Structural vector autoregressions (SVARs) represent a prominent class of time series models used for macroeconomic analysis. The model consists of a set of multivariate linear autoregressive equations characterizing the joint dynamics of economic variables. The residuals of these equations are combinations of the underlying structural economic shocks, assumed to be orthogonal to each other. Using a minimal set of restrictions, these relations can be estimated—the so-called shock identification—and the variables can be expressed as linear functions of current and past structural shocks. The coefficients of these equations, called impulse response functions, represent the dynamic response of model variables to shocks. Several ways of identifying structural shocks have been proposed in the literature: short-run restrictions, long-run restrictions, and sign restrictions, to mention a few. SVAR models have been extensively employed to study the transmission mechanisms of macroeconomic shocks and test economic theories. Special attention has been paid to monetary and fiscal policy shocks as well as other nonpolicy shocks like technology and financial shocks. In recent years, many advances have been made both in terms of theory and empirical strategies. Several works have contributed to extend the standard model in order to incorporate new features like large information sets, nonlinearities, and time-varying coefficients. New strategies to identify structural shocks have been designed, and new methods to do inference have been introduced.
George W. Evans and Bruce McGough
While rational expectations (RE) remains the benchmark paradigm in macro-economic modeling, bounded rationality, especially in the form of adaptive learning, has become a mainstream alternative. Under the adaptive learning (AL) approach, economic agents in dynamic, stochastic environments are modeled as adaptive learners forming expectations and making decisions based on forecasting rules that are updated in real time as new data become available. Their decisions are then coordinated each period via the economy’s markets and other relevant institutional architecture, resulting in a time-path of economic aggregates. In this way, the AL approach introduces additional dynamics into the model—dynamics that can be used to address myriad macroeconomic issues and concerns, including, for example, empirical fit and the plausibility of specific rational expectations equilibria. AL can be implemented as reduced-form learning, that is, the implementation of learning at the aggregate level, or alternatively, as discussed in a companion contribution to this Encyclopedia, Evans and McGough, as agent-level learning, which includes pre-aggregation analysis of boundedly rational decision making. Typically learning agents are assumed to use estimated linear forecast models, and a central formulation of AL is least-squares learning in which agents recursively update their estimated model as new data become available. Key questions include whether AL will converge over time to a specified RE equilibrium (REE), in which cases we say the REE is stable under AL; in this case, it is also of interest to examine what type of learning dynamics are observed en route. When multiple REE exist, stability under AL can act as a selection criterion, and global dynamics can involve switching between local basins of attraction. In models with indeterminacy, AL can be used to assess whether agents can learn to coordinate their expectations on sunspots. The key analytical concepts and tools are the E-stability principle together with the E-stability differential equations, and the theory of stochastic recursive algorithms (SRA). While, in general, analysis of SRAs is quite technical, application of the E-stability principle is often straightforward. In addition to equilibrium analysis in macroeconomic models, AL has many applications. In particular, AL has strong implications for the conduct of monetary and fiscal policy, has been used to explain asset price dynamics, has been shown to improve the fit of estimated dynamic stochastic general equilibrium (DSGE) models, and has been proven useful in explaining experimental outcomes.