A Semiotic Reading of Becker-Woessmann (2009): The Footnote Parabola as Interpretant, Not as a Competing Causal Model

This study offers a semiotic reading of Becker and Woessmann (2009), "Was Weber Wrong? A Human Capital Theory of Protestant Economic History," The Quarterly Journal of Economics, 124(2), 531-596. It does not propose a competing causal model, it does not re-estimate the econometric parameters, and it does not touch the reported Standard Error. Two layers are strictly separated. The first layer is causal and belongs to Becker and Woessmann: Protestantism affects literacy and economic prosperity, identified by distance to Wittenberg as an instrumental variable in a Two-Stage Least Squares (2SLS) framework. The second layer is semiotic and belongs to this study: the textual structure of the paper, in particular Footnotes 22, 23, and 45, is read through the parabolic interpretant f(x) = -x^2 + 45x + 0.25. The vertex x = 22.5, f(22.5) = 506.5, is mapped semiologically to the published IV coefficient 0.506 as an isomorphic marker, not as a new estimate. The Standard Error 0.081 remains in its proper econometric domain. The constant 0.25 = 1/4 is read as one in four: the testing goes up to four times. Test 1: Are Protestants more prosperous? Test 2: Are Protestants more literate? Test 3: Is it causal, tested via distance to Wittenberg? Test 4: If literacy is controlled, are Protestants still more prosperous? The footnote parabola is therefore an interpretant in Peirce's triadic sense: it reads a causal text, it does not replace causal inference.