Hello, i would like to have pointers on how to solve the assignments below. Thanks!
Department of Economics
Economic Data Analysis
Problem Set # 2
(due Tuesday, Apr.
12 in class
I. True/False/Uncertain – Brie?y explain. No credit without an explanation (5 marks each).
1. Some form of Granger causality should be present with unit root, co-integrated variables.
2. The GARCH model is not useful in the case of homoskedasticity.
3. 2SLS can be run only if the order condition is satis?ed.
4. The Hausman test can be used to test for both simultaneity bias and endogeneity in Random E?ects
5. The slope coe?cient in a Probit model cannot be above 1.
II. Problems – Use Stata for all your computations. You have to show your work. No credit
without an explanation (15 marks each).
1. The ?le ?CO2 data? contains monthly data on changes in CO2 levels in the atmosphere and temperature
changes. Let us use this data set to investigate two hypotheses:
Hypothesis I: Changes in CO2 levels cause temperature changes, i.e. man?s industrial activity increases CO2 , which in turn increases temperatures. Thus, global warming is man-made.
Hypothesis II: Changes in CO2 levels follow changes in temperature, i.e. the sun warms up the
oceans, which release more CO2 . Thus, global warming is not man-made.
(a) Plot the CO2 and temperature data on a time plot. Are they trending? (5 marks)
(b) Assume both changes in CO2 and temperature are stationary. Test if temperature changes
Granger-cause CO2 changes. Use ADL (4,4) in its original version. What do you conclude?
(c) Test if CO2 changes Granger-cause temperature changes. What do you conclude? (5 marks)
2. Consider the following T-ARCH model:
ht = ? + ?1 e2 + ?dt?1 e2
et < 0
et ? 0
(a) If ? = 0, what are the values of ht when et?1 = ?1, when et?1 = 0 and when et?1 = 1? (5 marks)
(b) If ? = 0, what are the values of ht when et?1 = ?1, when et?1 = 0 and when et?1 = 1? (5 marks)
(c) What is the key di?erence between ? = 0 and ? = 0? (5 marks)
3. Suppose that a fad for oats (resulting from the announcement of the health bene?ts of oat bran) has
made you toying with the idea of becoming a broker in the oat market. Before spending your money,
you decide to build a simple model of supply and demand for oats:
QDt = ?0 + ?1 Pt + ?2 Y Dt +
QSt = ?0 + ?1 Pt + ?2 Wt +
QDt = QSt
QDt = the quantity of oats demanded in time period t.
QSt = the quantity of oats supplied in time period t.
Pt = the price of oats in time period t.
Wt = the average oat farmer wages in time period t.
Y Dt = disposable income in time period t.
(a) There is no left-hand-side variable that appears on the right-hand-side of either equation. Does
this mean that OLS will have no simultaneity bias? Why or why not? (3 marks)
(b) Are your equations structural or reduced-form? (2 marks)
(c) How many and what are the endogenous and exogenous/predetermined variables? (2 marks)
(d) Are the demand and supply equations over-, under- or just identi?ed? (2 marks)
(e) You expect that when Pt goes up, QDt will fall. Does this mean that any simultaneity bias in
the demand equation will be negative, instead of the positive bias we typically have with OLS
estimation of simultaneous systems? Explain your answer. (3 marks)
(f) Carefully outline how you will apply 2SLS to this system. How many equations (including reducedform) would you have to estimate and which variables will be in which equation. (3 marks)
4. Consider the following ?xed e?ects model with panel data:
Yit = ?0 + ?1 Xit + ?2 D2i + vit
where it is a classical error term (satis?es the classical assumptions) and ai is a time-invariant, omitted
(a) What is the real world meaning of ai ? (3 marks)
(b) Why does a have one subscript, while v and
have two? (3 marks)
(c) Why do we need to remove ai from the equation? (3 marks)
(d) Show how the demeaned version of the equation removes ai from the error term. (6 marks)
5. The two most-used forms of mortgages are ?xed-rate mortgages and adjustable-rate mortgages. If a
borrower chooses a ?xed-rate mortgage, the interest rate that he pays is ?xed over the life of the loan.
If a borrower chooses an adjustable-rate mortgage, the interest rate that he pays is calculated as the
rate of short-term government bonds plus a risk premium and is adjusted up or down (following the
changes in the rate of government bonds) during the life of the loan. Since adjustable-rate mortgages
carry a risk of higher rates in the long run, they usually have a lower initial interest rate than do
In order to evaluate the factors in?uencing the choice between adjustable and ?xed rate mortgage
loans, we have run a Linear Probability Model (LPM) and Logit Model the results of which appear
below, based on 78 observations:
The dependent variable is a binary (dummy) variable taking the values of Di = 1 if the i-th borrower
chose an adjustable-rate mortgage and Di = 0 if the i-th borrower chose a ?xed-rate mortgage.
? Fi = The ?xed interest rate available to the i-th borrower, in %.
? Mi = The interest premium (di?erence) over the Treasury bills rate (that is included on the
adjustable rate) that is available to the i-th borrower, in %.
? Yi = The di?erence between the interest rate on long-term and short-term government bonds
available on the day of the i-th loan, in %. The interest rate on long-term bonds is normally
higher than the short-term rate to account for the unknown risks of the future.
(a) Hypothesize the expected signs of the explanatory variables and test the appropriate hypotheses at
the 5% level using the LPM and Logit models. Are the results from hypotheses testing consistent
across the two models? (Assume the critical value of the one-sided test is about 1.671) (3 marks)
(b) Transform the Logit slope estimates to make them comparable to the LPM estimates. Are they
consistent with the LPM estimates? How do you interpret the transformed logit coe?cient on F
in words? (4 marks)
(c) Using the two models calculate the probability of choosing an adjustable rate mortgage if F = 13%,
M = 2% and Y = 2% (use the untransformed Logit). (4 marks)
(d) Using the two models, what is the probability of choosing an adjustable rate mortgage if the ?xed
interest available now increases to 14%, with M and Y staying the same as in (c)? (4 marks)