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Problem Set 1
ECONOMETRICS
Prof. Oscar Jorda
Due Date: Friday, January 19
Instructions: The goal of the problem set is to understand what you are doing rather than just
getting the correct result. Please show your work clearly and neatly. No credit will be given to
late homework, regardless of the excuse. Please write your answers in the space provided.
1. [05 pts] Calculate VAR(aX + b), where a and b are constants and X is a random variable.
2. [05 pts] Show that 2 = E(X2) - E(X)2 .
3. [10 pts] Calculate the following probabilities using the tables in your book and show how you
obtained your results in the space provided:

X ~ N(1.5, 22); P[0.3  X  1] =___________

X ~ N(2, 1.52); P[-5.5  X  -0.3] = ___________

X ~ t5; Calculate x given that you know P[-x  X  x] = 0.05. x = ____

X ~ 12; Calculate x given that you know P[X  x] = 0.05. x = ____

X ~ F3,6 ; Calculate x given that you know P[x  X] = 0.01. x = ____
4. [05 pts.] Show VAR(a + cX) = c2 VAR(X)
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5. [10 pts] Suppose you are offered two dental insurance plans. The first one costs $50.00 per
year, has a $100.00 deductible and covers all costs thereafter. The second plan costs only
$35.00 per year but has a $250.00 deductible (it also covers any costs thereafter).
A. Assuming dental care expenses can be thought of as a uniform random variable U ~ [0,
3500], which option offers a better deal? (Hint: for each plan, write down the costs as a
function of U. Note that if U > deductible, then there are no additional costs).
B. What is the expected cost of dental care if you decide to go without insurance? Is this
insurance plan a good deal?
6. [10 pts] A recent article in the NY Times reports that high-tech industries are implementing a
new, virtually error-free quality control system they call "6 sigma." This makes reference to
the fact that the probability of shipping a product with a defect is beyond six standard
deviations. Assuming normality, calculate the probability of getting a defect-free product
from these companies. If INTEL ships 100 million chips a year, how many chips will contain
defects under this quality control system?
7. [05 pts] Calculate f(x|y) given that f(x,y) = xy. Calculate the ranges for X and Y that make
f(x,y) a true probability density function if you know that X, Y  0. (Hint: check that the p.d.f.
integrates to 1).
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EViews Exercise [50 pts]
For this exercise you will need to download the file: ps1.wf1 from my web-site. It contains
macroeconomic yearly data on the U.S. The range is 1961 - 2000. You can click each series to get
a more detailed description. You will need to manipulate some of the series as follows:

Calculate the annual rate of inflation by taking the log-difference of the GDP deflator as
follows:
Inflation = log(deflatort) – log(deflatort-1)
This can be accomplished by typing the following line in the command window and
hitting enter:
genr inflation = d(log(deflator))*100
Remark: This is an approximation to calculating percentage changes that is common in
econometric analysis. To convince yourself, generate the inflation series by calculating
the annual percentage change of the GDP deflator. Type the following in the command
window and then hit enter:
genr inflation2 = ((deflator - (deflator(-1))/deflator(-1))*100
Plot both series on a graph. Are you convinced?
You need to do the same to calculate output growth using the series GDP. Call the new
series "output" and "output2."

Calculate the ratio of the Trade balance to GDP ratio. Note that the trade balance data is
in nominal terms but that the GDP data is in real terms. First, we need to convert the
trade figures into real terms. To do this simply multiply the trade balance by the GDP
deflator. Note that your units of measurement have changed: instead of millions of
dollars, now you have hundreds of millions of dollars.
Now we can calculate the trade to GDP ratio but first note that GDP is reported in
billions of dollars. Therefore, if you want to report as a percentage of GDP, you will need
to multiply the GDP figures by 1000 (why?).
The trade to GDP ratio can therefore be calculated by typing the following in the
command window:
genr trade_ratio = trade*deflator/(gdp*1000)
Things you need to turn in:
1. [05 pts] Calculate basic statistics for Unemployment, Output, Inflation, Government Deficit
(as a percentage of GDP) and the Trade Deficit (as a percentage of GDP). Please report using
the appropriate units.
2. [10 pts] Subset your sample according to whether the president was a democrat or a
republican and calculate the sample statistics for the same variables as in point 1. What can
you say about the differences?
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3. [10 pts] Suppose instead, that you subset your sample after a president (democrat or
republican) has been in office for one year. How do your results vary? Do you think this
measure is a more accurate description of a president’s economic performance? Why?
4. [10 pts] Graph each series (Unemployment, Output, Inflation, Government Deficit and Trade
Deficit) for the whole sample in individual graphs (although all graphs can be in the same
page). Shade the periods corresponding to democrat presidents.
5. [15 pts] You are asked by the member of congress (for which you are interning) to report on
the relative economic success of democrat presidents versus republican presidents. Based on
the analysis you have conducted (not on your political belief, we are scientists…), write a
one-paragraph memo. Make sure you mention other factors that may affect your conclusions
(wars, oil crises, etc.). Make sure you state your conclusion clearly.
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