I would say that this influence has to be studied case by case.
Some general consideration would involve Maslow's pyramid. Fewer people would get to the top of it, where they require refined art, while more people would be at its bottom, busy with satisfying their basic needs for food, shelter, physical security, etc. Most people would seek simple entertainments not requiring deep spiritual involvement. And culture - art, literature, theatre, music, cinematograph - would cater to those requests in order to survive (dominance of pop culture). High and refined culture would be marginalized and brought to the verge of extinction.
If we mean broader culture - the way people dress, decorate their houses, celebrate their holidays, take care of their youngest and oldest, to what extent they are united, cooperative and tolerant, etc., this may depend on other factors even stronger than on the economy itself. A struggling economy is often accompanied by turbulent politics, and this may destroy the fabric of the society (communication and cooperation in it) even stronger than low incomes of the majority of people
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From @computergenie