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
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 memorabil
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 c
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
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 func
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
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 r
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)
e
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 avera
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 M
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 -
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?
ex
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 eac
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 M
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 enr
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 -
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?
ex
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 fo
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 d
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
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
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 bet
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 possibl
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 eor
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 eac
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 fo
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 d
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
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 Q