# Percent vs. Percentage Points…and…Exponential vs. Linear

One can talk about a percent increase in a profit margin… but that really only serves to confuse.

Suppose I wanted to look at an after tax profit margin (in this case “Profit per unit of real gross value added of nonfinancial corporate business: Corporate profits after tax with IVA and CCAdj (unit profits from current production)” (A466RD3Q052SBEA)).

**Figure 1:** Profit per unit real gross value added in nonfinancial corporate , after tax (blue). NBER defined peak-to-trough recession dates shaded gray. Red dashed lines at 1992Q4-2022Q4; arrows denote percent and percentage point growth between those dates. Source: BEA via FRED, NBER, and author’s calculations.

One could talk about a percentage growth rate of a profit margin (4.5%/yr in Figure 1), but it’s weird to calculate a percentage change on a percent. That’s why typically, when considering changes in ratios, one speaks of percentage point changes (0.4 ppts/yr in Figure 1), thereby avoiding needless confusion. (Those who deliberately want to confuse might want to use “percent change” of ratios, then).

When to use percent change? Well, when discussing something in levels. E.g., Figure 2 below.

**Figure 2:** Profit for nonfinancial corporate business sector, after tax, on log scale (blue). NBER defined peak-to-trough recession dates shaded gray. Red dashed lines at 1992Q4-2022Q4; arrows denote percentage point growth between those 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 mean it’s necessarily growing fast. Might be, might not be. For instance something growing at 0.01% per year might be increasing a lot slower than something growing at 0.01 units per year… Exponential just means that if the series is logged, the logged series grows linearly.

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