VARs and VECMs

Question 1

What is a VAR?

Answer 1

A system with more than one variable

It is a module that will capture interdependencies between multiple time series

It will also describe the dynamics which are common to these variables

Question 2

What is the structural form?

Answer 2

We move all the variables in time, t, to the LHS, and keep the lags and error terms on the RHS

Put into a matrix

Question 3

What is the reduced form?

Answer 3

Question 4

How do we represent the second set of shocks, v_1t and v_2t?

Answer 4

Question 5

How do we multiply the RHS by the inverse of the LHS matrix?

Answer 5

Question 6

How do we represent a VAR in MA form?

Answer 6

Question 7

What is an impulse response?

Answer 7

It shows us how a system reacts to a unit shock in a single time period

Question 8

How do we represent an impulse response?

Answer 8

Question 9

What does a variance decomposition do?

Answer 9

Identifies the contribution of each of the structural disturbances to overall variance of each of the variables in the VAR at different forecast horizons

Question 10

How can we derive the variance decomposition of the forecast error if structural errors are independent and serially uncorrelated?

Answer 10

Question 11

How can we interpret Supply and Demand shocks from a table?

Answer 11

Question 12

What assumptions do we make of a structural VAR when estimating the model?

Answer 12

Question 13

How do we estimate a VAR model?

Answer 13

Question 14

How do we find the variances of v₁, v₂ and the covariance between them?

Answer 14

Remember:

𝑣_1𝑡 = 𝜀_1t

𝑣_2𝑡 = 𝜀_2𝑡 − 𝑐₂₁𝜀_1t

Question 15

What is the generalisation of a higher order system (order 3) in the Cholesky decomposition?

Answer 15

Question 16

Why does the Cholesky decomposition permit the estimation of the VAR?

Answer 16

Question 17

If there are p variables in the VAR, how many sample moments do we need for estimation?

Answer 17

Question 18

What does Granger causality in a VAR imply?

Answer 18

Granger causality in a VAR implies a correlation between current values of one variable and the past values of other variables

Question 19

How do we identify unidirectional or bidirectional causality in terms of Granger causality?

Answer 19

Question 20

How do we determine if y Granger-causes x or vice versa?

Answer 20

All values of 𝛾_1p must = 0 to rej. null and conclude y Granger-causes x

All values of 𝛽_2p must = 0 to rej. null and conclude x Granger-causes y

Question 21

How do we represent the general form of a VAR in MA form (not a matrix)?

Answer 21

Question 22

Summary of the general forms of a VAR (structural and reduced)

Answer 22

Question 23

How do we represent the first or difference of a VAR?

Answer 23

Question 24

What is the problem with B having unit roots?

Answer 24

We cannot write the process in MA form

Question 25

What is the stability condition?

Answer 25

When the Eigenvalues are all within the unit circle

This is thanks to B having roots < 1