Elasticity

Elasticity is an important concept in economics. It measures how responsiveness one variable is to changes in another. Mathematically, the concept of elasticity is fairly simple:

percentage change in y Ay/y

percentage change in x Ax/x ‘

Подпись: є
Подпись: AE(y)/E(y) Ax/x image031 Подпись: (2.4)

In terms of the regression function, we are interested in the elasticity of average food expenditures with respect to changes in income:

E(y) and x are usually replaced by their sample means and в2 by its estimate. The mean of food_exp and income can be obtained by using the cursor to highlight both variables, use the

View>Summary statistics from the menu bar as shown in Figure 2.10, and the computation can be done by hand. However, you can make this even easier by using the gretl language to do all of the computations-no calculator needed! Simply open up a new script and type in:

1 ols food_exp const income —quiet

2 scalar elast=$coeff(income)*mean(income)/mean(food_exp)

This yields the output shown in figure 2.11.

Following a least squares regression, Gretl stores the least squares estimates of the constant and the slope in variables called $coeff(const) and $coeff(income), respectively. In addition, it uses mean(income) and mean(food_exp)to compute the mean of the variables income and food_exp. The —quiet option is convenient when you don’t want or need the output from the regression printed to the screen. The result from this computation appears below in Figure 2.12.

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