Univariate unobserved-component model with a nonrandom-walk permanent component

Abstract

In this article, we revisit the univariate unobserved-component (UC) model of the US GDP by relaxing the traditional random-walk assumption of the permanent component. Since our general UC model is unidentified, we investigate the upper bound of the contribution of the transitory component, and find the GDP fluctuation is dominated by the permanent component.

Keywords:

• unobserved-component model
• random-walk assumption
• permanent and transitory shocks

JEL Classification:

• C22
• C49
• E32

Acknowledgements

I am grateful to Yi Wen for his comments and continuous encouragement. I also thank Daqing Luo, Pengfei Wang and seminar participants at Shanghai University of Finance and Economics, Tsinghua University. Of course, all errors are mine.

Notes

Oh et al. (2008) also recommend this specification. They find that ARIMA (2,1,2) is preferred by the Akaike information criterion (AIC) and ARIMA (1,1,0) is preferred by the Bayesian information criterion (BIC). However, the latter specification is not able to capture the periodical behaviour of output due to its oversimplified structure.

The setting is infeasible, since this will make the order of MA part of (the RHS of Equation 2) exceed 2.

The mean growth rate μ is just the same as that in ARIMA representation.

Here, ‘feasible’ means that equation system 5 always has solution when .

The parameters are statistically significant, we calculate their t-statistics by bootstrapping method, but not reported here.

In their paper, Blanchard–Quah (BQ) decompose GDP based on a structural bivariate VAR system of (GDP, unemployment rate). They just identify the model by imposing a long-run restriction on the transitory component.

The dashed lines are 95% bootstrapped confidence interval computed (200 replications) by Hall’s percentile interval.

In fact, this point can be easily seen from a spectrum perspective: the spectrum of growth rate of GDP shares the same value with growth rate of permanent component at zero frequency, and this value is just the squared long-run effect multiplying the variance of innovation in ARIMA process.