Markup Estimation: Monetary Values or Physical Quantities?

The mainstream methods of production function estimation, such as Olley and Pakes (1996), Levinsohn and Petrin (2003), and Ackerberg et al. (2015), commonly used for markup estimation, require physical quantities of output and inputs. However, due to data limitations, most empirical work on production function parameters use \textit{monetary values} (revenue or expenditure) as proxies for physical quantities. In this paper, I show that using monetary values can result in an endogeneity problem and produce biased production function estimates that are not captured by current estimation methods. The root of this problem is a potential correlation between unobserved prices and input demands, which can also violate the optimal input demand assumption in Levinsohn and Petrin (2003), depending on the elasticity. I characterize this bias analytically and use simulated and actual data for French manufacturing firms to estimate markup using both physical quantities and monetary values. The results demonstrate that the bias in production function estimates is significant (35\%), which has implications for important firm-level variables such as markup.