\(\def\bfA{{\bf A}}

\def\bfB{{\bf }}

\def\bfC{{\bf C}}\)**Introduction**

In this blog post, I describe Stata’s capabilities for estimating and analyzing vector autoregression (VAR) models with long-run restrictions by replicating some of the results of Blanchard and Quah (1989). Read more…

**Introduction**

In a univariate autoregression, a stationary time-series variable \(y_t\) can often be modeled as depending on its own lagged values:

\begin{align}

y_t = \alpha_0 + \alpha_1 y_{t-1} + \alpha_2 y_{t-2} + \dots

+ \alpha_k y_{t-k} + \varepsilon_t

\end{align}

When one analyzes multiple time series, the natural extension to the autoregressive model is the vector autoregression, or VAR, in which a vector of variables is modeled as depending on their own lags and on the lags of every other variable in the vector. A two-variable VAR with one lag looks like

\begin{align}

y_t &= \alpha_{0} + \alpha_{1} y_{t-1} + \alpha_{2} x_{t-1}

+ \varepsilon_{1t} \\

x_t &= \beta_0 + \beta_{1} y_{t-1} + \beta_{2} x_{t-1}

+ \varepsilon_{2t}

\end{align}

Applied macroeconomists use models of this form to both describe macroeconomic data and to perform causal inference and provide policy advice.

In this post, I will estimate a three-variable VAR using the U.S. unemployment rate, the inflation rate, and the nominal interest rate. This VAR is similar to those used in macroeconomics for monetary policy analysis. I focus on basic issues in estimation and postestimation. Data and do-files are provided at the end. Additional background and theoretical details can be found in Ashish Rajbhandari’s [earlier post], which explored VAR estimation using simulated data. Read more…