Examination Paper 2020/21
MSIN0105: Financial Econometrics
TIME ALLOWANCE: 24 hours
There is ONE (1) section to the examination paper, which consists of four (4) compulsory
questions. The allocations of the marks are indicated in the brackets. Each of the four
questions has multiple subquestions.
MSIN0105 1 TURN OVER
Answer all questions. The value of each ques-
tion is provided in square brackets.
Q1. [20]. Judge if each statement given below is correct or incorrect, providing your reason-
ing. In these statements, (yi, xi) , i = 1, . . . , n, are iid observations of a dependent variable
yi and a vector of regressors xi = (1, x1i, . . . , xKi)
′.
1. Consider a linear model yi = x
′
iβ+ i with E (xii) = 0. This specification implies that
the conditional expectation of yi given xi is x
′
iβ.
2. The ordinary least square estimator for a linear probability model yi = x
′
iβ+i with yi ∈
{0, 1} is inconsistent due to heteroskedasticity of the errors, i.e., V ar(i|xi) depends
on xi.
3. In weighted least square estimation for linear regression model with heteroskedasticity,
an observation whose error variance is larger receives a higher weight in the estimation.
4. Consider a linear regression model with a regressor vector xi that includes an intercept
and two dummy (binary) variables d1i ∈ {0, 1} and d2i ∈ {0, 1}, where all the units
in the data have either one of d1i or d2i equal to 1. That is d1i + d2i = 1 holds for
all i. In this case, we cannot estimate the coefficients of d1i and d2i by OLS due to
multicollinearity.
MSIN0105 LSA 2 TURN OVER
CONTINUED
Q2. [25].
As a consultant working for a commercial bank, you would like to develop an econometric
model that assists bank’s decision for approving loan applications. Suppose you have access
to a database of the past borrowers containing binary Yi ∈ {0, 1} that indicates if borrower
i defaults (Yi = 1) or not (Yi = 0), together with the borrower’s characteristics including
the value of collateral Vi and the interest rate Ri of i’s borrowing. Including an intercept,
we denote other observable characteristics of borrower i by vector Xi. Denote the set of
regressors by Zi = (Vi, Ri, X
′
i)
′.
Consider a probit model
Pr(Yi = 1|Zi) = Φ(βV Vi + βRRi +X ′iβX), (1)
where Φ(·) is the cumulative distribution function of the standard normal random variable.
(a) [5]. Explain how you estimate the coefficient parameters in the probit model.
(b) [5]. Derive the marginal effect of the probability of default with respect to interest
rate Ri, i.e.,