Question 1
Identify the FALSE or INCORRECT statements in the following extract. Provide a brief explanation of your answers.
A researcher is interested in the relation between the yield on 20-yearBritish Government securities or gilts (denoted IG in the following Eviewsoutput) and the discount rate on 3-month sterling Treasury bills (denoted ITB in the Eviews output), for the period April 2001 to July 2016. The monthly data is from www.bankofengland.co.uk.
Dependent Variable: IG
Method: Least Squares
Sample: 2001M04 2016M07
Included observations: 184
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Variable
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Coefficient
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Std. Error
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t-Statistic
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Prob.
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C
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3.395172
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0.070661
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48.04854
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0.0000
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ITB
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0.255711
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0.022067
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11.58781
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0.0000
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R-squared
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0.424556
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Adjusted R-squared
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0.421394
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S.E. of regression
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0.619406
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Sum squared resid
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69.82689
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Log likelihood
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-171.9444
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Mean dependent var
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4.020043
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S.D. dependent var
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0.814300
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Akaike info criterion
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1.890700
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Schwarz criterion
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1.925645
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Hannan-Quinn criter.
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1.904863
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C330 Econometric Principles and Data Analysis
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Session One 2017
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F-statistic
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134.2774
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Durbin-Watson stat
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0.097931
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Prob(F-statistic)
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0.000000
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The population regression equation is
IGt 3.395172 0.255711ITBt
where IGt is the yield on gilts at time t, and ITBt is the discount rate on Treasury bills at time t.
There appears to be a positive relationship between IGt and ITBt . The estimated slope coefficient is 0.255711. The mean value for ITBt in the Eviews output is 4.020043.
To test the hypothesis that the slope coefficient is zero, we can use a t-test. It is a two- variable model estimated using monthly data, so the appropriate degrees of freedom for this test are 10. The calculated t-statistic of 11.58781 and Prob. value of 0.0000 indicate we would not reject the hypothesis that the slope coefficient is equal to zero at the 0.05 significance level. Approximately 42.46% of the variation in IGt is not
explained by the model. A 95% confidence interval for the slope coefficient would not include zero. The total sum of squares is less than 69.82689. The model is linear in the parameters to be estimated.
Question 2
Consider the two-variable regression model for which the population regression equation can be written in the following form:
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Yi 1 2 Xi ui
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(1)
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where Yi and Xi are observable variables, 1
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and 2
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are unknown regression
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coefficients, and ui is an unobservable population disturbance term.
The corresponding ordinary least squares sample regression equation is given by:
where ˆ1 and ˆ2 are the estimators of the constant and the slope parameter respectively, and ei is the sample residual for the ith observation.
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(a)
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Specify the ordinary least squares estimation criterion.
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[5 marks]
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(b)Derive the ordinary least squares normal equations to estimate
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equation (1). Explain your answer.
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[10 marks]
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(c)Discuss the conditions under which the estimators ˆ1 and ˆ2
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obtained from the equations derived in 2(b) are BLUE.
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[10 marks]
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C330 Econometric Principles and Data Analysis
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Session One 2017
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Question 3
The tab-delimited text file C330_A1_S1_2017_Q3.txt contains weekly data on the stock price of Hasbro Inc., the US multinational toys, games and entertainment company (HAS), and the Standard & Poor’s 500 index (SP500) from 27 August 2012 to 22 August 2016, giving 209 observations (the share price and stock index are closing prices, in US dollars, source: uk.finance.yahoo.com). For reference, for observation 27/8/2012 HAS = 37.51 and SP500 = 1406.58. For 4/9/2012 HAS = 37.64 and SP500 = 1437.92. And for 22/8/2016 HAS = 80.72 and SP500 = 2182.64. Use a 5% significance level in your analysis.
(a)Obtain a scatter plot of the weekly log return on the Hasbro Inc. stock
ln HASt ln HASt 1
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against the weekly log return on the S&P 500 index for the
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complete sample, and comment on the plot.
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[10 marks]
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(b)Use Eviews to estimate the following model using ordinary least squares over the full sample, and submit your output as your answer:
ln HASt ln HASt 1 1 2 ln SP500t ln SP500t 1 ut
[10 marks]
(c)Comment on the estimated parameters, including the relationship between the variables and the size of the estimated coefficient ˆ2 .
[10 marks]
(d)(i) Test whether the parameter 2 is significantly different from zero.
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(ii) Test whether the parameter 2 is less than 1.
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[10 marks in total]
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(e)Explain what the value of R2 means in the context of the estimation of this model. Use the F-test to test whether the
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calculated R2
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you obtain in Part (b) is significantly different from
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zero.
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Derive the ordinary least squares normal equations to estimate equation (1). Explain your answer.