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Hi, I am running a double log regression on the demand for bananas:

log(Y) = log(x1) + log(x2) + c

where Y = per capita banana sales
x1 = price
x2 = income
c = constant


I've been told to include a "time trend" in this regression however I have no idea what that means, or what the estimated coefficent shows I've been told that I can include a time trend in eviews by inputting the following into "estimate equation"

log(y) log(x1) log(x2) c @trend

but again, I don't know what the coefficient that I get for "@trend" actually shows, please help! thanks

If the coefficient of trend variable turns out be significant, then it will mean that per capita banana sales do change with respect to time in addition to price and income. In other words, time is an important determinant and effects the dependent variable. Trend variable is a general independent variable, which takes values between 1 and the number of observations in your sample in an ascending order. The associated coefficent measures the size of this impact.

Aside from this economic intrepretation, there may also be several econometric issues with this equation in terms of stationarity. You may consider to filter (detrend) your series beforehand or may prefer to use logarithmic difference as the transformation method. I think you will better off referring to econometric or time series analysis textbooks before going further...

thanks very much for your reply, I am running this regression for each of the 51 states of the USA, to see whether there are differences between the states. These were estimated using OLS and inflation has been removed from the values. Of my 51 regressions outputs, the majority of them have an r squared above 0.90, HOWEVER, often my coefficients are not significant. Overall, using the 10% level of significance,

LOG(LAGGEDSALES) is significant in 40 out of 51 regressions
LOG(PRICE) 23 out of 51
LOG(INCOME) 8 out of 51
C 6 out of 51
@TREND 9 out of 51

This strikes me as very low, I would have expected price and income to be significant more times then that. Do you think multicollinearity could be a problem? What topics would you suggest looking for in the econometric textbooks? Stationarity/nonstationarity... serial correlation (LM test as I have a lagged Y as an independent variable)...cointegration... anything else? thanks again

i suspected there could be multicollinearity as the r squared's were high, but the explanatory variables were often not significant. I calculated the VIF for each of my 51 regressions, and for 44 out of 51 regressions, the VIF was above 5 - in most cases it was WELL above 5. In fact, for the regressions where the R squared was 0.99, the VIF was over 100 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.

do you think transforming the variables by taking first differences will correct this problem of multicollinearity?

Exactly what problem do you think multicollinearity causes?

Exactly what problem do you think multicollinearity causes?

high standard errors - I'm thinking this is why I'm getting insignificant coefficients but a high r squared, which is often 0.99

That's certainly true. But why do you think that high standard errors are a problem? Sure, it would be nice if they were smaller. But unless you have prior information there isn't any way to get them smaller while still having unbiased coefficients.

The majority of my vifs seem way too big I'm hoping that after I've corrected for the multicollinearity that price and income will be significant in more cases, as it is in other papers. Even after i've corrected for multicollinearity, serial correlation may still be an issue. I don't know which one to correct first although I think I'll try correcting the multicollinearity first. With that said though, apparently you should often leave the multicollinearity unadjusted, so I may end up just correcting for the serial correlation

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.