Based on observed data 1976-2011, I got a model to estimate crop productivity like: Y= 0.18*time - 0.005*time^2 + 0.15*temp + 2.33. and then I want to estimate the impacts of climate change (high temperature) by 2100. Please note that [0.18*time - 0.005*time^2] is called technological trend/progress.
The issue for me is [0.19*time - 0.005*time^2] will be negative when time=39. if I set time = since 1976, time=38 corresponds with 2015. Any suggestion to prevent negative values of [0.18*time - 0.005*time^2] ?
Please list any related papers
First elementary consideration: are all the variable significant? Check with the t test. Second did you check for collinearity among variables and error correlation? A suggestion is to use the log transformation of variables. Eventually use dummy variables if there is presence of seasonality. Try it
Please go through the paper "http://ageconsearch.umn.edu/bitstream/196659/2/1-PS-Birthal.pdf ".
@Purushottam,
I downloaded the paper you suggested but I didn't see any explanation about setting of time variables.
Let's say observed data is from the period 1970-2014, Was this paper setting time variable = 1 starting from 1970 ?
And for the future prediction, Was this paper setting time variable = 1 again starting from 2015 ?
If time and time^2 are giving you non-sense results, perhaps you need to use another function that has a non-linear increase with time. Instead of time and time^2, try and exponential term.
Muhamad -
I agree with Andrew that the negative time-squared term seems to be a problem. If you overfit/over-complicate a model to a set of data without validation using other data, you will often have a problem, and in a time series like this, you already know that such a term would eventually be a problem.
For crop productivity, I would expect time to be of short-lived usefulness. Perhaps you should not be looking at a time series forecast at all, but rather prediction from cross-sectional data, if that is possible for you.
At any rate, I would look to subject matter theory to find other crucial independent variables. If time is still used, perhaps because you are looking at a newly developing area, I'd expect to use something that goes to zero quickly and you should reassess your model soon.
All you really have is temperature. What about precipitation? Maybe you could categorize by soil type. You don't want to over-complicate your model, but you don't want an underfit either, which could result in omitted variable bias. What other information may be crucial, and can you obtain it?
Cheers - Jim
PS - Ah! From the topic list you have, I see you are interested in climate change. It seems to me that both temperature and precipitation are tied to climate change. What else?
Muhamad -
I just glanced at that (apparently/hopefully open access??) article noted by Purushottam, and I think you should give it another look. At the end of page 146 they give a 'formula,' and then in the first column of page 147, they explain the terms. The full 'formula' may be more complex than you need or can justify with data available to you, and is rather nebulous, but the explanation in that first column of page 147 may give you some ideas.
Cheers - Jim
Muhamad, all these proposals are good, but please lay down more of your variables we would easily see how to go around the problem. the paper download investigates alot of channels to which climate change affects crop yield...what franco says up there is a good idea ...use time dummy to check for seasonality. xi: xtset (i.time*x1) either with fixed models or any other model that you are using...this would help you have an intuition of time significance...! good luck
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