QE Flashcards
F-Test Formula
Careful on your definiton of K
[n-k-1/q] [TSS-RSS/TSS]
^all unrestricted model.
RSSrest = TSSunrest
k is number of regressors, q is restrictions
Speciffy it as the homoskedastic only F-test
Confidence Interval Values
90% - 1.645
95% - 1.96
99% - 2.58
Standard Error Forumla
sigma/sqrt(n)
Variance formulae
Var(X)=E[(X-mu )^2]
= E[X^2] - E[X]^2
Covariance formulae
E(XY) - E(X)E(Y)
= E(X-E(X))(Y-E(Y)
R^2 Formula
1 - (SSR/SST)
Adjusted R^2
1 - [(n-1)/(n-k-1)] [SSR/SST]
LATE Assumptions
MIRE
like quagMIRE
LATE Definition
Average causal effect on COMPLIERS
TOT
Treatment effect On the Treated
WEIGHTED average of the causal effect on COMPLIERS and the causal effect on ALWAYS TAKERS
TOU
Treatment effect On the Untreated
WEIGHTED average of the causal effect on COMPLIERS and the causal effect on NEVER TAKERS
Bloom Result
If no never takers, LATE = TOT
5 Threats to internal validity
HIPCA
Individualistic treatment response (each person’s outcome depends only on his own treatment), contamination, Hawthorne effect, placebo, attrition
4 Threats to external validity
S A S S
Sampling, spillover effects, assignment differences, short durations (surrogate outcomes).
Type 1 Error
Incorrect rejection of a true null.
False positive.
Type 2 Error
Incorrectly accepting a false null.
False negative
IV Assumptions
Exogeneity of instrument (good as randomly assigned and exclusuion), and relevance
3 in total for QE
Testing IV independence assumption
Not directly testable.
- Distribution of covariates
- Baseline information
Derive Omitted Variable Bias formula
SRBeta = LRBeta + OVB
OVB = gamma (Cov(X,OmittedVar)/Var(OmittedVar))
OVB only does not equal to zero if
1. omitted var is correlated with outcome
2. omitted var is correlated with other instrument.
Autocovariance
Cov ( Yt , Yt-1 )
What is the summation equation?
Autocorrelation
Cov ( Yt , Yt-j ) / var (Yt)
Dickey-Fuller Test
Test if unit root is present.
I.e. H0: Beta1 = 0
WHAT DOES THIS DO
Chow Test
Testing for structural breaks
How is this done?
Spurious regression
Regression that provides evidence of a non-existent relationship between two variables. I.e. two random walks regressed on each other.
Spurious regression
Regression that provides evidence of a non-existent relationship between two variables. I.e. two random walks regressed on each other.
Granger causality test
Testing if additional variables in a time series have predictive power.
Use an F-test with H0 that BetaX = 0.
Problems with having a unit root/having trends
1 AR coeffcients are strongly biased towards zero. This leads to poor forecasts.
2 Some t-statistics do not have a standard normal distribution, even in large samples.
3 If y and x are both random walks then they can look related even when they are not - this gives us a spurious regression.
ATT Equation
write it
ATE Equation
write it
what to say in a t test
State what you are testing and say ceteris paribus
Outline H0 and H1
Under H0, define t-stat, and say that it is approximated N(0,1) by the CLT, assuming random (iid) and large (n observations) sample).
Decision rule.
Do the test.
Answer, and ceteris paribus.
IV Equations
Structural: D on Y
Reduced: Z on Y
First: Z on D
IV Estimator
equation
Contamination
People who arent assinged to treatment get it
RSMFE Equation
?
P Value
Is the chance of making a type 1 error when taking p value as your significance level
