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@leah_boustan My intuition; (@cjwich @marcfbellemare @KarenPence18’s are likely better): ln(a+•) emphasizes extensive margin more as a↓0. At extreme a=0, only extensive margin matters since e.g., f(1)–f(0)= –∞ Choosing a=1 is arbitrary. And measured using f(1)–f(0), sinh⁻¹ is like a≈0.7