Econometrics

Name: _______________________________________ Midterm Exam II

Predictive Analytics Midterm Exam II

Instructions: This exam contains five sections. Each section is worth 20 points. You have 48 hours to complete your exam. Your answers must be typed. Make sure to highlight your final answer. Section I Consider this DGP: 𝑦 = 𝛽$𝛽%&𝜆(, where 𝑒 is a random variable such that 𝑒~𝑁(0,𝜎0).

1. Explain how you would estimate this model. (15 points) 2. Find the estimators for the parameters. (5 points)

Section II Consider this DGP: 𝑦 = 𝑓(𝑥) + 𝑒, where 𝑒~𝑁(0,𝜎0), and you ignore the functional form of the determining function 𝑓.

1. Explain how you would estimate this model. (15 points) 2. How would you employ this model to predict the impact of a change in 𝑥 by 1 unit on a change in 𝑦. (5

points). Section III A colleague of yours wants to estimate a DGP that presents multicollinearity. Explain to your colleague the challenge of this task and advise him on what he can do in this case. (20 points)

Section IV Consider this DGP: 𝑦 = 𝛽$ + 𝛽%𝑥% + 𝛽0𝑥0 + 𝑒, where 𝑒~𝑁(0,𝜎0). A colleague wants to estimate this DGP by regressing on this equation: 𝑦 = 𝛽$ + 𝛽%𝑥 + 𝜀.

1. Explain to your colleague what will be the consequence of this estimation. (15 points) 2. Find the value of 𝐸7𝛽8%9. (5 points)

Section V Consider this DGP: 𝑦 = 𝛽$ + 𝛽%𝑥% + 𝛽0𝑥0 + 𝑒, where 𝐸[𝑒] = 𝐸[𝑒𝑥%] = 𝐸[𝑒𝑥0] = 0, but you ignore what kind of distribution follows the random variable 𝑒.

1. Can you estimate the parameters of the DGP? (5 points) 2. Can you construct the confidence interval of 𝛽%? (5 points) 3. Can you test the null hypothesis 𝛽% = 0? (5 points) 4. Assume you find that 𝛽8% = 0. What does this finding tell you about the DGP? (5 points)