In a comment on my most recent blog post, Andy Harless "[wishes he] had a better intuition for what is going on in [my] model." I took a stab at responding to Andy in the comment section, but my response became so long that I turned it into a post. Here is my answer to Andy. You can find additional comments over at Economist's View where Mark Thoma was kind enough to post an excerpt.
The model Andy is talking about (here) describes an endowment economy with no production. There are two types of people; patient and impatient. Impatient people have a higher rate of time preference than impatient people and, as a consequence, one group will become lenders and the other group will become borrowers. Both types die in any given period, with the same age-independent probability. They are replaced by new people so that the population of each type is stationary and there is an exponential age distribution for each type.
All asset market transactions occur through a zero profit financial intermediary. There are complete annuities markets and when a person dies, his wealth is returned to the financial intermediary. If a person borrows from the intermediary, he is required to take out life insurance.
In the special example in this post, there is no fundamental uncertainty. I will also assume, in this post, that there are only two shocks. Because of these special assumptions, I will need only two assets to complete the markets. These assets are short-term bonds and long-term bonds. The more general case, where long-term bonds and equity are different assets, is covered in the paper.
Short term bonds represent a claim to one unit of the endowment next period. Long term bonds represent a claim to one unit of the endowment in every period. The price of a long term bond is the same as the value of a new born agent’s human wealth because human wealth and long-bonds are claims to the same income streams.
When they are born, lenders sell a portion of their human wealth to borrowers: in return, they buy short-term debt. Lenders start out life as savers and in the early years of their life they consume less than their endowment in every period.
Borrowers, in contrast, sell sell short-term debt to lenders. In the early years of their life they consume more than their endowment in every period.
As lenders age, eventually they reap the benefits of their youthful choices and they begin to spend the interest on their asset portfolios. Lenders have an increasing consumption profile over time.
As borrowers age, eventually they reap the harvest of their youthful indiscretion and they begin to pay back the interest on their debts. Borrowers have a decreasing consumption profile over time.
So far so good. But what about uncertainty?
The trades I described above imply that a lender shorts long-term debt and goes long in short-term debt. A borrower takes the opposite side of these trades.
A long bond issued in period t is a claim to one unit of the endowment next period PLUS a claim to a long bond in period t+1. Just as in Keynes’ beauty contest example, the price of a long bond next period is worth what the market thinks it is worth. In the paper, we assume that there is a complete set of markets that are indexed to an observable ‘sunspot’ variable. That is simply a short cut for bringing ‘animal spirits’ or market sentiment into the pricing equation. The model displays what George Soros calls ‘reflexivity’.
Our model has many equilibria where a long-bond is worth exactly what the market thinks it is worth. If people think that long bonds are worth a lot; they WILL BE worth a lot. In that case, there will be a resource transfer from lenders to the new born agents and the borrowers. If people think that long bonds are worth less; they WILL BE worth less. In that case, there will be a resource transfer from the new born agents and the borrowers to the lenders.
Our model differs from a representative agent economy because, although borrowers and lenders each make trades that obey a transversality condition, there is no analog of these transversality conditions for the market as a whole. It is this feature that distinguishes our work from most other models. The trades that occur in our model are equilibrium trades in the sense in which that term is used in standard DSGE models. But unlike most existing models; these trades are NOT Pareto optimal. We think that this is a useful way to understand why financial crises are so painful.
In the special example in this post, there is no fundamental uncertainty. I will also assume, in this post, that there are only two shocks. Because of these special assumptions, I will need only two assets to complete the markets. These assets are short-term bonds and long-term bonds. The more general case, where long-term bonds and equity are different assets, is covered in the paper.
Short term bonds represent a claim to one unit of the endowment next period. Long term bonds represent a claim to one unit of the endowment in every period. The price of a long term bond is the same as the value of a new born agent’s human wealth because human wealth and long-bonds are claims to the same income streams.
When they are born, lenders sell a portion of their human wealth to borrowers: in return, they buy short-term debt. Lenders start out life as savers and in the early years of their life they consume less than their endowment in every period.
Borrowers, in contrast, sell sell short-term debt to lenders. In the early years of their life they consume more than their endowment in every period.
As lenders age, eventually they reap the benefits of their youthful choices and they begin to spend the interest on their asset portfolios. Lenders have an increasing consumption profile over time.
As borrowers age, eventually they reap the harvest of their youthful indiscretion and they begin to pay back the interest on their debts. Borrowers have a decreasing consumption profile over time.
So far so good. But what about uncertainty?
The trades I described above imply that a lender shorts long-term debt and goes long in short-term debt. A borrower takes the opposite side of these trades.
A long bond issued in period t is a claim to one unit of the endowment next period PLUS a claim to a long bond in period t+1. Just as in Keynes’ beauty contest example, the price of a long bond next period is worth what the market thinks it is worth. In the paper, we assume that there is a complete set of markets that are indexed to an observable ‘sunspot’ variable. That is simply a short cut for bringing ‘animal spirits’ or market sentiment into the pricing equation. The model displays what George Soros calls ‘reflexivity’.
Our model has many equilibria where a long-bond is worth exactly what the market thinks it is worth. If people think that long bonds are worth a lot; they WILL BE worth a lot. In that case, there will be a resource transfer from lenders to the new born agents and the borrowers. If people think that long bonds are worth less; they WILL BE worth less. In that case, there will be a resource transfer from the new born agents and the borrowers to the lenders.
Our model differs from a representative agent economy because, although borrowers and lenders each make trades that obey a transversality condition, there is no analog of these transversality conditions for the market as a whole. It is this feature that distinguishes our work from most other models. The trades that occur in our model are equilibrium trades in the sense in which that term is used in standard DSGE models. But unlike most existing models; these trades are NOT Pareto optimal. We think that this is a useful way to understand why financial crises are so painful.
Why are equilibria not Pareto optimal? The answer comes from our assumption that demographics limit participation. If the unborn could participate in the asset markets that occur before they are born, they would eliminate the inefficient sunspot fluctuations. Because everyone is assumed to dislike risk, in the absence of prenatal financial markets; everyone is worse off. The model captures a lot of what appears to have happened in the financial markets, within a framework that is very neoclassical in its structure. For me, that is a virtue.