Abstract
The idea that many macroeconomic variables are unit root processes serves voluminously as a preliminary result in empirical works, but it is just a result of misspecification or weak identification with respect to the structural breaks. This contribution raises the size or power in tests of a null of a stationary process/unit root by Fourier approximation which converts the estimation of location and style of breaks into the problem of appropriate frequency selection. An examination of China’s 15 representative macroeconomic series indicates that only the financial series have good reason to be regarded as unit root processes; most of others are better regarded as trend stationary with smooth transitions. The inference based on these results affirms that China’s real business cycles are indeed fluctuations around different deterministic trends, and it is not the noise component rather the historical events corresponding to the breaks that have persistent effects. The results also support that large government-initiated shocks aimed at improving fundamentals are indeed capable of positive effects on the balanced growth path.
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Notes
- 1.
Some tests, for instance, Bai and Perron (1998), have little power when a break happens near the end of a series.
- 2.
Simulation results are actually the same for the other β and γ.
- 3.
I’m indebted to the anonymous reviewer for pointing this out.
- 4.
I’m grateful to the referee for these refinements.
- 5.
Rodrigues and Taylor (2012) also come up with a unit root test using a Fourier series to approximate smooth breaks on an ADF basis. The difference is their test statistics is established according to the DF-GLS method, while Ender and Lee construct their test statistics according to the LM principle. Though DF-GLS is associated with higher test power for nonstructural settings, the penalty of sticking to this idea in Fourier approximated breaks is for the test statistics to suffer from asymptotically rank deficiency.
- 6.
Please refer to Enders and Lee (2012, pp. 580, 582) for critical values under single frequency and cumulated frequencies.
- 7.
Such an informal demonstration is available upon request.
- 8.
Source (In Chinese): http://jiuliyougancheng.blogchina.com/1373459.html
- 9.
Chinese economy is an investment-driven economy up until today. Investment, irrespective of private or public, rather than consumption, plays a determinant role in economic growth. In 1992, Mr. Deng Xiaoping, the former chairman of the CPC, made one of his most cited speeches in South China whose content was to encourage the existence of private economy for the sake of efficiency. The speech instigated an upsurge of investments, and the inflation during 1993–1996 was brought about by this round excessive investing.
- 10.
Here in the table, the DF-GLS test only reports among others the test statistic of the optimal lag selected by Ng-Perron sequential t statistics.
- 11.
The initial transition parameter is set to 10 for LSTAR estimation.
- 12.
5% data trimming is used.
- 13.
Consider the stationary process y t = ε t and the unit root process (1 − L)y t = (1 + θL)ε t where |θ| < 1; the observable implications are virtually the same as θ goes to −1. Again, consider the unit root process y t = y t − 1 + ε t and the stationary process y t = ρy t − 1 + ε t under |ρ| < 1 ; it is also difficult to distinguish between the two when ρ is close to 1 at finite time horizons.
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Barnett, W.A., Han, Q. (2018). Uncertainty and Stationarity in Financial and Macroeconomic Time Series—Evidence from Fourier Approximated Structural Changes. In: Jawadi, F. (eds) Uncertainty, Expectations and Asset Price Dynamics. Dynamic Modeling and Econometrics in Economics and Finance, vol 24. Springer, Cham. https://doi.org/10.1007/978-3-319-98714-9_1
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