Why use log me odels? o Log models are invariant to the scale of the variables since measuring percent changes e They give a direct estimate of elasticity e For models with y >0, the conditional distribution is often heteroskedastic or skewed, while In(y) is much less so o The distribution of In() is more narrow limiting the effect of outliers Economics 20- Prof anderson 6
Economics 20 - Prof. Anderson 6 Why use log models? Log models are invariant to the scale of the variables since measuring percent changes They give a direct estimate of elasticity For models with y > 0, the conditional distribution is often heteroskedastic or skewed, while ln(y) is much less so The distribution of ln(y) is more narrow, limiting the effect of outliers
Some rules of thumb e What types of variables are often used in log form? o Dollar amounts that must be positive Very large variables such as population o What types of variables are often used in level form? Variables measured in years o Variables that are a proportion or percent Economics 20- Prof anderson 7
Economics 20 - Prof. Anderson 7 Some Rules of Thumb What types of variables are often used in log form? Dollar amounts that must be positive Very large variables, such as population What types of variables are often used in level form? Variables measured in years Variables that are a proportion or percent
Quadratic models o For a model of the form y-Bo+ B-x+ B2x2+ u we cant interpret B, alone as measuring the change in y with respect to x, we need to take into account B, as well, since 4≈(B1+2B2 x|x、SO △ B+2B2x Economics 20- Prof anderson 8
Economics 20 - Prof. Anderson 8 Quadratic Models For a model of the form y = b0 + b1x + b2x 2 + u we can’t interpret b1 alone as measuring the change in y with respect to x, we need to take into account b2 as well, since ( ) x x y y x x 1 2 1 2 ˆ 2 ˆ ˆ ,so ˆ 2 ˆ ˆ b b b b + +