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ECON 138 Summer 2010
Problem Set 4
Due Wed 8/11
1. (Principle-Agent Problem with Risk Aversion)
An entrepreneur has cash and wants to invest > into a project. The project yields
> 0 with probability and 0 with probability 1 − . The probability of success is
<
if she shirks. The entrepreneur obtains private
if the entrepreneur works and
benefit if she shirks and 0 otherwise. All standard assumptions from the set-up in class
apply unless modified below.
Assume that
<
( −
−
)
and
>
+
a. Interpret the two assumptions intuitively.
In contrast with the risk-neutrality assumption in class, assume that the entrepreneur has
the following utility over his payoff,
≥
( )=
−∞
≤
This means that the entrepreneur is infinitely risk averse against payoff dropping below
the threshold . We assume that the amount of cash the entrepreneur has is large enough
by not entering into
so that ≥ , so that the entrepreneur can always get a utility of
a contract.
b. What is the minimum cash requirement when
c. What is the minimum cash requirement when
≤ 1?
= 1?
2. (Principle-Agent Problem with Repeated Investment)
Consider a risk neutral manager who has no cash on hand ( = 0) and an investment
project which returns when it succeeds and 0 when it fails. The cost of investment is .
If the manager works hard the project succeeds with probability , if she shirks she gains
private benefit but lowers the probability of success to . If the first project succeeds
then a second project arises with probability .
a. Show that the pledgable income for the first-period project is larger than the expected
pledgable income for the second-period investment.
b. Suppose investors cannot pre-commit to finance in the second period when the first
project succeeds. Will financing in the second period happen more easily than in the
one-shot case?
c. Now suppose that investors can pre-commit to financing in both periods. That is,
they can write contracts that guarantee financing of the second-period project
conditional on a project arising in the second period. Compute the expected pledgable
income and write down a condition for financing.
3. (Asymmetric Information)
Extending the basic model we discussed in class, imagine that for a faction of firms if
> , but
the manager shirks the probability of success is , while for the rest it is
both types of firms have the same
, , and . This represents a different type of
asymmetric information problem, one where outsiders don’t know the true effects of
shirking.
a. Write down a condition for a manager of each type to work hard.
b. Compute the investor’s value for financing to each type separately at the lowest Rm
that that type would accept.
c. Can the investor offer a contract that induces hard work among all managers whould
accept that contract? Can we find such a hard-work-inducing contract that only one
type of firm would want to accept?
d. What is the value to the firm of financing both types at the lowest Rm that induces
both types to work hard? Therefore what is the condition for financing to occur?
4. (Stata)
In this question you are asked to investigate whether “managers make a difference.” Do
different types of managers make different corporate finance decisions? You are asked to
test for an “Depression Babies” effect: Do managers who were born in the time of the
Great Depression (use “born in the 1920s or or 1930s”) make different types of corporate
decisions than managers who were born later and did not personally experience the Great
Depression? Specifically, test whether Depression Babies are more averse to debt than
their peers.
a. Obtain the largest possible data set of CEOs and CFOs and their companies from
wrds.wharton.upenn.edu (ExecuComp). Provide summary statistics (number of firms,
number of managers etc.)
b. Categorize the CEOs and CFOs into ‘Depression babies’ and ‘others’ (E.g. code a
CEOdummy variable equal to 1 if the CEO is a depression baby and code a CFOdummy variable equal to 1 if the CFO is a depression baby.) Include the dummy
variables in the summary statistics.
c. Download for the same companies, for which you have CEO and CFO data, all
relevant data from Compustat. In particular, you will need to construct a year-by-year
measure of ‘how much debt they have.’ (This could just be leverage, but if you have
an idea for a better measure of ‘debt aversion’, go ahead and define it and use it.)
Include the firm variables in the summary statistics, also including your debt measure.
d. Test whether debt is higher or lower in the group of firms run by Depression Baby
CEO and / or CFOs. A simple test of differences in means will give a first indication.
In a regression framework you can simultaneously test for CEO-Depression Baby
effects and CFO-Depression Baby effects. You can also include controls, which you
may think are important. Interpret your results; can we argue that there is a causal
effect of being a Depression Baby?