Recent Developments in Modeling Financial...

Recent Developments in Modeling FinancialIntermediation

by Stephen Williamson

Professor Kevin D. Salyer

UC Davis

May 2007

Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 1 / 11

Summary of Williamson article

Read �rst few sections carefully...nice historical overview and context.

Model is complicated...a LOT going on

Model Highlights

An overlapping generations model: each period a new generation isborn. People live for two periods.

Each generation consists of two types:

Lenders who need to save for old age consumption.Entrepreneurs who have heterogeneous investment projects and onlycare about old age consumption.

In contrast to all our earlier models, both types of agents arerisk-neutral.

Model Highlights

Lenders who need to save for old age consumption.

Entrepreneurs who have heterogeneous investment projects and onlycare about old age consumption.

Model Highlights

Model provides another motivation for banks: MoralHazard

Entrepreneurs are rational: it is in their interest to lie about returnsfrom investment.

Lenders (many lenders are needed to �nance project) must monitoroutput - this is costly.

The model demonstrates that banks can achieve monitoring at lowercost because of the Law of Large Numbers (again!)

Equilibrium

Due to high expected monitoring costs, some entrepreneurs will notget loans.

Exogenous to the model are:

The probability of successful production.The output of production.These are assumed to take on two possible sets of values...and arerandom.

We demonstrate that business cycles arise in equilibrium even thoughaverage levels of production are constant.

Equilibrium

The probability of successful production.

The output of production.These are assumed to take on two possible sets of values...and arerandom.

Equilibrium

The probability of successful production.The output of production.

These are assumed to take on two possible sets of values...and arerandom.

Equilibrium

Closer Look at the Model

All decision making is done by lenders and banks (entrepreneurs arepassive).

There are two assets for lenders: money and deposits.

Because lenders are risk neutral, expected rate of return on bothassets must be the same.

Outline of steps in the model

1 We �rst show that savings of lenders is increasing in expected returnsof assets.

2 We then show that costs of monitoring is lowered by banks.3 Banks do the following:

1 Take deposits from lenders and o¤er them certain return = expectedreturn from projects.

2 Receives payments from entrepreneurs that depends on the probability(π) of their success. (Projects produce either wt or 0.)

4 Because of low probability of success, some projects have lowexpected returns and will not get �nanced. This produces a cuto¤level of π�

2 We then show that costs of monitoring is lowered by banks.

3 Banks do the following:

Modeling of uncertainty

Entrepreneurs have di¤erent probabilities of success. These aredistributed uniformly over the interval

�πl ,πu

A successul project produces w units. An unsuccessful projectproduces 0.

The values�πl ,πu ,w

�are assumed to take on two values:

z1 =�πl1,π

u1 ,w1

�and z2 =

�πl2,π

u2 ,w2

Pr (zt+1 = z1 jzt = z1 ) = q1. Pr (zt+1 = z1 jzt = z2 ) = q2. It isassumed that q1 > q2.

State 1 is the "good" state. If in state 1, more likely to stay therethan go there from state 2.

Some Notation

N = number of agents born each period.α = fraction of agents that are lenders. (1� α) are entrepreneurs.H = stock of money (does not play a role).pt = price of money in terms of output (the inverse of the price level).

Example : If the price leve is Pt =$Pt

1 apple

so pt =1/Pt apples

1$(use Pt = 2).

Some Notation - continued

e = the endowment of lenders (received when born).β = monitoring costsv = payment made to banks if project is successful. Otherwise payment =0 and entrepreneur is bankrupt.

Now - On to the Model!

Recent Developments in Modeling Financial...

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