Intro to Econometrics
1. For two generic random variables Z. and W, the Law of Iterated Expectations (LIE) says
You are given the following regression model:
and you are told that 0.
a) Does A1 hold?
b) Is 3 the causal effect of X; on Y,!
c) Show that E(a) = 0. Interpret what it means.
d) Show that Cor(a), X1) 0. Interpret what it means.
2. Consider two randorn variables T; and G. To answer the following questions a simple sketch
a) Draw n scatter plot such that Gi) is positive and R² is high and close to 1.
b) Draw n scatter plot such that Cov(T). Gi) is positive and R² is low.
c) Draw n scatter plot such that Cov(T).Gi) is negative and R² is high and close to 1.
d) Draw a scatter plot such that Cov(T¿.G, = 0. What would be the value of the R² in
this case? Explain in detail. (Hinf: the the OLS estimator for the slope of a simple linear
regression to ansaber)
3. Suppose that the true relationship between the variables Y1 and X, is given by:
with 14, - W; Zis where W;, Z; are additional variables that you are ignoring and that end
up in the error term.
a) Suppose that Cov(Xi, W;) > 0 and that Cov(Xi, Zi) > 0. Is it possible that A1 holds in
this situation? Please explain why using both formality and intuition.
b) Suppose that Cov(Xi,W;) > 0 and that Coo(Xi, Zi) < 0. Is it possible that the regressor
is uncorrelated with the error term? Can you say precisely when this is the case?
c) Does =0 imply that A1 holds?
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