This assignment is designed to review the materials you learn in the lab. Be sure to comment your code to clarify what you are doing. Not only does it help with grading, but it will also help you when you revisit it in the future. Please use either RMarkdown or knitr to turn in your assignment. These are fully compatible with R and LaTeX. If your code uses random number generation, please use set.seed(12345) for replicability. Please post any questions on Piazza.

1) Checking Intuition

  1. Explain the logic of using a valid instrument \(\textbf{Z}\) to deal with the endogeneity of a true linear model \(Y = \textbf{X}\beta + \epsilon\). What assumptions do we need to make? How can those assumptions break down?
  2. Explain the frequentist definition of a confidence interval. What assumptions do we need to make? How can those assumptions break down?

2) Coding in R

The teengamb dataset in the faraway package studies teenage gambling in Great Britain.

  1. Load teengamb and describe, briefly, the substantive meaning of each variable.
  2. Run an OLS regression of income on gamble. Using summary(), explain the substantive meaning (i.e.ย more than just the mathematical interpretation) of Estimate, Std. Error, t value, and Pr(>|t|) with respect to income. In other words, how do we think about these outputs in the context of finite-sample inference?