The time-frequency dependence of unemployment on real input prices: a wavelet coherency and partial coherency approach

ABSTRACT

While the dependence of unemployment on real oil price and real interest rate is an important issue that has been addressed only in the time dimension, little is known about the movements of real input prices and their impact on unemployment in the time-frequency space. With a continuous wavelet coherency and partial coherency approach and monthly data of Japan and US from January 1960 to May 2017, this paper contributes to the literature by examining the characteristics of the dependence of unemployment on real input prices across frequencies and over time. The empirical results indicate that: First, a rise in real oil price leads to productivity growth slowdown and unemployment increase at the scale of 16–64 months after 1990 for Japan and 8–24 months after 2005 for US. Second, an increase in real interest rate results in higher unemployment at the 16–32-month scale before 1974 for Japan and 8–64-month scale before 2000 for US. Third, the degree of integration between labour market and energy market in US is higher than that in Japan. This study provides time-frequency evidence to the supply side hypothesis about the relationships between input prices and unemployment.

KEYWORDS:

• Real oil price
• real interest rate
• unemployment
• continuous wavelet analysis
• wavelet coherency
• wavelet partial coherency

JEL CLASSIFICATION:

• C87
• E24
• E31
• O57
• Q43

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ This is because the equilibrium unemployment is homogeneous of zero with respect to the total labour size and the rule that government employs to update unemployment benefit as technology improves in the model.

² The Census X-12 approach is developed by the US Census Bureau to decompose or adjust seasonality in time series. The core algorithm of Census X-12 approach is based on an autoregressive integrated moving average (ARIMA) model, where the multiplicative form of decomposition for time series $Y_t$ takes the form $Y_t=T{C}_t\cdot S_t\cdot {\delta }_t$, where $T{C}_t$ is the trend cycle, $S_t$ is the seasonal factor, and ${\delta }_t$ represents the irregular component.

³ For example, RWTI could have been affected by the 1970s oil crisis, UNEP_JP and RINR_JP may have been influenced by the 1997 Asian financial crisis, and UNEP_US and RINR_US might have been affected by the Great Recession during the early 2010s.

⁴ We separately estimate a standard $GARCH\left(p,q\right)$ model for real oil price, real interest rate in US, and real interest rate in Japan, where $p$ and $q$ are determined according to the information criteria.