代考计量经济学final-Econometrics代写-Final代写

ECMT5001: Final Examination (2020s2)

代考计量经济学final Using the same regression result in (2), test this hypothesis at the five percent significance level. Show all your steps.

The total score of this exam is 45 marks. Attempt all questions.

1.(Total: 15 marks) Mimi factory produces dog food Y using two inputs, namely labour L and capital K. The production function is given by 代考计量经济学final

Y = AL^α K^β ; (1)

where A > 0, and α, β ≥ 0 are the model parameters.

Carol, the Director of Mimi factory, wants to estimate the model parameters A, α and β using the data recorded over n days. After taking ECMT5001, Carol knows that linear regression is going to be useful.

(a) (3 marks) Set up the linear regression model for Carol. State clearly the relationship between the regression coe¢ cients and the three model parameters in (1). [Hint: take logarithm]

(b) (4 marks) Simon, who is the Chief Data Officer of Mimi factory, wants to examine whether the production line is at a constant returns to scale (i.e., α + β = 1). To this end, he proposes an alternative linear regression model and obtains the following result (standard error in parenthesis):

(2)

Using the above regression result, test Simonís hypothesis at the five percent signifi-cance level. Show all your steps. 代考计量经济学final

(c) (4 marks) Simon is also interested in testing whether the technological level is at unity (i.e., A = 1). Using the same regression result in (2), test this hypothesis at the five percent significance level. Show all your steps.

(d) (4 marks) Mimo, who is Simonís assistant, instead proposes the following linear regression model for Simonís test:

Mimo argues that this is a better model than what Simon proposed because it contains one more variable and hence has higher R². Do you agree with Mimo? Why or why not?

2.(Total: 14 marks) Consider the following linear regression: 代考计量经济学final

yt = a + bxt + εt.

After estimating the model for each dataset, Bob follows the good practice by examining the residuals The residual plot is given in Figure 1.

(a) What is the problem with the estimated regression? [3 marks]

(b) Will this problem affect the validity of the OLS estimate of b? Why or why not?[4 marks]

(d) What suggestion would you give to Bob so that correct statistical inference can be made on b? [3 marks]

3.(Total: 16 marks) Bao wants to examine the relationship between outdoor activities and COVID-19 infection. He considers the following linear regression model:

(3)

where casei denotes the number of confirmed cases of COVID-19 in region i, and outdoori is the average time (in hours) spent outdoors by each individual each day in region i.Based on a sample of 28 regions, the estimated regression line based on sampled data is given below (standard error in parenthesis):

(4)

(a) Interpret the coe¢ cient estimate of log(outdoor)_i. [2 marks]

(b) As a result of the lockdown policy in Sydney, people reduce their outdoor activities by 10%. Based on the estimated regression, what is the predicted percentage change in the number of confirmed cases of COVID-19 in Sydney? [2 marks] 代考计量经济学final

(c) Bao wants to see if there is a positive relationship between outdoor activities and COVID-19 infection. Perform a hypothesis test at the five percent significance level.

Show all your steps. [4 marks]

(d) Figure 2 shows the plot of regression residuals against log(outdoor)_i . Which assump-tion does the regression violate? What is a possible reason for such a violation? [4

marks]

(e) In light of the problem identiÖed in part (d), Bao included one more regressor to the regression:

where raini is the average amount of daily rainfall in region i. The estimated regres-sion line is

Based on the above regression result and the plot in Figure 2, do you expect to be larger than or smaller than 1.5 (the OLS estimate of the coe¢ cient of log(outdoor)i in (4))? Explain your answer. [4 marks]