Origins and Nature of Macroeconomic Instability in Vector Autoregressions
Abstract
For a general class of dynamic and stochastic structural models, we show that (i) non-linearity in economic dynamics is a necessary and sufficient condition for time-varying parameters (TVPs) in the reduced-form VARMA process followed by observables, and (ii) all parameters' time-variation is driven by the same, typically few sources of stochasticity: the structural shocks. Our results call into question the common interpretation that TVPs are due to "structural instabilities". Motivated by our theoretical analysis, we model a set of macroeconomic and financial variables as a TVP-VAR with a factor-structure in TVPs. This reveals that most instabilities are driven by a few factors, which comove strongly with measures of macroeconomic uncertainty and the contribution of finance to real economic activity, commonly emphasized as important sources of non-linearities in macroeconomics. Furthermore, our model yields improved forecasts relative to the standard TVP-VAR where TVPs evolve as independent random walks.
Summary
This paper addresses the origins and nature of macroeconomic instability in vector autoregressions (VARs). The authors theoretically demonstrate that nonlinearity in economic dynamics is a necessary and sufficient condition for time-varying parameters (TVPs) in the reduced-form VARMA process of observables, assuming typical exogenous dynamics. Furthermore, they show that the time variation in these parameters stems from a few common sources of stochasticity, namely the structural shocks. This challenges the conventional interpretation that TVPs are solely attributable to structural instabilities. Motivated by their theoretical findings, the authors propose a novel Factor-TVP-VAR model. This model allows intercepts, autoregressive coefficients, contemporaneous relationships, and stochastic volatilities to evolve according to a small number of latent factors, thereby reducing dimensionality and aligning with the theoretical insight that only a few underlying forces drive parameter changes. They also introduce a grouped-factor variant to improve interpretability by distinguishing factors influencing the propagation mechanism, the contemporaneous covariance structure, and stochastic volatilities. Empirical application to U.S. macro-financial data reveals economically meaningful factors and structural changes, demonstrating improved forecasting performance compared to standard TVP-VAR models.
Key Insights
- •Nonlinearity is Key: The paper establishes that nonlinearity in structural economic equations is both a necessary and sufficient condition for TVPs in reduced-form VARMA models under typical exogenous dynamics.
- •Reduced-Rank Variation: The analysis highlights that the time variation in VARMA parameters originates from a few structural shocks, implying a reduced-rank structure of parameter instability. This justifies imposing factor structures on TVPs.
- •Factor-TVP-VAR: The authors propose a Factor-TVP-VAR model that incorporates the reduced-rank nature of parameter instability by allowing all TVPs to evolve according to a small number of latent factors.
- •Grouped-Factor TVP-VAR: The introduction of a Grouped-Factor TVP-VAR allows for better interpretability by grouping VAR parameters into categories like regression coefficients, covariance states, and stochastic volatilities, each driven by distinct factors.
- •Improved Forecasting: The empirical application demonstrates that the Factor-TVP-VAR model yields improved forecasting performance relative to standard TVP-VAR models where TVPs evolve as independent random walks.
- •Structural Instabilities vs. Nonlinearities: The paper argues that the existence of TVPs in reduced-form processes is better explained by nonlinearities in the underlying economic structure rather than solely by structural breaks or instabilities.
- •Dimensionality Reduction: The Factor-TVP-VAR significantly reduces the dimensionality of the state space compared to traditional TVP-VARs, making it more computationally feasible for higher-dimensional systems.
Practical Implications
- •Macroeconomic Modeling: Researchers can use the Factor-TVP-VAR to model macroeconomic systems more efficiently and accurately, capturing the underlying commonalities in parameter instability.
- •Forecasting: Practitioners can leverage the improved forecasting performance of the Factor-TVP-VAR for better economic predictions.
- •Policy Analysis: Policymakers can benefit from the model's ability to uncover structural changes in transmission mechanisms and identify the factors driving these changes, informing better policy decisions.
- •Model Building: The theoretical framework provides guidance on how to build more structurally sound VAR models, linking time-varying parameters to underlying economic forces.
- •Future Research: The paper opens up avenues for further research, including single-step estimation of the Factor-TVP-VAR and extensions to handle non-smooth nonlinearities and censoring points.