Posts Tagged ‘vector autoregression’

Long-run restrictions in a structural vector autoregression

\def\bfB{{\bf }}


Structural vector autoregression models

\def\bfA{{\bf A}}
\def\bfB{{\bf B}}
\def\bfu{{\bf u}}
\def\bfI{{\bf I}}
\def\bfe{{\bf e}}
\def\bfC{{\bf C}}

\label{var1} \\



Vector autoregressions in Stata


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

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

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

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}

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…

Vector autoregression—simulation, estimation, and inference in Stata




\end{bmatrix} + \epsb_t


I set my sample size to 1,100 and Read more…