QUANTITATIVE ECONOMICS

Project
Using UK time series data, which is available in the CSO databank NAVIDATA, estimate
the aggregate consumption function. In doing this you will use the Stata package and
NAVIDATA data for years 1972-1995 inclusive.
1 Data exploratory and Labels l
y = consumers¡¦ expenditure (¢G million 1990 prices and defined in CSO, CCBH)
x2 = personal disposable income (¢G million in 1990 prices, CECO)
x3 = interest rates (Treasury Bill yield %, AJRP)
(Before running the regression in Stata, first transform the variables by dividing y and x2 by
10000. Y and X2 in the regression will thus be in units of ¢G10,000 million, i.e.
Y = 3 3
2
2 and X x
10000
x
, X
10000
y
ƒ­ ƒ­
Provide supporting theoretical arguments for the inclusion of variables described above and
any data exploratory analysis you consider useful.
2 Using Stata and data from 1972 to 1990, estimate the following models
Y = a1 + b1X2 + u (1)
Y = a2 + b2X3 + u (2)
a) Discuss the fit of the models.
b) Test the significance of a1, b1, a2, b2 using t test at 5% significance level ( for each test in
this report, indicate clearly The null hypothesis and the alternative hypothesis, the
distribution under the null hypothesis of the statistic used, the critical and acceptance
regions, the decision taken and why).
c) What is the marginal propensity to consume? Does it agree with the theory? State the
appropriate hypothesis and test it at 5% significance level.
3 Use Stata and data from 1972 to 1990 to estimate
Y = b1 + b2X2 + b3X3 +u (3)
Also:
a) Test at 5% significance level the hypothesis H0: 0 95 2 b ƒ­ . against HI: 0 95 2 b ƒ¬ . using a
t-test.
b) Calculate yourself a 95% confidence interval for 3 b .
c) Your output will include (i) the F-statistic and (ii) Residual sum of squares. Interpret these
numbers.
d) Print the estimated variance-covariance matrix of the coefficients. Explain.
e) Test the significance of b1, b2, b3 using p-values
ECO 2008
3
f) Rerun the regression adding a time trend. Let b4 be the parameter of the time trend.
g) Discuss the fit of the models. Which is the best model and why?
h) Test at 5% significance level the hypothesis H0: b3 = b4 = 0 against the alternative that at least one parameter is ¡Ú 0. (indicate clearly the critical and acceptance areas)
4 Use the model with the time trend which you have estimated in the previous section (3) to forecast consumption levels for the years 1991-1995.
a) Compare the forecasts with the actuals.
5 Estimate the relationship in (3) using the full sample in a log linear form, with and without a
time trend. Discuss the results.
6 Do you think any other significant variables are missing from your consumption equation according to standard consumption theory? Estimate using what you consider to be a more comprehensive formulation of the consumption function. Give reasons for the inclusion of additional variables and discuss the economic and econometric results. Note: any additional data needed for your project should be found by yourself.
7 Provide a working do file in an Annex.
The database, NAVIDATA, is accessible from the computers in the computer laboratories and those in the Seamus Heaney Library. Students must use exclusively the Stata econometric package, which is available on computers in the computer labs and in the Seamus Heaney and Main libraries.
Notes on accessing the NAVIDATA database, and using the Stata econometric package, are included in this package. Use of these computer facilities is also required in tutorials for the module. A handout is included giving brief notes on the use of logarithms in estimation, the retail price index and the inflation rate, and calculating the long run implication of dynamic econometric estimates, subjects which sometimes cause difficulty for students undertaking the project.