Term 2 Flashcards
Discuss Simple and Multiple Regressions
A ~ represents a simple
A ^ represents multiple
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
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>
What is bias equal to for B~1?
Bias(B~1)=B2D~1
What is asymptotic theory?
As N gets larger, the probability that Z is different from its mean falls
What is the CLT?
As a sample size increases, the sample becomes normally distributed
What is the consistency of OLS?
As sample size increases, a coefficient tends to its true value
What is the normality of OLS?
As the sample size increases, the distribution becomes normal
What are the consequences of heteroskedasticity?
OLS is unbiased,
Incorrect estimators therefore cannot use T and F tests
OLS no longer BLUE
How do you estimate variance of a coefficient under heteroskedasticity?
Sum(x-Xbar)^U2/ Variance
Why is it not a good idea to only compute robust SE?
They are worse than usual SE
How can we detect heteroskedasticity?
Graphs
The Breusch-Pagan Test
White Test
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
How do you perform the white test?
Same as BP but with indicators
How do you calculate the WLS?
Replace every coefficent by RootX
What is the difference between CS and TS data?
TS data is ordered, thus is not randomlyy sampled
There is therefore correlation
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
What is lag distribution and how is it calculated
Plots the coefficents of each lagged variable on a graph
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
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
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
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
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
What is contemporaneous exogenity?
A weaker assumption of TS3, that assumes no conditional mean for only variables within the same time period
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<dl>dU
Inconclusive if dL</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
