In the previous year, consumers' savings had decreased.
or
In the previous year, consumer savings had decreased.
Which one is valid and why?
You can say either, depending on the context. The term consumer savings is used by economists to describe broad trends in the behavior of a population. But you could use consumers' savings to refer to a specific set of consumers apart from the general populace.
Curiously, I hit exactly the same question with one of my children. We were in a hotel eating breakfast. He asked why this was called a hotel restaurant, rather than hotel's restaurant. It is a grammatical feature called apposition.
In this case, the word 'consumer' (no apostrophe) acts as a qualifier to the word 'savings'.
So, we begin with the head word 'savings' and explain what savings we are taking about by using the word 'consumer'.
'Consumer' then, performs much the same job as the determiner 'those'. We could say
those savings
and the grammatical structure would be quite the same.
Therefore, while you could say 'consumer's savings', the term you are after here is consumer savings.
N.B.: Generally, 'consumer's savings' would be preceded by the article 'the', as The Consumers in this sense would be a specific group of people, outlined elsewhere in its context.