Retrieving initial capital distributions from panel data

A common problem in the empirical production analysis at the firm-level is that the initial values of capital are often missing in the data. Most empirical studies impute initial capital according to some ad hoc criteria based on a single arbitrary proxy. This paper evaluates the bias of production function estimations that is introduced when these traditional initial value approximations are used. We propose a generalized framework to deal with the missing initial capital problem by using multiple proxies where the choice of proxies is data-driven. We conduct a series of Monte Carlo experiments where the proposed method is tested against traditional approaches and apply the method to the firm-level data.