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Economics
This is an open-note, open-book, open-room, open-laptop, open-kitchen, open-border, open to family & friends, but not an open discussion examination. Notations are as used in the class. Credit for each question is given in [ ]. Please write your answers “without a cloud” (a Chinese metaphor for clarity). FIVE bonus marks will be awarded for neatness. GOOD LUCK!!
Prof Bera’s Econ 503, What he taught in class
after the Midterm, Spring 2021
Prof Bera’s Econ 503 Final, Spring 2021 Exam,
as it appears to be
These pictures and captions were suggested by Utsoree Das, all the way from Kolkata, India. Herself a student, I think, Utsoree only had amiability in mind.
1. [10] (Geometry by OLS)
Explain the diagram as much as you can.
2. [15] (From Greek ε to English e)
Recall our definition of e = Y − X, where = (X′ X)−1X ′ Y in the context of the multiple regression model Y = Xβ + ε .
Write a character certificate (reference letter) on behalf of e [i.e. discuss its usefulness, and properties good (10 marks) and bad/ugly (5 marks)].
3. [10+10] (All important: An Application)
Consider the following model to explain CEOs salaries in terms of annual firm sales, return on equity (roe, in percentage form), and return on firm’s stock (ros, in percentage form):
log(salary) = β0 + β1 log(sales) + β2roe + β3ros + u
(i) In terms of model parameters, state the null hypothesis that after controlling for sales and roe, ros has no effect on CEO salary. State the alternative that better stock market performance increases CEO salary. Also, state the null hypothesis in matrix notation (Rβ = δ) we studied in class, i.e. specify the matrices, R, β, and δ .
(ii) Using data on 209 observations, the following equation was obtained through OLS (where the standard errors are given in parentheses):
Test the null hypothesis that ros has no effect on salary against the alternative that ros has positive effect, at the 10% level (t0.90,205 = 1.286). Would you include ros in a final model explaining CEO compensation in terms of firm performance? Explain.
4. [5+15] (All about Jingle-Bell {JB})
(i) What is the intuition behind the JB test for normality?
(ii) Compile the bad things about JB, and discuss how those can be overcome, if at all. Note: There is absolutely no constraint on how far you can go in answering this question.
5. [10+10] (On our favorite: Y`ı f¯angch¯a
(i) Discuss step-by-step how you would carry out a test for heteroscedasticity [Breusch-Pagan or White] in the context of the linear regression model.
(ii) Why do we need robust standard error (s.e.) in the presence of heteroscedasticity? And how is it calculated?
6. [5+10] (Dependence: It depends on your understanding)
In time-series context, for the regression model:
yt = x'tβ + εt
we considered two kinds of dependence for εt , namely,
AR(1) process:
E(εt |ψt) = ρεt−1, |ρ| < 1 (1)
and ARCH(1) process:
V (εt |ψt) = α0 + α1ε2t−1, |α1| < 1 (2)
where ψt represents all the past information.
(i) What are the consequences for the OLS estimator under AR(1) dependence, as in (1). (ii) Distinguish between these two kinds of dependence, i.e., between (1) and (2).