Bubbles are something thought to be irrational, like a feeding frenzy not linked to any fundamentals, but rather self-fulfilling expectations. Given that bubbles are essentially expectation based, it has been very difficult to prove their existence in the data. The reason is that they depend, by definition, on intangibles. But there are times where the guts just tell you that a bubble must have been there, and many feel so about housing in Anglo-Saxon countries in recent years. The question one can ask then is, how can such bublles happen?
Óscar Arce and David López-Salido make an interesting attempt at rationalizing housing bubbles. They build a model that features several equilibria, some bubbleless and under some conditions some with bubbles. They define a bubble as "the price of an asset that exceed the present discounted value of the dividends", in particular when households hold assets that do not earn any dividend. For this to happen, the interest rate needs to be equal to the growth rate (zero in the model), and the bubble represents the excess of savings, typically held by middle-aged households. Why? Because they have a collateral constraint on mortgages.
What does this mean? First, a policy of low interest rates encourages bubbles. That is something we knew. Second, high collaterals encourage bubbles. That seems a bit odd given the recent US experience, where there is a widely held belief that the lack of collateral constraints led to a surge in housing prices. I think this has to do with the definition of a bubble: it is not the price of the asset, it is the portion that is above what can be justified by fundamentals. With the decrease in collaterals, the bubble portion may have decreased, while the fondamental portion may have increased more.
As said, bubbles are very difficult to measure. This paper seems to make it even more difficult.