8
Week 8 Consistency and Estimator Variance
8.1
Chebyshevs Inequality
1. Use Chebyshevs Inequality to solve this problem. Show your work. A machine
used to ll cereal boxes dispenses on average ounces per box. The manufacturer wants the
actual amount dispe
1
Economics 240a: Week 1
1.1
Probability Assignment
You are advising an e-commerce company that is trying to understand how customers behave on
their website. The company sells Three Stooges memorabilia and has provided you with some sales
data from which
2
Week 2: Random Variables and Distributions; Variance
and Covariance
2.1
Random Variables
A contestant on a quiz show is presented with two questions, 1 and 2, which she must attempt to
answer. She can choose the order that she answers. If she answers th
3
Week 3: Stochastic Models and Identication
3.1
Stochastic Models
You are interested in analyzing the eect of education, age and age-squared on wages.
Wi = 0 + 1 Educi + 2 agei + 3 age2 + ui
i
1. Is this a linear model? Why?
2. How do you interpret 0 ?
3
4
Week 4 Method of Moments and Least Squares Estimations
4.1
Method of Moments
You gather data from a random sample of n observations, Yi . . . Yn . The data possess a uniform
probability density function over the interval (0, ).
1. What is the method of
5
Week 5 Exogeneity and Estimator Bias
For this question you will use the dataset murder2.csv, which includes:
rate = Murder rate per 100,000
convictions = Number of convictions divided by number of murders
executions = Average number of executions div
6
Week 6
6.1
Conditional Expectations and Bias Assumptions
We are interested in modeling a mans height as a function of his fathers height (in inches):
Hi = 1 Fi + Ui .
Suppose that there is another relevant variable, mothers height (Mi ), in the error te
7
Week 7
7.1
Mean Squared Error
Using your model and code from last weeks simulation where:
The number of simulations (loop iterations) is 100
The number of observations is n = 1, 000
Fi N (, 4)
ei N (0, 2 )
Ui = 0.5 Fi + ei
1 = 1.1
Hi = 1 Fi + Ui
8
Week 8: Chebyshev and Estimating Estimator Variance
8.1
Chebyshevs Inequality
1. Use Chebyshevs Inequality to solve this problem. Show your work. A machine
used to ll cereal boxes dispenses on average ounces per box. The manufacturer wants the
actual am
1
Economics 240a: Week 1
1.1
Probability Assignment Question
First it helps to write down all the probabilities using set notation:
Let C=the probability of the Curly Wig, M=the probability of the Moe bust, and L the probability of the Larry boxer shorts.
2
Week 2 Random Variables and Distributions; Variance
and Covariance
2.1
Quiz Show Question
Let the probability that she answers Question 1 correctly P (Q1) = p1 and the probability that she
answers Question 2 correctly P (Q2) = p2 . Remember that these e
7
Week 7: Mean Squared Error and Estimator Distribution
7.1
Mean Squared Error
OLS in each of the following
Report the bias, variance, and mean squared error of your estimates for 1
scenarios:
1. = 10 and 2 = 1 and n = 1000:
7.1.1 - Bias of B1ols = 0.5001
Identication
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
You are a military analyst who needs to answer: How many tanks
could Germany produce each month during the Second World
War?
also used for V2 r
Condence Intervals
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
October 2011
Initial Question
How do you determine the accuracy of an estimate?
Do we really have evidence how eort responds to
co-worker wages?
How many people do we ne
Estimation: Method of Moments
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Does China have an abnormally low number of female births?
Stochastic Model
Mi - fraction of male births in country i
Ci - ind
Estimation : Least Squares
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Do SAT scores predict success in college?
Stochastic Model - i indexes enrolled college students
Ci - college GPA
Hi - high schoo
Exogeneity
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Does additional education lead to higher wages?
Stochastic Model - i indexes workers
Wi - (log) wage
Si - years of schooling (education)
Ji - yea
Stronger Exogeneity Assumptions
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Do certain mutual fund managers produce consistently high
returns?
excess returns: fund return - average of all fund returns
Estimator Bias
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Is it sensible to purchase bottles of wine as an investment?
vintage - harvest year for wine grape
bottled wine - often resold at auctions
Ho
Estimator Variance
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
What is a fair bet in a game of chance?
You are oered to bet on the outcome of a die roll
payout - $1 for each pip showing
For a given di
Estimator Mean-Squared Error
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
What is the value of a call option on a stock?
You are oered a contract that allows you to buy 1000 shares
of IBM at $190 per s
Estimator Distribution
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Can marathon runners change their pace after 25 miles, to
break the four hour barrier?
The nish times are grouped into 5 minute inter
Estimator Consistency
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
October 2011
Initial Question
Statistics graduate students from Berkeley made a substantial
amount of money betting on roulette in Las Vegas
Were they simply lucky? I
Variance Estimation
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
October 2011
Initial Question
How do you characterize uncertainty for an estimator?
What are the range of possible values for monthly
German tank production?
Do we real
8
8.1
Week 8: Chebyshev and Estimating Estimator Variance
Chebyshevs Inequality
First lets write down the Inequality:
P (|Y | k) 1
1
k2
1
Now nd a value of k that makes 1 k2 = .93 Depending on how precise you want to be,
anything between 3.8 and 4 will w
3
3.1
3.1.1
Week 3: Stochastic Models and Identication
Stochastic Models
Is this a linear model?
Yes. Even though the model includes a quadratic term (age2 ), we classify stochastic models as
linear when they are linear in the coecients. Because none of t
Estimator Consistency
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
October 2011
Initial Question
Statistics graduate students from Berkeley made a substantial
amount of money betting on roulette in Las Vegas
Were they simply lucky? I
Variance Estimation
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
October 2011
Initial Question
How do you characterize uncertainty for an estimator?
What are the range of possible values for monthly
German tank production?
Do we real
Estimator Distribution
Lecture for Economics 240A
Douglas G. Steigerwald
UC Santa Barbara
September 2011
Initial Question
Can marathon runners change their pace after 25 miles, to
break the four hour barrier?
The nish times are grouped into 5 minute inter