Econometrics

Question 1

Student’s t-test for correlation coefficient

Answer 1

t = r*sqrt(n - 2) / sqrt(1 - r^2)

Test is applicable only if the two populations are normally distributed

Question 2

Formula for slope coefficient in a univariate regression

Answer 2

cov(X,Y) / std(Y)

Question 3

List Gauss-Markov assumptions

Answer 3

OLS is BLUE under:

1) Correct specification (linear model)
2) Spherical errors (constant variance and zero correlation terms)
3) Exogeneity of independent variables
4) Sample data matrix has full rank

Question 4

What if residuals are not normally distributed?

Answer 4

This does not lead to biased estimation of the coefficients

However, t-tests might not work on small samples

Question 5

What would heteroscedasticity lead to?

Answer 5

Heteroscedasticity does not lead to biased estimation of the coefficients
Incorrect measurement of standard errors of the coefficients

Question 6

Student’s t-test for regression coefficients

Answer 6

Two-tailed test: b_X / SE(X)

Degrees of freedom: n - k - 1

Question 7

(M)ANOVA parameters

Answer 7

SST = RSS + SSE
SST = var(Y), RSS = var(Y_est), SSE = sum((Y -Y_est)^2)
MSR = RSS / k
MSE = SSE / (n - k - 1)
Degrees of freedom for total = n - 1
F-test = MSR / MSE (H0 - all coefficients equals zero, test is rejected if F > F_crit - one-way test!)

Question 8

R_2 and R_2_adj

Answer 8

R_2_adj = 1 - (1 - R_2)*(n - 1)/(n - k - 1)

Question 9

Testing for heteroscedasticity

Answer 9

Breusch-Pagan test for conditional heteroscedasticity
BP = n * R_2 (regression of squared residuals on an independent variable). Test is Chi-square, one-way, k degrees of freeedom

Question 10

Correction for heteroscedasticity

Answer 10

White SEs - usually higher than normal ones

Question 11

Serial correlations - outcomes

Answer 11

In a cross-section setting positive serial correlation leads to artificially low SEs, but does not lead to biased estimation of the coefficients
In a time-series setting serial correlation may make parameters estimated inconsistent

Question 12

Durbin - Watson statistics

Answer 12

DW = sum((Resid_t - Resid_t-1)^2)/sum((Resid_t)^2) = 2(1 - r) for large sample size
Serial correlation exists if DW significantly differs from 2

Question 13

Correction for serial correlations

Answer 13

Hansen method to adjust SEs

Question 14

Assumptions of AR models

Answer 14

Covariance stationarity:

1) Constant and finite expected value (mean-reversion level is calculated by fitting Y_t = Y_t-1 and solving for Y_t)
2) Constant and finite variance of Y
3) Constant and finite covariance of Y_t and T_t-1

Question 15

Test for serial correlation of AR models

Answer 15

Special type of t-test: t = corr(Resid_t, Resid_t-1)*sqrt(T)

Two-tail test with T-2 degrees of freedom

Question 16

Test for unit-roots

Answer 16

Dickey - Fuller test:

Y_t - Y_t-1 = b0 + g * Y_t-1, H0: g = (b1 - 1) equals zero.

Question 17

When a regression of two time series on each other is correct?

Answer 17

1) If both X and Y and covariance stationary

2) If both X and Y are cointegrated unit-roots

Question 18

Chow test

Answer 18

Test for structural difference in two subsamples

F(k, n - 2k) = (RSS_full - RSS_1 - RSS_2) /(RSS_1 + RSS_2) * (n - 2k)/k