Gumpertz Function with Iterative Least Squares

[makaveli]

Hello,

I am a beginner in using EViews (hence, this is my first post here). I have run some linear regression models but now it comes to including a more complex model. It is panel data about the vehicles per capita in several countries in the world over a certain period of time. I try to test a model which I have found in this very paper.

Basically they test for the influence of income on vehicle rates with the help of a Gompertz function which looks like this:

Code: Select all

V(t) = gamma*teta*exp(alpha*exp(beta*GDP(t)))+(1-teta)*V(t-1)

Where:
- gamma = maximum saturation (let's assume that it is 850 vehicles per 1,000 persons)
- teta = speed of adjustment
- alpha, beta = as usual

They state that they used an "iterative least squares" method of which I assume that it is just normal OLS which is iterative because of the inclusion of the previous period. Is that correct?

Anyway, I tried to implement this model into EViews by entering an equation (in Estimate Equation) and using least squares:

Code: Select all

v = 850*c(1)*exp(c(2)*exp(c(3)*gdp))+(1-c(1))*v(-1)

What I get is an Error: "Overflow". If this seems utterly stupid to you, I am sorry, but I could not figure out any solution by using e.g. the EViews Illustrated Tutorial or searching in the EViews Help. What do I have to do differently?

If there might be any mistakes in my post, I am not a native speaker, so sorry for that, too.

Thank you very much!

[startz]

You might try to set some of the parameters close to those in the paper before the estimation. Enter

Code: Select all

c(2) = -5

or whatever.

[makaveli]

Sorry, this does not help. Still the same problem.

What comes next would be to estimate a country-specific c(3). But first I wanted to keep it as simple as possible.

[startz]

Did you also set c(3) to some appropriate negative value?

[makaveli]

Yes. Approximately -0.2. Why is there such a problem? Is the calculating capacity of EViews too low? Unfortunately I do only own the Student Version (poor guy).

[startz]

EViews an excellent job at these calculations. But computers are not mathematically perfect.

You might want to post your EViews workfile and the exact commands you've used to see if anyone has an idea what to do.

[makaveli]

Well unfortunately I cannot post my workfile, but all I did was loading the panel data and entering the equation above in Estimate Equation choosing least squares. A normal linear regression like

Code: Select all

ls v c gdp urb

,where urb is urbanisation rate, is easily possible. So I assume that it has to do something with this double-exponential formula. Is that possible?

[startz]

The problem is almost certainly due to the highly nonlinear formula.

[makaveli]

Well, shouldn't EViews at least take some time to calculate? The "Overflow"-Error pops up almost immediately after I press the Estimate-button. It seems to me that there is some sort of mistake in the formula or a problem with including the panel data in such a formula where there is no distinction between countries. But on the other hand the mistake cannot be THAT simple, can it?

[EViews Gareth]

Type this at the command line:

Code: Select all

series test = 850*c(1)*exp(c(2)*exp(c(3)*gdp))+(1-c(1))*v(-1)

Does that generate an error?

[startz]

What are the minimum and maximum values of GDP in your file?

[makaveli]

Sorry for the delayed reply:

Type this at the command line:

Code: Select all

series test = 850*c(1)*exp(c(2)*exp(c(3)*gdp))+(1-c(1))*v(-1)

Does that generate an error?

This does work perfectly well.

What are the minimum and maximum values of GDP in your file?

This could be a problem. Due to the limited capacity of observations in the Student Version of EViews, I had to reduce the sample to low income countries (as a concentration on these is the purpose of my estimation). I will test a complete sample (with higher incomce countries) on Monday when I am back in the office, where I have access to a full version.

Meanwhile I am going to reduce the model to something similar like this (p. 4). I will report again on Monday.

But thanks a lot for your help!!!

[makaveli]

What I did now is:

I entered the complete equation with all dummy variables that have been used in the paper. This looks like this:

Code: Select all

v = (850 + c(1)*d + c(2)*u)*(c(3)*r+c(4)*f)*exp(c(5)*exp(c(6)*gdp)) + (1-c(3)*r-c(4)*f)*v(-1)

I also defined the coefficients c(1) to c(6) with values similarly to the paper before I ran my regression, i.e.

- d for population density (if larger than the density of the US, its di = di - dUSA; otherwise 0)
- u for urbanisation (same) --> these two form the formula for a country specific saturation rate
- r = 1 if GDP(t) > GDP(t-1); 0 otherwise
- f = 1 if GDP(t) < GDP(t-1); 0 otherwise --> these two make up the formula for the speed of adjustment

Moreover I have enlarged the number of iterations in the "options"-tab of least squares in "Estimate Equation" to a dimension of something like 5000000. After running this, I still get an "Overflow"-Error.

BUT the coefficients have changed to some extent when I check them after the failed regression (which seems to be good, doesn't it?).

What I think could still cause this problems:

- I did not define c(6) as a cross-sectional coefficient (what Dargay & Gately have done), meaning that every country has its own beta (or c(6)). How do I do that?
- least squares is the wrong method to estimate it (even though those guys said that they have used iterative least squares). Is there another possibility?
- I have not yet weighted my observations by population.
- I did not yet estimate low income countries as one pooled group (so that it becomes something like a pooled cross-sectional regression).

Does anyone of you guys have some sort of idea why I'm still confronted with the Overflow-Error?

Thanks a lot!