Economic Project - Statistics and Econometrics

(1) Per capita expenditure a specific food or food group (FX)

(2) Unemployment Rates for a period of 12 years (UR)

You will be told your years and food choices. You must then assemble the data,

Sources: Data can be obtained via ONS for example in the Annual Abstract of Statistics.

The specific data for FX can be found on a spreadsheet in this page

https://www.gov.uk/government/statistical-data-sets/family-food-datasets

which will be placed in Blackboard.

1. Present your data in a table showing the names of the variables. Make sure the full definitions and sources of each variable are given.

[5 marks]

2. The first equation to be estimated is :

FX i = b0 + b1 URi +ui

Where u is a disturbance term and the i subscript represents year.

Answer these questions:

(i) In terms of economic theory what sign would you expect to find for the coefficients in the regression equation ?

[5 marks]

(ii) Explain why we are using per capita data for food rather than the total value as the dependent variable?

[5 marks]

(iii) Why is there a constant term in the equation with no variable attached?

[5 marks]

(iv) Why do these types of equations have a ‘u’ term ?

[5 marks]

3. Estimate equation (1) by OLS and present the results in a suitable table

(i) Comment on the result for the coefficient on the UR variable.

[5 marks]

(ii) Comment on the R squared statistic.

[5 marks]

(iii) Is the estimated value of b0 positive or negative? Does it matter for the reliability of your estimates for b1 whether b0 is positive or negative?

[5 marks]

(iv) Examine the residuals of your estimated equation to determine whether any of your years might be considered an outlier in the regression.

[5 marks]

(v) Calculate the elasticity of FX with respect to UR at the sample means and comment on it?

[5 marks]

4. You are now required to estimate the following form of the model using OLS:

FX i = b0 + b1 URi + b2 UR i 2 +ui

where u is a classical disturbance term.

Carry out the following hypothesis tests

(i) b0=0 against the two sided alternative at the 10% level for both equations

[5 marks]

(ii) b1=0 against the two sided alternative at the 5 % level for both equations

[5 marks]

(iii) b1=b2=0 against the one sided alternative at the 5% level for the second equation

[5 marks]

(iv) Establish whether your second equation has one of the following shapes:

[5 marks]

(a) U-shaped

(b) Inverted U-shape

(c) Non-linear upward sloping

(d) Non-linear downward sloping

(e) Linear upward sloping

(f) Linear downward sloping

(g) None of the above

5. Having estimated both equations, compare their results and consider whether equation 2 is an improvement over equation 1.

[5 marks]

6. Economists would think that the model you have estimated so far is not satisfactory in terms of the independent variables. You should now change this model by introducing up to a maximum of two additional variables. Explain why these variables have been chosen and give full sources and definitions for them. Present and interpret the regression results for this new model.

[5 marks]

7. You should now write a short report of 450-600 words. This should briefly summarize your findings- marks will be given for further exploration of your model involving the provision of new estimates and suggestions for improvement of the model you have estimated.

[20 marks]

References

Department for Environment, Food & Rural Affairs. (2013). Statistical data set: Family Food Data Set. Available: https://www.gov.uk/government/statistical-data-sets/family-food-datasets. Last accessed 13th March 2014.

Office of National Statistics (2003) Annual Abstract Statitics. London: Pelgrave Macmillan. Pg 96.

Office of National Statistics (2010). Annual Abstract Statitics . London: Pelgrave Macmillan. Pg 101.