I am estimating the impacts of climate on crop productivity.
Y= (0.1272*time - 0.00424*time^2) - 0.09*temperature + constant
"(0.1272*time - 0.00424*time^2)" is a representation of technological progress and "-0.17*temperature" is the impacts of temperature Y (crop productivity).
This model is regressed from observed data 1976-2011.
so time is 1 from 1976 and so on, (time=36 in 2011)
I want to forecast the effects of climate on crop productivity in future.
But, the effects of technological progress will be negative
as "(0.1272*time - 0.00424*time^2)" will be negative after time > 72.
Can I reformulate the coefficients "0.1272" and "0.00424" so
the effects of technological progress will not negative ?
If yes, what are scientific background ?
Why not recalibrate your analysis around different planting sessions, scaled into temptation changes, or perhaps consider your remodelling along different scales of maturation - e.g. arable, yearly, biennial and permanent crop?
I think these suggestions will reshape your outcomes.
Dear Muhamad,
It probably would be a better model if you try to capture technology with a different variable besides Time. It could be a dummy variable that capture different methods used to grow crops. 1976-2011 is a long time, so you might have changed the use of fertilizer for instance.
You can still have time. The model can be:
Yield = f(Time, Method, Temperature)
You must also follow the normal procedure to ensure that the independent variables are not correlated. Also, keep the observation in time order to test for auto-correlation.
If you want to keep working with your polynomial time variable, then you should try some other specifications. If you hope to capture returns to scale, then you can look at the work of Robert Lucas Jr, and Paul Romer for other specifications as related to the Cobb-Douglas type.
Good luck in your research.
I think, you should better include sin(time/a) and cos(time/a) to model the temporal/seasonal structures (if there are e.g. centuries of better crop productivity and vice versa). These Fourier series you can also adjust for the length of the periodicity of your data. Maybe you also have to include more than one seasonal structure.
What is the rationale behind including the squared temporal trend? As the crop productivity is probably no process with an polynomial trend (of order 2 and more), the regressor "time squared" would always lead to bad forecasts over a longer period of time. If you include higher order polynomials, that effect could vanish. However, the limit of the temporal trend is still (plus or minus) infinity as t approaches infinity.
@Lall, Are there any supporting papers explain to add more variables other than time to capture technological trend ?
@Philipp, a linear time variable relates to acceleration of techno progress and squared term relates to deceleration of techno progress
@Andrey, I'm not sure the domain means ?
How do you measure Y, what values can Y take?
Is it a positive number?
If is always positive, you can apply Box-Cox transformations to Y and it then never will be negative.
Given the fact that you observe this technological progress and the deceleration of this progress, a logarithmic dependence could possibly also help to solve your problem.
If you think of technical progress as a growth process (i e. It tends to incease at a % rate) then you should model it usinG logs of your variables. If Y=100 or 200 an increase of 5% implies increases of 5 or 10 respectively if you are using growth rates. You are also likely to have less heteroskedasticity if you use logs. Of course you should also check for unit roots and include other variables to improce your model
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