G023 - Problem set 1 - December 10, 2007
1. Suppose that you estimate the model Yt = Yt
1 +"t
by OLS and that "t is an AR(1) process.
(a) Write the expression for the OLS estimator b for a sample of size T
(b) Show that the OLS estimator b is inconsistent

University College London
Department of Economics
G023: Econometric Theory and Methods
Answers to Exercise 4
1. Heteroskedasticity.
(a) The formula given is just (X X)1 X y for the case in which X and
y are vectors. The variance of the OLS estimator is gi

University College London
Department of Economics
G023: Econometric Theory and Methods
Answers to Exercise 3
1. Prepare and examine the data.
(a) The survey is designed to be representative of Great Britain. However because of non-response it tends to hav

University College London
Department of Economics
G023: Econometric Theory and Methods
Exercise 1: Sketch answers
1. This problem characterizes the expected value as the best predictor in the
sense of minimizing the mean squared error. Note that the value

University College London
Department of Economics
G023: Econometric Theory and Methods
Exercise 2: Sketch answers
1. (a) In each case the coecients after the unit changes are denoted by
2
a , a , a .
2
i. a = , a = 1000, a = 2 .
2
ii. a = /1000, a = , a =

University College London
Department of Economics
MC3: Econometric Theory and Methods
Exercise 5
20/11/2006
The data used in this exercise are the same as used in Exercise 3. Details
are given there. They are records from a UK household survey conducted i

University College London
Department of Economics
MC3: Econometric Theory and Methods
Exercise 3
21.10.2005
The data used in these exercises are records from a UK household survey
conducted in 1998. The data are also available via a link at the course web

University College London
Department of Economics
MC3: Econometric Theory and Methods
Exercise 4
23/10/2005
1. Heteroskedasticity. Consider the model
yi = xi + "i
in which yi and xi are scalar, i = 1; : : : ; n, with xi > 0 for all i, and
E["i jxi ] = 0,

University College London
Department of Economics
MC3: Econometric Theory and Methods
Exercise 1
6.10.2006
1. Optimal prediction. You have to predict the value taken by a random
variable, X, which has a known distribution. Let xp denote the prediction
you

University College London
Department of Economics
MC3: Econometric Theory and Methods
Exercise 2
6.10.2005
1. Interpreting and formulating linear models. An econometric model species the relationship between household expenditure on housing ( per
year) an