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\begin{document}

\title{Differences in Exposure to International Trade Across Demographic Groups}
\author{David Riker}
\date{\vspace{1.5in}%
\today}

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{\Large  \textbf{DIFFERENCES IN EXPOSURE TO}} \\
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{\Large  \textbf{INTERNATIONAL TRADE}} \\
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{\Large  \textbf{ACROSS DEMOGRAPHIC GROUPS}} \\


\vspace{0.75in}

{\Large David Riker} \\

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{\large ECONOMICS WORKING PAPER SERIES}\\ 
Working Paper 2023--05--A \\ \vspace{0.5in}
U.S. INTERNATIONAL TRADE COMMISSION \\
500 E Street SW \\
Washington, DC 20436 \\
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May 2023 \\

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\vfill

\noindent The author thanks Peter Herman, Ross Jestrab, and Bill Powers for helpful comments and suggestions on an earlier draft. Office of Economics working papers are the result of ongoing professional research of USITC Staff and are solely meant to represent the opinions and professional research of individual authors. These papers are not meant to represent in any way the views of the U.S. International Trade Commission or any of its individual Commissioners.

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Differences in Exposure to International Trade Across Demographic Groups \\
David Riker \\
Economics Working Paper 2023--05--A \\ 
May 2023 \\~\\
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\begin{abstract}
\noindent We estimate the exposure of demographic groups of U.S. workers to international trade using employment-weighted averages of the trade intensities of U.S. manufacturing industries in 2021. Differences in the race and education of the workers have larger effects on the measures of trade exposure than differences in their gender, ethnicity, or occupation. The measures of trade exposure are based on publicly available data and can be applied to many different demographic aggregations and years of data. They can be applied broadly to U.S. trade with all countries or narrowly to U.S. trade with specific partner countries.
\end{abstract}

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David Riker \\
Research Division, Office of Economics \\
david.riker@usitc.gov \\
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\section{Introduction \label{sec: section1}}

International trade is one of many factors that can shift U.S. labor demand and lead to changes in employment levels.\footnote{Other factors that shift labor demand include changes in domestic demand, technology, and cost of materials and other inputs in production.} Exposure to trade can be measured as the impact on U.S. employment from negative or positive trade shocks, including changes in tariff rates, transport costs, and foreign production costs. Exposure to trade in a particular industry depends on the industry's trade intensity, measured by its import penetration rate (i.e., the share of imports in total U.S. expenditure on the production of an industry) and its export share (i.e., the contribution of exports to the total shipments of a domestic industry). Exposure to trade also depends on the substitutability of foreign and domestic varieties of the industry's products in consumer demands.

There are often large differences in the average trade exposure of demographic groups due to differences in the distribution of their employment across manufacturing industries. To quantify these differences, we calculate prospective, model-based measures of trade exposure for several demographic groups in 2021. The measures are straightforward to calculate with publicly available data.

The measures that we calculate are similar to measures of import and export exposure in \citeasnoun{Ebenstein}. In order to estimate the impact of globalization on U.S. labor market, \citeasnoun{Ebenstein} estimate a retrospective econometric model that regresses the wages of U.S. workers on their individual characteristics and exposure measures that are employment-weighted averages of imports, exports, and offshoring at the industry- and occupation-level.\footnote{The sample period in \citeasnoun{Ebenstein} is 1984--2002.} 

Like \citeasnoun{Ebenstein}, we calculate employment-weighted average measures of trade exposure, but for a different purpose.\footnote{\citeasnoun{ADH2013} also use employment share-weighted measures of exposure to imports and exports. They focus on the economic impact of imports from China between 1990 and 2007.} Our measures of trade exposure are derived from an industry-specific partial equilibrium simulation model and are not used in a retrospective econometric analysis like \citeasnoun{Ebenstein}. Our model generates prospective estimates of U.S. workers' potential exposure to changes in labor demand due to future import and export shocks. We also adopt a different assumption about labor supply: the wage model in \citeasnoun{Ebenstein} assumes upward-sloping labor supply, while our employment model assumes perfectly elasticity labor supply.

Section \ref{sec: section2} introduces our theoretical model and derives the formulas for the import and export exposure of U.S. workers. Section \ref{sec: section3} describes the data sources. Section \ref{sec: section4} reports estimates of trade exposure by demographic group. Section \ref{sec: section5} focuses on the workers' exposure to trade with specific partner countries. Section \ref{sec: section6} concludes with ideas for extending the analysis.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Measures of Trade Exposure \label{sec: section2}}

First, we derive the measures of trade exposure based on an industry-specific partial equilibrium model of international trade with conventional functional forms. We assume that the value of domestic shipments of industry $i$ has the constant elasticity of substitution (CES) form in equation (\ref{eq:1}).

\begin{equation}\label{eq:1}
v_i = \theta_i \ Y \ (P_i) \ ^{\sigma_i \ - \ 1} \ (p_i) \ ^{1 \ - \ \sigma_i}
\end{equation}

\noindent $p_i$ and $v_i$ are the prices and value of shipments of each domestic producer in the industry. $Y$ is aggregate expenditure in the domestic market, $\theta_i$ is the expenditure share of products in industry $i$, $\sigma_i$ is the elasticity of substitution between domestic and imported varieties, and $P_i$ is the CES industry price index in equation (\ref{eq:2}). 

\begin{equation}\label{eq:2}
P_i = \left( \ n_i \ (p_i) \ ^{1 \ - \ \sigma_i} \ + n_i^* \ (p_i^* \ \tau_i) \ ^{1 \ - \ \sigma_i} \ \right)^{\frac{1}{1 \ - \ \sigma_i} \ }
\end{equation}

\noindent $n_i$ and $n_i^*$ are the numbers of domestic and foreign varieties in the industry, $p_i^*$ is the price of foreign varieties, and $\tau_i > 1$ is a trade cost factor for imports that is increasing in tariffs, transport costs, and any other domestic barriers to trade.

Equations (\ref{eq:3}) and (\ref{eq:4}) are comparable equations for the value of industry exports and the industry's CES price index in the foreign market.

\begin{equation}\label{eq:3}
v_i^* = \theta_i^* \ Y^* \ (P_i^*) \ ^{\sigma_i \ - \ 1} \ (p_i \ \tau_i^*) \ ^{1 \ - \ \sigma_i}
\end{equation}

\begin{equation}\label{eq:4}
P_i^* = \left( n_i \ (p_i \ \tau_i^*)^{1 \ - \ \sigma_i} \ + n_i^* \ (p_i^*)^{1 \ - \ \sigma_i} \right)^{\frac{1}{1 \ - \ \sigma_i}}
\end{equation}

\noindent $Y^*$ is aggregate expenditure in the export market, $\theta_i^*$ is the expenditure share of products of industry $i$, and $\tau_i^* > 1$ is the trade cost factor for exports that is increasing in foreign tariffs, transport costs, and any other foreign barriers to trade.

We assume that production in industry $i$ has a Leontief technology that combines labor and materials in fixed proportions. $w$ is the marginal cost of labor, and $c$ is the marginal cost of materials. $a_{wi}$ and $a_{ci}$ are industry-specific unit factor requirements. Equation (\ref{eq:5}) is the domestic producers' margin cost of production in industry $i$.

\begin{equation}\label{eq:5}
mc_i = a_{wi} \ w \ + a_{ci} \ c 
\end{equation}

Finally, we assume that there is monopolistic competition in the domestic and export markets.\footnote{The models of monopolistic competition and trade in differentiated products in \citeasnoun{Krugman}, \citeasnoun{Melitz}, \citeasnoun{Chaney}, \citeasnoun{HMR}, and subsequent studies also assume that consumers have CES preferences.} 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 decisions of firms: each firm takes the industry's price index as given, since its own contribution to this price index is infinitesimal. Each firm perceives that the own-price elasticity of demand for its variety is a constant, so its price is a constant mark-up over its marginal cost of production.

\begin{equation}\label{eq:6}
p_i = \left( \frac{\sigma_i}{\sigma_i \ - \ 1} \right) \  \left( a_{wi} \ w \ + \ a_{ci} \ c \right)
\end{equation}

\noindent Using the approach to calibrating $\sigma_i$ from \citeasnoun{AhmadRiker}, equation (\ref{eq:6}) implies equation (\ref{eq:7}):

\begin{equation}\label{eq:7}
\sigma_i = \frac{p_i}{p_i - a_{wi} \ w - a_{ci} \ c} = \frac{V_i}{V_i - W_i - C_i}
\end{equation}

\noindent $V_i$ is the value of total shipments of domestic producers in industry $i$, $W_i$ is total domestic wage payments in the industry, and $C_i$ is the industry's total cost of materials.

Equations (\ref{eq:8}), (\ref{eq:9}), and (\ref{eq:10}) are percent changes in domestic labor demand, imports, and exports in industry $i$ resulting from changes in the trade cost factors. They are first-order log-linear approximations evaluated at the initial equilibria in the domestic and foreign markets. To simplify these expressions, we hold all other economic fundamentals constant, including $Y$, $Y^*$, $w$, $c$, $a_{wi}$, $a_{ci}$, $\theta_i$, $\theta_i^*$, and $\sigma_i$.\footnote{We also hold the foreign producer price ($p_i^*$) constant. The delivered price in the domestic market ($\tau_i \ p_i^*$) is not constant when $\tau_i$ changes. We assume that $n_i$ and $n_i^*$ remain fixed in the short run.}

\begin{equation}\label{eq:8}
\hat L_i = \left( \frac{L_i \ - \ L_i^*}{L_i}  \right) \hat M_i \ + \ \left( \frac{L_i^*}{L_i}  \right) \hat E_i \ - \ \hat p_i
\end{equation}

\begin{equation}\label{eq:9}
\hat M_i = \left(\sigma_i \ - \ 1 \right) \mu_i \ \hat \tau_i 
\end{equation}

\begin{equation}\label{eq:10}
\hat E_i = \left(1 \ - \sigma_i \right) \left( 1 \ - \ \chi_i\right) \ \left( \hat \tau_i^* \ + \ \hat p_i \right) 
\end{equation}

\noindent $L_i$ is total employment of domestic manufacturers in industry $i$, and $L_i^*$ is their employment associated with exports, so $\frac{L_i^*}{L_i} = \frac{E_i}{V_i}$, where $E_i$ is the value of the industry's exports. $\hat L_i$ is the proportional (or percent) change in employment in the domestic industry, $\frac{dL_i}{L_i}$, and $\hat \tau_i$ and $\hat \tau_i^*$ are the proportional changes in the foreign and domestic trade cost factors.  $\mu_i$ and $\chi_i$ are the industry's import penetration rate and its exports as a share of expenditures in the foreign market. $L_i$, $M_i$, and $E_i$ are endogenous variables that change in response to changes in trade costs. $p_i$ is an endogenous variable that does not change, because it is fixed according to equation (\ref{eq:6}). 

Equations (\ref{eq:11}) is the reduced-form expression for the percent change in domestic labor demand in response to the changes in trade costs. It is derived by substituting Equations (\ref{eq:9}) and (\ref{eq:10}) into Equation (\ref{eq:8}).

\begin{equation}\label{eq:11}
\hat L_i = \left( \frac{L_i \ - \ L_i^*}{L_i}  \right) \left(\sigma_i \ - \ 1 \right) \mu_i \ \hat \tau_i \ + \ \left( \frac{L_i^*}{L_i}  \right) \left(1 \ - \sigma_i \right) \left( 1 \ - \ \chi_i\right) \ \hat \tau_i^* 
\end{equation}

\noindent The first term on the right-hand side of equation (\ref{eq:11}) is the labor demand effects of trade shocks through imports, and the second term is the labor demand effects through exports.

Equation (\ref{eq:12}) is an accounting identity that links the percent change in total labor demand for domestic workers in group $g$ to the industry-specific shifts in labor demand in equation (\ref{eq:11}). 

\begin{equation}\label{eq:12}
\hat L_g = \sum_i \left( \frac{L_{gi}}{L_g}  \right) \ \hat L_i 
\end{equation}

\noindent $L_g = \sum_i L_{gi}$ is total domestic employment of workers in group $g$ across all industries, and $L_{gi}$ is domestic employment of group $g$ workers in industry $i$. 

Equation (\ref{eq:13}) is the percent change in labor demand for workers within group $g$ due to changes in foreign and domestic trade cost factors in all of the industries ($\hat \tau_i$ and $\hat \tau_i^*$).

\begin{equation}\label{eq:13}
\hat L_g = \sum_i \left(\frac{L_{gi}}{L_{g}} \right) \ \left(  \left(\frac{V_i - E_i}{V_i}\right) \left(\frac{M_i}{V_i - E_i + M_i}\right) \ \hat \tau_i - \left(\frac{\ E_i}{V_i}\right) \ \hat \tau_i^* \right)  (\sigma_i \ - \ 1)
\end{equation}

\noindent $M_i$ is the value of its imports. We simplify equation (\ref{eq:13}) by assuming that the industry's exports account for only a negligible share of the total export market, so $\chi_i$ in equation (\ref{eq:11}) is set equal to zero.\footnote{This simplifying assumption can be relaxed if there are data available on total expenditures on products of the industry in the foreign market.} As long as labor supply is perfectly elastic or wages are otherwise fixed, equation (\ref{eq:13}) is also the percent change in employment of workers in group $g$.\footnote{Alternative assumptions about labor supply would break the equivalence between the percent changes in labor demand in equation (\ref{eq:13}) and the percent changes in domestic industry employment. For example, differences in adjustment costs across the demographic groups would result in additional differences in employment effects.}

Equations (\ref{eq:14}) and (\ref{eq:15}) are the measures of exposure to imports ($imp$) and exports ($exp$) for group $g$. They are equal to the percent change in $L_g$ for simultaneous ten-percent increases in trade costs on imports and exports ($\hat \tau_i = \hat \tau_i^* = 0.10$).

\begin{equation}\label{eq:14}
X^{imp}_g = \sum_i \left( \frac{L_{gi}}{L_{g}} \right) \left(\frac{V_i - E_i}{V_i}\right) \left(\frac{M_i}{V_i - E_i + M_i}\right) (\sigma_i \ - \ 1) \ 0.10
\end{equation}

\begin{equation}\label{eq:15}
X^{exp}_g = \sum_i \left( \frac{L_{gi}}{L_{g}} \right) \left(\frac{E_i}{V_i}\right) (1 \ - \ \sigma_i) \ 0.10
\end{equation}

\noindent Since $\sigma_i > 1$, the measure of exposure to imports is positive (an increase in tariffs on imports increases domestic labor demand), and the measure of exposure to exports is negative (an increase in foreign tariffs on exports reduces domestic labor demand). 

According to equation (\ref{eq:11}), the exposure of an industry's total labor demand depends on its trade intensity and the extent of substitution between domestic and imported varieties. According to equations (\ref{eq:14}) and (\ref{eq:15}), the exposure of a specific group of workers depends on these factors and also on the distribution of the employment of group members across the industries.

The exposure measures to imports and exports can be combined together or considered separately, as in equations (\ref{eq:14}) and (\ref{eq:15}). When the net exposure $X^{imp}_g \ - \ X^{exp}_g$ is positive, it indicates that reciprocal ten-percent increases in trade costs on imports and exports will increase labor demand for group $g$. The sign of a group's net exposure depends on employment shares and trade intensities. Its magnitude, but not its sign depends on the value of $\sigma_i$. 

To simplify the model, we have assumed that the effects of trade shocks on labor demand are industry-specific. The model could be generalized by incorporating inter-industry input-output linkages and economy-wide resource constraints. In that case, trade shocks in one industry would spill over to other industries, and reduced-form exposure measures would not be simple weighted averages based on industry shares of employment. \citeasnoun{CP2022} makes this point using several different examples. The data requirements of these generalizations would be difficult to meet.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Data Sources \label{sec: section3}}

We focus on the U.S. manufacturing sector. We use data on shipments, payrolls, and costs of materials by NAICS three-digit manufacturing industries in 2021, the most recent release of the U.S. Census Bureau's Annual Survey of Manufactures (ASM).\footnote{These data are publicly available at \url{https://www.census.gov/programs-surveys/asm/data/tables.html}.} We use data on the 2021 free alongside value of domestic exports and the landed duty-paid value of imports for consumption by NAICS three-digit industry from the U.S. International Trade Commission's Trade Dataweb.\footnote{These data are publicly available at \url{https://dataweb.usitc.gov/}.} We calibrate the elasticity of substitution parameters for each industry using equation (\ref{eq:7}).

In addition to these industry-level data, we use individual-level data that record the demographic characteristics of U.S. workers. The data on industry and occupation of individual workers, as well as their age, education, race, ethnicity, and gender are public use micro-data files from the Annual Social and Economic (ASEC) supplement of the Current Population Survey.\footnote{These data are publicly available at \url{https://cps.ipums.org/cps/}.}

Table 1 reports the estimated elasticity of substitution ($\sigma_i$), export share of shipments $\left( \frac{E_i}{V_i} \right)$, and import penetration rate $\left( \frac{M_i}{V_i \ - \ E_i \ + \ M_i} \right)$ for each of the 21 NAICS three-digit manufacturing industries. There is significant variation in these three elements of trade exposure. The elasticity of substitution values range from 1.81 for beverage and tobacco products to 4.54 for transportation equipment. Export shares range from 4.90\% for beverages and tobacco products to 51.40\% for leather and allied products. Import penetration rates range from 8.15\% for printing and related products to 95.23\% for leather and allied products.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Characteristics of the Manufacturing Industries in 2021}
\begin{tabular}{p{7cm} r r r }	
Manufacturing Industry & Elasticity of & Export Share & Import \\
Name and NAICS Code & Substitution & of Shipments & Penetration \\
\ & \ & (\%) & (\%) \\
\toprule
Food manufacturing (311) & 3.33 & 8.41 & 10.08 \\
Beverage and tobacco products (312) & 1.81 & 4.90 & 16.90 \\
Textile mills (313) & 3.54 & 29.48 & 37.38 \\
Textile product mills (314) & 3.24 & 11.74 & 62.82 \\
Apparel (315) & 3.19 & 31.90 & 94.24 \\
Leather and allied products (316) & 3.44 & 51.40 & 95.33 \\
Wood products (321) & 2.74 & 5.00 & 20.00 \\
Paper manufacturing (322) & 2.96 & 12.10 & 12.46 \\
Printing and related products (323) & 2.91 & 6.00 & 8.15 \\
Petroleum and coal products (324) & 4.86 & 14.94 & 12.63 \\
Chemical manufacturing (325) & 2.08 & 28.08 & 34.99 \\
Plastic and rubber products (326) & 2.88 & 11.80 & 25.73 \\
Nonmetallic mineral products (327) & 2.56 & 7.71 & 19.81 \\
Primary metal products (331) & 2.90 & 21.18 & 39.04 \\
Fabricated metal products (332) & 2.97 & 10.05 & 21.82 \\
Machinery manufacturing (333) & 3.19 & 31.60 & 44.92 \\
Computers and electronics (334) & 2.88 & 35.84 & 69.48 \\
Electrical equipment et al. (335) & 2.92 & 30.33 & 62.94 \\
Transportation equipment (336) & 4.54 & 22.50 & 35.96 \\
Furniture (337) & 3.10 & 5.57 & 47.00 \\
Miscellaneous manufacturing (339) & 2.39 & 27.37 & 60.32 \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

Table 2 reports the manufacturing share of employment $\frac{L_{gi}}{L_g}$ within 16 different groups based on workers' education, age, gender, race, ethnicity, and occupation and for an aggregate of all U.S. workers. The share of each group's U.S. workers employed in the manufacturing sector is larger for high school graduates who have not graduated from college, workers who are forty or older and male, and workers who are Asian, Hawaiian, Pacific Islander and not Hispanic. 

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Manufacturing Share of U.S. Employment by Demographic Group}
\begin{tabular}{p{10cm} r}
\ & Manufacturing Share \\
Demographic & of Group Employment \\
Group & in 2021 (\%) \\
\toprule
\textbf{Education} & \ \\
Not a High School Graduate & 9.804 \\
High School, Not College, Graduate & 10.323 \\
College Graduate & 7.444 \\
\ & \ \\
\midrule 
\textbf{Age} & \ \\
Forty and Older & 9.835 \\
Younger Than Forty & 8.220 \\
\ & \ \\
\midrule
\textbf{Gender} & \ \\
Female & 5.668 \\
Male & 12.190 \\
\ & \ \\
\midrule
\textbf{Race} & \ \\
American Indian, Aleut, or Eskimo Only & 8.560 \\
Asian, Hawaiian, or Pacific Islander Only & 10.140 \\
Black Only & 7.494 \\
White Only & 9.292 \\
All Other & 8.286 \\
\ & \ \\
\midrule
\textbf{Ethnicity} & \ \\
Hispanic & 8.567 \\
Not Hispanic & 9.218 \\
\ & \ \\
\midrule
\textbf{Occupation} & \ \\
Production Worker & 66.940 \\
Not a Production Worker & 5.976 \\
\ & \ \\
\midrule
\textbf{All Workers} & 9.102 \\
\ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Estimates of Trade Exposure \label{sec: section4}}

Table 3 reports our estimates of trade exposure by demographic group. The estimates provide a relative measure, a ranking of trade exposure across the groups within each category. They also provide an absolute measure with a clear economic interpretation: the import exposure measure is the percent increase in labor demand for U.S. workers in the demographic group resulting from a ten-percent increase in trade costs on imports, and the export exposure measure is the percent decrease in labor demand for U.S. workers in the group resulting from a ten-percent increase in trade costs facing U.S. exports in the industry.

According to Table 3, trade exposure for both imports and exports is larger (in absolute value)  for college graduates, workers who are younger than forty and male, workers who are Asian, Hawaiian, or Pacific Islander and not Hispanic, and non-production workers.\footnote{This first set of calculations groups workers by each demographic characteristic in isolation. Later we group workers by combinations of the demographic characters.} Differences in race and education have larger effects on the measure of trade exposure than differences in age, gender, ethnicity, or occupation. This is indicated by the ratio of the highest value within each category to the average for all workers at the bottom of the table. 

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{U.S. Workers' Exposure to Trade by Demographic Group in 2021}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\textbf{Education} & \ & \ \\
Not a High School Graduate & 5.005 & -3.126 \\
High School, Not College, Graduate & 5.750 & -4.181 \\
College Graduate & 6.145 & -4.843 \\
\ & \ & \ \\
\midrule 
\textbf{Age} & \ & \ \\
Forty and Older & 5.735 & -4.292 \\
Younger Than Forty & 5.943 & -4.353 \\
\ & \ & \ \\
\midrule
\textbf{Gender} & \ \\
Female & 5.746 & -4.209 \\
Male & 5.853 & -4.362 \\
\ & \ & \ \\
\midrule
\textbf{Race} & \ \\
American Indian, Aleut, or Eskimo Only & 5.064 & -3.799 \\
Asian, Hawaiian, or Pacific Islander Only & 6.301 & -4.894 \\
Black Only & 5.687 & -4.219 \\
White Only & 5.807 & -4.287 \\
All Other & 5.627 & -4.063 \\
\ & \ & \ \\
\midrule
\textbf{Ethnicity} & \ \\
Hispanic & 5.499 & -3.850 \\
Not Hispanic & 5.886 & -4.411 \\
\ & \ & \ \\
\midrule
\textbf{Occupation} & \ \\
Production Worker & 5.757 & -4.077 \\
Not a Production Worker & 5.861 & -4.462 \\
\ & \ & \ \\
\midrule
\textbf{All Workers} & 5.822 & -4.317 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\newpage
It is straightforward to redefine the demographic groups by combining two or more worker characteristics. Table 4 reports two examples, one that combines ethnicity and education and a second that combines gender and age.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Exposure to Trade for Groups that Combine Demographic Characteristics}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\ & \ & \ \\
Hispanic college graduate & 6.528 & -5.029 \\
Non-Hispanic college graduate  & 6.110 & -4.826 \\
Hispanic non-college graduate & 5.290 & -3.610 \\
Non-Hispanic non-college graduate & 5.755 & -4.168 \\
\ & \ & \ \\
\midrule
\ & \ & \ \\
Females forty and older & 5.759 & -4.250 \\
Males forty and older  & 5.728 & -4.310 \\
Females younger than forty & 5.727 & -4.151 \\
Males younger than forty & 6.034 & -4.438 \\
\ & \ & \ \\
\midrule
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\noindent The trade exposure measures are largest (in absolute value) for non-Hispanic college graduates and males who are younger than forty. While the ranking of the groups by the magnitude of their import and export exposure measures are often the same, including for all of the groups in Table 3, that are not always the case. Table 4 provides a counter-example. While females forty or over are the group that is second-most exposed to imports, they are the group third-most exposed to exports, behind males forty and over. This difference in ranking reflects differences in the industry shares of employment of older male and female workers in the data.

It is also possible to define the demographic groups more finely than the aggregated groups in Tables 2, 3 and 4. For example, Table 5 reports exposure measures for all 19 race groups in the ASEC data for 2021.\footnote{The names of the rows in Table 5 correspond to the names of the race groups reported in the ASEC data.} Table 6 reports exposure measures for a more detailed breakout of education into five groups. Table 7 reports exposure measures for a more detailed breakout of age into six groups. Table 8 reports exposure measures for a more detailed breakout of ethnicity into nine groups. 

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Race Detail on Trade Exposure of U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\ & \ & \ \\
American Indian-Asian & 5.856 & -4.031 \\
American Indian-Hawaiian/Pacific Islander & 9.867 & -7.968 \\
American Indian/Aleut/Eskimo & 5.064 & -3.799 \\
Asian only & 6.340 & -4.927 \\
Asian-Hawaiian/Pacific Islander & 3.297 & 0.867 \\
Black & 5.687 & -4.219 \\
Black-American Indian & 6.761 & -5.475 \\
Black-Asian & 8.627 & -5.218 \\
Four or five races, unspecified & 6.112 & -3.818 \\
Hawaiian/Pacific Islander only & 5.391 & -4.104 \\
Two or three races unspecified & 1.464 & -1.147 \\
White & 5.807 & -4.287 \\
White-American Indian & 5.005 & -3.700 \\
White-American Indian-Hawaiian/Pacific Islander & 2.148 & -1.957 \\
White-Asian & 6.540 & -5.351 \\
White-Black & 6.483 & -4.169 \\
White-Black-Hawaiian/Pacific Islander & 2.717 & -3.033 \\
White-Black-American Indian & 5.339 & -4.446 \\
White-Hawaiian/Pacific Islander & 4.166 & -2.158 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\newpage

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Education Detail on Trade Exposure of U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\ & \ & \ \\
Less than high school diploma & 5.005 & -3.126 \\
High school diploma or equivalent & 5.690 & -4.096 \\
Associate's degree & 6.021 & -4.567 \\
Bachelor's degree & 6.079 & -4.709 \\
Graduate degree & 6.279 & -5.117 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Age Detail on Trade Exposure of U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\ & \ & \ \\
20s & 6.046 & -4.347 \\
30s & 5.935 & -4.427 \\
40s & 5.560 & -4.197 \\
50s & 5.873 & -4.412 \\
60s & 5.680 & -4.201 \\
70s and above & 6.425 & -4.470 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Ethnicity Detail on Trade Exposure of U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\ & \ & \ \\
Central American (Exclusing Salvadoran) & 5.577 & -3.432 \\
Cuban & 5.164 & -3.544 \\
Dominican & 5.239 & -3.602 \\
Mexican & 5.450 & -3.789 \\
Puerto Rican & 5.865 & -4.516 \\
Salvadoran & 4.936 & -3.656 \\
South American & 5.699 & -4.358 \\
Other Hispanic & 6.323 & -4.517 \\
\ & \ & \ \\
Not Hispanic & 5.866 & -4.411 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}
\newpage

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\section{Exposure To Specific Trade Partner Countries \label{sec: section5}}

The export shares and import penetration rates reported in Table 1 and the estimates of trade exposure in Section 4 aggregate U.S. imports across all source countries and aggregate U.S. exports across all destination countries. In this section, we focus instead on certain trade partners, specifically Brazil, China, and India, and we only consider trade cost shocks that are specific to the country's trade with the United States. In this way, we assess the relative \textit{country exposures} of specific groups of U.S. workers. 

Table 9 reports the import penetration rate for these three specific trade partner countries for each of the NAICS three-digit U.S. manufacturing industries. This is a key input of the import exposure measure. There is significant variation across the manufacturing industries and across the three countries. China stands out among the three, with generally higher import penetration rates, though Brazil's import penetration rates exceeds China's in beverage and tobacco products, petroleum and coal products, and primary metal products, and India's rate exceeds China's rate in petroleum and coal products.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Import Penetration Rates by Country in 2021}
\begin{tabular}{p{7cm} r r r }	
Manufacturing Industry & Brazil & China & India \\
Name and NAICS Code & (\%) & (\%) & (\%) \\
\toprule
Food manufacturing (311) & 0.28 & 0.48 & 0.24 \\
Beverage and tobacco products (312) & 0.04 & 0.03 & 0.02 \\
Textile mills (313) & 0.12 & 8.74 & 4.53 \\
Textile product mills (314) & 0.16 & 44.42 & 20.38 \\
Apparel (315) & 0.35 & 75.26 & 36.52 \\
Leather and allied products (316) & 7.51 & 79.91 & 18.48 \\
Wood products (321) & 1.51 & 2.56 & 0.25 \\
Paper manufacturing (322) & 0.87 & 2.02 & 0.17 \\
Printing and related products (323) & 0.02 & 3.97 & 0.19 \\
Petroleum and coal products (324) & 0.34 & 0.02 & 0.55 \\
Chemical manufacturing (325) & 0.22 & 2.98 & 1.79 \\
Plastic and rubber products (326) & 0.23 & 10.05 & 0.61 \\
Nonmetallic mineral products (327) & 0.91 & 6.35 & 1.11 \\
Primary metal products (331) & 2.00 & 1.40 & 0.72 \\
Fabricated metal products (332) & 0.19 & 7.98 & 0.79 \\
Machinery manufacturing (333) & 0.61 & 10.42 & 1.11 \\
Computers and electronics (334) & 0.09 & 35.84 & 0.81 \\
Electrical equipment et al. (335) & 0.49 & 31.20 & 1.09 \\
Transportation equipment (336) & 0.27 & 2.79 & 0.33 \\
Furniture (337) & 0.54 & 25.90 & 1.40 \\
Miscellaneous manufacturing (339) & 0.30 & 29.04 & 9.96 \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\newpage

Table 10 includes the same demographic groups as Table 3, but it is specific to shocks to U.S. trade with Brazil. The exposure measures for trade with Brazil are much smaller than the measures for all imports in Table 3, reflecting the smaller import penetration rates in Table 9. The ranking of groups by the magnitude of the exposure measure is the same as Table 3 for exports (more exposure for college graduates, young males, Asian, Hawaiian, or Pacific Islander and non-Hispanic workers, and non-production worker) but different than Table 3 for imports for the race, education, ethnicity, and occupation groups (more exposure for American Indian, Aleut, or Eskimo and Hispanic workers, non-high school graduates, and production workers). Another important difference in the Brazil-specific measures is that the export exposure measure for all workers at the bottom of the table is greater in absolute value than the import export measure, which means that a ten-percent increase in the trade costs on both U.S. imports and exports would lower combined trade exposure. (For the calculations in Table 3 for all imports, the opposite is the case.) Tables 11 and 12 reports similar measures for trade with China and India.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Brazil-Specific Trade Exposure Measures for U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\textbf{Education} & \ & \ \\
Not a High School Graduate & 0.097 & -0.058 \\
High School, Not College, Graduate & 0.091 & -0.099 \\
College Graduate & 0.074 & -0.125 \\
\ & \ & \ \\
\midrule 
\textbf{Age} & \ & \ \\
Forty and Older & 0.083 & -0.104 \\
Younger Than Forty & 0.091 & -0.105 \\
\ & \ & \ \\
\midrule
\textbf{Gender} & \ \\
Female & 0.080 & -0.096 \\
Male & 0.088 & -0.108 \\
\ & \ & \ \\
\midrule
\textbf{Race} & \ \\
American Indian, Aleut, or Eskimo Only & 0.122 & -0.090 \\
Asian, Hawaiian, or Pacific Islander Only & 0.057 & -0.114 \\
Black Only & 0.097 & -0.105 \\
White Only & 0.087 & -0.104 \\
All Other & 0.098 & -0.087 \\
\ & \ & \ \\
\midrule
\textbf{Ethnicity} & \ \\
Hispanic & 0.087 & -0.084 \\
Not Hispanic & 0.086 & -0.109 \\
\ & \ & \ \\
\midrule
\textbf{Occupation} & \ \\
Production Worker & 0.093 & -0.094 \\
Non-Production Worker & 0.082 & -0.110 \\
\ & \ & \ \\
\midrule
\textbf{All Workers} & 0.086 & -0.104 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{China-Specific Trade Exposure Measures for U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\textbf{Education} & \ & \ \\
Not a High School Graduate & 1.938 & -0.227 \\
High School, Not College, Graduate & 2.107 & -0.323 \\
College Graduate & 2.357 & -0.424 \\
\ & \ & \ \\
\midrule 
\textbf{Age} & \ & \ \\
Forty and Older & 2.159 & -0.351 \\
Younger Than Forty & 2.203 & -0.347 \\
\ & \ & \ \\
\midrule
\textbf{Gender} & \ \\
Female & 2.446 & -0.341 \\
Male & 2.065 & -0.353 \\
\ & \ & \ \\
\midrule
\textbf{Race} & \ \\
American Indian, Aleut, or Eskimo Only & 2.254 & -0.290 \\
Asian, Hawaiian, or Pacific Islander Only & 3.170 & -0.497 \\
Black Only & 1.811 & -0.316 \\
White Only & 2.126 & -0.341 \\
All Other & 2.229 & -0.319 \\
\ & \ & \ \\
\midrule
\textbf{Ethnicity} & \ \\
Hispanic & 2.250 & -0.291 \\
Not Hispanic & 2.163 & -0.361 \\
\ & \ & \ \\
\midrule
\textbf{Occupation} & \ \\
Production Worker & 2.073 & -0.305 \\
Non-Production Worker & 2.241 & -0.376 \\
\ & \ & \ \\
\midrule
\textbf{All Workers} & 2.177 & -0.349 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{India-Specific Trade Exposure Measures for U.S. Manufacturing Workers}
\begin{tabular}{p{10cm} r r}
\ & Index of & Index of \\
Demographic & Exposure & Exposure \\
Group & to Imports & to Exports \\
\toprule
\textbf{Education} & \ & \ \\
Not a High School Graduate & 0.470 & -0.029 \\
High School, Not College, Graduate & 0.405 & -0.045 \\
College Graduate & 0.370 & -0.059 \\
\ & \ & \ \\
\midrule 
\textbf{Age} & \ & \ \\
Forty and Older & 0.388 & -0.049 \\
Younger Than Forty & 0.413 & -0.048 \\
\ & \ & \ \\
\midrule
\textbf{Gender} & \ \\
Female & 0.562 & -0.047 \\
Male & 0.330 & -0.049 \\
\ & \ & \ \\
\midrule
\textbf{Race} & \ \\
American Indian, Aleut, or Eskimo Only & 0.567 & -0.037 \\
Asian, Hawaiian, or Pacific Islander Only & 0.481 & -0.064 \\
Black Only & 0.366 & -0.044 \\
White Only & 0.392 & -0.048 \\
All Other & 0.426 & -0.043 \\
\ & \ & \ \\
\midrule
\textbf{Ethnicity} & \ \\
Hispanic & 0.555 & -0.039 \\
Not Hispanic & 0.367 & -0.050 \\
\ & \ & \ \\
\midrule
\textbf{Occupation} & \ \\
Production Worker & 0.427 & -0.042 \\
Non-Production Worker & 0.381 & -0.052 \\
\ & \ & \ \\
\midrule
\textbf{All Workers} & 0.398 & -0.048 \\
\ & \ & \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

\newpage
Tables 13 and 14 report the exposure measures for imports from different partner countries side-by-side. Table 13 reports the trade exposure measure for female workers and the ratio between the measure for females and the measure for all workers. A ratio above one means that female workers are more exposed to import shocks from the particular country than the average of all workers. According to Table 13, female workers are exposed more than the average of all workers to imports from China and India and less than the average for imports from Brazil and the aggregate of imports from all countries. 

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Comparison of Import Exposure Measures Across Countries: Gender}
\begin{tabular}{p{8cm} r r r r}
Group & All Imports & Brazil & China & India \\
\toprule
Female & 5.746 & 0.080 & 2.446 & 0.562 \\
Ratio to All Workers & 0.99 & 0.93 & 1.12 & 1.41 \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

Table 14 is a similar comparison for American Indian, Aleut, and Eskimo workers. This group is more exposed than the average of all workers for imports from Brazil, China, and India, and less exposed than the average for the aggregate of imports from all countries.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Comparison of Import Exposure Measures Across Countries: Race}
\begin{tabular}{p{8cm} r r r r}
Group & All Imports & Brazil & China & India \\
\toprule
American Indian, Aleut, or Eskimo & 5.064 & 0.122 & 2.254 & 0.567 \\
Ratio to All Workers & 0.87 & 1.42 & 1.04 & 1.42 \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

Finally, Table 15 is a similar comparison for college graduates. This group is more exposed than the average of all workers for imports from China and the aggregate of imports from all countries, and less exposed than the average for imports from Brazil and India.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Comparison of Import Exposure Measures Across Countries: Education}
\begin{tabular}{p{8cm} r r r r}
Group & All Imports & Brazil & China & India \\
\toprule
College Graduates & 6.145 & 0.074 & 2.357 & 0.370 \\
Ratio to All Workers & 1.06 & 0.86 & 1.08 & 0.93 \ \\
\bottomrule
	\end{tabular}
	 \end{threeparttable}
\end{table}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newpage

\section{Conclusions \label{sec: section6}}

The theory-based model of exposure to trade shocks in manufacturing industries translates differences in the distribution of a group's employment across industries and differences in the trade exposure of industries into differences in the exposure of specific demographic groups of U.S. workers to negative and positive trade shocks.

The measure of trade exposure are straightforward to calculate using publicly available data. There are many opportunities to expand the analysis in different directions. Demographic groups can be more narrowly defined, limited only by the detail available in the ASEC data. The groups can be defined as combinations or intersections of demographic characteristics. The measures can focus on trade with different partner countries and in different years. As a prospective measure of trade exposure, the model can identify groups of U.S. workers most likely to be affected by shocks in trade with specific partner countries, and it can identify trade partners likely to have the most effect on particular groups of U.S. workers. The model can also be used for retrospective analysis, for example to attribute a portion of the historical changes in the U.S. employment of specific groups to coinciding changes in trade costs.

\newpage
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\bibliography{biblio}

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