Questions from Econometrics

Q: Read the box “Social Class or Education? Childhood Circumstances and

Read the box “Social Class or Education? Childhood Circumstances and Adult Earnings Revisited”. a. Construct a 95% confidence interval for the difference in the household earnings of people whose fath...

Q: This exercise shows that the sample variance is an unbiased estimator of

This exercise shows that the sample variance is an unbiased estimator of the population variance when Y1, ……, Yn are i.i.d. with mean Y and var...

Q: a. Y is an unbiased estimator of Y. Is

a. Y is an unbiased estimator of Y. Is Y2 an unbiased estimator of 2Y? b. Y is a consistent estimator of Y. Is Y2 a consistent estimator of 2Y?

Q: Suppose X is a Bernoulli random variable with Pr (X =

Suppose X is a Bernoulli random variable with Pr (X = 1) = p. a. Show E(X4) = p. b. Show E(Xk) = p for k > 0. c. Suppose that p = 0.53. Compute the mean, variance, skewness, and kurtosis of X.

Q: Let Y be a Bernoulli random variable with success probability Pr (

Let Y be a Bernoulli random variable with success probability Pr (Y = 1) = p, and let Y1, ……, Yn be i.i.d. draws from this distribution. Let p^ be the fraction of successes (1s) in this sample. a. Sho...

Q: Suppose (Xi, Yi) are i.i.d

Suppose (Xi, Yi) are i.i.d. with finite fourth moments. Prove that the sample covariance is a consistent estimator of the population covariance; that is where sXY is defined in Equation (3.24). Data...

Q: Show that the pooled standard error [SEpooled (Ym – Yw

Show that the pooled standard error [SEpooled (Ym – Yw)] given following Equation (3.23) equals the usual standard error for the difference in means in Equation (3.19) when the two g...

Q: Suppose Yi∼ i.i.d. N (Y

Suppose Yi∼ i.i.d. N (Y, 2Y) for i = 1, ……, n. With 2Y known, the t-statistic for testi...

Q: In a poll of 500 likely voters, 270 responded that they

In a poll of 500 likely voters, 270 responded that they would vote for the candidate from the democratic party, while 230 responded that they would vote for the candidate from the republican party. Le...

Q: Using the data in Exercise 3.3: a.

Using the data in Exercise 3.3: a. Construct a 95% confidence interval for p. b. Construct a 99% confidence interval for p. c. Why is the interval in (b) wider than the interval in (a)? d. Without doi...