Transcribed TextTranscribed Text

Intro to Econometrics 1. For two generic random variables Z. and W, the Law of Iterated Expectations (LIE) says that Ez(E|W;|Zi] E(Z) 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 is enough. 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?

Solution PreviewSolution Preview

This material may consist of step-by-step explanations on how to solve a problem or examples of proper writing, including the use of citations, references, bibliographies, and formatting. This material is made available for the sole purpose of studying and learning - misuse is strictly forbidden.

Introduction to Econometrics
    $23.00 for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Econometrics Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Upload a file
    Continue without uploading

    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats