Flashcards in Term 2 Deck (69):

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

31

## How do you calculate the corr of strongly dependant data?

### Root(t/t+h)

32

## What is the consequence of strongly dependant data?

### Beta never converges to its true value as sample size increases

33

## What is the spurious regression problem?

###
Running a regression with two or more random walks

As they can coincide, R2 is large

34

## What is the assumption of stationarity?

### All joint distributions of TS data are constant over time

35

## What assumptions are required for consistency of OLS?

### For beta to be its true value, TS1-3

36

## What assumptions are required for Normality?

###
For OLS to be normally distributed

TS4-5

37

## Define Serial Correlation?

###
A correlation of the error term with other error terms

Positive - Error does not cross enough

Negative - Crosses too much

38

## How do you model serial correlation?

###
Autoregressive Models

Order ()

Error correlated will all previous

First Order Moving Average

Error correlated with immediate previous

39

## What is the effect of Serial Correlation

###
Does not Effect Bias

Tests Statistics are incorrect

OLS is no longer BLUE

40

## Under what circumstances does serial correlation invalidate R2?

###
IF explanatory variables have unit roots

If the data is weakly dependant, okay

41

## What is the method for treating heteroskedasticity in TS data without serial correlation?

### Same as CS

42

## What are HAC? How do you treat serial correlation?

###
Heteroskedasticity an autocorrelation consistent errors

Allow the error to be correlated only two periods in the past

This creates the HAC?

43

##
How do you calculate

HAC errors?

### Se(B1) = ROOT [ SumWU+ Sum Sum WtWsUtUs

44

## What does large differences in errors and HAC imply?

### Serial correlation is present

45

## How can you test for serial correlation?

###
Create a model that allows for serial correlation and compare

H0:P=0

46

## What does the test becomeif strictly exogenous?

### A test to see that the error is not dependant on the next two x's

47

## What does the test become if contemporaneously exogenous?

### Same as strict but will all eplanatory variables also tested

48

## What is an alternative test method?

###
Larrange Muliplier

LM=(n-p)R^2

Chi squared distribution

49

## What is the Durbin Watson Statistic

###
A test for serial correlation

d=Sum(Ut-ut-1)^2 / Sum Ut^2

Related to P as =2(1-P)

50

## What is the bounds test for positive autocorrelation?

###
H1:P>0

Reject H0 if ddU

Inconclusive if dL

Inconclusive if dL

51

## What is the bounds test for negative autocorrelation

###
H1:P<0

Reject H0 if d>4-dL

Do not Reject if d<4-dU

Inconclusive if 4-dU

52

## How do you correct for serial correlation?

### Create Feasible Generalized Least Squares

53

## How do you calculate P for GLS?

### Sum( UtUt-1) / Sum Ut-1^2

54

## Define endogenous variables?

### Variables that are not correlated with the error term

55

## How can endogeneity occur?

###
Omitted Variables - If the omitted variable is correlated

Measurment Errors - A mis measurment will cause it

56

## How can you fix endogeneity?

###
Add control varaibles, in the hope it becomes exogenous

Find one Instrument Variable (IV) for the endogenous explanatory variables (EEV)

57

## What is an instrumental variable?

###
A variable that is correlated with an endogenous explanatory varaible

If must satisfy

Cov(Z,U)=0

Cov(Z,X)=!0

58

## How do you get a variiable that satisfys the above?

###
Take Z's cov with both sides

As Cov(Z,U)=0

B1=Cov(Z,Y)/Cov(Z,X)

Where Cov=(x-xbar)(y-ybar)

59

## Discribe this IV estimator?

###
Consistent but not unbiased

Large Variance

1/rxz

Correlation

60

## What is Two Stage Least Squares?

### If we have more IV than necessary, becomes a two stage least squares

61

## How do you test whether a variable is exogenous?

###
Add AY2 into the regression

Regress Y2 on all other coefficents

If the error term is correlated with the original error, perfect collinearity

62

## What is a panel data set?

### The same units are sampled in two or more time periods

63

## What is the main benefit of panel data?

### We can control for unobserved characteristics that do not change

64

## What is heterogeneity bias?

###
Where unobserved effects cause bias over time?

Cov(Xit,a)=!0

A is unobserved constant effect

65

## How can we remove heterogeneity bias via Fixed Difference?

### Take time period 2 away from time period one

66

## What is the other advantage of panel data?

### More data = more precise estimators

67

## What is the fixed effects estimation?

### Average an equation by T and take this away from the original, A is thus removed

68

## If there is a difference between FD and FE what does this indicate?

### No Strict Exogenity (The unobserved effect is uncorrelated with X)

69