Vector Autoregressive (VAR) Model

Background

The Vector Autoregressive (VAR) model is a powerful statistical tool used in econometrics for understanding the interdependencies among multiple time series data. Unlike univariate models which consider a single time series, VAR models simultaneously regress multiple variables on their own lagged values and the lagged values of every other variable in the system.

Historical Context

Developed initially by Christopher Sims in the early 1980s, the VAR model allowed economists and statisticians to treat all variables within the multivariable time series as endogenous. This marked a significant departure from traditional modeling that often differentiated between endogenous and exogenous variables.

Definitions and Concepts

A Vector Autoregressive model (VAR) is defined as a multivariate extension of the univariate autoregressive (AR) model. In a VAR model, each variable in the system is a linear function of its own past values and the past values of all other variables in the model.

The general form can be expressed as:

\[ Y_t = c + A_1 Y_{t-1} + A_2 Y_{t-2} + \ldots + A_p Y_{t-p} + \varepsilon_t \]

where:

• \( Y_t \) is a (k x 1) vector of endogenous variables.
• \( c \) is a (k x 1) vector of intercept terms.
• \( A_i \) are (k x k) coefficient matrices for lag \( i \).
• \( \varepsilon_t \) is a (k x 1) vector of error terms.

Major Analytical Frameworks

Classical Economics

VAR models have been used extensively to understand macroeconomic relationships and shocks, providing an empirical backbone to theories of economic fluctuations.

Neoclassical Economics

In this framework, VAR models help in exploring the dynamic relationship between macroeconomic variables such as output, interest rates, and prices without imposing restrictions based on theoretical models.

Keynesian Economics

Keynesian economists utilize VAR models to assess how changes in fiscal policy, monetary policy, and other exogenous shocks affect macroeconomic variables over time.

Marxian Economics

VAR models are employed to analyze the dynamic interactions among economic variables that are pertinent to Marxist economic theories, such as the relationships between different types of capital.

Institutional Economics

In institutional economics, VAR models assist in investigating how institutional changes impact economic variables, observing both short-term and long-term effects.

Behavioral Economics

These models are leveraged to explore how psychological factors and market sentiments influence the interactions among economic time series.

Post-Keynesian Economics

Post-Keynesian economists use VAR models to study the effects of policies and external economic shocks while considering the inherent uncertainties in the economy.

Austrian Economics

Though less common in Austrian economics, VAR models nonetheless can provide insights into the temporal structure of capital and business cycles.

Development Economics

VAR models are particularly useful for evaluating the impact of development policies and international aid on multiple economic indicators in developing countries.

Monetarism

Monetarists apply VAR models to study the impact of changes in the money supply on other macroeconomic variables such as inflation and unemployment.

Comparative Analysis

VAR models offer the advantage of modeling the dynamic relationship between multiple time series without requiring pre-specified causal linkages. However, they also require large datasets to estimate numerous parameters, making them sensitive to overfitting and multicollinearity issues.

Case Studies

In practice, VAR models have been used in various studies, for example:

• Examining the effect of monetary policy on economic output and interest rates.
• Analyzing the dynamic relationship between stock prices and corporate earnings.
• Understanding the transmission mechanisms of fiscal policy shocks on aggregate demand.

Suggested Books for Further Studies

1. Time Series Analysis by James D. Hamilton
2. New Introduction to Multiple Time Series Analysis by Helmut Lütkepohl
3. Applied Time Series Econometrics by Helmut Lütkepohl and Markus Krätzig

Related Terms with Definitions

• Univariate Autoregressive Model (AR): A model where a single time series is regressed on its past values.
• Endogenous Variable: A variable that is determined within the model.
• Exogenous Variable: A variable that influences endogenous variables but is determined outside the model.
• Lagged Values: Past values of a variable used in regression to predict current values.
• Impulse Response Function: A representation of the reaction of variables in a VAR model to external shocks.
• Granger Causality: A statistical hypothesis test for determining whether one time series can predict another.

By reviewing the historical development, key definitions, and the analytical frameworks within which