U.S. Elasticities of Substitution and Factor Augmentation at the Industry Level

Abstract

We provide industry-level estimates of the elasticity of substitution (σ) between capital and labor in the United States. We also estimate rates of factor augmentation. Aggregate estimates are produced. Our empirical model comes from the first-order conditions associated with a constant-elasticity of substitution production function. Our data represent 35 industries at roughly the 2-digit SIC level, 1960SIC level, -2005. We find that aggregate U.S. σ is likely less than 0.620. σ is likely less than unity for a large majority of individual industries. Evidence also suggests that aggregate σ is less than the value-added share-weighted average of industry σ's. Aggregate technical change appears to be net labor-augmenting. This also appears to be true for the large majority of individual industries, but several industries may be characterized by net capital augmentation. When industry-level elasticity estimates are mapped to model sectors, the manufacturing sector σ is lower than that of services; the investment sector σ is lower than that of consumption.

Public Capital and the Labor Income Share

“…First, it embeds the widely-used Cobb-Douglas technology for σ = 1, in which case public capital augments private capital and labor in the same proportion (Hicks neutrality) [48]. However, the empirical evidence overwhelmingly suggests a value of σ lower than one [10][11][12][13][14], which raises the possibility of public capital being biased towards a particular factor. If σ < 1, then public capital that disproportionately augments private capital (i.e., η K > η L ) winds up biased towards labor; conversely, public capital that disproportionately augments labor (i.e., η K < η L ) winds up biased towards private capital.…”

“…If private capital and labor are sufficiently substitutable between each other-meaning an elasticity of substitution larger than one-a decrease in the price of capital goods induces firms to substitute from labor to capital, which decreases the labor share. A difficulty of this theory, however, is that the overwhelming majority of empirical studies find substitution elasticities that are much smaller than one [10][11][12][13][14].…”

Factor Substitution and Productivity in New Zealand

“…() suggest that factor substitutability is easiest in US agriculture, with about 1.6 in agriculture, 0.8 in manufacturing (an aggregation of mining, electricity and gas, manufacturing and construction) and 0.75 in aggregated service industries. On the other hand, estimates from other estimation approaches are generally significantly below unity for these industries for US data in Young () and Lawrence ().…”

A Dynamic Model of Firm Valuation

“…This is a standard procedure in the empirical economics literature (see, e.g., Balistreri, McDaniel and Wong, ; Fox and Smeets, ; Young, ).…”

“…This type of analysis could help practitioners improve the implementation of the model. 7 This is a standard procedure in the empirical economics literature (see, e.g.,Balistreri, McDaniel and Wong, 2003;Fox and Smeets, 2011;Young, 2013).…”