Since the output and input variables used in the production function are based on monetary values (deflated at the industry-year level), the resulting estimated measures of efficiency are revenue based (Klette and Griliches 1996). Observing output prices allows us to compute physical quantity produced by the firm and hence isolate demand factors from revenue-based productivity (Foster, Haltiwanger, and Syverson 2008). TFPQit is the Hicks-neutral measure of physical total factor productivity we are interested in estimating. Using the method in Foster, Haltiwanger, and Syverson (2008), a simple measure of technical efficiency is constructed: tfpqit = tfprit /lnpit. Although firm-level prices are observed and output is in physical quantity, capital and material inputs are still based on expenditure deflated with an industry-specific price index. This implies that for any deviation from a perfectly competitive input market, capital and material inputs would also include unobserved idiosyncratic input price variation. To correct for the “input price” bias arising from the correlation between input prices and quantities, Grover and Maloney (2021) rely on Blum et al. (2018), which extends the Gandhi, Navarro, and Rivers (2020) method to recover estimates of markups using output price data. Following De Loecker et al. (2016), this methodology is extended to address the input prices bias stemming from unobserved firm-level input prices, henceforth TFPQit , along the lines of De Loecker et al. (2016). After estimating the production function parameters, firm-level markups (μit) can be recovered from marginal costs (mcit) and output prices. Specifically, markups are calculated based on the expression derived from the first order condition of the firm’s cost minimization of the flexible material inputs: µit = ln α itm − lnSit − εit (2A.2) where α mit is the output elasticity of materials estimated from the production function; Sit is the share of material inputs expenditure (Mit) over total sales (Rit); and εit is the ex post shocks to the estimated production function. As markups are the wedge between prices and marginal costs, mcit = lnPit − μit.
Notes 1. See https://www.worldbank.org/en/topic/urbandevelopment/overview#1. 2. See Chauvin et al. (2017) for the United States, China, and India; Combes, Duranton, and Gobillon (2008) for France; De la Roca and Puga (2017) for Spain; and Henderson, Nigmatulina, and Kriticos (2019) for Africa. 3. They use building heights to develop a measure of density adjusted for floor area and show that by not taking into account the quality of built structures, naive measures of population density end up conflating crowding and livable densities.
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Place, Productivity, and Prosperity
