Econometrics 2

Question 1

Time-Series Data

Answer 1

Data across a period of time

e.g. GDP over 20 years

Question 2

Cross-Section Data

Answer 2

Specific time period, unit of observation is varied e.g. worker

Question 3

Panel (longitudinal data)

Answer 3

Varies across both time and a unit e.g. countries and time

Question 4

Regression analysis

Answer 4

Study of relationship between dependent variable and explanatory variable(s)

Estimating and/or predicting the (population) mean or average value of the dependent variable on the basis of the known or fixed values of the explanatory variables

Question 5

Population Regression Line (PRL)

Answer 5

Gives mean value of dependent variable corresponding to each value of explanatory variable (X)

Line that passes through the conditional mean of Y

Question 6

Ordinary Least Squares (OLS)

Answer 6

Method for estimating the unknown parameters in a linear regression model

b1 and b2 should be chosen such that the residual sum of squares (RSS) are minimised

Question 7

Linear functional form

Answer 7

Yi = B1 + B2 Xi + ui
B2 measures the unit change in Y for a 1 unit
change in X

Question 8

Log-lin model

Answer 8

ln Yi = B1 + B2 Xi + ui
B2 measures the relative change in Y for an
absolute change in X

Question 9

Lin-log model

Answer 9

Yi = B1 + B2 ln Xi + ui
B2 measures the absolute change in Y for a
relative change in X

Question 10

Log-linear model

Answer 10

lnYi = B1 + B2 ln Xi + ui
B2 measures the elasticity of Y with respect to X, that is the percentage change in Y for a
given percentage change in X

Question 11

Properties of the regression line

Answer 11

1. The regression line passes through the
   sample means of X and Y
2. The mean value of the estimated Y
   equals the mean value of the actual Y
3. The mean value of the residuals ei is
   zero
4. The residuals ei are uncorrelated with
   the predicted Yi
5. The residuals ei are uncorrelated with Xi

Question 12

What is TSS

Answer 12

TSS = total sum of squares
ESS = explained sum of squares
RSS = residual sum of squares

TSS = ESS + RSS

Question 13

What is r squared?

Answer 13

r squared is the (sample) coefficient of determination, it measures the proportion or percentage of the total variation in Y explained by the regression model

R-squared is a statistical measure of how close the data are to the fitted regression line

Question 14

What are the properties of r squared?

Answer 14

1. It is a non-negative quantity

2. Its limits are: 0 < r squared < 1

Question 15

Gauss-Markov theorem

Answer 15

Given the assumptions of the classical linear
regression model, the OLS estimators, in the class of unbiased linear estimators, have minimum variance; that is, they are BLUE

Question 16

OLS estimators b1 and b2 are said to the best
linear unbiased estimators (BLUE) of B1 and
B2 if they are…

Answer 16

1. Linear
2. Unbiased
3. Minimum Variance

Question 17

Homoscedasticity

Answer 17

if all random variables in the sequence or vector have the same finite variance

also known as homogeneity of variance

Question 18

Why use adjusted R squared

Answer 18

The problem with the multiple coefficient of

determination, R squared is that it increases as the number of explanatory variables (k) increases

Question 19

What is a dummy variable

Answer 19

Qualitative rather than quantitative in nature
i.e. variable with no natural scale of measurement
Examples: Gender, race, religion, education level
binary i.e. equal to 1 or zero

Question 20

What are the two different approaches to comparing two regressions?

Answer 20

Chow Test

Dummy Variable Approach

Question 21

What are the advantages of dummy variable approach over chow test
for structural stability?

Answer 21

1. Only need to estimate one regression in the dummy variable approach
2. The dummy variable approach more flexible.
3. Chow test does not tell us which of the coefficients have changed over time
4. Pooling (under the dummy variable approach) increases the degrees of freedom

Question 22

Points to note about dummy (explanatory) variables

Answer 22

1. If a qualitative variable has m categories introduce m-1 dummy variables
   Because of the dummy variable trap
2. The assignment of 1 and zero to the two categories is arbitrary. The important point is to know which way round they have been assigned
3. The group or category that is assigned the value zero is the base, control or omitted category.
4. The coefficient attached to the dummy variable D can be called the differential intercept coefficient

Question 23

Classical (multiple) Linear Regression Model

assumptions

Answer 23

Assumption 1: E(ui | X2i , X3i … Xki) = 0
Assumption 2: cov(ui , uj) = 0, i not equal to j
Assumption 3: var(ui) = sigma squared
Assumption 4: cov(ui , X2i) = cov(ui , X3i) = … = cov(ui , Xki) =0
Assumption 5: The regression model is correctly specified
Assumption 6: ui ~ N (0 , sigma squared)
Assumption 7: No exact linear relationship between the explanatory variables

Question 24

How do we judge a model to be “good”?

Answer 24

Parsimony
Identifiability
Goodness of fit
Theoretical consistency
Predictive power

Question 25

Detection of heteroscedasticity

Answer 25

(a) Informal methods:
Graphical method
(b) Formal methods:
Park test
Glejser test
Breusch-Pagan test
Goldfeld-Quandt test
White’s general heteroscedasticity test

Question 26

Tests of specification errors

Answer 26

(a) Detecting the presence of unnecessary variables:
Individual (t-test) and joint (F-test) tests of significance
(b) Tests for omitted variables and incorrect functional forms:
Examination of residuals
Ramsey RESET test
Lagrange Multiplier (LM) test