帮写ECON3013: Applied Econometrics (Semester 2, 2023/2024) –– Assignment 1代做Java程序

ECON3013: Applied Econometrics (Semester 2, 2023/2024) -- Assignment 1

Submitted to the TA or teacher in hard copy before 5:00pm, Friday, 22 March 2024

Using AI tools in doing this Assignment is strongly prohibited!!!

This assignment paper has a total of 100 marks, and contributes 25% to the course’s overall assessment.

CLEARLY write down your answers/solutions to each question with your Name and Student Number on some clean paper.

Necessary steps/formulas/calculations/arguments MUST be included in your answers as a good practice.

Keep FOUR (4) decimals for all calculations/results for relatively higher accuracy, unless clearly unnecessary.

For Q8 and Q9, do and ONLY do the REQUIRED part based on your Student Number’s being even or odd.

The t-table as appeared in the lecture notes IS included at the end of this assignment paper for your easy use.

Economy	CO2 per capita	Urbanization
Afghanistan	0.277459	25.56191
Armenia	2.279488	63.9
Australia	14.77265	87.31742
Azerbaijan	3.430466	54.9
Bangladesh	0.508222	38.177
Bhutan	1.382237	42.316
Brunei Darussalam	21.70213	78.25
Cambodia	1.153169	24.232
China, People's Republic of	7.750536	63.89027
Fiji	1.153466	57.247
Georgia	2.75471	59.23241
India	1.62184	34.3
Indonesia	2.08434	56.641
Japan	8.058622	91.782
Kazakhstan	11.29504	58.84898
Kiribati	0.476398	55.6
Korea, Republic of	10.99003	81.414
Kyrgyz Republic	1.3919	34.2
Lao People's Democratic Republic	2.652316	36.29
Malaysia	7.55437	75.1
Maldives	2.608418	40.669
Marshall Islands	2	77.794
Mongolia	6.230794	69
Myanmar	0.617924	31.141
Nauru	3.541488	100
Nepal	0.508668	62.36
New Zealand	6.160799	84
Pakistan	0.835353	36.75427
Palau	8.988636	78.9
Papua New Guinea	0.572634	13.345
Philippines	1.22411	47.408
Samoa	1.022657	18.75403
Singapore	7.686684	100
Solomon Islands	0.321471	24.67
Sri Lanka	0.996683	18.713
Tajikistan	0.991487	26.3
Thailand	3.819351	54.78681
Timor -Leste	0.338354	31.3
Tonga	1.177782	21.5186
Tuvalu	0.624785	64.014
Uzbekistan	3.376304	50.56481
Vanuatu	0.404333	25.16202
Viet Nam	3.641251	36.82282
Source: Asian Development Bank

The table above contains information of 43 Asian economies on their year 2020 CO2  emissions (‘000 metric tonnes per capita) and degree of urbanization, measured by urban population as a percentage of total population. The following sample sums have been calculated from the sample for convenience, with y being CO2  emissions,x being urbanization and i the country index:

∑i(4)1 xi  = 2233.17735,  ∑i(4)1 yi  = 160.97935,  ∑i(4)1 xi(2) = 139792.3132,  ∑i(4)1 yi(2) = 1452.88189,

∑i(4)1 xiyi  = 11230.30771.

Part A. Basic Statistical Assessment (30 marks)

Q1 (3 marks): Is this a cross-sectional data set, a time series data set or a panel data set? What is the reason for considering CO2 emissions on a per capita basis instead of the absolute levels (‘000 metric tonnes)?

Q2 (10 marks): Find the sample means or averages (x andy), the sample standard deviations (sx  and sy) of the two (random) variables x andy. Find also the sample covariance sxy  and the sample correlation coefficient rxy  between the two variables.

Q3 (17 marks): The Chief Economist of the World Bank claims that the average CO2 emissions per capita in Asia should  be 7.00 (‘000 metric tonnes per head), about the same level in the EU counterparts. The intuition is that while the Asian  economies tend to be less economically developed, have fewer industrial activities and hence less emission comparatively, their bioenergy adoption is also lower which inhibits CO2  reduction. To verify his claim, you decided to perform a test  on this hypothesis using the conventional 5% significance level. Write down the detailed test procedures including the  type of test, the null and alternative hypothesis, the relevant test statistics and other information needed to run the test.  What is your conclusion? Will your conclusion differ if a more demanding 1% significance level is used instead? Show  your work carefully and clearly. Based on your findings, do you think equal contribution by all countries in emission  reduction as advocated by Western countries a fair and appropriate policy? Briefly explain.

Part B. Test Relationships (70 marks)

This Part relates to a simple linear regression model estimated using the above sample data (with the results in Part A)

and the ordinary least squares (OLS) method:  yi  =β(̂)0  +β(̂)1 xi  + ûi =̂(y)i  + ûi, wherê(y)i  =β(̂)0  +β(̂)1 xi  is the model-fitted or

forecast values of yi  with respect to xi  and ûi is the corresponding residual for economy i (i = 1, 2, … , 43).

Q4 (12 marks): Find the sample-estimated values ofβ(̂)1  andβ(̂)0 , and explain their (practical) meanings. Do they make

sense to you?

Q5 (18 marks): Find the coefficient of determination (R2) and the standard error of regression (̂(σ)). and briefly explain their (practical) meanings. Do you think they are small (low) or large (high)? [Hint: make your judgment by referencing to some benchmark to get a meaningful picture of their magnitudes.]

Q6 (12 marks): Find the standard error ofβ(̂)1  and briefly explain its (practical) meaning. Is this standard error small or large? What is the standard error ofβ(̂)0 ?

Q7 (3 marks): In terms of model fitness, do you think we can get better results by regressing urbanization (x) on CO2 emissions (y) instead?i.e. using urbanization as dependent variable and CO2  emissions as independent variable.

If the last digit of your Student Number is even, do the following Q8-even and Q9-even. If it is is odd, do the following Q8-odd and Q9-odd.

Q8-even (5 marks): For Indonesia, find the model-fitted CO2 emissions and briefly comment on the actual emissions as compare to this.

Q8-odd (5 marks): For New Zealand, find the model-fitted CO2 emissions and briefly comment on the actual emissions as compare to this.

Q9-even (20 marks): Suppose an alternative simple linear regression exercise is performed with CO2 emissions replaced

by de-meaned CO2 emissions with everything else remain the same,i.e. yi(*) = a0  + a1xi+ εi  and  yi(*) = yi  —  . Using

the properties of the summation operator ∑, show that = 0. Find the estimated values of  and . Are they different

from  and  you estimated before. What can you say about the correlation between yi(*) and xi , and the R2 of this new

model? Show your step clearly and show the calculated values wherever possible.

Q9-odd (20 marks): Suppose an alternative simple linear regression exercise is performed with urbanization replaced

by de-meaned urbanization with everything else remain the same,i.e. yi   = a0  + a1xi(*) + εi  and  xi(*) = xi  —  . Using the

properties of the summation operator ∑, show that  = 0. Find the estimated values of   and . Are they different

from  and  you estimated before. What can you say about the correlation between xi(*) and yi , and the R2  of this new

model? Show your step clearly and show the calculated values wherever possible.