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THE UNIVERSITY OF HULLThe Business School
赫尔大学的商学院
Level 6 Examination
六年级考试
January 2012
Empirical Economics
实证经济学
Date: 24thJanuary 2012
Time: 1.30 pmTime
Allowed: 2 hours
Answer ALL parts of Question 1 (Section A)Answer any TWO questions from Section BAll questions are equally weighted. At the end of each sub-question, the break down of marks is shown in [ ]. http://www.ukassignment.org/ygkczy/ As far as practicable, explain your derivations and results using logic based on relevant economic theory.
回答所有的问题1（A部分）回答任何节球问题的两个问题是相同的权重。结束时的各子问题，打破马克在[]中所示。在切实可行的情况，说明你的使用根据相关经济理论的逻辑推导和结果。
Do not open or turn over this exam paper, or start to write anything until told to by the Invigilator. Starting to write before permitted to do may be seen as an attempt to use Unfair Means.
不要打开或关闭这项考试的纸张，或直到被告知监考员，开始写东西。开始写之前允许这样做可能被视为试图使用不正当手段。
Section A: Compulsory
A部分：强制
Question Q1. Global population reached 7 billion on October 31, 2011. As a researcher you would like to test a hypothesis that the population growth rate (Yi) depends on the life expectancy of individuals (Xi) as follows:
问题Q1。 2011年10月31日，全球人口达到7亿美元。作为一名研究人员，你想测试一个假设，即人口增长率（百分比）取决于个人的预期寿命（十一）如下：
a. Discuss the economic logic behind this model and list the OLS assumptions on error terms ei.
一。讨论这种模式背后的经济逻辑，并列出了OLS假设误差项EI。
b. Find the OLS estimators of 1and 2 that minimise the sum of squared errors.[10]
二。查找OLS估计量的1和2，最大限度地减少误差平方和。[10]
c. The cross section data in 2005 across 199 countries was summarised as given below.
C。如下面给出的，在2005年横跨199个国家的横截面数据进行了总结。
d. What are total sum square (TSS), regression sum square (RSS) and error sum square(ESS) in this model? What are the variances of Yiand ei? [10]
e. Determine the overall signi…cance of this model by an F -test at a 5 percent level ofsigni…cance. [Critical value of F for df(1,197)'3.84] [10]
f. What is the estimate of R2? How does it relate to the F-statistic? [10]
g. Estimate the variances and standard errors ofb1andb2. [10]
h. Computing relevant t-statistics, determine whether parametersb1andb2are statisti-cally signi…cant at a 5 percent level of signi…cance. [Critical value of t for a 5% level ofsigni…cance for 197 degrees of freedom is about 1.96 (i.e. t0:05;197'1:96) ]How do variancesof these parameters a¤ect their t-statistics? [10]
i. What is the prediction of population growth rate (Y ) for a country in which the lifeexpectancy (X) is estimated to be equal to 80 years? What would this imply for thefertility rate (children per woman of child bearing age)? [5]
j. Reformulate the model to include the ratio of health sector spending to GDP (H) as anew variable in the model. What will happen to this estimation if the life expectancyand the ratio of health sector spendings are inexactly correlated? Illustrate on thebasis of the variance in ation factor. [10][26163] [Continued...]2
k. Modify the model appropriately including relevant dummy variables to investigatewhether the population growth rate varies by four continents; namely Asia, Africa,Europe and America. How would you determine the signi…cance of these dummy vari-ables? [5]
Section B: Answer Any Two Questions Q2. Consider a multiple regression model in which level of per capita output of a country(Yi) depends on energy consumption per capita (X1;i) and e￠ ciency of energy use (X2;i) as:
B部分：选答两题Q2。考虑多元回归模型中，一个国家的人均产出（沂）水平取决于人均能源消费量（X1）和E¢作为能源使用效率的（X2）：
a. Provide a reasonable theoretical basis for the speci…cation of a per capita output func-tion of this sort (e.g. producer optimisation or a supply function). [10]
b. Write normal equations to derive the OLS estimators of0;1and2. [10]
c. Derive estimators of0;1and2: (hint: use matrix inverse on the deviation formand/or Cramer’s rule). [10]
d. Write the expression for the variance of the error term and explain when this wouldtend to be smaller. [14]
e. What is the covariance matrix of0;1and2? Write an expression for the variancesof0;1and2. [14]
f. Determine the test statistic that helps to i) determine the statistical signi…cance of eachestimated parameterb0;b1andb2and ii) test the overall signi…cance of the model,i.e.0= 0;1= 0;and2= 0. Explain brie y. [14]
g. What would happen to the OLS estimators derived above if the energy consumption percapita (X1;i) and e￠ ciency of energy use (X2;i) are perfectly correlated as X2;i= 5X1;ifor all i ? What can be done to improve the validity of the model in such a situation?[14]
h. Assume that instead of estimating Yi=0+1X1;i+2X2;i+ eia researcher estimatedYi=0+1X1;i+ ei. How could you determine the omitted variable bias and thestatistical signi…cance of the revised model? [Hint: F-test for restriction]. [14]3
Q3. Consider the Gauss-Markov theorems for a linear regression of the demand for a normalgood (Yi) on its own prices (Xi) as:Yi=1+2Xi+ eii = 1 :::N
(2)where eiis randomly distributed white noise.a. Prove that the OLS estimators of1and2are linear in Yi. [16]b. Show that the OLS estimators of1and2are unbiased. [16]
c. Verify that the OLS estimators of1and2have minimum variance and are consistentcompared to any other linear and unbiased estimator, b. [20]
d. Discuss the nature of the problem which arises when E(Xiei)6= 0: What can be doneto solve this problem? [16]
e. Describe what happens to the OLS estimators of1and2when the error variancesare not constant, i.e. var(ei) =2i. [16]
f. Analyse what happens to the OLS estimators of1and2when E(eiej)6= 0:
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