# CS计算机代考程序代写 finance Excel Assignment 1

Assignment 1
Empirical Finance: Methods and Applications January 25, 2021
• Datasets for problems 4, 5, and 6 are available on insendi.
• You should submit a single pdf solution containing answers to all sub-parts of all problems (including
4-7). Typewritten solutions are preferred but handwritten and scanned solutions are acceptable.
• Marks for each problem are listed below.
• In addition, please submit code for problems 4-7 in the form of an R project. This should be a zipped folder that contains an R Project, a single R file with answers to all relevant parts of all problems, and all csv files (including those for 4-6 and any you download for problem 7). I should be able to download and run your R file directly. Please comment your code to make it as easy to interpret as possible.
• Your marks depend on clarity of exposition in solutions and code. This includes figures and regression results.
• You may discuss all problems with classmates but each student must independently write and submit their own solution. Solutions and code that have been clearly copied will cause the full assignment to receive 0 marks and may invite further disciplinary action.
Problem 1 (5 marks)
Suppose we see 5 observations of yi, Di, shown in the table below:
Consider the following linear model:
yi Di 10 81 41 00 31
yi = δ0 + δ1Di + vi.
Suppose we estimate this model on the data above via OLS. Please explicitly find δˆOLS and δˆOLS. 01
1

Problem 2 (10 Marks)
Relative to the United Kingdom, the United States has borrower friendly laws surrounding residential mort- gage default. Many US states are Non-Recourse—that is, if borrowers stop making the mortgage payments, lenders cannot hold them responsible beyond seizing the home itself. On the other hand, the United King- dom has Full-Recourse: lenders may seize cars, investments, garnish wages, et cetera. Many believe that the relative leniency of laws in the United States is responsible for higher rates of mortgage default.
For the sake of simplicity, assume laws may take only two forms: Non-Recourse (in the United States) or Full-Recourse (in the United Kingdom). Imagine we are interested in the causal (treatment) effect of Non-Recourse laws on mortgage default.
(a) Denote mortgage default for a borrower i by Di. In potential outcomes notation, write the average treatment effect of Non-Recourse laws on default. (3 marks)
(b) Suppose we compare the average default rates in the United States to the average default rates in the United Kingdom. Write this comparison in potential outcomes notation. (3 marks)
(c) Why does the expression in part (a) differ from that in part (b)? Please provide an explanation that is not simply mathematical, but that provides some intuition. Would you expect the answer in (b) to be higher or lower than that in (a)? Why? (4 marks)
Problem 3 (10 marks)
Suppose the relationship between yi and xi is as follows:
yi = β0 + β1xi + vi,
where xi is observable, E[vi|xi] = 0 and E[xi] = 0. However, suppose we do not see yi, but instead observe
yi∗ = yi + ηi. Consider the regression:
You may assume that ηi has mean 0 and variance ση2.
y i∗ = β 0 + β 1 x i + u i ,
(a) Suppose that Cov(x , η ) = 0. Will the OLS estimator βols using y∗ instead of y be biased for β ? Show
ii1ii1 why or why not. (5 marks)
(b) Suppose instead that ηi = γxi +εi, where γ ̸= 0 and Xi and εi are independent. Will the OLS estimator
βols using y∗ instead of y be biased for β ? Show why or why not. (5 marks) 1ii1
2

Problem 4 (20 marks)
The dataset rollingsales manhattan.xls contains details on 2020 real estate transactions in Manhattan.1
(a) Load the data into R and perform the following basic data cleaning exercises: 2
• Relabel the column names to remove any spaces