ch 7.1-3: linear regression on change

[Phlos]

Hello, in the first examples for linear regression on US consumption expenditure (section 7.1 to 7.3), the linear regressions are made on the change in the different values. The reason for this is not mentioned explicitly. I suppose it has something to do with (a) the change is the relevant signal we want to study, not the absolute value, and/or (b) the linear regression wouldn't work otherwise. I'm not an economist so for me this is not very clear. Could you comment on this? (Adding an explicit explanation in the text in the book would also be beneficial I think)

[robjhyndman]

Both of the reasons you suggest are valid here.

(a) The change in this example is the relevant signal to study from an economic point of view. The actual value of each economic variable depends on the scale chosen, but the % change is consistent across scales. Also, these variables are changing all the time (due to inflation, population growth, etc.) By taking % changes, we remove the effect of the underlying growth (it becomes part of the intercept), and let the parameters measure the remaining relationship.

(b) A linear regression assumes that the errors are iid, and that would not happen with the original absolute values. In particular, you can't estimate a linear regression on nonstationary data. We discuss it later in the book 10.1.