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My two cents worth:
Recent statistical analysis of remaining records shows that Allied victory claims vastly exceed corresponding German losses. No argument from me there. I have read that these claims in fact exceed total German production of aircraft during the war, let alone losses.
The reasons for many of these discrepancies have been well-covered here: the difference between a victory and a kill, the fog of war, a single aircraft credited to multiple pilots, "accounting" errors on the German or Allied side (date/time don't match), missing records and so on.
Where the research has to target itself, IMHO, is those claims where a German aircraft is clearly claimed as destroyed or captured and there is no corresponding loss in the German records. If we have multiple witnesses to the destruction of a German aircraft, or the body of its pilot in Allied hands, or the aircraft itself sitting in an Allied hangar, and there is no corresponding German loss reported, then we have to question the accuracy of those records. I don't know that this has been done yet.
I don't believe that the answer to this issue has to be that one side or the other were deliberate liars. Overclaiming is to be expected for victories and underclaiming is to be expected for losses, if you ask me. The real issue is deliberately lying about it, and the destroyed aircraft are the key to this.
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