Monday, February 02, 2015

Discounting taxes

Samson is having trouble with this post, about why you can't "save money" by moving to a place with lower property taxes.

Let us picture three homes, identical in every respect. (This is a thought experiment, OK?)

Each is priced at $100,000.

Now the property tax fairy descends on the area, placing a tax of $1000 per year on home B, and $10,000 per year on home C, while ignoring home A. Furthermore, assume that there are no benefits from the higher taxes, such as better schools: the tax fairy just whisks the money off to fairy-land.

The market of potential owners is, on average, planning to occupy their next home for ten years. The present value of the tax payments on home B for a ten-year period, discounting at 5%, is roughly -$7500, and that on home C roughly -$75,000. (Should we discount in perpetuity? Maybe, but that doesn't really change the outcome of our exercise.)

If all three homes (aside from taxes) are identical to me, I will pay $100,000 for home A, $92,500 for home B, and $25,000 for home C. I do not save a penny by buying home A with low property taxes: in an efficient market, the burden of future property tax payments is already priced into the home.

What will be a benefit or loss to the homeowner will be unexpected changes in property taxes. Also, if property taxes are providing some large benefit, like top-notch public schools, but I have no interest in that service, I may be better off going to a lower tax location.


  1. ' The present value of the tax payments on home B for a ten-year period, discounting at 5%, is roughly -$7500, and that on home C roughly -$75,000"

    Wouldn't people have different rates of time preference, or different expectations about future inflation , and for that reason value different combinations of house price + future tax payments differently ?

    1. Yes, rob, that is absolutely true! But note that the current discount rate is the outcome of all of their time preferences, and so is a sort of "average." We can take our model and qualify it in all sorts of ways, and get all sorts of people who might want the lower-taxed house: those with an aversion to taxation for moral reasons, say.

      But this simple model shows that, for the "representative house buyer," it isn't true that he "saves money" by buying the lower-taxed house.

  2. I was going to say what rob said, (and speculate that people with higher time preference than the market rate, i.e, almost everyone, would actually prefer houses in higher tax areas because it effectively reduces the down payment and increases 'financing' at a rate below the rate implied by their time preference) and also ask about effects on house quality & neighborhood 'evolution' --

    It seems just from observation that places with higher rates would tend to have lower quality houses, because builders will tend to build only when the cost of construction is less than what they could sell for. Pushing down the house price means they won't build as high quality. On the other hand, it might just be that this gets pushed on to the factors of production. I can't really tell how it plays out, but it does seem to me that the houses are lower quality where taxes are higher.

    I don't know. I do know that as a landlord, I don't bear much of the burden, if any (as long as I have tenants in my houses). It also seems to me that higher taxes seem to invite people like me and lower income buyers into the market because of the lower down payments, so that over time you wind up with poor(er) people and renters in the high-tax neighborhoods, and the 'top-notch' school districts approach tends to backfire in the long run.

    But I can't really say for sure. I know incomes are lower here (Texas) than the coastal areas, where you pay more taxes on income. Is it because of property taxes, pushing down the value of means of production (i.e., us)? I completely understand the 'tax-discount' idea, I use it all the time, but I have a hard time thinking about this stuff the further out it plays.

    1. Absolutely Scott: see my subsequent post on models. We can determine what goes on in a simple model like mine above, but carrying that through to the real world is very, very tricky business!

  3. I had the same problems as Samson, and was going to write something up, but I concur with your new, weaker claim. The original couple you overheard could well have been saving a lot of money by moving.

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  5. I think to the average person “save money with lower property taxes” means something quite different. It is a reminder to take all expenses into account, including property taxes. In an economists’ thought experiment, it is natural to assume that everyone’s doing all the math. Often we also assume that everyone is good at weighing incommensurables against each other. But, of course, the actual property buyer has a lot of potential distractions and is not purchasing a commodity, so they can potentially forget to do all the math.

    I’m not criticizing the economist thought-experiment here. This post makes perfect sense. From the property-buyer’s perspective, it implies a more general principle, which is “don’t extrapolate that the overall price is a good value simply because one particularly salient expense is a good value.”



"If your approach to mathematics is mechanical not mystical, you're not going to go anywhere." -- Nassim Nicholas Taleb