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EDA > Term 2 > Flashcards

Term 2 Flashcards

1
Q

Discuss Simple and Multiple Regressions

A

A ~ represents a simple

A ^ represents multiple

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2
Q

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

A

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

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3
Q

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

A

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<b></b>

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4
Q

What is bias equal to for B~1?

A

Bias(B~1)=B2D~1

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5
Q

What is asymptotic theory?

A

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

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6
Q

What is the CLT?

A

As a sample size increases, the sample becomes normally distributed

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7
Q

What is the consistency of OLS?

A

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

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8
Q

What is the normality of OLS?

A

As the sample size increases, the distribution becomes normal

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9
Q

What are the consequences of heteroskedasticity?

A

OLS is unbiased,

Incorrect estimators therefore cannot use T and F tests

OLS no longer BLUE

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10
Q

How do you estimate variance of a coefficient under heteroskedasticity?

A

Sum(x-Xbar)^U2/ Variance

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11
Q

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

A

They are worse than usual SE

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12
Q

How can we detect heteroskedasticity?

A

Graphs
The Breusch-Pagan Test
White Test

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13
Q

How do you perform the Breusch-Pagan Test?

A

Estimate the Regression, Square the residuals

Regress U^2 using explanatory variables, F test for joint significance

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14
Q

How do you perform the white test?

A

Same as BP but with indicators

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15
Q

How do you calculate the WLS?

A

Replace every coefficent by RootX

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16
Q

What is the difference between CS and TS data?

A

TS data is ordered, thus is not randomlyy sampled

There is therefore correlation

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17
Q

What are the types of TS data models?

A

Static: Same time period

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

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18
Q

What is lag distribution and how is it calculated

A

Plots the coefficents of each lagged variable on a graph

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19
Q

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

A

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

Short run instantaneous elasticity

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20
Q

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

A

The sum of all lag coefficents

Tells us what happens if Z permanently increases

Called long run elasticity

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21
Q

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

A

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

Order is number of lags

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22
Q

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

A

TS1 - Linear in Paramaters

TS2 - No perfect collinearity

TS3 - Errors conditional mean is zero

These assumptions allow OLS to be unbiased

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23
Q

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

A

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

TS5- No serial correlation (errors are not correlated)

TS6 - Normality

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24
Q

What is contemporaneous exogenity?

A

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

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25
Q

What are the three types of correlaton?

A

Explanatory variables over time
Violates TS2

Explanatory variables and errors
Violates TS3 and bais

Errors over time
Violates TS5

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26
Q

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

A

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

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27
Q

What is the problem associated with TS data and R2

A

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

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28
Q

What is weakly dependant data?

A

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

Correlation between observations gets smaller as time between grows

29
Q

How do you calculate the corr for weakly dependant data?

A

Coefficent of Yt-1 raised to time period in advance

30
Q

What is strongly dependant data?

A

Weakly dependant does not occur

Corr does not fall as time between observations grows

31
Q

How do you calculate the corr of strongly dependant data?

A

Root(t/t+h)

32
Q

What is the consequence of strongly dependant data?

A

Beta never converges to its true value as sample size increases

33
Q

What is the spurious regression problem?

A

Running a regression with two or more random walks

As they can coincide, R2 is large

34
Q

What is the assumption of stationarity?

A

All joint distributions of TS data are constant over time

35
Q

What assumptions are required for consistency of OLS?

A

For beta to be its true value, TS1-3

36
Q

What assumptions are required for Normality?

A

For OLS to be normally distributed

TS4-5

37
Q

Define Serial Correlation?

A

A correlation of the error term with other error terms
Positive - Error does not cross enough
Negative - Crosses too much

38
Q

How do you model serial correlation?

A 
Autoregressive Models
Order () 
Error correlated will all previous
First Order Moving Average
Error correlated with immediate previous
39
Q

What is the effect of Serial Correlation

A

Does not Effect Bias
Tests Statistics are incorrect
OLS is no longer BLUE

40
Q

Under what circumstances does serial correlation invalidate R2?

A

IF explanatory variables have unit roots

If the data is weakly dependant, okay

41
Q

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

A

Same as CS

42
Q

What are HAC? How do you treat serial correlation?

A

Heteroskedasticity an autocorrelation consistent errors

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

This creates the HAC?

43
Q

How do you calculate

HAC errors?

A

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

44
Q

What does large differences in errors and HAC imply?

A

Serial correlation is present

45
Q

How can you test for serial correlation?

A

Create a model that allows for serial correlation and compare
H0:P=0

46
Q

What does the test becomeif strictly exogenous?

A

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

47
Q

What does the test become if contemporaneously exogenous?

A

Same as strict but will all eplanatory variables also tested

48
Q

What is an alternative test method?

A

Larrange Muliplier

LM=(n-p)R^2

Chi squared distribution

49
Q

What is the Durbin Watson Statistic

A

A test for serial correlation

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

Related to P as =2(1-P)

50
Q

What is the bounds test for positive autocorrelation?

A

H1:P>0

Reject H0 if d<dl>dU
Inconclusive if dL</dl>

51
Q

What is the bounds test for negative autocorrelation

A

H1:P<0

Reject H0 if d>4-dL
Do not Reject if d<4-dU
Inconclusive if 4-dU

52
Q

How do you correct for serial correlation?

A

Create Feasible Generalized Least Squares

53
Q

How do you calculate P for GLS?

A

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

54
Q

Define endogenous variables?

A

Variables that are not correlated with the error term

55
Q

How can endogeneity occur?

A

Omitted Variables - If the omitted variable is correlated

Measurment Errors - A mis measurment will cause it

56
Q

How can you fix endogeneity?

A

Add control varaibles, in the hope it becomes exogenous

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

57
Q

What is an instrumental variable?

A

A variable that is correlated with an endogenous explanatory varaible

If must satisfy
Cov(Z,U)=0
Cov(Z,X)=!0

58
Q

How do you get a variiable that satisfys the above?

A 
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
Q

Discribe this IV estimator?

A

Consistent but not unbiased
Large Variance
1/rxz
Correlation

60
Q

What is Two Stage Least Squares?

A

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

61
Q

How do you test whether a variable is exogenous?

A

Add AY2 into the regression
Regress Y2 on all other coefficents

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

62
Q

What is a panel data set?

A

The same units are sampled in two or more time periods

63
Q

What is the main benefit of panel data?

A

We can control for unobserved characteristics that do not change

64
Q

What is heterogeneity bias?

A

Where unobserved effects cause bias over time?
Cov(Xit,a)=!0
A is unobserved constant effect

65
Q

How can we remove heterogeneity bias via Fixed Difference?

A

Take time period 2 away from time period one

66
Q

What is the other advantage of panel data?

A

More data = more precise estimators

67
Q

What is the fixed effects estimation?

A

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

68
Q

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

A

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

69
Q

What is the random effects estimation?

A

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

EDA (2 decks)

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