We can talk about a percentage increase in a profit margin…but that really only serves to confuse.
Suppose I want to look at an after-tax profit margin (in this case, “Profit per unit of real gross value added of non-financial enterprises: after-tax corporate profits with IVA and CCAdj (unit profits of current production)” (A466RD3Q052SBEA) ).
Figure 1: Profit per unit of real gross value added in non-financial corporations, after tax (blue). The NBER has defined peak-to-trough recession dates as shaded. Red dotted lines at 1992Q4-2022Q4; arrows indicate percentage and percentage point growth between these dates. Source: BEA via FRED, NBER and author’s calculations.
We could talk about a growth rate as a percentage of a profit margin (4.5%/year in Figure 1), but it’s weird to calculate a percentage change on a percentage. This is why, when considering changes in ratios, we usually speak of changes in percentage points (0.4 percentage points/year in Figure 1), thus avoiding unnecessary confusion. (Those deliberately confusing may want to use “percentage change” in ratios, then).
When to use percentage change? Well, when you discuss something in the levels. For example, Figure 2 below.
Figure 2: Profit of the non-financial corporate sector, after tax, in billions of Ch2012$ SAAR, on a logarithmic scale (blue). Profits deflated by the GDP deflator. The NBER has defined peak-to-trough recession dates as shaded. Red dotted lines at 1992Q4-2022Q4; the arrows indicate percentage point growth between these dates. Source: BEA via FRED, NBER and author’s calculations.
The other point I want to make is that technically something growing exponentially doesn’t necessarily mean it’s growing rapidly. Maybe, maybe not. For example, something growing at 0.01% per year may grow much slower than something growing at 0.01 units per year… Exponential simply means that if the series is recorded, the recorded series grows linearly.