经济助攻代写经济考试代写经济作业代写

ECON 308: ECONOMETRICS MIDTERM EXAM

经济助攻代写 1.Consider a regression function of the form y = β0+ β1x + s. a. Formally state the homoskedasticity assumption (SLR5).

1.

Consider a regression function of the form y = β₀+ β₁x + s.

a. Formally state the homoskedasticity assumption (SLR5).

b. What does this meanintuitively?

c. Draw some hypothetical data on an (x, y) scatterplot that would be consistent with this

d. On a second set of x and y axes, draw some hypothetical data that would exhibit heteroskedasticity, in violation of this

2. 经济助攻代写

Formallystate the zero conditional mean assumption for a multiple linear regression (MLR 4). What might cause this assumption to be violated?

3.

Supposeyou have data on the real (inflation-adjusted) incomes of men at age 40 (y) as well as the mens’ fathers’ real incomes at age 40 (x) (so each observation is a father-son pair of real incomes at age 40). Your estimated regression is yˆ = βˆ0 + βˆ1x.

a. Supposeyour estimated βˆ1 is equal to How would you interpret this?

b. Supposeyour estimated βˆ1 is equal to How would you interpret this?

c. Supposeyou wanted to allow βˆ1 to vary by race, with two racial How would you alter the above regression?

d. Supposeinstead there are R racial How would you alter the above regression?

4. 经济助攻代写

Supposethe population regression function is y = β₀ + β₁x + s, where y is an indicator for whether or not a child eventually attends college and x is the child’s score on a 5th grade academic assessment (which ranges from 0 to 100, with mean µ and variance σ²). Assume the Gauss-Markov assumptions

a. Writethe expression for βˆ1 in the estimated regression of y on x.

b. Whatis the interpretation for βˆ1?

c. Supposethat, instead of using x in the regression, we use z, which is x standardized to have a mean of 0 and variance of 1. What is the expression for β₁ now? How do we interpret its magnitude?

d. Showthat β₁ = σβˆ1.

5. 经济助攻代写

Supposethe population regression function is y = β₀ + β₁x₁ + β₂x₂ + s, where β₂ = 0, e., β₂ has no linear relationship with y. Jorge suggests that you exclude x₂ when you estimate your regression, as this will lead to better results. Torrance argues instead that it doesn’t matter whether you include x₂ or not, as you will get the same results. Who is correct , and under what circumstances?

6. 经济助攻代写

Suppose you wish to estimate a linear regression of Y on X₁and X₂. Write a model de- scribing each of the following scenarios, and fill in actual numbers which match the patterns described.

a. Y increases at an increasing rate with both X₁and X₂, and the coefficients on both continuous predictors can be interpreted as

b. Y increases with X₁and X₂, but the rate of change of Y with X₁ is larger when X₂ is larger.

c. Y increases at a constant rate with X₁and X₂, but X₂ only matters for Y when Y is greater than 10,000.

7. 经济助攻代写

Inthe potential outcomes model with a binary treatment D,

N AT E = AT E + E[Y ⁰ | D = 1] − E[Y ⁰ | D = 0] + (1 − P(D = 1))(AT T − AT U ).

a. Under what assumption on the relationship between D and (Y ¹, Y ⁰) does N AT E=

AT E?

b. What does E[Y ⁰| D = 1] − E[Y ⁰ | D = 0] represent?

c. What is the formal definition ofAT T ?

d. What does AT T − AT U represent? Intuitively, why is thisimportant?

Below, I reiterate some of the formulas I presented in class and present some useful generalizations. Throughout the handout, let X, Y , and Z denote random variables while a and b denote arbitrary constants (numbers).

Conditional probabilities: Suppose the set S_X = {x₁, x₂, . . . , x_n} contains all possible values of the random variable X, and each value is distinct. In other words, the events of S_X are mutually exclusive and exhaustive. Then, the law of total probability states that