Midterm I, Econ120C
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Midterm I, Econ120C
Spring 2019
1. (28 points, 4 points each) Do you agree or disagree with the following statements? Circle your answer. You do not need to provide any explanation. Should you decide to change an answer, please write in words what your Önal answer is. For example, you may write ìMy Önal answer to this question is ëAgreeîí.
(a) In an observational study, if X and Y are not correlated, then X cannot cause Y and Y cannot cause X .
Agree Disagree
(b) If X is correlated with Y , and Y is correlated with Z , then X and Z must be correlated.
Agree Disagree
(c) Even if the correlation coe¢ cient between X and Y is 1, it is still possible that there is no causal relationship between X and Y:
Agree Disagree
(d) In a competitive market, the demand curve is QD = a + b . P + u, and the supply curve is QS = c + d . P + v where b < 0; d > 0 and u is independent of v with E(u) = E(v) = 0: If we regress Q on P by OLS based on independent market observations (Qi; Pi), then the OLS estimator of the slope coe¢ cient is expected to be larger than b.
Agree Disagree
(e) Consider a linear causal model Y -_ a+X8+Zy+v where 8 > 0, y < 0, cov(X; Z) > 0 and v is independent of X and Z: If Z is omitted from the regression, then the OLS estimator of 8 is expected to be smaller than 8 in large samples.
Agree Disagree
(f) The di§erence between passive prediction and active prediction lies in whether more obser- vations are actively collected.
Agree Disagree
(g) Consider a data set that contains two variables X and Y , each of which has a positive sample variance. The slope coe¢ cient estimates produced by the Stata commands ìreg y xîand ìreg x y,rîmust have the same sign.
Agree Disagree
2. (26 points) Consider the following causal model
x - 2(1 + y + u) ;
y - 4 _ x + v:
Suppose that the values of (u; v) are generated from
Ui ~iid N (0; 7u(2)); Vi ~iid N (0; 7v(2)) .
Assume that Ui is independent of Vj for all i; j = 1; 2; :::; n: We do not observe (Ui; Vi) but we observe the equilibrium solution (Xi ,Yi), which satisÖes
Xi = 2(1 + Yi+ Ui);
Yi = 4 _ Xi + Vi ;
for i = 1; 2; :::; n:
(a) [6 points] Consider the special case with 7u(2) = 0 but 7v(2) 0. What is the best linear (passive)
prediction of Y given X = 2? (i.e., suppose I give you the value of X but withhold the value of Y; what would be your best guess of Y according to the MSE criterion?)
(b) [6 points] Consider the special case as in (a) with 7u(2) = 0 but 7v(2) 0: What is the best linear (passive) prediction of X given Y = 5?
(c) [8 points] Now suppose
7u(2) = 7v(2) = 1:
Calculate cov (X; Y) :
(d) [8 points] Under the same assumption in (c), what is the best linear (passive) prediction of Y given X = 4?
3. (15 points, 5 points each) Consider a simple model to estimate the causal e§ect of the class attendance on studentsíperformance in Econ120C at UCSD:
Scorei = a + 8 x Attendancei + vi
based on an observational study, where Attendancei is the variable indicating the percentage
of the times that a student attends the class during the attendance surveys, Scorei is some aggregate score for Econ120C, and vi contains all other unobserved causal variables. (a) Using the terminology from this class, explain, in words, what does the causal e§ect mean?
(b) In an observational study, do you agree that vi is likely to be positively correlated with Attendancei? Explain.
(c) In view of your answer in (b) about the nature of the correlation between vi and Attendancei ; what is the bias property of the OLS estimator OLS of 8? In other words, do you expect OLS _8 to be positive, negative or zero in large samples?
(24 pts) Consider the causal model
Y - a + Xf8 + Xf(2)(y + Xo)
where Xf stands for the causal factor of interest, and Xo stands for other causal factors. (a) (6 pts) What is the ceteris paribus causal e§ect of Xf on Y? Please provide a mathematical
deÖnition.
(b) (6 pts) Does the ceteris paribus causal e§ect deÖned in (a) depend on the levels of Xf and Xo? Explain.
(c) (12 pts) Suppose (Xfi; Xoi) are iid draws from independent standard normal distributions, i.e., Xfi ~ iidN (0; 1); Xoi ~ iidN (0; 1), {Xfi} and {Xoi} are independent. We observe Xfi and
Yi = a + Xfi8 + Xf(2)i(y + Xoi)
for i = 1; :::; n: Suppose the sample size n is large, and Y is regressed on a constant and Xf: What do you expect the coe¢ cient estimator associated with Xf to be? Please present your answer in terms of the parameters a; 8; and y:
2022-08-18