Forecasting macro variables with a Qual VAR business cycle turning point index

Abstract

One criticism of Vector Autoregression (VAR) forecasting is that macroeconomic variables tend not to behave as linear functions of their own past around business cycle turning points. A large amount of literature therefore focuses on nonlinear forecasting models, such as Markov switching models, which only indirectly capture the relation with turning points. This article investigates a direct approach to using information on turning points from the National Bureau of Economic Research (NBER) chronology to model and forecast macroeconomic data. Our Qual VAR model includes a truncated normal latent business cycle index that is negative during NBER recessions and positive during expansions. We motivate our forecasting exercise by demonstrating that if starting from a linear specification, a truncated normal variable is an omitted variable, then forecasts of the remaining variables will become nonlinear functions of their own past. We apply the Qual VAR model to recursive out-of-sample forecasting and find that the Qual VAR improves on out-of-sample forecasts from a standard VAR.

Notes

¹ Many nonlinear models perform well in-sample but fail when it comes to out-of-sample forecasting (see, for instance, Dacco and Satchell, 1999; Bessec and Bouabdallah, 2005).

² A discussion of the sampling distribution of the latent turning point index is in the appendix.

³ The estimation of the Bayesian VAR uses code generously supplied by John Robertson and Ellis Tallman, which implements directly the Bayesian VAR proposed by Sims and Zha (1998). The hyperparameters are defined in Robertson and Tallman (2001) and we set the parameters controlling the priors to the values suggested by Robertson and Tallman (2001): λ₀ = 0.6, λ₁ = 0.1, λ₂ = 1, λ₃ = 0.1, μ₁ = 5 and μ₂ = 5.

⁴ Though the number of iterations is comparatively low, the fact that both models are estimated recursively to generate the out-of-sample forecasts poses limits in terms of computation time on the number of iterations.

⁵ With a threshold of 0.5 both models are unable to forecast the 2001 recession at the 6 and 12 month horizon.

⁶ We thank Ellis Tallman for providing code to draw these VAR coefficients.