BUFN 745 Final
Spring 2021
Professor Alex He
Due: Friday 3/11/2020 at noon EST
1 Short Questions (Choose any 4, for 5 points each)
Please answer with a brief explanation in one or two sentences or mathematical expressions. For
questions asking whether a statement is True/False/Uncertain, correct answers without explanation
do not receive credit. You should answer 4 questions of your choice. If you answer more
than 4 questions, we will only grade the first 4.
1. (True/False/Uncertain) If fixed effects model and random effects model give very different
estimates, then the estimate from the random effects model must be inconsistent.
2. (True/False/Uncertain) Suppose we are using Cox Proportional Hazard model to estimate the
duration of mortgage loans. The partial likelihood will be the same if one of the borrowers
defaults after 3 years since the loan started or 5 years since the loan started, as long as no
other borrower defaults between 3 years and 5 years and there is no time-varying predictor
variable.
3. Suppose we have a dataset on firms’ revenue and employment, and firms with less than 50
employees are more likely to have missing revenue because firms with fewer than 50 employees
don’t have to report their revenue (but we still observe the employment for these firms). Is
this Missing Completely at Random, Missing at Random or Missing Not at Random?
4. (True/False/Uncertain) The optimal bandwidth for the kernel regression is the same as the
is the same as the optimal bandwidth for kernel density of the predictor variable.
5. (True/False/Uncertain) In a quantile regression where stock returns are regressed on an in-
dicator variable for recession (which equals to 1 if it’s in a recession and 0 otherwise), if the
coefficient is -0.1 for the 10th percentile, then it means that the stock at the 10th percentile
of the return distribution earns 10% less returns during recessions.
2 Long Question: Covid and Firms (60 Points)
In this question, you will work with a dataset of about 2000 publicly listed firms over two years
(2019 and 2020) to understand the determinants of firms’ stock market performance and acquisitions
during the current recession. You have the following variables:
• gvkey: firm ID
• year
• conm: firm name
• csho: number of shares outstanding (in millions)
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• dlc: short-term debt
• dltt: long-term debt
• pstk: preferred stock (in million dollars)
• revt: revenue
• prcc_f : share price (in dollars)
• acquisition: equals to 1 if the firm acquires another firm in that year, and 0 otherwise
1. (4 points) Create a new variable logmarketcap that equals to log market capitalization (number
of shares multiplied by share price), and another variable logrevt that equals to log revenue.
2. (6 points) Estimate an OLS regression of log market capitalization on log revenue:
logmarketcapi = βlogrevti + i
For a 10% increase in revenue, how much does market capitalization change? List at least one
reason why the estimate for β is not BLUE.
3. (10 points) Estimate an fixed effects regression of log market capitalization on log revenue
with firm fixed effects and year fixed effects. For a 10% increase in revenue, how much
does market capitalization change? How does the effect compare to part 2? List one potential
explanation for the difference.
4. (10 points) Estimate an first difference regression of log market capitalization on log revenue.
To do this, calculate the difference in log market capitalization d_logmarketcap and the dif-
ference in log revenue d_logrev, and regress d_logmarketcap on d_logrev. How does the effect
compare with part 3? Why?
5. (10 points) Winsorize d_logmarketcap and d_logrev from part 4, and rename the new variables
d_logmarketcap_w and d_logrev_w. Estimate a kernel regression of d_logmarketcap_w on
d_logrev_w, and plot the prediction from the kernel regression. Is the relationship linear?
6. (20 points) In the last part, we want to understand which firms make acquisitions in 2020.
Keep only observations where year is equal to 2020.
(a) (10 points) Use firms with firm ID (gvkey) not divisible by 3 as the training set, and
firm ID divisible by 3 as the test set. In the training set, use change in log market
capitalization (d_logmarketcap_w), change in log revenue (d_logrev_w) and leverage
(equals to short term debt plus long term debt divided by firm value, and firm value is
total debt plus market capitalization plus preferred stock) to predict whether the firm
makes an acquisition in 2020. Report the coefficients from the logit model (you don’t
need to do bootstrap for standard errors).
(b) (5 points) If revenue is 10% higher, what is the change in the probability of acquisition?
(c) (5 points) Choose a method to evaluate the prediction from the logit model in the test
set.
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