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<p>This paper examines the relationship between the Consumer Price Index (CPI) and the Producer Price Index (PPI) in France over the period 1970–2022 using wavelet coherence and partial wavelet coherence (PWC). PWC is employed as a de-trending device in the time–frequency domain: by conditioning the CPI–PPI relationship on M3, it isolates direct producer-to-consumer transmission from co-movement driven by a common monetary trend. The results show that the CPI–PPI relationship is time-varying and frequency-dependent, with PPI leading CPI at medium frequencies and during crisis episodes, consistent with a cost-push mechanism. Occasional reversals around the subprime crisis suggest that transmission is state-dependent rather than structural. Conditioning on M3 substantially reduces low-frequency coherence, indicating that part of the long-run co-movement reflects a common monetary trend rather than direct pass-through, a result not previously documented in the wavelet literature. Headline CPI exhibits stronger coherence with PPI than core CPI, confirming the amplifying role of food and energy prices.</p>

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Studying CPI-PPI Dynamics Across Cycles Using Partial Wavelet Coherence: Evidence from France

  • 期刊论文

  • 发表日期：

    2026年6月22日

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  • Marie Bidan,
  • Roman Mestre

摘要

This paper examines the relationship between the Consumer Price Index (CPI) and the Producer Price Index (PPI) in France over the period 1970–2022 using wavelet coherence and partial wavelet coherence (PWC). PWC is employed as a de-trending device in the time–frequency domain: by conditioning the CPI–PPI relationship on M3, it isolates direct producer-to-consumer transmission from co-movement driven by a common monetary trend. The results show that the CPI–PPI relationship is time-varying and frequency-dependent, with PPI leading CPI at medium frequencies and during crisis episodes, consistent with a cost-push mechanism. Occasional reversals around the subprime crisis suggest that transmission is state-dependent rather than structural. Conditioning on M3 substantially reduces low-frequency coherence, indicating that part of the long-run co-movement reflects a common monetary trend rather than direct pass-through, a result not previously documented in the wavelet literature. Headline CPI exhibits stronger coherence with PPI than core CPI, confirming the amplifying role of food and energy prices.