Module XI·Article II·~2 min read
VAR Models and Empirical Macroeconomics
Modern Macroeconomic Models
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Vector Autoregressions and Applied Analysis
Vector Autoregressions (VAR) are statistical models widely used for the empirical analysis of macroeconomic dynamics, forecasting, and the evaluation of policy effects. Unlike structural DSGE models, VAR models are atheoretical and allow the data to "speak for themselves."
Structure of a VAR Model
A VAR describes a system of variables in which each variable depends on its past values and the past values of all other variables in the system. The simplest VAR(1) for two variables:
$y_{1t} = a_{11}y_{1,t-1} + a_{12}y_{2,t-1} + \varepsilon_{1t},$
$y_{2t} = a_{21}y_{1,t-1} + a_{22}y_{2,t-1} + \varepsilon_{2t}.$
VAR models do not require a priori theoretical restrictions on the structure of the economy. They estimate dynamic relationships between variables from the data.
Forecasting
VAR models are widely used for macroeconomic forecasting. They capture the autoregressive structure and interrelationships between variables. VAR forecasts are often comparable to or outperform structural models over short horizons.
A drawback: the large number of parameters requires long time series.
Bayesian VARs (BVAR) use prior information for regularization and improving forecasts.
Impulse Response Functions
Impulse Response Functions (IRF) show the dynamic response of the system’s variables to a one-time shock in one of the variables. IRFs answer the question: how does variable Y change in periods $t, t+1, t+2...$ after a shock to variable X in period t?
Identification of shocks is a key problem. Structural VARs (SVAR) impose restrictions (theoretical or statistical) to identify “pure” structural shocks (monetary, technological, etc.).
Analysis of Monetary Policy
VAR models are actively used to assess the effects of monetary policy. A typical model includes GDP, inflation, and the interest rate. The impulse response to an interest rate shock shows how policy tightening affects output and inflation.
Standard results: a rate increase reduces output and inflation with a lag of several quarters. The maximum effect on output occurs after 4-8 quarters, on inflation — even later.
Variance Decomposition
Variance Decomposition shows what share of the fluctuations of each variable is explained by different shocks. This helps to understand the relative importance of different sources of fluctuations.
Application for Investors
The results of VAR analysis inform about typical time lags of policy and shock effects on the economy. This helps to form expectations regarding the timing of effect realization. Impulse response functions from published studies provide an understanding of the magnitude of typical responses—for example, how much GDP declines when the rate is raised by 100 basis points.
VAR forecasts are used as one of the inputs in the process of forming expectations. Comparing VAR forecasts with the consensus may reveal discrepancies and potential trading opportunities.
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