Econ B S3

Question 1

What does it mean if CML4 is violated?

Answer 1

Perfect multicollinearity therefore OLS estimator can’t be computed; problems also arise when variables are close to PC

Question 2

What does it mean if CML5 is violated?

Answer 2

Heteroscedasticity (HTSC) and autocorrelation (AC); OLS is no longer efficient but remains consistent

Question 3

What are the 3 distinct assumptions for CLM1?

Answer 3

1) The random term error enters in additively
2) The model is linear in regression coefficients (partial derivatives functions of only known constants and regressors)
3) The population regression coefficients beta(j) are unknown constants that don’t vary across observations

Question 4

What does “The population regression coefficients beta(j) are unknown constants that don’t vary across observations” mean for cross sectional and time-series data?

Answer 4

For cross sectional data, it means there aren’t any sub groups of the population that have different marginal effects on the dependent variable

For time-series data, it means the effect of the x variable x(k) on y is constant in time

Question 5

What does CLM6 allow us to do if it holds?

Answer 5

Confidence intervals/hypothesis testing using a t distribution (SEE NOTES)

Question 6

See

Answer 6

Read pages 8&9 of note, see and learn ‘assuming x is random’ and then try proving beta1 is consistent

Question 7

Why is CLM2 normally violated? What does this mean?

Answer 7

In economics, it is normally violated since x is random (stochastic) since the explanatory variables aren’t chosen and inputted.
Means that assuming x and u are independent is too strong, but uncorrelated is not enough (u may be uncorrelated to x but correlated to x^2) *

Question 8

What does * lead to?

Answer 8

New assumption: Zero Conditional Mean Assumption/Mean Independence: the expected value of u doesn’t depend on the value of x:
E(u|x)=0
tf variable x is now ‘exogenous’

Question 9

What does the Zero Conditional Mean Assumption/Mean Independence assumption imply? (2)

Answer 9

1) Unconditional mean of the population values of u equals 0: E(u|x)=0 tf E(u)=0

2) x and u have 0 covariance (uncorrelated):
E(u|x)=0 -> Cov(x,u)=0

Question 10

Why does E(u|x)=0 -> E(u)=0?

Answer 10

Law of iterated expectations states E(E(u|x))=E(u)

Therefore: E(u)=E(E(u|x))=E(0)=0

Question 11

What does E(u|x)=0 -> Cov(x,u)=0 lead to? Prove that E(u|x)=0 -> Cov(x,u)=0.

Answer 11

It means no linear correlation, but also that x and u are mean independent (tf x is strictly exogenous to u). Proof is page 10 of notes

Question 12

Why do we need a new set of assumptions?

Answer 12

Since x is now random, we need new assumptions with everything conditional on x

Question 13

Which 2 assumptions don’t change?

Answer 13

CLM1 and CLM 4

Question 14

What is MLR2?

Answer 14

The error u has an expected value of zero, given any values of the IVs

E(u|x1,x2,…,xk)=0

Question 15

What is MLR4?

Answer 15

The errors are conditionally homoskedastic:
V(u|x1,…,xk)=σ^2

and conditionally uncorrelated:
Cov(ui,uj|x)=0 for all i not equal to j

Question 16

What is MLR5?

Answer 16

The population error u, conditionally on x, is normally distributed with zero mean and variance σ^2

u|x~N(0,σ^2)

Question 17

What is the second new assumption?

Answer 17

the sample observations are statistically independent

Question 18

What does the 2nd new assumption imply? (2)

Answer 18

1) Error terms u(i) and u(j) are also statistically independent
cov(u(i),u(s)|x)=0 for all i not equal to s

2) Dependent variables y(i) and y(j) are also statistically independent
cov(y(i),y(s)|x)=0 for all i not equal to s

Question 19

Why is random sampling assumption usually suitable for cross sectional models but rarely for time-series data?

Answer 19

see notes

Question 20

2 points about cross sectional data?

Answer 20

• sample of observations taken at a single point/period in time
• individual observations have no natural ordering

Question 21

3 points about time series data?

Answer 21

• sample observations taken on one or more variables over successive periods
• individual observations have natural ordering; a chronological one
• often exhibit a high degree of time dependence, tf cannot be assumed to be generated by random sampling

Question 22

What is a stochastic/time series process?

Answer 22

A sequence of RVs indexed by time

Question 23

Why do we think of TS data as an outcome of random variables?

Answer 23

When we collect TS data we obtain 1 possible outcome of the stochastic process, since we can’t go back and realize it again with different historical conditions. BUT if conditions had been different, we’d obtain a different result to the process. Tf the set of all possible realizations is equivalent to the population

Question 24

What is a static model?

Answer 24

When a model models a contemporaneous relationship between x and y (*happening in the same time period tf change in x immediately causes change in y)

Question 25

Which assumptions are suitable for time series models?

Answer 25

MLR1,3&4

Question 26

finish notes and make flashcards on them (3.5)

Answer 26

now

Question 27

What is omitted variable bias?

Answer 27

When we omit a variable that belongs in the true/population model (underspecifying the model) -> OLS estimator being biased (See example in my notes)

Question 28

When a variable is omitted, say in a simple regression model, the incorrect model error will be:
v=β2x2+u
Show that this will result in failure of mean independence.
What happens if we estimate β(hat)1?

Answer 28

See my notes p3 2nd side at bottom

Question 29

Learn lecture 4 proof!!!

Answer 29

in my notes pages 4&5