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I want to come up with predictions of final energy demand per capita (fe) for a panel of countries. Explanatory variables are GDP per capita (gdp) and population density (pop) -- all variables are expressed in natural logarithms. I use R and the plm package for estimation.

My model is based on the following equation and I use the pgmm function of plm, which does an Arellano-Bond estimation:

$\text{log(fe)}_{it} = \delta \, \text{log(fe)}_{i,t-1} + \beta_1 \,\text{log(gdp)}_{it} + \beta_2 \,\text{log(gdp)}_{it}^2 + \beta_3 \,\text{log(pop)}_{it} + \beta_5 \, \text{log(year)}$

Now I want to forecast future values of final energy demand using scenarios for GDP per capita and population density and a logarithmic (sic!) time trend. If I understand the procedure correctly, this should work like this:

$\text{fe}_{it} = exp(\delta \, \text{log(fe)}_{i,t-1} + \beta_1 \,\text{log(gdp)}_{it} + \beta_2 \,\text{log(gdp)}_{it}^2 + \beta_3 \,\text{log(pop)}_{it} + \beta_5 \, \text{log(year)}) + exp(s^2/2)$ (where $s^2$ is the mean squared error of the residuals.).

I know simply plug in my scenario values and the final energy demand of the previous year, the numbers that I get are not even close to what I expected but rather off by several (dozens) orders of magnitude. For convenience, I leave out the term $exp(s^2/2)$, but since this is positive, it would only make my problem even larger.

What am I doing wrong?

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