If CPI is a 10 out of 10 on a scale of economic data that causes bond market volatility, PPI is never more than a 5. It's a good thing too. All it took was a 0.1% deviation from expectations for CPI to send bond yields 15+ bps higher on Tuesday. Contrast that to today's PPI deviation of a whopping 0.4% (specifically, m/m core PPI came in at 0.5 versus a median forecast of 0.1). If this had been CPI, 10yr yields would likely have jumped 30+ bps, but that's assuming anyone would believe the number.
This level of deviation is all but unheard of on CPI. On the other hand, PPI is historically much more volatile.