Econometrics Flashcards
Gauss-Markov Conditons
Expected errors given each X is 0. Variance of errors given each X is the same Errors are uncorrelated. E [uiuj | x1,x2,…xn] = 0
Six OLS Assumptions
- Linear in parameters
- Full rank. X is an n*k matrix of rank k.
- Conditional expectation. E [ui | x] = 0
- Homoskedascity and nonautocorrelation. E [U U’ | X] = varianceU * Identity Matrix
- Fixed or random regressors
- Normality: Errors are normally distributed.
Effect of OLS Assumptions
1) allows the beta to exist. 2) and 3) allow for unbiasedness. 4) and 5) mean the standard errors are valid. 6) allows for exact inference in finite samples. (without 6 we can still perform inference with large samples right?)
Wald Test
Diffrentiate c’Ac
(A + A’ ) c
Other Variance eqaution NEED FOR variance of estimand
E ( X - MU ) ^ 2
Consistency Assumptions
Write the maths all down
C1) Linear
C2) Independence
C3) Rank
Weak Stationarity conditions
Mean Lag formula
B is top fraction, C is bottom fraction Mean Lag = B’(1)/B(1) - C’(1)/C(1) (Plug in 1)
Spurious Regression Beta
Converges to random variable
T-Test under spurious regression
t-ratio significance test does not possess a limiting distribution, but actually diverges as the sample size T -> ∞.”
R^2 under spurious regression
R^2 has a non-degenerate limiting distribution as T ! ∞.”
How to do Whites’ Test
- Estimate the model by OLS and compute the OLS residuals
- Regress the squared residual on all regressors, their squared terms and all their interactions
- Test the null (homoscedasticity) hypothesis: H0 : α2 =α3 =γ2 =γ3 =δ=0
White Test Test Statistic
nR^2, which is distributed according to chi-squared statistic, with p-1 as the level. X^2, sub-text p-1
Testing format
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.
What to do with heteroskedascity
Heteroscedasticity and autocorrelation-robust (HAC) standard errors
Ergodic Condition
Sum of the covariances is less than infinity
Autocorrelation formula
How to perform a Confidence Interval
- State the distributtion of the sample mean
- State the confidence interval rule
- Define terms in the confidence interval
- Compute the Standard Deviation, which is equal to 1/n * sum of the covariances
- Summation within a summation trick
- Difference of two squares trick - Sub it back into the confidence interval rule. Remember to take the root of everything.
Autocovariance for an AR(1)
Memorize Hessian Matrix
Probit Formula
Logit Formula
Reproduce an IV
DO it
Is the linear model XB or BX
XB
Dude with two tongues stuck out
What are the matrix dimensions of the linear model
Y : n by 1 (vertical)
X: n by k
beta: n by 1 (vertical)
mu: n by 1 (vertical
Total multiplier
Plug a 1 into your lag term for your combined polynomial
Impact Multiplier
Same as total, but plug in 0
Types of Iterative formulae
My one: Newton-Raphson
Others: Gauss-Newton, high-low, gradient descent, Levenberg-Marquardt (the most effective).
Time Series Distribution of the Sample mean due to CLT
