# How to estimate Vector Autoregression (VAR) modelsPart 1

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## What is a vector autoregression (VAR) model?

VAR stands for vector autoregression, and was proposed by Christopher Sims in his paper “Macroeconomics and Reality (1980)”. VAR models generalize univariate models as it allows for multiple endogenous variables. Recall that on previous tutorials, we have estimated univariate models. Now it’s time to estimate multivariate models. We will allow for more endogenous variables in the model.  Nowadays, VAR models are widely used in the economics field.

## vector autoregression formalities

VAR models allow for the interaction between diverse variables and are called endogenous variables.  Each endogenous variable is explained by its own past lags, the past lags of the other variables in the model and a serially uncorrelated error term.

#### Example: Bivariate var (x,y)

Let’s go through an example. Let’s suppose we have two variables (x) and (y) and, only one lag: Bivariate VAR(1). Observe that inside brackets there is a (1). It is indicating that the model only incorporates one lag in each variable. We would write the model the following way:

$y_t=a_1+b_{11}y_{t-1}+b_{12}x_{t-1}+u_{t}$
$x_t=a_2+b_{21}y_{t-1}+b_{22}x_{t-1}+v_{t}$

As we can see $y_t$ is explained by its own lag $(y_{t-1})$, the lag of the other variable in the model $(x_{t-1})$ and a serially uncorrelated error term $(u_t),(v_t)$.

## How to estimate var models in stata Part 2

• Impulse Response Functions (IRF)
• Cholesky Decomposition
• How to order the variables in a VAR model
• Variance Decomposition
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