Question

I'm confused on the Var model and its applications, along with the impulse-response that goes along with the Var model

Answer 1

Vector autoregression (VAR) is a stochastic process model used to capture the linear interdependencies among multiple time series. VAR models generalize the univariate autoregressive model (AR model) by allowing for more than one evolving variable. All variables in a VAR enter the model in the same way: each variable has an equation explaining its evolution based on its own lagged values, the lagged values of the other model variables, and an error term.

Applications :

1. VAR models as providing a theory-free method to estimate economic relationships

2. VAR models are also increasingly used in health research for automatic analyses

Impulse response analysis:

It is an important step in econometric analyes, which employ vector autoregressive models. Their main purpose is to describe the evolution of a model’s variables in reaction to a shock in one or more variables. This feature allows to trace the transmission of a single shock within an otherwise noisy system of equations and, thus, makes them very useful tools in the assessment of economic policies. This post provides an introduction to the concept and interpretation of impulse response functions as they are commonly used in the VAR literature.

Since all variables in a VAR model depend on each other, individual coefficient estimates only provide limited information on the reaction of the system to a shock. In order to get a better picture of the model’s dynamic behaviour, impulse responses (IR) are used. The departure point of every impluse reponse function for a linear VAR model is its moving average (MA) representation, which is also the forecast error impulse response (FEIR) function. Mathematically, the FEIR Φi for the ith period after the shock is obtained by

Φi=∑j=1iΦj−1Aj, i=1,2,...

with Φ0=IK and Aj=0 for j>p, where K is the number of endogenous variables and p is the lag order of the VAR model.