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I am creating a panel dataset for earnings based on English local authorities (local administrative districts). In 2009 and 2019, some local authorities were combined to create a single local authority. In order to make comparisons, I am using the boundaries set in 2019, which means I need to combine several local authorities (multiple observations into a single observation). There are datasets from the ONS that have mean and median earnings, however they use the old (not combined) local authorities. The combined local authorities are geographically adjacent to each other, which means that the variance in earnings is not particularly large, but I still need to obtain combined/ consolidated values for the new local authorities.

My approach so far, has been to take a weighted (based on number of jobs) mean of the old local authorities mean and median earnings, to get a single value for the new local authority. It seems likely that these values would be quite close to the actual (unobseved) values, however, I feel like I am comitting a statistical blunder by take a weighted mean of a mean/ median. For reference, this affects about 2% of my dataset.

Any suggestions for whether you think it's acceptable to carry forward my approach or if there is a more orbust way to proceed? I could omit these observations (local authorities) but then I would be subject to a selection bias, and this seems unecessary because the values for the local authorities that have been combined are so close together anyway that it is unlilely that I would be getting unreasonable values, I just want to make sure I am handling this properly. Thank you

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    $\begingroup$ I think your approach is a very natural starting point. I also think as a robustness check you can leave these out. If I were sitting in an economics presentation and someone described this, I would not question it. I'm making this a comment rather than an answer only because I don't have a substantial alternative suggestion. I think it's fine. $\endgroup$ Jun 27, 2023 at 7:32

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