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1

Discuss Simple and Multiple Regressions

A ~ represents a simple
A ^ represents multiple

2

What is the simple relationship between B~1 which does not control for X2 and B^1 which does (Bias)

B~1=B^1+B^2d~1

3

What are the two cases of B~ and B^?

If x2's effect on Y is positive, x1 and x2 are positive correlated
B~1>B^1

If x1 and x2 are negatively correlated
B~1

4

What is bias equal to for B~1?

Bias(B~1)=B2D~1

5

What is asymptotic theory?

As N gets larger, the probability that Z is different from its mean falls

6

What is the CLT?

As a sample size increases, the sample becomes normally distributed

7

What is the consistency of OLS?

As sample size increases, a coefficient tends to its true value

8

What is the normality of OLS?

As the sample size increases, the distribution becomes normal

9

What are the consequences of heteroskedasticity?

OLS is unbiased,

Incorrect estimators therefore cannot use T and F tests

OLS no longer BLUE

10

How do you estimate variance of a coefficient under heteroskedasticity?

Sum(x-Xbar)^U2/ Variance

11

Why is it not a good idea to only compute robust SE?

They are worse than usual SE

12

How can we detect heteroskedasticity?

Graphs
The Breusch-Pagan Test
White Test

13

How do you perform the Breusch-Pagan Test?

Estimate the Regression, Square the residuals
Regress U^2 using explanatory variables, F test for joint significance

14

How do you perform the white test?

Same as BP but with indicators

15

How do you calculate the WLS?

Replace every coefficent by RootX

16

What is the difference between CS and TS data?

TS data is ordered, thus is not randomlyy sampled

There is therefore correlation

17

What are the types of TS data models?

Static: Same time period

Finite Distributed Lag (FDL): Y can be affected by upto Q periods in the past

18

What is lag distribution and how is it calculated

Plots the coefficents of each lagged variable on a graph

19

What is the impact propensity? What occurs if log form?

The coefficent of Z in the current time period - immediate change

Short run instantaneous elasticity

20

What is the long run propensity? What occurs if log form?

The sum of all lag coefficents

Tells us what happens if Z permanently increases

Called long run elasticity

21

What is an autoregressive model? What does its order determine?

A model where past Y's influence current Y's

Order is number of lags

22

What assumptions are required for finite sample OLS to be unbiased? (1-3)

TS1 - Linear in Paramaters

TS2 - No perfect collinearity

TS3 - Errors conditional mean is zero

These assumptions allow OLS to be unbiased

23

What assumptions are required for finite sample OLS to be unbiased? (4-6)

TS4- Homoscedaticity (Variance does not depend on X or change over time

TS5- No serial correlation (errors are not correlated)

TS6 - Normality

24

What is contemporaneous exogenity?

A weaker assumption of TS3, that assumes no conditional mean for only variables within the same time period

25

What are the three types of correlaton?

Explanatory variables over time
Violates TS2

Explanatory variables and errors
Violates TS3 and bais

Errors over time
Violates TS5

26

How do you calculate variance of a coefficent in a TS model?

Variance(B) = Var/SST(1-R2)

27

What is the problem associated with TS data and R2

If their is a high trend within the data, R2 will be higher than it should be

28

What is weakly dependant data?

The condition that we impose on TS data to ensure CLT and LLN holds

Correlation between observations gets smaller as time between grows

29

How do you calculate the corr for weakly dependant data?

Coefficent of Yt-1 raised to time period in advance

30

What is strongly dependant data?

Weakly dependant does not occur

Corr does not fall as time between observations grows