Theory Coherent Shrinkage of Time Varying Parameters in VARs: Conclusion and References

Table of Links

Abstract and Introduction

Theory coherent TVP-VAR

Forecasting with the TC-TVP-VAR

Response analysis at the ZLB with the TC-TVP-VAR

Conclusion and References

A Appendix

5 Conclusion

TVP-VAR are flexible statistical models used both for prediction and policy analysis in macroeconomics. Despite their flexibility allows to capture changes in the dynamic relationship among the macroeconomic variables, these models can easily become too flexible with the risk of over fitting the data. This translate into poor forecasting performances and imprecise inference on the time-varying parameters and of typical objects of interests such as the impulse responses. On the other side, models from the economic theory typically provide a more tightly parameterized representation of the macroeconomy and therefore have the opposite tendency of fitting the data rather poorly. This paper exploits the restrictions implied by economic theory to formulate a prior for the parameters of TVP-VARs so as to enhance inference within this class of models. It does so by introducing a shrinkage prior that centers the time varying coefficients at each time period on the cross equation restrictions implied by an underlying economic theory about the variables in the system. The paper shows that “economic shrinkage” can be successfully used to obtain more accurate forecasts and more precise estimates of typical objects of interests such as the impulse responses.

Future research For future research the prior proposed in this paper could be modified to accommodate for multiple competing theories `a la Loria et al. (2022). As well, the model could be extended to embed stochastic volatility, adapting the algorithm in Bognanni (2018). More in general, restrictions from economic theory could successfully be used to reduce overfitting and sharpen inference in non-parametric VARs and Gaussian Procesess VARs (Hauzenberger et al. 2022).

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