Tobin’s Q: A Wily Trickster and Slightly Vacuous


I was writing an article this morning for an internet website about the recent IMF proclamations that there may be a global housing bubble underway. The article, if it runs, should be online next week and I will link to it here.

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,

OLYMPUS DIGITAL CAMERAWhere: 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,


OLYMPUS DIGITAL CAMERAWell, 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.



About pilkingtonphil

Philip Pilkington is a macroeconomist and investment professional. Writing about all things macro and investment. Views my own.You can follow him on Twitter at @philippilk.
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6 Responses to Tobin’s Q: A Wily Trickster and Slightly Vacuous

  1. rumplestatskin says:

    I find it strange that there is a while literature on real options investment that details why uncertainty and expectations matter ti investment, but then the Bank of England ignore it in a paper about the exact topic these theories where designed to explain.

    Indeed, back in 1994 Dixit and Pindyck wrote a textbook summarising the real options in relation to investment. The main application of this work is to building and housing investment.

    The general solution, the optimality condition, under real options is that land owners invest in developing buildings when their expected rate of return from investing is equal (or higher) than from delaying investment.

    Price levels are irrelevant.

    There is a 1985 AER paper by Sheridan Titman that explain that tightening planning controls can increase housing investment because it reduces the payoff from delaying investment (it destroys part of the real option).

    Rant over. Good post as always.

    • The book looks interesting. Are these guys Keynesians?

      The solution sounds basically like Keynes’ marginal efficiency of capital which, to a very large extent, begs the question. But better to leave it open than to provide an incorrect answer.

  2. Dan Sullivan says:

    Good observations. To take it further, the speculation is in land, not house prices (which aggregate land and capital together). The price of land one pays in order to build is offset by the expectation that the land component will be available, with either a loss or a gain, to the owner of the completed house in the future. This expectation of future land value is factored in to what the builder/buyer is willing to pay for land on which he can build. The question then becomes what determines the price the current land holder is willing to accept

    Where land value is more heavily taxed, the expectation of a gain in land value is lowered, but so is the purchase price of land in the present. Also, where land value is heavily taxed, something else must be more lightly taxed, or additional services must be provided. This enhances the desirability of living at that location, and enhances land value.

    The important distinction is that a land value tax interferes with the option of holding land for speculative gain. Even if the land is more desirable to the builder/occupant, it becomes less valuable to idle speculator, who is induced to sell.

    To the user of land, a higher tax on land value and a lower tax on buildings is normally a net gain, for his land will have a brand new building on it. Similarly, replacing wage taxes with land value tax should be a net gain for an occupant who plans to pay off his purchase with wages. Similarly, a reduction in business taxes should usually be a net gain for someone paying off his new facility from business revenues.

    To the speculator in buildable land, however, land value tax is a killer. The speculator is not capturing the rental value of the land, as he is not putting it to use, or at least not to a full-market use. Rather, he is gaining only the capitalized gain between the current rental value and the expected increase. The builder/user of developed land, on the other hand, is realizing both.

    If we assume a return to capital of 4% and an increase in land value of 7%, with no land value tax, then the land speculator has a competitive advantage over the true capitalist. However, a land value tax of 3% wipes out that advantage, and additionally gives the speculator a cash-flow problem that the capitalist doesn’t have. That is, the capitalist pays his current taxes out of current revenues, while the speculator must pay his taxes from some other source and hope to recapture them in a future sale.

    If we further assume that this 3% land value tax offsets some other tax that is paid by either labor or capital (or both), land speculation becomes such a burden to the speculator that he becomes willing to sell now. So are other land speculators, and the price of land falls.

    While it is true that the price of land will be lower in the future as well, the fact that it is lower today, coupled with the increased profitability of working where profits are taxed less or living where wages are taxed less, tips the balance in favor of building.

  3. Nick Edmonds says:

    In defence of Tobin, his Q is just the ratio of (current) market valuation to replacement cost, rather than anything involving expected future values.

  4. Pingback: Will real estate bubbles again sink the global economy? | Walter Unger CCIM

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