On the difference between an accounting identity and a model,
[T]here is a crucial difference between this law [β = s(avings)/g(rowth)] and the law α = r × β, whch I called the first fundamental law of capitalism in Chapter 1. According to that law, the share of capital income in nationa income, α, is equal to the average rate of return on capital, r, times the capital/income ratio, β. It is important to realize that the law α = r × β is actually a pure accounting identity, valid at all times in all places, by construction. Indeed, one can view it as a definition of the share of capital in national income (or of the rate of return on capital, depending on which parameter is easiest to measure) rather than as a law. By contrast, the law β = s/g is the result of a dynamic process: it represents a state of equilibrium toward which an economy will tend if the savings rate is s and the growth rate g, but that equilibrium state is never perfectly realized in practice.
— Thomas Piketty, Capital in the Twenty-First Century (Cambridge: The Belknap Press, 2014), pp. 168–169.