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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 d
dU
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

What is the random effects estimation?

You keep a in the regression, and quantify the total variance that can be explained by A