Using a time trend to measure technical change is an implicit acknowledgment that at least the dependent variable (e.g., factor demands or fac¬tor shares) is nonstationary.
Many studies based on duality models use a linear deterministic time trend to measure such an omitted variable (e.g., Binswanger; Lopez; Fulginiti and Perrin; Mos- chini; Shumway and Alexander).
Furthermore, in the absence of a direct measure of technical change, a time-series ap¬proach to estimating duality models allows a richer specification of the process representing technical change.
When no direct measure of this variable is available, technical change becomes an omitted variable when estimating empirical relationships (Clark, Furtan, and Taylor).
For example, modeling tech¬nical change as a random walk with drift in¬cludes the deterministic time trend as a special case.
While realizations of a random walk with drift and a deterministic time trend appear similar when plotted against time, there are fundamen¬tal differences between them (Nelson and Kang; Dickey, Bell, and Miller).
The effect of technical change is to increase fac¬tor productivity or to change the income shares among factors or the revenue shares among out¬puts.
The differences lead to serious econometric consequences if a deter¬ministic time trend is incorrectly used in a regression model.
In particular, for a regression in the levels of the data, OLS coefficient esti¬mates will be inefficient, significance levels will be inflated, and there will be a high probability of concluding that there is a significant rela¬tionship among the variables when in fact no relationship exists.
If the data are non¬stationary, estimating duality models becomes a time-series problem as well as a regression problem.
However, this is only one of many representations of technical change and an unduly restrictive one at that.
This result has been well established for many macroeconomic time se¬ries (Nelson and Plosser).
A single iteration of the Cochrane-Orcutt procedure to correct for serial correlation will not correct these problems (Nel¬son and Kang).