You raised a very interesting question on one of the most famous "unknown" in econometrics yet it appears most often in econometric models and has received most of the critics as well as stimulated emny econometricians to find new more creative roads in order to avoid the use of that famous "unknown" in the estimation of time series models. (eg. someone has already mentioned cointegration)
When I include a linear time trend in my economic model To, To+1, To+2,...,To+n) where n: number of observations, and estimate its coefficient which is often interpreted as a measure of the impact of a multitude of known and unknown factors (subjectively, as a matter of fact). Logically - and strictly speaking too - that kind of interpretation or inference is applicable to the estimation time periods only. Outside the estimation time periods, one never knows what those subjective known and unknown unmeasurable factors behave both qualitatively and quantitatively. Furthermore, the linearity of the time trend poses many questions: (i) why should it be linear? (ii) if the trend is non-linear then under what conditions its inclusion does not influence the magnitude as well as the statistical significance of the estimates for other parameters in the model? (iii) the law of nature, especially in economics, commonly accepted is "what goes up must come down one day, and the reverse is also true" so why including the
linear time trend in your model which blatantly violates this law when n --> infinity ?
Some known efforts of mathematicians, statisticians, econometricians, economists have been published in well-known and less known journals to respond to to those questions (eg. the work of John Blatt (mathematical meaning of a time trend), C Granger and many other econometricians (on cointegration and related issues), Ho-Trieu & Tucker (on logarithmic time trend which is
non-linear with results alluding to a proof rejecting the existence of linear trend, and linear trend is just a misnomer of a special form of cyclical trend when periodicity is large; please see
http://ideas.repec.org/a/ags/remaae/12288.html for further details).
So, to conclude, you are not the only econometrician who is wondering about the meaning of the simple but amazing "unknown" time trend in your econometric model for banana consumption in the USA. All the best.
I've been told that I can include a time trend in eviews by inputting the following into "estimate equation"
Interestingly, for the regressions that had a low VIF (i.e <5), their R squared was often far smaller, i.e around 0.5 or 0.6 as opposed to an R squared of 0.90 for regressions with a high VIF.