lenders who are better at evaluating their true risk and providing any specific services
they need8.
In this case, a low observation wi ll always yield an offer of k + 02 in the first period
since p- < 1- < 1, which means (2-2) does not hold.
1-PL PL
If 92(02 -0) = 1, both lenders are always separating. Since all signals are
S,
informative -- < 1 and P- > Lp > 1, which means that by strategy OS both
1-pL p 1-p PH
lenders always have the same policy, they are both always separating borrowers
according to their independently observed signal.
Proposition 4: When the accurate lender is separating according to its signal, so
that an observation of L gets a high interest rate offer and an H gets a low one, all
borrowers will approach the accurate lender in the first period.
If the accurate lender is separating, safe borrowers will prefer the accurate lender
since they will get an H observation and an offer of k+01 with higher probability. But then
the inaccurate lender knows that all its pool of first time applicants is risky, which implies
all the offers will be high interest rates. Hence, the accurate lender will be at least
weakly preferred. The formal proof can be found in the Appendix.
This proposition also implies that if one lender has privileged information regarding
a particular borrower, due to previous lending relationships for example, this lender will
be approached first by such borrower when it is separating. Note that when this lender
is not separating, this is not necessarily the case, the borrower may prefer to break the
relationship and look for a new lender with its new project. This case is analyzed next.
8 Berger et al. (2001); Detragiache et al. (2008).