## Tuesday, August 17, 2010

### Linking Liquidity Constraints to Network Formation...

For some time now I have been struggling to develop a mechanism to link liquidity constraints with the agent's network formation decision.  I suspect that this has a lot to do with the fact that while I have read quite a lot on network theory, I have not yet got around to reading much of anything having to do with liquidity constraints.  All of my knowledge of liquidity constraints has come from the two weeks we spent talking about them during my MSc.  What follows is my first attempt to link the two concepts together.  The idea follows closely to the textbook treatment of consumption decisions of agents facing liquidity constraints.

The agent has two choice variables each time period: consumption, ct, and the number of neighbors in the network, nt.  The agent has wealth wt and anticipates some uncertain future income yt+1. This agent's savings can be defined to be st=wt-ct.  Typically an agent then maximizes something like the sum of his current utility plus the expected discounted sum of future utility subject to the constraint that next period's wealth wt+1=Rt+1(st+yt+1), where Rt+1 is the interest rate.  A liquidity constraint in this scenario would require that the agent's savings st be non-negative (i.e., agents can not borrow)

What I want to do is allow agents to borrow funds from neighbors in the network (assuming that they have excess savings to lend).  Agents would become liquidity constrained if neither themselves nor any of their neighbors had funds to lend them.  In this scenario, an agent's consumption decisions over time are affected by his position in the network (i.e., his access to credit from his neighbors).  Clearly there are a number of issues to work out with the framework.  Such as how to specify the interest rate, the income stream, the appropriate utility function, the information set, etc.   Also this is definitely not going to be analytically tractable (but them neither are more traditional liquidity constraint problems). Ideally it would also be nice to be able to model agent default.  Maybe this could be done by specifying some type of stochastic income stream where there is some positive probability of the agent unexpectedly ending up in the "low" income state and is thus unable to repay his loan.

This is pretty much wild speculation at this point...I just wanted to get these thoughts down on digital paper...