Firm-level productivity studies: Illusions and a solution

Applied economists often wish to measure the effects of policy changes (like trade liberalization) or managerial decisions (like R&D expenditures or exporting) on firm-level productivity patterns. But firm-level data on physical quantities of output, capital, and intermediate inputs are typically unobservable. Therefore, when constructing productivity measures, most analysts proxy these variables with real sales revenues, depreciated capital spending, and real input expenditures. Our first objective is to argue that the resultant productivity indices have little to do with technical efficiency, product quality, or contributions to social welfare. Nonetheless, they are likely to be correlated with policy shocks and managerial decisions in misleading ways. Our second objective is to develop an alternative approach to inference. We assume firms' costs and revenues reflect a Bertrand-Nash equilibrium in a differentiated product industry, as in Berry [Berry, Steven (1994) "Estimating discrete-choice models of product differentiation," Rand Journal 25(2), pp. 242-262.]. This allows us to impute each firm's unobserved marginal costs and product appeal from its observed revenues and costs. With these in hand, we calculate each firm's contribution to consumer and producer surplus. Further, we link these welfare measures to policy and managerial decisions by assuming that marginal costs and product appeal indices follow vector autoregressive (VAR) processes, conditioned on policy proxies and/or managerial choice variables. We estimate the demand system parameters and VAR parameters jointly using Bayesian techniques. Applying our methodology to panel data on Colombian paper producers, we study the relation between our welfare-based measures and conventional productivity measures. We find that the two are only weakly correlated with one another. Further, they give contrasting pictures of the relationship between firms' performances and their participation in foreign markets. One reason is that product appeal variation has little effect on standard productivity indices, but it is captured by welfare-based performance measures.