When a firm hires a worker, they have incomplete information on the workers' productivity. Firm's goal is to hire the most productive workers, and they estimate productivity of the workers given the observable characteristics in a resume/interview.
I have seen a paper that uses wage increase as a proxy for the workers' productivity. Presumably, the underlying assumption behind this choice is that once worker gets hired, employer can observe the productivity of the worker better, and 'rewards' the productive worker by increasing their wage. However, this is not a good proxy to use because wage increase can be due to many other reasons that have nothing to do with productivity (eg. racism, which is observable, and personality clash, which is not observable to econometrician).
Is there any other ways to measure the productivity of the workers in a data like NLSY? I cannot partial out the observable characteristics in wage change, because I'm trying to predict productivity of the workers given the observable characteristics.