you substitute away from one in favour of another. (More tea, less coffee in this example.)

What if I taxed labour (with an income tax)? That causes some distortions as well right? Depending on disposition, people may substitute away from labour to leisure or, since they feel poor, they may start working even more to compensate. Most labour theorists argue that very poor people will tend to work more, since they cannot afford to not work, but wealthier people may cut back on work and purchase more "leisure" because working becomes more "expensive" since they are taxed.

So here is what bothers me. A lot is said of "non-distortionary taxes". People like to argue that a certain tax is not distortionary for such and such reasons. The most frequent example is the lump sum tax. This tax is basically a per-head tax - every person has to pay $X just for existing. The end. People seem convinced that, theoretically, it just shrinks a person's overall income, but doesn't really distort their incentives to purchase some goods over others. It just shrinks their overall budget. This makes sense right? (You should be shaking your head "no", since I am going to argue that it doesn't.)

In fact, I was talking to a TA of mine who went to Harvard for his undergraduate education. He was telling me how in his basic macro class there, they taught him that concept. Same I've heard from people going to all sorts of schools for undergrad, including schools as far and wide as MIT, UT Austin, Columbia, Berkeley, and -yes- even U Chicago! (Note: this isn't done at the graduate level, or even at an advanced undergraduate level, as I understand it. But most business folk do not pursue Ph.D.s in economics, so they run off into the business world with stupid ideas like these...)

So what is my problem with the notion that there are some non-distortionary taxes? Well, I like the Sala-i-Martin mantra that "all taxes of distortionary - people are just stupid". Here's why. Take the example of the lump sum tax. The common argument goes: since lump sum tax paid cannot be changed by individual behavior, i.e. since I pay $X no matter what, there is no reason to view it as changing my choices. In all other choices, I pay $Tax based on how much coffee I buy or how much work I do, or whatever. But here, I am stuck paying $X - too bad, so sad.

See, the thing is, the argument is flawed because if we look at this way, we aren't looking at the right model. I will show that the model excludes a key market and therefore appears to be non-distortionary, even though it clearly is! For an analogy, say we take a model where we fix how many hours we work per week. Say I work 40 hours per week no matter what, and my wage is held constant. And in this model I examine the effect of a tax on consumption (sales tax) and a tax on wage (income tax). But since from year to year my wage is still taxed at the same rate and I am stuck, by assumption, in a state of working 40 hours per week, it looks like this tax isn't distortionary. I am stuck paying the tax no matter what, and I cannot avoid it by substituting leisure for labour! But wouldn't it be silly to conclude from this model that wage taxes aren't distortionary? It would seem so because my model assumes that I cannot change my behaviour by reducing labour hours. Obviously, in the real world, there would be effects - the problem here is with the model. My model made labour exogenous (outside of the model) - it was fixed. And therefore, that key market was missing from the analysis so it seemed as though income tax was non-distortionary!

Similarly, here is the thing. There is a market for children. The number of children "bought" varies per income level. Introducing a lump sum tax per head is basically a tax per how many coffee cups are bought - i.e. how many children are bought. Right? It is just that most models treat the "fertility market" as exogenous (outside of the model). Since the models exclude markets such as these, they obviously fail to see that the lump sum tax has distortionary effects!

In sum, all taxes are distortionary. There are just people who distort reality and conclude otherwise, and those who do not.