What's Vector Auto Regression (VAR)

 o VAR

Generally, VAR is considered as an extension of a single equation (ARDL) model which we will discuss later (in upcoming blogs).

VAR can be considered as the hybrid of the ARDL and the structured model (simultaneous equation models) and VAR is used profusely in Econometrics.

Its known to all that most of the econometric model are structural in nature (relationship between variable are determined by the economic theory).

There are many conditions that in which the economic theory won't be sufficient to determine the right model, i.e. the specification of the model should be based on the Econometric approach too. Now, there's a confusion about the correctness of the theory.

Say, the data, rather than the Econometricians specify the dynamic structure of the data. Let, the data determine what is the correct model. So, with this spirit, the VAR model was developed.

We will discuss clearly about the Simultaneous Equation Models (in upcoming blogs), now in the Simultaneous Equation Models, the classification of the endogenous and exogenous variables was arbitrary and identification is achieving by imposing "0" restrictions on the coefficients of the variables on the equation. These two decisions were subjective and this was criticized by "Sims".

According to Sims,. if there's two Simultaneity  between the variables they should be treated equally. There should not be distinction between endogenous and exogenous i.e. all the variables should be treated as endogenous and this spirit led "Sims" to develop a VAR  model.

In VAR thus, there's no distinction between the endogenous and exogenous variables (if included the model will will be biased).

A variable which is exogenous in one model is endogenous in the other:

In VAR model we have to specify two things (2 dimensions):

i) We have to select the variables supposed to be interacting with each other (m).

ii) Determine the largest number of the lags (to ensure that the entre relationships between these variables are captured into the model (p).

Say, that we consider the two variables, money supply and interest rates (Ms and r).

Now, in the VAR model Ms is related not only on the past values of the Ms but also on the past values of r. Similar case is with the "r" as well.

Now, we specify the VAR with 2 variables as :

Mst = alpha + Sum(j to k; j=1)beta j * Mt-j + Sum(j to k; j=1) gamma j * R t-j + U1t _________ eq (a)

Rt = alphaprime + Sum(j to k; j=1) theta j * Mt-j + Sum(j to k; j=1) lamda j * R t-j +U2t______ eq (b)

These two system of the equations are used in the context of the Granger Causality (will discuss later in coming blogs).

U1t and U2t are assumed to be uncorrelated and U1t and U2t are the impulses/innovations/shocks.

TO BE CONTD...

Aditya Pokhrel

MBA, MA Economics, MPA.