Regular readers of this blog will know that I consider that a good thing.

The financial crisis is motivating a search for new models of asset markets and their interaction with the real economy.  It seems obvious that, for example the housing bubble can only be explained by a model in which asset prices are bid up by the activity of highly optimistic investors or speculators.  Models which build in these divergent beliefs (and not just differences in information) are, perhaps very surprisingly to outsiders, only recently coming to mainstream economic theory.

Alp Simsek asks whether the presence of optimistic traders can inflate the price of assets, say housing prices.  It seems obvious, but remember that investment in housing is leveraged using collateralized loans where the house itself is the collateral.  If the optimists are borrowing from the “realists” to buy houses at overinflated prices, and they are offering up the house as collateral, then surely the realists aren’t willing to lend?

Alp shows that this logic sometimes holds, but not always.  And he formalizes a precise way of measuring optimism which determines whether the presence of optimists will inflate asset prices, or alternatively their optimism will be filtered due to realists’ witholding of credit.

Suppose that you are a realist and you are making a loan to me to purchase a house.  A year later we will see whether housing prices have gone up or down.  If they go up, I will pay off the loan and realize a profit.  If they go down I will default on the loan.  A key idea is to understand that the loan effectively makes us partners in the purchase of the house.  I own it on the upside (and I pay you back your loan) and you own it on the downside.  We pay for the house together too: you contribute the loan amount and I contribute the down pament.

The equilibrium price of the house will be determined by how much we, as partners, are willing to pay.  I am an optimist and I would like to pay a lot for it, but I am financially constrained so my contribution to the total price is some fixed amount, my down payment.  Thus, our total willingness to pay is determined by how much you are willing to pay to enter this partnership.

Now we can see how my optimism plays a role.  Suppose I am more optimistic than you in the sense that I think there is a lower probability of default than you.  It turns out this doesn’t make our willingness to pay any higher than it would be if I were a realist just like you.  That’s because you own the house in the event of default so it’s the probability that you assign to default that enters into our total value, not the probability that I assign.  It’s true that I assign a higher probability to the good event that the price goes up, but I am already putting all of my cash into the partnership.  I can’t do anything more to leverage this form of optimism.

But suppose instead that the way in which I am more optimistic than you is slightly different.  We both assign the same probability to default, i.e. the event that the price falls.  Where we differ is in terms of our beliefs conditional on the price going up.  In particular I think that conditional on the upside, the expected price increase is higher than you think it is.  Now we have a new way to leverage our partnership.  Since I expect to have a higher upside, I am prepared to offer you a higher payment in the event of that upside.  (That is, I am willing to pay back a larger loan amount.)  And the promise of that higher payment on the upside coupled with the same old house on the downside makes this a strictly more attractive partnership for you and you are willing to pay more to enter it.  (That is, you are willing to loan more to me.)

Indeed these collateralized loans seem to be the ideal contracts for us to make the most of our differences in beliefs.  And once we see how that works, it is easy to go from there to a theory of a dynamic housing bubble.  Tomorrow there might be optimistic investors who will partner will creditors to bid up housing prices.  Today, you and I might have differences in beliefs about the probability that those optimistic investors might materialize.  If I am more optimistic than you about it, you and I can enter into a partnership which leverages our different beliefs about tomorrow’s differences in beliefs, etc.

There is an important thing to keep in mind when considering models with heterogenous beliefs.  We don’t have a good handle on welfare concepts in these models.  For example, in Simsek’s model the efficient allocation is to give the asset to the optimists.  Indeed, the financial friction is only an impediment to achieving an efficient allocation.  A planner, faced with the same constraint, would not do anything different than the market.  If we apply standard welfare notions like this, then these models are not a good framework for discussing financial reform.