Econometrics

Question 1

What is a density function?

Answer 1

Denoted PDF. The probability of a variable taking on a specific value, x. f(x) = P(X=x)

Question 2

Conditional density

Answer 2

Assigns a density for the dependent variable, y, for each value of the explanatory variable, x. f(y|x) = f(y,x) / f(x)

Question 3

Stability of coefficients

Answer 3

Recursive estimation over the sample to see the development in the coefficient. Does it converge to a value?

Question 4

Time series

Answer 4

The realization of a stochastic process {Y_t; t€T}

Question 5

First order Markov process

Answer 5

The conditional density of Y_t given the entire past of y_t-1, y_t-2,…, depends only on y_t-1. f(y_t | y_t-2, y_t-1) = f(y_t | y_t-1)

Question 6

What is a distribution function?

Answer 6

Denoted CDF. The probability of a variable taking on a value lower than or equal to a specific value? Goes from 0 to 1. F(x) = P(X<=x)

Question 7

Law of large numbers

Answer 7

Consistency. Increasing the sample size (no. of observations) will give a more accurate estimate. Theta^ →^p Theta

Question 8

Unbiasedness

Answer 8

Take many samples, each with an estimated parameter, theta^. The average of the estimates will be equal to the true population parameter, theta, when the no. of samples approaches infinity.

Question 9

Autocovariance

Answer 9

Cov(Y_t, Y_t-j) =: E [(Y_t - E(Y_t)) (Y_t-j - E(Y_t-j))]

Question 10

Autocorrelation function (acf)

Answer 10

ζ_j,t =: Cov(Y_t, Y_t-j) / Var(Y_t)

Question 11

Final equation

Answer 11

When a variable of a dynamic system (VAR) is written in terms of its own lags and exogenous variables, we call that equation the final equation for the variable.

Question 12

Weakly stationarity

Answer 12

When the autocovariance does not depend on time itself, but only the timedifference, j, between the variables. Then the process is covariance stationary (weakly stationary).

Question 13

Stationary time series

Answer 13

The variance and autocovariance is time independent, and the autocovariances is symmetric forward and backwards.

Question 14

Stationary VAR

Answer 14

Global aysmptotically stable. All the eigenvalues from the companion form must lie within the unit circle, and the disturbances must be stationary (constant mean and covariance matrix).

Question 15

ADL/ARDL-model (Autoregressive distributed lag)

Answer 15

The conditional model of Y given X, from a VAR-model. Together with the marginal model of X from the VAR, it gives a regression representation of the VAR.

For a VAR(1):

Y_t = φ₀ + φ₁Y_t−1 + β₀X_t + β₁X_t−1 + ε_t

ADL(p,q), where p denotes no. of lags on y and q denotes no. of lags on x.

Question 16

Weak exogeneity

Answer 16

Weak exogeneity (WE) is the case where statistically efficient estimation and inference can be achieved by only considering the conditional model and not taking the rest of the system into account.

WE is defined relative to the parameters of interest.

Question 17

Strong exogeneity

Answer 17

X_t is strongly exogenous if X_t is weakly exogenous in the conditional model and Y_t is not Granger-causing X_t (the parameter on Y_t-1 in the marginal model of X_t is 0).

Question 18

Super exogeneity

Answer 18

X_t is super exogenous in the conditional model if X_t is weakly exogenous and the parameters of the conditional model are invariant with respect to structural breaks (interventions) in the marginal model of X_t.

Does not require strong exogeneity.

Question 19

ADL(1,1)

Answer 19

y_{t =} beta₀ + beta₁*y_t-1 + gamma₀*x_t + gamma₁*x_t-1 + u_t