Using gret l for Principles of Econometrics, 4th Edition
Growth Model
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.
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Figure 4.17: The plot of the residuals from a linear model. There is some visual evidence of serial correlation, suggesting that the linear model is misspecified. |
1 open "@gretldirdatapoewa-wheat. gdt"
2 series lyield = log(greenough)
3 ols lyield const time
This produces
Lgreenough = -0.343366 + 0.0178439 time
(0.058404) (0.0020751)
T = 48 R2 = 0.6082 F(1, 46) = 73.945 a = 0.19916
(standard errors in parentheses)
The estimated coefficient b2 = ln(1 + g) = 0.0178. This implies that the growth rate in wheat yield is approximately 1.78% annually over the course of the sample.[20]
