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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
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 2 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 3 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 3 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 3 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 3 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 3 / 11
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!)
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 4 / 11
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!)
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 4 / 11
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!)
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 4 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 5 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 5 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 5 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 5 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 5 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 5 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 6 / 11
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�
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 7 / 11
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�
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 7 / 11
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�
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 7 / 11
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�
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 7 / 11
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�
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 7 / 11
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�
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 7 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 8 / 11
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).
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 9 / 11
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.
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 10 / 11
Now - On to the Model!
Professor Kevin D. Salyer (UC Davis) Williamson article 05/06 11 / 11