How to estimate production function by looking at the output, labour and capital only? Normally it is impossible, capital and labor does not work on its own to produce the output, there are managers with skills and connections, so simple projection of output into the column space of labor and capital would be terribly misleading, i.e. the estimates would pick up an effect of a missing variable, and any prediction exercises would not be very meaningful.
Well, still you can do a lot, by thinking explicitly about how the data was generated. It was generated by dynamically optimising firms and economists now a lot about how a rational firm behaves, and this knowledge allows us to control for unobservables. The presentation of a method developt by ACF summarized this approach.