Government intervention in credit allocation: a collective decision making
model
Ruth Ben-Yashar and Miriam Krausz*
Bar-Ilan University, Israel
Abstract
The purpose of this study is to address the important issue of government
intervention in credit markets through government loan programs. This topic has
significance for the economic development of certain weaker sectors in society
ultimately affecting overall economic and social conditions. We apply a collective
decision making model to a bank's credit decision process to show the effect of
government loan programs on credit allocation. This allows us to analyze the effect of
the decision making structure of a bank (the collective decision rule, e.g., centralized
and decentralized), as a crucial factor in determining the effectiveness of government
intervention.
Key words: government loan programs, collective decision making.
JEL classification: G21, G28, D71
*Corresponding author, email: kerausm1@mail.biu.ac.il
Government intervention in credit allocation: a collective decision making
model
1. Introduction
In this research we focus on the government's efforts to increase the amount of
credit available to certain types of borrowers such as minorities, women and
developing regions or industries. We apply a collective decision making model to a
bank's credit decision process to show the effect of government intervention on credit
allocation. The combination of these two strands of research allows us to analyze the
decision making structure of a bank as a crucial factor in determining the
effectiveness of government intervention.
Financial intermediaries have an important role in the economy of transferring
funds from investors to productive enterprises. But, due to asymmetry in information,
banks are not always able to perform their task fully and phenomena such as credit
rationing (Stiglitz and Weiss, 1981) are observed. Governments intervene in the credit
market in order to provide loans in cases where private markets will not. They may be
acting in response to general credit rationing in the market or to difficulties faced by
certain sectors such as small businesses.
Government loan programs have macro-economic implications (Espinosa-Vega,
Smith and Yip, 2002) as well as affecting certain targeted sectors. Indeed weak
sectors such as minorities, students and small businesses constantly face credit
rationing implying that no intermediary will supply them with credit even when they
are willing to pay high interest rates. Consequently, many governments have loan
programs (e.g SBA loan program, Fannnie Mae, Sally Mae and Freddie Mac in the
U.S., student's loan program in Canada and SBS loan guarantees in the U.K.)
designed to increase the supply of loans to these targeted sectors. Such loan programs
effectively constitute government intervention in the credit market. The two most
common methods of intervention are loan guarantees and loan subsidies involving
either existing intermediaries or special lending institutions. However, once these
tools are in place, banks are not obliged to use them. The usual loan screening
1
methods and credit scoring techniques are applied to loan requests and the bank
decides whether or not to grant the loans. If a government in a free economy does not
wish to impose credit on intermediaries, and leaves the bank to make its own decision
within the framework of a credit program, the government cannot be ensured that the
supply of credit will match its expectations even when governments establish special
intermediaries for credit programs. By analyzing the bank's credit decision process we
wish to provide an explanation as to why governments sometimes only partially
succeed in increasing the supply of credit and how governments should act in order to
increase lending to target populations.
In the field of banking a large body of literature deals with credit scoring methods
(Mester, 1997, Altman and Saunders, 1997 and Allen, Delong and Saunders, 2004),
while a much smaller amount of research has been devoted to the design of the
decision making process in banks. Most notably Stein (2002) discusses the effect of
centralized vs. decentralized decision making on the share of small business lending.
His focus is on the effect of the bank's decision making design on the ability of soft
information, concerning small business loans, to compete with loan requests made by
large firms. Stein (2005) discusses the design of cut-off methods for credit decisions
when a credit score is provided and Andersson (2004) carries out an experimental
study that determines the role of a decision maker's experience in the decision to lend.
In this paper the bank's credit decision whether to accept or reject a specific
loan request is analyzed within the framework of a collective decision making model,
which focuses on the aggregation of the decisions of a group of experts, i.e, the
(collective) decision rule. The subject of optimal group decision-making in a
committee of fixed size that is subject to human fallibility has attracted a great deal of
attention in the past couple of decades or so. Nitzan and Paroush (1982, 1985),
Grofman et al. (1983) and Shapely and Grofman(1984) are the first works which lay
the theoretical foundations of the binary choice model. Ben-Yashar and Nitzan (1997)
defined the optimal decision rule in a more general framework, which allows
asymmetric choice. Other studies analyzed the optimal decision rule under constraints
(Ben-Yashar, Kraus and Khuller, 2001; Ben-Yashar and Kraus, 2002), the optimal
decision rule in polychotomous choice (Ben-Yashar and Paroush, 2001) and other
aspects of collective decision–making. The results obtained by several studies are
2
applicable to a variety of economic fields such as labor economics (e.g., Nitzan and
Paroush 1980), Management (e.g., Ben-Yashar and Nitzan, 1998) and Investment and
Reliability Theory (e.g., Sah and Stiglitz 1988 and Sah 1990, 1991).
The collective decision making model assumes a team of decision makers
whose task is to approve or reject a project so as to maximize the expected utility of
the organization. The decisions of the team members are aggregated by a central
planner under a collective decision rule, to provide a final decision whether to accept
or reject the project. Within our application of the decision making model, each team
member has expertise in determining whether or not a loan should be granted. The
group of team members can also be interpreted as a group of criteria used in a credit
decision model. Both loan guarantees and subsidies can directly affect the specific
decision but not necessarily the decision process. This depends on whether the bank
always adopts the optimal decision rule or abides to a fixed decision rule that may not
necessarily be optimal. In the former case the decision process will change when
governments intervene and this must be taken into consideration by the government.
In the latter case the decision process does not change when the government
intervenes.
The distinction between the case where the process is affected and the case where
it is not, is important because different institutional frameworks are used by
governments for their loan programs. In some countries government loan programs
are operated through private lending institutions that provide financial services to the
general population including loans. In other countries special lending institutions are
established to deal only with government loans. Different institutions may differ in
their willingness or ability to adjust their decision process. However, in both cases the
lending institution employs screening methods and credit decision making procedures
in order to extend credit to high quality borrowers that are most likely to repay the
loan. We therefore analyze government loan programs both when the decision and the
decision process are affected as well as when only the specific decision is affected.
We consider government intervention when banks follow the optimal decision
rule/structure and when banks keep to a rigid decision structure which may not
necessarily be optimal.
3
2. The model
We assume that there are n decision makers in a bank1 whose task is to
approve or reject a loan application so as to maximize the bank's expected profit.
There are two kinds of loan requests, good (1) or bad (-1). A good loan provides the
bank with a profit while a bad loan creates a loss. We denote by xi decision maker i’s
decision, where xi=1 (accept) or xi=-1 (reject), and a decision profile x={x1,…,xn}. Let
us denote by x + the number of decision makers who decide in favor of accepting the
loan. The individual's decision regarding the type of loan is based on his information
such as past experience in lending to the applicant, the loan applicant's leverage and
other attributes of the borrower and the loan application. Decision maker i’s
decisional skill is represented by pi (the probability that individual i accepts a good
loan and rejects a bad one). We assume that the decisional skill is 1/2< pi <1 and
decisional skills are statistically independent across decision makers. A collective
decision is reached by the bank manager who applies a decisive decision rule that is a
function f that assigns 1 (approval) or -1 (rejection) to any x in Ω={1,-1}n, f: Ω→{1,1}.
Each loan of size L at an interest rate r finances a project with a return which
is known to the applicant but not to the bank. The bank faces a cost r0 of financing
the loan, such that r > r0 . All applicants require the same loan size such that size of
the loan is set by the applicant. Prices are set competitively in the loan market. Facing
asymmetric information, the bank signs a standard debt contract with the borrower in
order to minimize monitoring costs. The state of a loan can be good with a priori
probability 1 > α > 0 , and bad with a priori probability 1 − α . The state is determined
as a function of the random return on the project being financed, R, which is drawn
from a known distribution of returns in the population of borrowers, represented by
the density h(⋅) such that the state is 1 (good) if R > Lr0 and -1 otherwise. The
distribution of returns in the population of borrowers is known to the bank manager
while an individual decision maker gains information only about the particular loan
she is facing.
1
The decision makers may be interpreted as components of a computerized credit decision model.
4
The government can intervene in two ways. It can give a loan guarantee which
is activated in the case of bankruptcy (when R < Lr ) such that the bank is
compensated by a proportion g of missing income, Lr − R . The government can also
subsidize the loan by reducing the bank's cost of funds, r0 , which is activated whether
or not there is bankruptcy. When there is government intervention, the state is good if
⎛ r − gr ⎞
⎛ r − gr ⎞
⎟⎟ . Note that Lr0 > L⎜⎜ 0
⎟⎟ . Therefore, the prior probability that the
R > L⎜⎜ 0
⎝ 1− g ⎠
⎝ 1− g ⎠
loan is good increases with g and/or with the reduction in r0 .
The profit associated with the approval (1) (reject (-1)) of a good (1) loan is
denoted by B(1,1) (B(-1,1)), where B(1,1)>B(-1,1). Similarly, the profits associated
with approval and rejection of a bad (-1) loan are denoted by B(1,-1) and B(-1,-1),
respectively, where B(-1,-1)>B(1,-1). B(1)=B(1,1)-B(-1,1) is the positive net profit
from a good loan and B(-1)=B(-1,-1)-B(1,-1) is the positive net profit from a bad loan.
Without loss of generality, we assume that rejection of a project (good or bad) is
associated with zero profit. That is, B(-1,1)=0 and B(-1,-1)=0. Hence, B(1)=B(1,1)
and B(-1) = -B(1,-1). Note that,
B(− 1) = −
⎛ r − gr ⎞
⎟⎟
L ⎜⎜ 0
⎝ 1− g ⎠
∫ (R + g ( Lr − R) − Lr )h(R )dR
(1)
0
−∞
and
∞
Lr
B (1) =
∫ (R + g ( Lr − R) − Lr )h(R )dR + L(r − r ) ∫ h(R )dR .
0
0
⎛ r − gr ⎞
⎟⎟
L ⎜⎜ 0
⎝ 1− g ⎠
(2)
Lr
The net profits are also affected by the loan guarantee and by the subsidy as
described later on in the paper. The expected profit is given by
α[B(1,1)T(f:1)+B(-1,1)(1-T(f:1))]+(1-α)[B(-1,-1)T(f:-1)+B(1,-1)(1-T(f:-1))]
where T(f:1) and T(f:-1) are respectively the probabilities of reaching a correct
collective decision when the state is 1 (good) and -1 (bad), given the decision rule f.
The above expected profit can be reduced to the following form
E=αB(1)T(f:1)+ (1-α)B(-1)T(f:-1)- (1-α)B(-1).
5
(3)
The optimal rule (Ben-Yashar and Nitzan, 1997) fˆ is a qualified weighted
majority rule and given by:
n
fˆ = sign[∑ wi xi + λ +δ ] .
(4)
i =1
where
⎧1 M > 0 ⎫
pi
α
B(1)
sign{M } = ⎨
, λ = ln
, δ = ln
.
⎬, wi = ln
1 − pi
1−α
B(−1)
⎩− 1 M ≤ 0 ⎭
The optimal rule is defined by the optimal weight wi that is assigned to
individual i’s decision2 and by some bias components determining the extent of the
optimal bias toward one of the alternatives: λ and δ. λ reflects the asymmetry in the
priors of the two states, δ reflect the asymmetry of the profits associated with the two
states. Notice that λ+δ represent the combined bias due to a priori probabilities and
the profits, which are a function of g and r0 so that government intervention affects
the bias too.
We
assume
that
individuals
have
homogeneous
skills,
that
is
pi = p j = p ∀ i ≠ j . In this case the optimal rule is a qualified majority rule. That is
[
]
p
. Note that the qualified
fˆ = sign w∑ xi + λ + δ , where w = wi = w j = ln
1− p
majority rule can be represented by k (Ben Yashar and Nitzan 1997), where more than
kn decision makers are required to decide in favor of the loan in order to accept a
loan. More precisely,
⎧1 x + > kn
fk = ⎨
⎩− 1 otherwise
We can point to several interesting rules. k = 1
2
is the simple majority rule,
that is if the number of decision makers is odd the minimum number of decision
2
Under the assumption that
pi > 1 , the weight is non-negative.
2
6
makers in favor of the loan must be
n +1
in order to approve the loan. Two extreme
2
decision making systems can be identified, hierarchy and polyarchy. In a polyarchy
(decentralized), the acceptance of the loan by one decision maker implies that the loan
is approved (i.e., 0 ≤ k < 1 ). In a hierarchy (centralized) the bank approves a loan
n
only if it is accepted by all decision makers ( 1 − 1 ≤ k < 1 ).
n
The optimal k, k̂ , is given by:
1
δ +λ
kˆ = −
.
2 2n ln⎛ p
⎞
⎜ 1− p⎟
⎝
⎠
(5)
In the symmetric case where B(1)=B(-1) and α = 1 , the bias elements
2
vanish and the optimal aggregation rule is the simple majority rule, kˆ = 1
2
. If
δ + λ > 0 , the bias is in favor of accepting the loan request and therefore kˆ < 1 2 ,
i.e., less than half of the decision makers are required to decide in favor of the loan in
order for an accept decision. In the extreme case, when the bias is very large, only one
decision maker is required to make a positive decision. This is a polyarchy. The
opposite is true when δ + λ < 0 .
It is possible that the bank will not necessarily use the optimal decision rule.
This is because there may be constraints on the bank that determine the weights
and/or the bias. In this case we assume that the decision rule is a qualified majority
rule represented by the minimum number of decision makers, q, required to decide in
favor of a loan in order for the loan to be approved ( q = min (⎡kn ⎤, kn + 1) ). For
example, if n is an odd number then q SMR =
n +1
, where q SMR is the simple majority
2
rule. We analyze both cases where the optimal rule is used and where it is not.
7
3. Results
As shown above, government intervention is reflected in g and r0 such that
⎛ r − gr ⎞
⎟⎟ . That is
when there is government intervention, the state is good if R > L⎜⎜ 0
⎝ 1− g ⎠
∂α
∂g
> 0 and ∂α
∂r0
< 0 . The net profits from good and bad loans are also affected
by government intervention such that B(1) increases with g and decreases with r0
while B(-1) decreases with g and increases with r0 .3 That is
∂B(1)
∂B(1)
> 0,
< 0 and
∂g
∂r0
∂B(− 1)
∂B(− 1)
< 0,
> 0 . All the following results are presented for the case of a
∂g
∂r0
government guarantee where g is increased but hold also for the case of a subsidy
where r0 is decreased.
Our first set of results assumes that the decision rule is fixed and is represented
by q. Note that in this case, since the decision rule remains unchanged, the
probabilities of accepting good projects, T (q : 1) , and of rejecting bad projects,
T (q : −1) , do not change as a result of government intervention. We assign the
probability of approving a loan under the decision rule q by Pr ob(accept : q ) .
Result 1: The probability of approval increases with the magnitude of government
intervention, that is in the case of a guarantee:
∂prob(accept : q )
> 0.
∂g
Proof:
Pr ob(accept : q ) = αT (q : 1) + (1 − α )(1 − T (q : −1)) ,
3
Using Liebnitz rule for differentiating an integral,
in this case
and since
Lr −R > 0 )
( )
. Also,
r − gr
L 0
< Lr
1− g
,
∂B( −1)
∂g
Lr − R > 0 ).
∂B( 1)
∂g
=
Lr
∫
( ( Lr − R ) ) h( R ) dR + 0 > 0
⎛ r0 − gr ⎞
⎜
⎟
L
⎜ 1− g ⎟
⎝
⎠
⎛ r − gr ⎞
⎟
L⎜ 0
⎜ 1− g ⎟
⎝
⎠
∫ ( ( Lr − R ) ) h( R ) dR + 0 < 0
= −
−∞
. (Note that in this case
The same method leads us to the results for
8
r0
.
(Note that
R<L
( )
r0 − gr
1− g
n
⎛n⎞
n− j
where T (q : 1) = ∑ ⎜⎜ ⎟⎟ p j (1 − p ) ,
j =q ⎝ j ⎠
n
⎛n⎞
j
and (1 − T (q : −1)) = ∑ ⎜⎜ ⎟⎟(1 − p ) p n − j .
j =q ⎝ j ⎠
∂prob(accept : q ) ∂α
∂α
(1 − T (q : −1))
T (q : 1) −
=
∂g
∂g
∂g
=
∂α
(T (q : 1) − (1 − T (q : −1)))
∂g
=
∂α
∂g
n
∑∆
j =q
j
{
}
⎛ j⎞
n− j
j
where ∆ j = ⎜⎜ ⎟⎟ p j (1 − p ) − (1 − p ) p n − j .
⎝n⎠
Since (a) ∂α
∂g
(b) ∀j >
> 0.
n
, ∆ j > 0 .4
2
(c) ∀j = a, ∆ a = −∆ n − a .5
If q > n , then from (a) and (b)
2
n
know that
∑∆ j =
j =q
with (a)
∂prob(accept : q )
> 0 . If q < n , then from (c) we
2
∂g
n
∑∆
j = n − q +1
j
. Since n-q+1>n/2, this last term is positive from (b), and
∂prob(accept : q )
> 0.
∂g
Q.E.D.
Result 1 is a straightforward result that implies that given a fixed decision
making structure in the bank, the probability of accepting loans increases with
government intervention. This is achieved simply by the fact that the share of good
projects has, from the bank's point of view, increased due to government intervention.
4
p
5
∆ j >0 ⇔
1− p
( )( )
p j
p n− j
>
⇔ j >n− j ⇔ j >n
2
1− p
1− p
. (Note that under the model's assumptions p>1/2 and hence
>1 ).
∆a =
( )[
n
a
p a ( 1− p )
n−a
−( 1− p )
a n−a
p
] and
∆ n−a =
( )[
n
n−a
a
n−a a
p n − a ( 1− p ) −( 1− p )
p
9
]. Hence,
∆ a = −∆ n−a
.
The implication is that some loans that would have been rejected before the guarantee
was introduced will now be approved and the government succeeds in increasing the
number of loans allocated. Furthermore, the larger the guarantee, the greater the
increase in lending. Also, the bank will always wish to participate in the loan program
because the guarantee increases the bank's utility from lending. This can be seen by
deriving E=αB(1)T(f:1)+ (1-α)B(-1)T(f:-1)- (1-α)B(-1) (equation (3)) with respect to
g:
⎡ ∂α
⎡ ∂α
∂E
∂B(1) ⎤
∂B(− 1) ⎤
B(1) + α
B(− 1) + (1 − α )
= T ( f : 1)⎢
− (1 − T ( f : −1))⎢−
>0
⎥
∂g
∂g ⎦
∂g ⎥⎦
⎣ ∂g
⎣ ∂g
We have determined that the government can use the guarantee as a tool to
increase lending. We now show that the structure of decision making in the bank has
crucial importance in determining the magnitude of the effect of government
intervention on the probability of loan acceptance.
Result 2: The effect of government intervention on the probability of accepting a
loan increases as a symmetric function of the decision rule, as the simple majority
rule is approached from either side. In other words, it is determined as a symmetric
function of q that peaks at the simple majority rule.
That is:
∂prob(accept : q SMR ) ∂prob(accept : q SMR + i ) ∂prob(accept : q SMR − i )
>
=
∂q
∂q
∂q
⎛ ∂prob(accept : q SMR + i ) ⎞
⎟⎟
∂⎜⎜
∂q
⎝
⎠ < 0 where i is an integer.
and
∂i
Proof:
From (c) above, if q <
n
n
then ∑ ∆ j =
2
j =q
n
∑∆
j = n − q +1
j
, therefore:
∂prob(accept : q ) ∂prob(accept : n − q + 1)
.
=
∂q
∂q
Specifically this is true when q is q = q SMR − i , then by substituting q SMR =
n − q SMR + i + 1 = q SMR + i .
10
n +1
,
2
Hence,
∂prob(accept : q SMR − i ) ∂prob(accept : q SMR + i )
.
=
∂q
∂q
Recall that,
∂prob(accept : q ) ∂α
=
∂g
∂g
n
∑∆
j =q
n
j
and from (b) above,
∑∆
j = q SMR
j
>
n
∑∆
j = q SMR + i
j
.
Furthermore, the term on the RHS of this inequality decreases with i.
Q.E.D.
Result 2 implies that structure of decision making in the bank affects the
success of the government in implementing a loan program. The government can
expect the highest degree of success when the bank uses the simple majority rule to
approve a loan request. Thus if the government decides to establish a special lending
institution that grants loans within the government's loan program, these institutions
should embrace the policy of the simple majority rule. Also, the government can
achieve the same level of success whether the bank implements a poliarchy rule
whereby only one decision maker is required to approve a loan or a hierrachy rule,
whereby all decision makers must approve a loan. However, in both these cases the
government achieves the lowest level of success. Furthermore, there is symmetry in
the level of success that can be achieved when moving away from the simple majority
rule towards hierarchy and poliarchy. The implication of this result is that as a bank is
either more centralized in its decision making process or more decentralized its
decision making process, the level of success of a loan program is reduced. The worst
case from the government's point of view is to face either extreme centralization or
extreme decentralization.
When the government decides to implement its loan program through the
commercial banking system, the government will probably not be able to impose a
decision making process on the lending institution. At the same time, a utility
maximizing institution is likely to adopt the decision rule that maximizes its utility.
However, the optimal decision rule is a function of the a priori probabilities and the
expected returns, both of which are affected by the guarantee. Hence when a
guarantee is introduced the optimal rule changes. In other words, government
intervention affects the way in which bank make their decisions concerning loan
approval. In the following set of results we show how the optimal rule is affected by
11
government intervention and we analyze the level of success of such intervention
under the optimal rule.
From equation (5) above it follows that the optimal decision rule, k̂ is
negatively related to δ + λ . Since B(1) increases with g and B(-1) decreases with g,
⎛ B(1) ⎞
⎛ α ⎞
⎟⎟ increases with g. Also, because α increases with g, λ = ln⎜
δ = ln⎜⎜
⎟
⎝1− α ⎠
⎝ B(− 1) ⎠
increases with g. That is if g increases then the optimal structure of the bank becomes
more lenient toward approval of the project, i.e., a smaller proportion of decision
makers is necessary for collectively choosing to approve the project.
∂kˆ
=−
∂g
That is
1
< 0 . Note that this derivative is not a function of the decision
⎛ p ⎞
⎟⎟
2n ln⎜⎜
⎝1− p ⎠
rule. We denote by q̂ the minimum number of decision makers required to approve
the loan so that the loan is accepted under the optimal decision rule.
Result 3: When the bank chooses the optimal decision rule:
(a) The probability of accepting a project increases with g.
(b) Given a decision rule q̂ , the effect of g on the probability of approval is
greater when q̂ is an optimal decision rule that changes optimally with g,
rather than when it is a fixed rule.
Proof:
(a) Pr ob(accept : qˆ ) = αT (qˆ : 1) + (1 − α )(1 − T (qˆ : −1))
ˆ
ˆ
∂prob(accept : qˆ ) ∂α
∂α
(1 − T (qˆ : −1)) + α ∂T (q : 1) + (1 − α ) ∂(1 − T (q : −1))
T (qˆ : 1) −
=
∂g
∂g
∂g
∂g
∂g
Note that the sum of the first two terms on the RHS is positive (from Result 2).
Also,
∂T (qˆ : 1)
> 0 since
∂g
∂T (qˆ : 1) qˆ ⎛ n ⎞ j
n− j
= ∑ ⎜⎜ ⎟⎟ p (1 − p ) , lˆ < qˆ ,
∂g
j =lˆ ⎝ j ⎠
where lˆ is the new optimal rule (i.e., the minimum number of decision makers
required to be in favor of a loan under the new optimal rule, in order for the loan
12
to be accepted). As we have shown the rule is more lenient in accepting loans as a
result of the increase in g therefore lˆ < qˆ .
Also,
∂ (1 − T (qˆ : −1))
> 0 , since
∂g
∂ (1 − T (qˆ : −1)) qˆ ⎛ n ⎞
j
= ∑ ⎜⎜ ⎟⎟(1 − p ) p n − j , lˆ < qˆ .
∂g
j =lˆ ⎝ j ⎠
Hence,
∂prob(accept : qˆ )
>0.
∂g
(b) Note that
(1)
∂prob(accept : qˆ )
is composed of two elements:
∂g
∂α
∂α
(1 − T (qˆ : −1)) , which is the effect of g on the probability of
T (qˆ : 1) −
∂g
∂g
acceptance when the rule is fixed, q̂ ,
and (2) α
∂T (qˆ : 1)
∂ (1 − T (qˆ : −1))
, which is the effect of g on the
+ (1 − α )
∂g
∂g
probability that arises from changing the optimal rule. Thus, given a decision rule
q̂ , the effect of g on the probability of approval is greater when q̂ is an optimal
decision rule rather than when q̂ is applied as a fixed decision rule.
Q.E.D.
Result 3 implies that it is in the interest of the government that the lending
institution adjusts its decision making process to the optimal rule rather than
remaining with the same rule which performs as a fixed rule, because then the
government can achieve a greater increase in lending. Thus, when facing a lending
institution with any type of decision making process, the government will always
achieve more when the institution adjusts its decision making process as a result of
the government loan program instead of remaining with its rule fixed.
It is also important to note that the utility of the bank increases when it
participates in the government loan program under the optimal decision rule. This can
be seen by the fact mentioned above that the bank's utility increases under a fixed
rule. Since optimizing the decision rule always improves utility it must be that banks
that optimize their decision rule certainly increase utility in the presence of
13
government intervention. Furthermore, the utility increases more when the bank
optimizes the decision than when a fixed rule is used.
4. Conclusion
In this paper we have shown that the structure of decision making in banks is a
crucial factor in determining the effect of government loan programs on the amount of
lending. This has important policy implications for governments that wish to increase
lending to certain sectors. In essence our results point to the conclusion that
governments can achieve better results from their programs when facing banks that
have neither centralized nor decentralized decision making systems. In fact, the closer
the decision making process is to the simple majority rule, the greater the effect of the
government program. Furthermore, the government can achieve superior results when
lending institutions are versatile in their decision making process, choosing the
optimal decision rule in accordance with the level of government intervention.
In our analysis the government always succeeds in increasing lending and
banks always find it worthwhile to participate in the government program. There may
however be cases where banks will not be willing to extend loans through a
government program, or alternatively extend far fewer loans than the government
intended. In our model this can be explained by adverse selection that affects the a
priori probabilities. A larger number of bad loans will enter the market, knowing that
there is an increase in the probability of loan approval. This will change the
distribution of population of borrowers faced by the bank and accordingly will affect
the prior probabilities of facing good and bad loans.
14
Literature
Allen, L., DeLong G. Saunders A., 2004 "Issues in the Credit Risk Modeling
of Retail Markets" Journal of Banking and Finance, 28(4) 727-52.
Altman and A. Saunders, 1997, "Credit Risk Measurement: Developments
over the Last Twenty Years", Journal of Banking and finance 21(11-12) 1721-42
Andersson P., 2004, "Does experience matter in lending? A process-tracing
study on experienced loan officers' and novices decision behavior", Journal of
Economic Psychology, 25, 471-492.
Ben-Yashar, R. and Kraus, S. ,2002, “Optimal collective dichotomous
choice under quota constraints,” Economic Theory 19, 839–852.
Ben-Yashar, R., Kraus, S., and Khuller, S. , 2001, “Optimal collective
dichotomous choice under partial order constraints,” Mathematical Social
Sciences 41, 349–364.
Ben-Yashar, R. C. and Nitzan, S. , 1997, “The optimal decision rule for
fixed-size committees in dichotomous choice situations: The general result,”
International Economic Review 38, 175–186.
Ben-Yashar, R. and Nitzan, S., 1998, “Quality and structure of
organizational decision making,” Journal of Economic Behavior and
Organization 36, 521–534.
Ben-Yashar, R. and Paroush, J., 2001, “Optimal decision rules for
fixed-size committees in polychotomous choice situations,” Social Choice and
Welfare 18, 737–746.
Espinosa-Vega M. A., Bruce D. Smith, Chong K. Yip, 2002, "Monetary policy
and government credit programs", Journal of Financial Intermediation 11, 232-268.
Grofman, B., Owen, G., Feld, S.L., 1983, "Thirteen theorems in search
of the truth". Theory and Decision 15, 261-278.
Mester L. J., 1997, "What's the point of credit scoring?", Business Review,
September/October, 3-16.
Miron J. A. , 1986, "Financial panics, the seasonality of the nominal interest
rate, and the founding of the Fed", American Economic Review 76(1) 125-40.
15
Nitzan, S., Paroush, J. , 1980. "Investment in human capital and social self
protection under uncertainty". International Economic Review 21, 547-557.
Nitzan, S. and Paroush, J., 1982, “Optimal decision rules in uncertain
dichotomous choice situation,” International Economic Review 23, 289–297.
Nitzan, S. and Paroush, J., 1985, Collective Decision Making: An
Economic Outlook. Cambridge: Cambridge Univ. Press.
Sah, R. K. ,1990, “An explicit closed-form formula for profitmaximizing k-out-of-n systems subject to two kinds of failures,”
Microelectronics and Reliability 30, 1123–1130.
Sah, R. K. , 1991, “Fallibility in human organizations and political
systems,” The Journal of Economic Perspectives 5, 67–88.
Sah, R. K. and Stiglitz, J. E., 1988, “Qualitative properties of profitmaking k-out-of-n systems subject to two kinds of failures,” IEEE
Transactions on Reliability 37, 515–520.
Shapley, L. and Grofman, B., 1984, “Optimizing group judgmental
accuracy in the presence of interdependencies,” Public Choice 43, 329–343.
Stein R. M., 2005, "The relationship between default prediction and lending
profits: Integrating ROC analysis and loan pricing, bank runs", Journal of Banking
and Finance 29, 1213-1236.
Stein, J. C., 2002, "Information Production and Capital Allocation:
Decentralized versus Hierarchical Firms", Journal of Finance 57(5) 1891-1921
Stiglitz and Weiss, 1981, “Credit Rationing in Markets with Imperfect
Information” American Economic Review 393-410
16