\begin{document} \title{Estimating the Elasticity of Substitution and Import Sensitivity by Industry\vspace{0.5in}% } \author{Saad Ahmad and David Riker} \date{\vspace{1.5in}% \today} \thispagestyle{empty} \begin{center} {\Large A NEW METHOD FOR ESTIMATING THE ELASTICITY OF SUBSTITUTION \\ \vspace{0.25in} AND IMPORT SENSITIVITY BY INDUSTRY} \\ \vspace{1.5in} {\Large Saad Ahmad and David Riker} \\ \vspace{0.75in} {\Large May 2019}\\ \vspace{1.5in} \begin{abstract} \noindent We estimate the elasticity of substitution for specific manufacturing industries using a structural model of international trade in differentiated products and data on industry profit margins from the 2012 Economic Census. Then we use these elasticity estimates, along with import penetration rates in U.S. manufacturing industries, to estimate the sensitivity of domestic shipments to changes in tariffs and other import costs. \end{abstract} \end{center} \clearpage \newpage \doublespacing \setcounter{page}{1} \section{Introduction \label{sec: section1}} Demand elasticities are important inputs into model-based analysis of trade policy. The elasticity of substitution between products from different countries determines the magnitudes of changes in trade patterns in response to changes in tariff rates and other trade costs. There is a large econometric literature devoted to estimating the elasticity of substitution for different industries. Within this literature, there is considerable variation in estimates of the elasticity, reflecting differences in data sources and estimation techniques. [Saad: cite the literature, including \citeasnoun{HHIK2007}, and summarize in one paragraph.] In this paper, we contribute to this literature with a new set of elasticity values that add to the estimates in the literature. We develop a practical method for estimating the elasticity of substitution for detailed manufacturing industries using publicly available, industry data for the U.S. economy. Our calculations are consistent with the structural models of trade in differentiated products in \citeasnoun{Krugman1980} and the more recent literature with firm heterogeneity in \citeasnoun{Melitz2003}, and \citeasnoun{Chaney2008}.\footnote{[Add more recent examples of the constant mark-up literature...]} We use data from the 2012 Economic Census for manufacturing industries at the level of three-digit, four-digit, and six-digit NAICS codes. At the three-digit level, we estimate that the industries with the largest elasticity of substitution values are petroleum and coal products, primary metals, food manufacturing, wood products, and transportation equipment.\footnote{We report estimates for all of the detailed industries in the Appendices.} Our industry-specific elasticity estimates can be used as inputs into complex simulation models or in simpler calculations of economic effects. As an illustrative application, we combine the elasticity estimates with data on industry-level import penetration rates to calculate the changes in the domestic shipments of incumbent U.S. producers that would result from a hypothetical 10\% increase in the costs of competing imports. This import sensitivity measure can be used to quantify the impact of change in tariffs, exchange rates, or other types of foreign cost shocks. At the three-digit level, we estimate that the U.S. industries that would be most impacted by changes in the costs of imports are manufactures of leather, apparel, transportation equipment, and primary metals. The rest of the paper is presented in five parts. Section \ref{sec: section2} presents the theoretical framework. Section \ref{sec: section3} describes data sources and limitations. Section \ref{sec: section4} reports our estimates of the elasticity of substitution by industry. Section \ref{sec: section5} applies the estimates to calculate import sensitivity of U.S. manufacturing industries. Section \ref{sec: section6} concludes. \section{Theoretical Framework for Estimating the Elasticity \label{sec: section2}} The models of monopolistic competition and trade in differentiated products in \citeasnoun{Krugman1980}, \citeasnoun{Melitz2003}, \citeasnoun{Chaney2008}, \citeasnoun{HMR2008}, and subsequent studies assume that consumers have constant elasticity of substitution (CES) preferences with elasticity $\sigma$.\footnote{The monopolistic competition framework was introduced in \citeasnoun{DixitStigliz1977}.} In these models, there is a continuum of firms, each with monopoly power in the unique variety that it produces. The assumption of a continuum of varieties simplifies the pricing decision of the firms. Each firm takes the industry price index as given, since its own contribution to this index is infinitesimal by assumption. In this case, each firm perceives the own-price elasticity of demand for its product to be a constant that is equal to $-\sigma$. The mark-up of each firm, $m$, is the difference between price ($p$) and marginal cost ($c$) divided by price. \begin{equation}\label{eq:1} m = \frac{p \ - \ c}{p} \end{equation} \noindent At the firm's profit-maximizing price, this mark-up is equal to the reciprocal of the absolute value of the constant own-price elasticity. The elasticity of substitution $\sigma$ is simply the reciprocal of this mark-up. \begin{equation}\label{eq:2} \sigma = \frac{1}{m} = \frac{p}{p \ - \ c} \end{equation} \noindent Within the modeling framework, this inverse relationship between $\sigma$ and $m$ applies to the data for each firm in the industry as well as aggregated data for the industry as a whole. (This is true even in Melitz-Chaney models with firm heterogeneity in costs within the industry.) Marginal costs are constant and equal to average variable costs. \section{Data Sources and Limitations \label{sec: section3}} The source for the data on industry mark-ups is the 2012 Economic Census of the United States.\footnote{These data are available at \url{https://www.census.gov/data/tables/2012/econ/census/manufacturing-reports.html}.} In this paper, we analyze industries at the level of three-digit, four-digit, and six-digit NAICS codes. The total value of shipments and receipts for services ($TVS$) is a measure of net selling values at the factory gate. Annual payroll ($PAY$) includes all forms of compensation for all employees. Production worker annual wages ($PWW$) includes all compensation for workers up through the line-supervisor who engaged in fabricating, processing, assembling, and related production activities. The total cost of materials ($TCM$) are the direct charges for materials consumed, including parts, fuel, power, resales, and contract work. The source for the U.S. import and export data that we use in the import sensitivity calculations is the USITC's Trade Dataweb.\footnote{These data are available at \url{https://dataweb.usitc.gov/}.} Annual industry imports for consumption are valued on a landed duty paid basis. Domestic exports are valued on a free along-side ship basis. We calculate two alternative measures of mark-ups, based on different assumptions about whether cost items are fixed or variable. This generates a range for the estimated mark-up, and consequently for the estimates of $\sigma$. The high estimate $m_1$ assumes that only the wage payments to production workers are variable costs.\footnote{It assumes that wage payments to non-production workers are fixed costs.} The low estimate $m_2$ assumes that all wage payments are variable costs, so $m_2 < m_1$. \begin{equation}\label{eq:3} m_1 = \frac{TVS - PWW - TCM}{TVS} \end{equation} \begin{equation}\label{eq:4} m_2 = \frac{TVS - PAY - TCM}{TVS} \end{equation} \noindent The cost of materials may include some fixed costs, but we assume they are all variable costs. We assume that all other expenses of the industries are fixed costs. \noindent We use $m_1$ and $m_2$ to calculate a high and low estimate of the elasticity of substitution for each industry. \begin{equation}\label{eq:5} \sigma_1 = \frac{1}{m_1} \end{equation} \begin{equation}\label{eq:6} \sigma_2 = \frac{1}{m_2} \end{equation} \noindent $m_2 < m_1$ implies that $\sigma_1 < \sigma_2$. One advantage of our approach to estimating the elasticity of substitution is that the simple calculations generate a full set of $\sigma$ estimates for detailed manufacturing industries. A second advantage is that the data are from a reliable official census that is relatively recent and periodically updated.\footnote{It will be easy to update the estimates with the release of 2017 Economic Census data scheduled for September 2019, or they can be updated using Annual Survey of Manufactures data for other years.} The greatest limitation of our approach is that the calculation of marginal costs from the available data are at best approximate. \section{Estimates of the Elasticity of Substitution \label{sec: section4}} Table 1 reports our high and low estimates of the elasticity of substitution for the NAICS three-digit industries. They range from 1.8 to 7.0. The highest values are for the petroleum and coal products industry, followed by the primary metals, food manufacturing, wood products, and transportation equipment industries. Table 2 reports the mean, minimum, and maximum values of the elasticity of substitution at different levels of aggregation.\footnote{Appendix A reports the full set of estimates for the three-digit, four-digit, and six-digit NAICS industries.} $\sigma_2$ is always greater than $\sigma_1$. The estimates of the elasticity are similar at different levels of industry aggregation; they are not necessarily larger when the industries are further disaggregated. [Saad: do you have ideas for other interesting ways to summarize these estimates?] [Saad: please add a discussion about how these values relate to estimates of $\sigma$ in the econometrics literature.] \section{Import Sensitivity Calculations \label{sec: section5}} The elasticity of substitution is an important input in complex industry-specific or economy-wide simulation models, but it can also be combined with import share data to generate a simple estimate of the sensitivity of U.S. manufacturing firms to changes in import costs. We calculate the industry import penetration ratio $S$ using data on the values of imports ($M$), exports ($X$), and total shipments of the domestic industry ($Y$) for the NAICS code corresponding to the estimate of $\sigma$. \begin{equation}\label{eq:7} S = \frac{M}{Y-X-M} \end{equation} Equation (\ref{eq:8}) is a log-linear approximation of the percent change in the quantity of domestic shipments of incumbent domestic producers ($Q$) resulting from a hypothetical 10\% increase in the cost of all imports in the industry.\footnote{In the terminology of \citeasnoun{Chaney2008}, it is the adjustment along the intensive margin of trade.} \begin{equation}\label{eq:8} \% \Delta Q \ = \ (\sigma-1) \ S \ 10\% \end{equation} \noindent This is an estimate of the effect on each incumbent producer in a Krugman model with representative firms or in a Melitz-Chaney model with heterogeneous firms, as long as prices are exogenously determined by wage rates in other sectors, as in \citeasnoun{Chaney2008}.\footnote{\citeasnoun{Chaney2008} shows that aggregate trade effects do not depend on $\sigma$ when there is firm heterogeneity and a Pareto distribution of productivities, however, because the larger in negative adjustment on the intensive margin of trade with a larger value of $\sigma$ is exactly offset by the larger positive adjustment on the extensive margin of trade.} We calculate import penetrationrates and import sensitivity for the NAICS three-digit and four-digit codes.\footnote{We do not calculate these measures for the six-digit codes, because it is more difficult to concord domestic production data to trade data at this level of aggregation.} Table 3 reports the import penetration rates for all U.S. imports and, separately, for U.S. imports from China. Table 4 reports the sensitivity estimates for both categories of imports for the NAICS three-digit industries using $\sigma_1$, the low estimate of the elasticity of substitution.\footnote{Appendix B reports the full set of estimates for all of the NAICS three-digit and four-digit industries and both categories of imports.} In the column corresponding to an increase in the cost of all imports, the largest impacts are in the leather and allied product manufacturing and apparel industries, both over 10\%. These mostly reflect the very high import penetration rates in these industries. The second highest group, with effects between 9 and 10\%, are the transportation equipment and primary metals industries. These mostly reflect relatively high values of $\sigma$. The third highest group, with effects between 6 and 9\%, are the electrical equipment, computer and electronic products, and textile manufacturing industries. These mostly reflect high import penetration rates. In the column corresponding to an increase in the cost of imports from China only, the largest impacts are in the leather, apparel, and textile product industries. \section{Conclusions \label{sec: section6}} Our approach to estimating the elasticity of substitution for detailed manufacturing industries has practical data requirements yet it produces useful information and a starting point for further analysis. The strength of the approach is its simplicity. The greatest challenge is quantifying marginal costs. The approach could be further refined with more specific cost data. \clearpage \newpage \bibliographystyle{dcu} \bibliography{biblio} \newpage \begin{table}[tbph] \centering \begin{threeparttable} \caption{Estimates of the Elasticity of Substitution for Three-Digit Industries} \begin{tabular}{l r r} \toprule Industry (NAICS code) & $\sigma_1$ & $\sigma_2$ \\ \midrule Food Manufacturing (311) & 3.4 & 3.7 \\ Beverage and Tobacco Product Manufacturing (312) & 1.8 & 1.9 \\ Textile Manufacturing (313) & 3.1 & 3.6 \\ Textile Product Manufacturing (314) & 3.1 & 3.8 \\ Apparel Manufacturing (315) & 2.6 & 3.4 \\ Leather and Allied Product Manufacturing (316) & 3.1 & 3.9 \\ Wood Product Manufacturing (321) & 3.4 & 4.1 \\ Paper Manufacturing (322) & 2.6 & 2.8 \\ Printing and Related Support Activities (323) & 2.2 & 2.8 \\ Petroleum and Coal Products Manufacturing (324) & 6.7 & 7.0 \\ Chemical Manufacturing (325) & 2.3 & 2.5 \\ Plastics and Rubber Products Manufacturing (326) & 2.7 & 3.2 \\ Nonmetallic Mineral Product Manufacturing (327) & 2.3 & 2.6 \\ Primary Metal Manufacturing (331) & 3.8 & 4.2 \\ Fabricated Metal Product Manufacturing (332) & 2.5 & 3.1 \\ Machinery Manufacturing (333) & 2.6 & 3.1 \\ Computer and Electronic Product Manufacturing (334) & 2.0 & 2.7 \\ Electrical Equipment, Appliance, and Component Manufacturing (335) & 2.4 & 2.9 \\ Transportation Equipment Manufacturing (336) & 3.4 & 4.1 \\ Furniture and Related Product Manufacturing (337) & 2.4 & 2.9 \\ Miscellaneous Manufacturing (339) & 1.8 & 2.2 \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} \begin{table}[tbph] \centering \begin{threeparttable} \caption{Summary of Elasticity Estimates} \begin{tabular}{l r r r r r r} \toprule Level of Aggregation & Mean & Min & Max & Mean & Min & Max \\ \ & $\sigma_1$ & $\sigma_1$ & $\sigma_1$ & $\sigma_2$ & $\sigma_2$ & $\sigma_2$ \\ \midrule Three-Digit Industries & 2.9 & 1.8 & 6.7 & 3.4 & 1.9 & 7.0 \\ Four-Digit Industries & 2.9 & 1.3 & 6.7 & 3.3 & 1.3 & 5.4 \\ Six-Digit Industries & 2.8 & 1.3 & 11.6 & 3.4 & 1.3 & 12.8 \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} \begin{table}[tbph] \centering \begin{threeparttable} \caption{U.S. Import Penetration Rates (Percentage Points)} \begin{tabular}{l r r} \toprule NAICS & \ & Imports \\ Three-Digit & All & from \\ Industry & Imports & China \\ \midrule Food Manufacturing (311) & 7.8 & 0.6 \\ Beverage and Tobacco Product Manufacturing (312) & 12.4 & 0.0 \\ Textile Manufacturing (313) & 28.5 & 7.4 \\ Textile Product Manufacturing (314) & 50.9 & 28.1 \\ Apparel Manufacturing (315) & 91.2 & 36.6 \\ Leather and Allied Product Manufacturing (316) & 94.9 & 64.6 \\ Wood Product Manufacturing (321) & 16.2 & 4.2 \\ Paper Manufacturing (322) & 11.5 & 1.6 \\ Printing and Related Support Activities (323) & 6.8 & 3.2 \\ Petroleum and Coal Products Manufacturing (324) & 15.8 & 0.0 \\ Chemical Manufacturing (325) & 26.6 & 2.1 \\ Plastics and Rubber Products Manufacturing (326) & 20.7 & 6.9 \\ Nonmetallic Mineral Product Manufacturing (327) & 18.5 & 6.4 \\ Primary Metal Manufacturing (331) & 34.9 & 1.6 \\ Fabricated Metal Product Manufacturing (332) & 17.6 & 5.4 \\ Machinery Manufacturing (333) & 37.6 & 6.6 \\ Computer and Electronic Product Manufacturing (334) & 65.0 & 29.1 \\ Electrical Equipment, Appliance, and Component Manufacturing (335) & 55.7 & 21.6 \\ Transportation Equipment Manufacturing (336) & 36.4 & 1.5 \\ Furniture and Related Product Manufacturing (337) & 33.9 & 19.6 \\ Miscellaneous Manufacturing (339) & 50.1 & 18.3 \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} \begin{table}[tbph] \centering \begin{threeparttable} \caption{Estimates of Import Sensitivity (Percentage Points)} \begin{tabular}{l r r} \toprule NAICS & \ & Imports \\ Three-Digit & All & from \\ Industry & Imports & China \\ \midrule Food Manufacturing (311) & 1.8 & 0.1 \\ Beverage and Tobacco Product Manufacturing (312) & 1.0 & 0.0 \\ Textile Manufacturing (313) & 6.1 & 1.6 \\ Textile Product Manufacturing (314) & 10.6 & 5.8 \\ Apparel Manufacturing (315) & 14.8 & 6.0 \\ Leather and Allied Product Manufacturing (316) & 19.9 & 13.5 \\ Wood Product Manufacturing (321) & 4.0 & 1.0 \\ Paper Manufacturing (322) & 1.8 & 0.2 \\ Printing and Related Support Activities (323) & 0.8 & 0.4 \\ Petroleum and Coal Products Manufacturing (324) & 9.1 & 0.0 \\ Chemical Manufacturing (325) & 3.5 & 0.3 \\ Plastics and Rubber Products Manufacturing (326) & 3.6 & 1.2 \\ Nonmetallic Mineral Product Manufacturing (327) & 2.4 & 0.8 \\ Primary Metal Manufacturing (331) & 9.9 & 0.5 \\ Fabricated Metal Product Manufacturing (332) & 2.6 & 0.8 \\ Machinery Manufacturing (333) & 5.9 & 1.0 \\ Computer and Electronic Product Manufacturing (334) & 6.2 & 2.8 \\ Electrical Equipment, Appliance, and Component Manufacturing (335) & 7.9 & 3.1 \\ Transportation Equipment Manufacturing (336) & 8.8 & 0.4 \\ Furniture and Related Product Manufacturing (337) & 4.8 & 2.8 \\ Miscellaneous Manufacturing (339) & 4.0 & 1.5 \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} \newpage APPENDIX A [Detailed table to be added.] APPENDIX B [Detailed table to be added.] \end{document}