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经济助攻代写 经济考试代写 经济作业代写

2021-05-14 16:57 星期五 所属: 经济作业 浏览:60

经济助攻代写

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).

 

经济助攻代写
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).

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 SX  = {x1, x2, . . . , xn} contains all possible values  of    the random variable X, and each value is distinct. In other words, the events of SX are mutually exclusive and exhaustive. Then, the law of total probability states that

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经济助攻代写
经济助攻代写

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