Econometrics

Question 1

Gauss-Markov Conditons

Answer 1

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

Question 2

Six OLS Assumptions

Answer 2

1. Linear in parameters
2. Full rank. X is an n*k matrix of rank k.
3. Conditional expectation. E [ui | x] = 0
4. Homoskedascity and nonautocorrelation. E [U U’ | X] = varianceU * Identity Matrix
5. Fixed or random regressors
6. Normality: Errors are normally distributed.

Question 3

Effect of OLS Assumptions

Answer 3

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?)

Question 4

Wald Test

Answer 4

Question 5

Diffrentiate c’Ac

Answer 5

(A + A’ ) c

Question 6

Other Variance eqaution NEED FOR variance of estimand

Answer 6

E ( X - MU ) ^ 2

Question 7

Consistency Assumptions

Answer 7

Write the maths all down

C1) Linear

C2) Independence

C3) Rank

Question 8

Weak Stationarity conditions

Answer 8

Question 9

Mean Lag formula

Answer 9

B is top fraction, C is bottom fraction Mean Lag = B’(1)/B(1) - C’(1)/C(1) (Plug in 1)

Question 10

Spurious Regression Beta

Answer 10

Converges to random variable

Question 11

T-Test under spurious regression

Answer 11

t-ratio significance test does not possess a limiting distribution, but actually diverges as the sample size T -> ∞.”

Question 12

R^2 under spurious regression

Answer 12

R^2 has a non-degenerate limiting distribution as T ! ∞.”

Question 13

How to do Whites’ Test

Answer 13

1. Estimate the model by OLS and compute the OLS residuals
2. Regress the squared residual on all regressors, their squared terms and all their interactions
3. Test the null (homoscedasticity) hypothesis: H0 : α2 =α3 =γ2 =γ3 =δ=0

Question 14

White Test Test Statistic

Answer 14

nR^2, which is distributed according to chi-squared statistic, with p-1 as the level. X^2, sub-text p-1

Question 15

Testing format

Answer 15

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.

Question 16

What to do with heteroskedascity

Answer 16

Heteroscedasticity and autocorrelation-robust (HAC) standard errors

Question 17

Ergodic Condition

Answer 17

Sum of the covariances is less than infinity

Question 18

Autocorrelation formula

Answer 18

Question 19

How to perform a Confidence Interval

Answer 19

1. State the distributtion of the sample mean
2. State the confidence interval rule
3. Define terms in the confidence interval
4. Compute the Standard Deviation, which is equal to 1/n * sum of the covariances
   - Summation within a summation trick
   - Difference of two squares trick
5. Sub it back into the confidence interval rule. Remember to take the root of everything.

Question 20

Autocovariance for an AR(1)

Answer 20

Question 21

Memorize Hessian Matrix

Answer 21

Question 22

Probit Formula

Answer 22

Question 23

Logit Formula

Answer 23

Question 24

Reproduce an IV

Answer 24

DO it

Question 25

Is the linear model XB or BX

Answer 25

XB

Dude with two tongues stuck out

Question 26

What are the matrix dimensions of the linear model

Answer 26

Y : n by 1 (vertical)

X: n by k

beta: n by 1 (vertical)
mu: n by 1 (vertical

Question 27

Total multiplier

Answer 27

Plug a 1 into your lag term for your combined polynomial

Question 28

Impact Multiplier

Answer 28

Same as total, but plug in 0

Question 29

Types of Iterative formulae

Answer 29

My one: Newton-Raphson

Others: Gauss-Newton, high-low, gradient descent, Levenberg-Marquardt (the most effective).

Question 30

Time Series Distribution of the Sample mean due to CLT

Answer 30