Essays on Firms Production Function, Markups, and the Share of their Income Going to Workers

Overview & Synopsis

Firms production function link their use of input factors to their production level. Production function estimates are at the same time important and untrustworthy. Important, because key indicators for policy design, such as the measure of aggregate markups, are derived from those estimates. Untrustworthy because they rely on identification assumptions.This project studies the assumptions underlying the usual techniques for estimating production functions: both their functional forms and the often assumed inputs flexibility. It then leverages production function estimates, to assess how firms ability to price over marginal income and the share of their income going to workers have evolved over the last 30 years.In Chapter 1 we provide evidence on the input flexibility assumption grounding production function estimation: the quasi instantaneous adjustment of either material or labor and delayed adjustment of capital hold. We rely on the existence of notches; values where after-tax profits decrease in before-tax sales in the French tax code.We identify which type of firms adjust their size in response to a transient notch. We do this by studying the ex-ante characteristics of firms below the tax cutoff. We find that firms who bunch tend to have larger elasticity of output with respect to materials and lower elasticity of output with respect to capital. Consistently, we also show that to adjust their remaining production firms, tend to primarily reduce spending on material.In Chapter 2 we leverage evidence on inputs flexibility to recover firm level markups of the universe of firms in France over the 1984-2016 period. De Loecker and Warzynski (2012) show that a firm’s markup proportionates the inverse of one of its flexible inputs revenue share. We analyze the evolution of aggregate markups in France and document that the rise of concentration correlates with a reallocation of market share towards high markup firms. We also show that the evolution of the labor share mirrors the evolution of markups: reallocation tends to decrease labor share while within firms, labor share rises.The choice of a functional form to describe firms production process is a compromise between theory and empirics. The workhorse production function is Cobb-Douglas and imposes a constant (and equal to 1) elasticity of substitution. Recent evidence in the empirical literature has however estimated a micro-elasticity of substitution significantly lower than one. While CES production functions allow for non-unit elasticity of substitution, they assume constant elasticity within industry and imply that the ratio of input use doesn’t depend on firm size.In Chapter 3, we show that the latter production function cannot account for IT inputs use in firms.With detailed data on software and hardware investments among French firms, we document that the firm-level demand for IT inputs relative to other inputs grows in the firm’s scale of operation. Theoretically, a non-homothetic CES production function helps rationalizing this empirical fact.We then analyze how the interaction of the fall of IT prices and the non-homothetic characteristics of IT inputs also help rationalize the empirical facts documented in chapter 2. First, since larger firms are more IT intensive in the cross-section, they benefit disproportionally from the fall in IT prices, rationalizing the rise of concentration. Similarly, since larger firms are more IT intensive in the cross-section, they operate at lower returns to scale and therefore have higher profit shares and lower labor shares. This explains how the rise in concentration drives a decline in aggregate labor shares. Finally, the comparative statistics of the model predicts that the fall of IT prices imply that when firms substitute toward IT they operate at higher returns to scale and therefore tend to have larger labor share, explaining the positive contribution to aggregate labor share of the within component.