Tobin’s Q: A Wily Trickster and Slightly Vacuous

November 10th, 2017
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Article of the Week from Fixing the Economists

by Philip Pilkington

I was writing an article recently for an internet website about the recent IMF proclamations that there may be a global housing bubble underway

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While examining the potential impacts on the global economy if the IMF turns out to be correct I came across an interesting paper that the Bank of England published back in 2008 entitled Understanding Dwellings Investment. It’s a good paper, well put together and very coherent. Quite what I’d expect from the BoE. But it does show the Q-theory up to be rather vacuous, if only unintentionally.

Tobin’s Q for housing, as the paper lays it out, is as follows,


Where: Hn is the price of new housing, L is the price of land per hectare, D is is density of development per hectare, C is the cost of construction, P is the cost of planning obligations, F is the cost of fees, and O is all other costs including the cost of finance.

Note that the variable for house prices is lagged forward. This is because, and this is where things start to break down, the authors note that it is not the house price now that matters to stimulate investment but rather the expected house price in the future. The authors write:

There is a lag between the decision to start construction work and the sale of a completed dwelling, so house builders must form an expectation about what house prices will be when the property is sold. (p396 — My Emphasis)

It seems to me better to note this explicitly in the algebra so that we all have a very clear conception of what is going on. So,




Well, that third variable in that last equation is a bit of a puzzle, now isn’t it? Indeed, if we had any concrete idea as to what it might be we might be better suited to property speculation than macroeconomics. Rather than engage in crystal ball-gazing — thank God — the ever practical authors just lag the variable to the real data. They write,

For simplicity, this article uses the actual value of house prices three quarters in the future as a proxy for builders’ expectations. This lead on house prices is based on data from the National House Builders Council (NHBC) that show the average time between the date builders notify the NHBC of an intention to start work and the date of completion is about ten months. (ibid)

No problem at all. But this all seems a bit retrospective, does it not? I mean, the authors take actual house prices as they developed three quarters out as a proxy for investors’ expectations. There is nothing inherently wrong with this. But it does lead to the question as to what the utility of the exercise is in the first place.

Think of it this way: the independent or exogenous variable here is the expected house price three quarters out. But then what is the dependent variable? Well, its the Q, right? But what is the point of the Q? Well, generally it is seen as a means to approximate the future course of prices.

Feeling a bit dizzy yet? Yes? Well, you should. We’re firmly placed here in the land of tautology and retrospective 20/20 vision. And that is why Tobin’s Q is ultimately pretty vacuous. It is basically in line with Keynes’ marginal efficiency of capital but while the latter never pretends to give this any concrete existence outside of the mind of the investor, the former at least hints at this even though when good practical economists try to use the tool they soon find it slightly… hollow.

By my reading the BoE economists basically recognised this. But they do seem to have made a rather odd omission. They produce the following graph measuring their estimation of the Q against the actual development of dwelling investment:


In the paper the authors note,

Q rose in the late 1980s as house prices rose faster than costs, prompting a house-building boom. Then, as housing market prospects deteriorated, so did the expected return and, with it, house building. Q quickly dropped and remained low until 2001, when rising house prices relative to costs again boosted the returns to house building. It is perhaps puzzling why house building did not rise more quickly given the increased returns. (p398)

The reason they give for the slower response of investment after 2001 has to do with increased planning regulations. But looking at the data they produce this does not seem to explain the lag. Rather the authors should have probably looked to what was driving expectations and hence investment.

In the late-1980s the UK was undergoing an investment boom due to the deregulation of the City of London under the Thatcher government. This was known as the ‘Big Bang‘. This led to a sort of mania in the City and ultimately to a housing and stock market boom followed by a slump.

We can see this clearly in the data where the rise in property investment followed the Q estimate. Investment followed expectations of future price increases. By contrast, after 2001 investment lagged future price increases. The latter was probably a more ‘natural’ housing bubble than the former in this regard as it was the result of investors eyeballing the price increases for a period before engaging in speculation. While in the 1980s everyone just went, well, a bit mad as Thatcher appeared on television telling the City that she was taking the leash off from around their collective neck.

What should we learn from all this? Well, simply that estimates like Tobin’s Q are slightly vacuous. In trying to bury uncertainty about the future they lead people to seek information in the data that can probably only be gleaned from a better comprehension of economic history. Everything that can be counted does not necessarily count; everything that counts cannot necessarily be counted.

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