Does allowing for heterogeneity necessarily mean the model is HANK?

I came across this text in a paper I read,

“Mankiw (2000) therefore proposed that economic model should allow for the cohabitation of optimizing and non-optimizing (or rule-of-thumb) households (HANK)”.

Is that really HANK or TANK instead?

I know Mankiw’s paper proposes heterogeneity in consumer behavior, but that is not necessarily HANK, right? More like a TANK model (savers-lenders model). Or HANK still applies here?

Thanks for any reply.

I think this is just a naming separation. As soon as you have >1 agents you can correctly talk about heterogeneity, so the quote is in general correct. What we, however, have established as HANK is having a whole distribution of agents.
Thus, I would say that it is just an evolution of naming.

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Thanks for the reply. So basically the statement was supposedly made before the evolution of the naming, right? Like in the current state of the literature, that would still be correct? Or maybe incorrect? Or maybe it does not really matter?

2 is still bigger than 1. So 2 agents indeed usually implies heterogeneity. But I would not get bogged down by the naming conventions. Ultimately, you have to decide what you are after.

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