I hate looking at my published papers because there are often typos in them which I didn't catch at the proofs stage... One of our PhD students, Nitin Gupta, found a typo in my paper: Elasticities of substitution and complementarity, Journal of Productivity Analysis 36(1): 79-89. The formula in equation (20) for the Allen Elasticity of Substitution between inputs Xi and Xj, AESij, should be:
The denominator is wrong in the formula in the paper. The formula for AESii is correct. Note that these formulae only make sense if you have normalized the data in some way. If, for example, you have indexed all variables to one in the first year then the formula will give the elasticity in the first year. It makes the most sense when like me you have normalized on the sample mean for each variable and so this elasticity is at some notional mean point. If you want to calculate the elasticity at different points in time or you haven't normalized the data then you can't use this formula. This is because the parameters associated with the first order terms in the translog function depend on the units used.
The good news is that I used the correct formula in all the calculations in the paper. The bigger picture message is don't believe that a formula is correct just because it is printed in a refereed journal!