falling household savings While reading Mazzucato's "The value of everything", I come across this


  The rise in private debt in the US and UK has resulted in household
  savings falling as a percentage of disposable income - income minus
  taxes - especially in periods of sustained economic growth (during the
  1980s, the late 1990s and the beginning of the 2000s.


I wonder if this is based on observation or if there is a cause and effect (as suggested by "resulted"), in which case I'd be grateful if anyone could provide some intuition of why such a relationship would exist.
If household debt rises, it means that more households consume more than they earn. This is the same as saying they save less. This means that the causal channel in your quote is by definition. 

Now one may ask why do savings decrease in a period of growth. I could imagine two causal channels. It could be that growth is a consequence of low interest rates, causing both higher private debt and hence more investment. One could also think of sustainable growth causing positive expectations, so households are worrying less about the future and hence save less for precautionary reasons.