Vector Autoregressive (VAR) models in Stata

Juan D'Amico

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Vector autoregression (VAR) is a powerful statistical model used to measure and analyze the relationships between multiple variables over time. It is a stochastic process model, meaning it models randomness in the form of data points that can be observed at different moments in time. VAR has been widely used in economics, finance, marketing, and other disciplines where there are multiple variables to consider when making decisions or predictions.

Variables Yt and Xt are assumed Stationary. (Logs and Differences can be applied if required.)

ut and vt are white noise disturbances. Commonly called innovations or shock terms.

The coefficients in the main matrix (b11, b12, b21, b22) are estimated by OLS.

The engle and granger test will show the relationship between variables. If one variable causes the other one, it means that it helps to predict future values of the other variable. For example, the inflation rate can help us predict the future values of the interest rate (if inflation goes up, interest rates will eventually go up).

Once you have estimated your VAR model, you should check for the lag length criteria. The lag length defines the number of lags that will be included as explanatory variables in the model, and has a substantial impact on its performance. The choice of an appropriate lag length is not always straightforward and requires careful consideration by the user.

An impulse response function will show how each endogenous variable evolves over time after it has been hit by an exogenous shock. For example, if there is a sudden surge in oil prices, this would be considered as an exogenous shock. The impulse response function would allow economists to observe the effect of this shock on various endogenous variables like inflation, interest rates and GDP over time. This information can then be used to make informed economic policy decisions that address short-term fluctuations while also considering long-term effects.

In this example, we can see that a shock in unemployment will decrease the Fed. Rate. The Fed will have to loosen monetary policy to try to activate the economy and recover from unemployment.

Variance decomposition is an important tool for data analysis. It helps to measure the proportion of variation in a dependent variable explained by each of the independent variables. The variance decomposition is obtained after fitting the VAR model.

The VAR model estimates parameters in an equation system which describes the variation in the dependent variable as a function of its own lagged values and independent variables. By estimating and comparing these parameters, one can determine how much variation in the dependent variable is explained by each of its covariates. This technique is useful for identifying influential factors when conducting forecasting or regression analysis.

Consequently, variance decomposition provides an efficient way to measure the relative importance of different independent variables on dependent variables. Furthermore, it helps to identify relationships between two or more time series that may not be immediately apparent from visual inspection alone.

We can see the effect of an unemployment shock in Unemployment and the Fed. Rate.

Also, we can see the effect of the fed rate on unemployment and the fed rate.

If you are interested in learning how to estimate a var model in Stata, then please watch the videos below. I explain the steps in an easy-to-follow tutorial that is perfect for those who may not have experience with this type of modeling but would still like to learn.

Also, you can buy the package to estimate VAR models. This package includes all the slides with the pictures featured in this article, plus detailed explanations and files that will help you easily replicate the content.

I understand that it can be difficult trying to understand complex equations and models so we want to make sure you have all the tools necessary to succeed. Watching these videos will provide you with an introduction into the world of VAR models and how they work in Stata. You’ll be on your way to becoming a pro at estimating VAR models quickly and easily!

Visit my website:

www.jdeconomics.com

Visit my store to buy the Slides and DO file of the model: www.jdeconomisctore.com

Best Regards,

Juan D’Amico

JD Economics