Measuring Returns to Scale in Nineteenth-Century French Industry

Gross-output vs value-added production function. With the Cobb-Douglas form used by Sicsic (1994), increasing returns to scale in the value-added production function are equivalent to increasing returns to scale in the gross-output production function. The choice between value-added and gross-output production function is nevertheless not innocuous because returns to scale estimated from the value-added production function overstate (understate) the degree of returns to scale in the case of increasing (decreasing) returns. To see this, let i = 1, . . . , N index observations and let yi denote output, li labor, mi materials, and ki capital. Consider the gross-output production function yi = e 0ll i m βm i k βk i e 2i