Below you will find a script that reproduces the results from the growth model example in section 4.5.1 of POE4. If yield grows at a constant rate of g, then yield at time t = 1 will be yieldl = yields (1 + g). For constant growth rates, repeated substitution produces
yieldf = yield0(1 + g)* (4.9)
Taking the natural log
ln(yieldt) = ln(yieldg) +1 ln(1 + g) = ві + (4.10)
add an error and you have a regression model. The parameter, в2 = ln(1 + g). This is an example of a log-linear model where the independent variable is time. The slope coefficient in such a model measures the approximate annual growth rate in the dependent variable.
1 open "@gretldirdatapoewa-wheat. gdt"
2 series lyield = log(greenough)
3 ols lyield const time
Lgreenough = -0.343366 + 0.0178439 time
T = 48 R2 = 0.6082 F(1, 46) = 73.945 a = 0.19916
(standard errors in parentheses)