econometricsA trend is usually used to proxy technical change in translog speciifcation of production, cost, profit, distance, etc functions. But can anyone explain why the trend is commonly specified as $t$ rather than $ln(t)$ like all other variables in a translog specification? I think the use of $t$ implies technology takes the form $e^t$.
Does the common use of $t$ instead of $ln(t)$ imply the exponential form is better than the alternative, and if so, why?
Yes. What is the mathematical consequence of this setup? Constant technological advance will mean that production becomes more efficient by the same factor between two sequent periods. The specification $ln(t)$ would imply that technology has a larger inpact between periods 2 and 3 than between periods 10 and 11.
Compare with interest yield, where the specification is $i^{t}$.
Thanks mzuba! I also found that $lnt$ is not invariant to the starting point of $t$; i.e., $t$=1,2,3.. may give a different result than $t$ = 5, 6, 7….This may explain the popularity of the $t$ specification which is free from this problem though at the cost of being restrictive. A short and clear discussion of the issues is in a paper by Watts and Quiggins (1984) below http://ageconsearch.umn.edu/bitstream/12259/1/52020091.pdf
All content is licensed under CC BY-SA 3.0.