Term 2 Flashcards by Jake Skelton

Discuss Simple and Multiple Regressions

A ~ represents a simple

A ^ represents multiple

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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

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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<b></b>

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What is bias equal to for B~1?

Bias(B~1)=B2D~1

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What is asymptotic theory?

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

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What is the CLT?

As a sample size increases, the sample becomes normally distributed

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What is the consistency of OLS?

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

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What is the normality of OLS?

As the sample size increases, the distribution becomes normal

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What are the consequences of heteroskedasticity?

OLS is unbiased,

Incorrect estimators therefore cannot use T and F tests

OLS no longer BLUE

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How do you estimate variance of a coefficient under heteroskedasticity?

Sum(x-Xbar)^U2/ Variance

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

They are worse than usual SE

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How can we detect heteroskedasticity?

Graphs
The Breusch-Pagan Test
White Test

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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

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How do you perform the white test?

Same as BP but with indicators

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How do you calculate the WLS?

Replace every coefficent by RootX

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What is the difference between CS and TS data?

TS data is ordered, thus is not randomlyy sampled

There is therefore correlation

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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

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What is lag distribution and how is it calculated

Plots the coefficents of each lagged variable on a graph

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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

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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

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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

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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

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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

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What is contemporaneous exogenity?

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

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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

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

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

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

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

How do you calculate the corr for weakly dependant data?

Coefficent of Yt-1 raised to time period in advance

What is strongly dependant data?

Weakly dependant does not occur Corr does not fall as time between observations grows

How do you calculate the corr of strongly dependant data?

Root(t/t+h)

What is the consequence of strongly dependant data?

Beta never converges to its true value as sample size increases

What is the spurious regression problem?

Running a regression with two or more random walks As they can coincide, R2 is large

What is the assumption of stationarity?

All joint distributions of TS data are constant over time

What assumptions are required for consistency of OLS?

For beta to be its true value, TS1-3

What assumptions are required for Normality?

For OLS to be normally distributed TS4-5

Define Serial Correlation?

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

How do you model serial correlation?

``` Autoregressive Models Order () Error correlated will all previous First Order Moving Average Error correlated with immediate previous ```

What is the effect of Serial Correlation

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

Under what circumstances does serial correlation invalidate R2?

IF explanatory variables have unit roots If the data is weakly dependant, okay

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

Same as CS

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?

How do you calculate | HAC errors?

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

What does large differences in errors and HAC imply?

Serial correlation is present

How can you test for serial correlation?

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

What does the test becomeif strictly exogenous?

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

What does the test become if contemporaneously exogenous?

Same as strict but will all eplanatory variables also tested

What is an alternative test method?

Larrange Muliplier LM=(n-p)R^2 Chi squared distribution

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)

What is the bounds test for positive autocorrelation?

H1:P>0 Reject H0 if d

dU Inconclusive if dL

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

How do you correct for serial correlation?

Create Feasible Generalized Least Squares

How do you calculate P for GLS?

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

Define endogenous variables?

Variables that are not correlated with the error term

How can endogeneity occur?

Omitted Variables - If the omitted variable is correlated | Measurment Errors - A mis measurment will cause it

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)

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

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)

Discribe this IV estimator?

Consistent but not unbiased Large Variance 1/rxz Correlation

What is Two Stage Least Squares?

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

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

What is a panel data set?

The same units are sampled in two or more time periods

What is the main benefit of panel data?

We can control for unobserved characteristics that do not change

What is heterogeneity bias?

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

How can we remove heterogeneity bias via Fixed Difference?

Take time period 2 away from time period one

What is the other advantage of panel data?

More data = more precise estimators

What is the fixed effects estimation?

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

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

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

What is the random effects estimation?

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