Section A – True / False Questions – Single-word answers are not acceptable

1. Consider the following model that purports to explain investment decisions as a function of interest rate as
   INV _t = ₀ + ₁ RATE _t + _t , where t = 1,…, n. In order to have accuracy in our estimated coefficients, we should choose a sample of observations during a relatively stable interest rate period. (3 points)
2. If \[{{\hat{\beta }}_{1}}\] is positive in the equation (1) Y _i = ₀ + ₁ X _1i + ₂ X _2i + _i , it could be negative in the equation (2) Y _i = ₀ + ₁ X _1i + ₂ X _2i + ₃ X _3i + _i , . (3 points)
3. When all of the explanatory variables are zero, the intercept is also zero. (3 points)

Question 1 ( 29 points)

Download the data on US Savings and Disposable Income.

1. Estimate the following model, S _t = ₀ + ₁ * DI _t + _t . Write down your results in full reporting mode. (3 pts)
   Where S _t = Annual Total Savings in the U.S. in $ billion for the period 1970 – 1995
   DI _t = Annual Disposable Income in the U.S. in $ billion for the period 1970 – 1995
2. Since you are using time-series data, you want to check for the existence of Serial Correlation. Use the estimated residuals to calculate the Durbin-Watson d-statistic and make an assessment about the existence of serial correlation on the basis of it. (4 points)

1. Plot a scatter graph of the residuals from your equation in (a) above against time to visually verify the existence of serial correlation. (4 points)
2. Assuming that you have proof of positive serial correlation, calculate the estimated rho directly from the DW d-statistic. (3 points)
   
3. Apply the rho you have estimated in (d) above to correct your data and run a Generalized Least Squares Regression. Show the formulation of the model and write down your results. (5 points)
   
4. Calculate the residuals from (e) above and re-estimate the DW d-statistic. Report your conclusions. (4 points)
5. Compare the equations from (a) and (e) above. Which of the two models do you prefer? Explain. (6 points)

Question 2 ( 3 1 points)

Download the data on Markets. These data refer to 179 Cities and come from "The Canadian People, Markets".

1. Estimate the following model, S _i = ₀ + ₁ * POP _i + ₂ * HH _i + ₃ * INC _i + _i
   Where: S = Total Retail Sales in the i-th city, in $ million.
   POP = Total Population of the i-th city, in 000’s.
   HH = Number of Households of the i-th city, in 000’s.
   INC = Total Personal Income of the i-th city, in $ million.
   and write down your results in full reporting mode. (3 points)
2. Since you are using cross-sectional data, you want to check for the existence of Heteroskedasticity. You do not have any specific correction factor in mind. So, you decide to run a White-test. Describe the procedure and report on the work and conclusions in full reporting mode. (8 points)
3. Assuming that you have rejected the null hypothesis of Homoskedasticity, you suspect that HH may be the variable that is causing Heteroskedasticity. Run a Park test to check your suspicions, write down your results and report your conclusions. (6 points)
4. Plot a scatter graph of the residuals from your equation in (a) above against the HH variable to visually verify the existence of heteroskedasticity. (3 points)
5. Assuming that you have confirmed your suspicions, proceed with the necessary transformation of your data to run a Weighted Least Squares regression, and write down your results. (4 points)
6. Explain the differences between the two models that you have estimated in (a) and (e) in terms of formulation, and signs and sizes of estimated coefficients. Which of the two models (a) or (e) do you prefer? Explain. (7 points)

Question 3 ( 31 points)

Download the data on Pepsi. The file contains 1460 observations for the following series:

Pepsi: A dummy variable where 1 denotes choice of Pepsi by the i-th customer and 0 otherwise

Price_P: The price of a 2-liter bottle of Pepsi at the time of purchase

Price_7: The price of a 2-liter bottle of 7-Up at the time of purchase

Price_C: The price of a 2-liter bottle of Coke at the time of purchase

Disp_P: A dummy variable where 1 denotes whether Pepsi was displayed at the time of purchase and 0

otherwise

The purpose of this exercise is to determine the factors that explain the choice of Pepsi over other types of colas.

1. Using these data, estimate the probability (proportion) of a customer choosing Pepsi for (i) all cases; and (ii) for the cases where Pepsi is displayed. (3 points)
2. Assuming that a relationship exists between choosing Pepsi as the dependent variable and the rest as the independent variables, hypothesize the signs of the β _k coefficients. (4 points)

1. Run 3 regressions of this relationship using a linear probability model, a logit model, and a probit model, and make a summary table including the estimated coefficients with their t/z ratios, R ² , coming from the 3 models. (6 points)
2. Calculate the proportion of correct predictions coming from the 3 models. (6 points)
3. Without running a significance test, evaluate the estimated coefficients. (3 points)
4. Create a second table with the transformed coefficients of the logit and probit models to make them comparable to those of the linear probability model E. (3 points)
5. Using the 3 models, evaluate the probability of choosing Pepsi when Pepsi is displayed and when Pepsi is not displayed while the prices of all three drinks are equal at $1.50 per 2-liter bottle. (6 points)

Price: $36.11

Solution: The downloadable solution consists of 18 pages, 1811 words and 2 charts.
Deliverable: Word Document