I am working on a panel data modeling research aiming to find labor force dynamics which are affecting employment of young newly graduated women engineers in Turkey. We employed the latest Labor Force Survey to build our model, however as you would realize, for country level inferences Turkstat provides weights for each observation, each observation represent a specific share of the Turkish population. However after filtering all female, young, new graduates, who have an engineering degree and works in a role related to engineering my sample fell to 726 from 370,000. From that point I think I am no longer trying to make an inference on Turkish population and should I keep using weights in modeling and discussion part? Or should I treat data as an ordinary random sampled survey and give the same weight for each individual.
There is a bit of controversy in labour market analysis about whether to use sample weights in modelling exercises. If your model is well specified and you don't generalize beyond the population of interest, I don't think the sampling weights are necessary or useful. That, however, is an economist's answer. Statisticians usually disagree but have never been able to explain to me why I should use sampling weights in this situation.
One thing to keep in mind is that you can't use the original sampling weights anymore, since you excluded 370,000-726 observations from the original data set, so the the original sampling weights are no longer valid. Calculating new sampling weights for your sub-sample would be very hard to do. Also, when and why to use sampling weights, i found this very useful: https://blogs.worldbank.org/impactevaluations/tools-of-the-trade-when-to-use-those-sample-weights
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