Abstract: Growth models in the tradition of Solow and Romer are framed in terms of production functions. Consequently, they are equally subject to a criticism developed by, among others, Phelps Brown (1957), Simon (1979a), and Samuelson (1979). These authors argued that production function estimations are flawed exercises because output, labor and capital stock, are definitionally related through an accounting identity. The identity argument helps demystify two illusions in the literature: (i) finding the Holy Grail: total factor productivity is, by construction, a weighted average of dollars per worker and a pure number (the rate of profit or the rental rate of capital); and (ii) the possibility of testing: if estimated properly, production function regressions will yield: (a) a very high fit, potentially an R2 of unity; and (b) estimated factor elasticities equal to the factor shares, hence they must always add up to 1. We illustrate these points through a series of well-known growth accounting exercises and models directly derived from production functions. They are futile exercises. We conclude that we know substantially less than we think about growth and that many of the discussions in the neoclassical growth literature are Kuhnian puzzles that only make sense within this paradigm.