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.


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]

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