Lags and logs

[Diego Straniero]

Hello all,

I am estimating a model where both I use a variable in natural logarithm form and its first lag. My question is should the lagged values be in logs as well or actual values. Does this depend on the variable itself and what will it change for interpretation and results? Thank you.

[Nick Cox]

If thinking or working with logs makes sense, then differences should be calculated on that scale. Change or difference is essentially multiplicative.

If thinking or working on the original scale makes sense, then differences should be calculated on that scale. Change or difference is essentially additive.

I can't think of a case for mixing modes of expression, but would be interested to hear of examples to the contrary.