In general we can establish causality for socioeconomic theories using natural studies. For instance your question can be answered by comparing the timing of in

In general we can establish causality for socioeconomic theories using natural studies. For instance your question can be answered by comparing the timing of introduction of technology into the home and the rise of women in the workplace. You can ask people how much time they spend doing housework and compare to what people with technical alternatives spend. This is a relatively easy natural study since so much of the data was well collected at the time. Harder ones that are more recent ask things like whether or not raising the minimum wage increases unemployment. You’ll be able to find studies that used Seattle’s minimum wage law to determine the answer to that question. In the narrow case of women entering the work force, the biggest factor was the employers being willing (forced) to hire women because they were the only workers available quite suddenly. Women would have entered the work force in more substantial ways before that but they were perceived as taking jobs from men. WW2 changed all that. One reason they were able to keep working after the war is because they had money and the products were available to allow them to get the housework done in less time. It was a status symbol in the 50s (and probably still today) to have a very bored wife at home.