经济计量学练习题(全英文)

ECONOMETRIC METHODS (U20451)

ASSIGNMENT, FEBRUARY 2014

An Excel file has been uploaded on the Moodle site for the unit, which is entitled ‘Assignment Data’. This file contains annual data from 1994 to 2012 on three variables:

Y = purchases of vehicles in the UK (constant prices);

X = UK real household disposable income;

Z = an EU measure of consumer confidence for the UK.

Please copy the data from the Excel file into an EViews workfile.

Descriptive Element (10 marks)

Produce a line graph of each of the time series. Using no more than 200 words, describe the behaviour of each of the variables over the nineteen-year period.

Two-Variable Linear Regression Model (20 marks)

There is presented below a population regression function:

Y t = B0 + B1X t + u t, t = 1994, 1995, ………, 2012.

B0 and B1 are population parameters. u t denotes a random disturbance term.

Assume that E[u t] = 0, t = 1994, 1995, ………, 2012.

Proceed to provide interpretations of the population parameters.

Apply Ordinary Least Squares estimation to the population regression function.

Indicate the point estimates of the two parameters.

Proceed to produce a 95 per cent confidence interval for B1, explaining the manner of its construction.

Adopting two different approaches (i.e., consulting the statistical table and using the probability value), perform a test of null hypothesis, Ho: B1= 0, against the alternative hypothesis, Ha: B1≠ 0.

The validity of the confidence interval and the test of the hypothesis rests partly on the disturbance terms being normally distributed.

Adopting two different approaches (i.e., consulting the statistical table and using the probability value), perform a suitable test in order to assess whether or not the disturbance terms are normally distributed.

Three-Variable Linear Regression Model (25 marks)

There is presented below a three-variable population regression function:

Y = B0 + B1X t + B2Z t + u t, t = 1994, 1995, ………, 2012.

(B2 is a population parameter.)

Assuming that E[u t] = 0, t = 1994, 1995, ………, 2012, provide an interpretation of each of the population parameters.

Apply to the regression equation Ordinary Least Squares estimation.

Adopting two different approaches (i.e., consulting the statistical table and using the probability value), perform a test of the joint hypothesis, Ho: B1= 0, B2= 0, against the alternative hypothesis, Ha: at least one of B1≠ 0, B2≠ 0

With respect to the estimated versions of the two- and three-variable regression functions, compare the values of each of the following statistics:

- The residual sum of squares;

- The coefficient of determination;

- The standard error of the regression;

- The adjusted R-squared statistic.

Account for the change in the value of each of the statistics in moving from the two- to the three-variable regression equation.

Three-Variable Log-Linear Regression Model (20 marks)

Alternative specification

log.(Y t) = B0 + B1log.(X t) + B2Z t + u t, t = 1994, 1995, ………, 2012.

Explain why a logarithmic transformation was not applied to the variable, Z.

Provide an interpretation of each of B1 and B2.

Apply to the logarithmic model Ordinary Least Squares estimation.

In terms of the fit of the sample data on Y, how does the three-variable log-linear model compare with the three-variable linear specification?

An Extension of the Three-Variable Linear Regression Model (15 marks)

Consider, once again, the three-variable linear regression equation:

Y t = B0 + B1X t + B2Z t + u t, t = 1994, 1995, ………, 2012.

The previous Labour Government implemented a car scrappage scheme in 2009 that was intended to encourage the purchase of new cars. The suggestion has been made that this policy had the effect of redistributing expenditure on vehicles, specifically, making this higher than it would otherwise have been in 2009 but lower than it would otherwise have been in 2010.

Construct two dichotomous/dummy variables to capture these effects and add them to the above model as explanatory variables.

Estimate the extended model using Ordinary Least Squares. On the basis of the estimation output that is produced by EViews, is there statistical evidence to support the contention that a redistribution of vehicle purchases occurred?

Limitations of the Regression Models (10 marks)

On the basis of your knowledge of the factors that determine household expenditure on durable goods, suggest some further explanatory variables that possibly should have entered this analysis.

For the purpose of undertaking this assignment, students are permitted to work either individually or in the form of a pair. If two students are officially working together then please ensure to show both of the student numbers.

Given the quantitative nature of the assignment then no word limit is applicable.

Submission Date: 25th April 2014

Robert Gausden, February 2014