ETF2100/5900 Introductory Econometrics

ETF2100/5900 Introductory Econometrics

Assignment 1 — A Case Study on the House Price of Stockton California

Important notes:

1. This is an individual assignment. This assignment is worth 20% of this unit’s total mark. Marks will be deducted for late submission on the following basis: 10% for each day late, up to a maximum of 3 days. Assignments more than 3 days late will not be marked.

2. Submission deadline for coursework is 12 pm noon Friday of Week 7 (i.e., 23/04/2021). Please submit a soft copy through Moodle. Name the soft copy as follows: student ID Name.doc (or .pdf). Pdf file is preferred, but word file is also fine. Also, on the title page, please make sure you provide the student ID and name correctly.

3. Notation used in the assignment needs to be typed correctly and properly. Incorrect (or inconsistent) notations are treated as wrong answers.

Please pay attention to the words in bold.

        There are 6660 observations of data on houses sold from 1999-2002 in Stockton California in the file “hedonic1.xls”. Use the data of 2001 only to estimate the next linear model and answer the associated questions below.

LSP = β01 + β02 SFLA + β03 BEDS + β04 BATHS + β05 STORIES +β06 VACANT + β07 AGE + u,

where u is an error term. Note that the sub-index i of each variable has been suppressed in the above equation.

        P = ln(Selling Price), which is a function of:

• SFLA – Size of Living Area (in square feet)

• BEDS – Number of Bedrooms

• BATHS – Number of Bathrooms

• STORIES – Number of Stories

• VACANT – Vacancy Status (1 if vacant, 0 if not at the time of the sale)

• AGE – Age of the House in Years

Questions: (20 marks in total)

1. Calculate the descriptive statistics for LSP and all explanatory variables (i.e., 7 VARI-ABLES IN TOTAL), and report them in a table. (2 points)

2. Estimate the above hedonic model for the houses sold from in Stockton California.

(a). Write down the estimated model (including estimates of the coefficients and the associated standard deviations, and R2 at least). (3 points)

(b). Discuss the estimation results using Goodness of fit. (1 points)

3. Keep two decimals for the calculation involved.

(a). At the 5% significance level, test the OVERALL significance of the model. What is the restricted model in this case? Write down the details of your test. (3 points)

(b). At the 5% significance level, test if “the age of the house in years” has NEGATIVE impacts on “ln(Selling Price)”. (3 points)

4. Write the model (1) using a vector form in a sample version as follows:

yi = β01xi1 + β02xi2 + · · · + β07xi7 + ui = x0iβ0 + ui,

where i = 1, . . . , N, β0 = (β01, . . . , β07)0, xi = (xi1, . . . , xi7)0 = (1, SFLA, . . . , AGE)0 , and the definition of yi should be obvious. Further define X = (x1, . . . , xN )0 in case one may need this notation to answer the following questions.

(a). To obtain the OLS estimate of β0 of (2), we need to minimize an objective function. Please write down the correct function form of the objective function. (1 point)

(b). Describe the basic assumptions of the classic linear regression models using the nota-tions of (2). (2 points)

(c). Provided that these assumptions hold, what conclusions can you make about the OLS estimators? (1 points)

5. For ETF2100 students only! Let’s simplify the model (2). Suppose that there is only one regressor, and we do not even include an intercept for the new model. So it becomes 

yi = β0xi + ui,

where every variable is a scalar. Suppose that (xi , ui) is independent and identically distributed across i, and {ui | i = 1 . . . , N} is independent of {xi | i = 1 . . . , N}. ui is an error term satisfies that E[ui] = 0 and = 1. In addition, let E[xi] = 1 and  = 2. While calculating the standard errors, one always needs to consider the value of . Please calculate its value and provide the detailed steps. (4 points)

5. For ETF5910 students only! Provide detailed steps to prove that by minimizing the ob-jective function in question (4), your OLS estimate has the form . We assume that  is invertible. (4 points)