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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 2011Empirical EconomicsDate : 26 January 2011日期:2011.01.26Time : 9.30amTimeAllowed : 2 hours

Answer ALL questions from section Aand ANY TWO questions from section BMarks are indicated at the end of each subquestion in [ ]回答所有的问题,从部分A和部分B两题

Do not open or turn over this exam paper, or start to writeanything told to by the Invigilator. Starting to writebefore permitted to do so may be seen as an attempt to useUnfair Means.不要打开或关闭这项考试,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 QuestionA:必答题Q1. Consider a regression of the supply of a product (Yi) on its own prices (Xi) as followsYi=1+2Xi+ eii = 1 :::Nwhere eiis a randomly distributed error term for observation i.

a. Discuss the economic theory behind this model and list the OLS assumptions on errorterms ei. [5]

b. Derive the normal equations and the OLS estimatorsb1andb2: [10]b1andb2: [10]c. A supplier observed the data on quantities and prices as given in Table 1 below. Whatare the OLS estimatesb1andb2implied by these data?[15]Table 1: Data on Quantities and PricesQuantities (Yi) 5 3 7 9 6 4Prices (Xi) 7 5 8 10 8 5d. What are the variances of eiand Yi?

d. What are the variances of eiand Yi?

f. Determine the overall signi…cance of this model by F -test at a 5 percent level of sig-ni…cance. [Critical value of F for df(1,4) =7.71] [10]

g. What are the variances and standard errors ofb1andb2?

b1andb2? [10]h. Compute t-statistics and determine whether parametersb1andb2are statisticallysigni…cant at a 5 percent level of signi…cance. [Critical value of t for a 5% signi…cance for4 degrees of freedom is 2.776 (i.e. tcrit;0:05;4= 2:776) ] [10]i. What is the prediction of Y when X is 15?

j. What is the elasticity of supply evaluated at the mean values of Yiand Xi? [5]k. Reformulate the model to include the price of a related product in the model. What willhappen to this estimation if the two prices are exactly correlated ? [5]你会如何​​决定是否供应此产品,即夏,秋,冬,春四季变化?l. How would you decide whether the supply of this product varies by four seasons, namelySummer, Autumn, Winter and Spring? [5]

Section B: Answer Any Two Questions想出一个对某种产品的需求的多元回归模型,其中质量取决于产品的价格(X1 )和个人的收入(X2):

Q2. Consider a multiple regression model for the demand for a certain product, where thequantity (Yi) depends on price of the product (X1;i) and the income of individuals (X2;i) as:

Yi=0+1X1;i+2X2;i+ eii = 1 :::N

a. Provide a reasonable theoretical basis for the speci…cation of a demand function of thissort (e.g. consumer optimisation with Cobb-Douglas utility function). [10]b. Write normal equations to derive the OLS estimators of0;1and2. [10]c. Derive estimators of0;1and2: (hint: use deviation form and/or the Cramer’s rule).[10]d. Write the expression for the variance of the error term. [14]e. What is the covariance matrix of0;1and2? Write an expression for the variancesof0;1and2: [14]f. Determine the test statistics for signi…cance of each of0;1and2and to test thegeneral hypothesis that0= 0;1= 0;and2= 0: [14]g. What would happen to the OLS estimators derived above if X2;i= 5X1;ifor all i ? Whatcan be done to improve the validity of 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 statistical signi…cance of the revisedmodel? [14]

Q3. Consider the Gauss-Markov theorems for a linear regression of the demand for a normalgood (Yi) on its own prices (Xi) asYi=1+2Xi+ eii = 1 :::N

where eiis a 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 consistent.[20]d. Discuss the nature of the problem which arises when E(Xiei)6= 0 [16]e. Describe what happens to the OLS estimators of1and2when var(ei) =2i. [16]f. Analyse what happens to the OLS estimators of1and2when E(eiej)6= 0: . [16][26163] [Continued…]3Q4. A piece of research using the UK data aims to study whether the level of unemployment(Yi) relates to the level of the bene…t-claimant count (X1;i), numbers of stoppages (X2;i) andwork hours (X3;i) taking data from the Labour Force Survey for 19 years (N = 19) asfollowing:Yi=0+1X1;i+2X2;i+3X3;i+ "ii = 1 :::Nf. Consider estimates put forward by a researcher on the aggregate supply function for UKusing quarterly data from 1960:1 to 2006:1 provided in tables 3 to 6 above. Criticallyjustify which ones of these results stands to the scrutiny of Durbin-Watsonstatistics and other statistical tests. Is there evidence for an aggregatesupply function? [20]Note: For K =2 the relevant Durbin-Watson dLand dUstatistic at a 1 percent and 5 percentlevel of signi…cance are given Table 7 below.Table 7: Relevant Part of Durbin-Watson Table1% 5%dLdUdLdUN=150 1.598 1.651 1.706 1.760N=200 1.653 1.693 1.748 1.789


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