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\title{Imports of Plastic and Rubber Products from China}
\author{David Riker}
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{\Large \textbf{DIFFERENT TYPES OF TRADE SHOCKS}} \\
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{\Large \textbf{IN AN UPSTREAM-DOWNSTREAM PE MODEL}} \\
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{\Large David Riker} \\
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{\large ECONOMICS WORKING PAPER SERIES}\\
Working Paper 2022--06--A \\ \vspace{0.5in}
U.S. INTERNATIONAL TRADE COMMISSION \\
500 E Street SW \\
Washington, DC 20436 \\
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June 2022 \\
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\noindent 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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Different Types of Trade Shocks in an Upstream-Downstream PE Model \\
David Riker \\
Economics Working Paper 2022--06--A \\
June 2022 \\~\\
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\begin{abstract}
\noindent I present a partial equilibrium model of trade that links upstream and downstream industries. The model demonstrates that two types of upstream trade shocks -- tariff changes and foreign productivity shocks -- have similar effects on the upstream industry but can have very different effects on the downstream industry. I apply the model to 2020 data for the upstream rubber and plastic products industry and the downstream furniture industry, in simulations of the effects of hypothetical tariff reductions and foreign productivity shocks that increase U.S. imports from China.
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David Riker \\
Research Division, Office of Economics\\
U.S. International Trade Commission \\
david.riker@usitc.gov \\
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\section{Introduction \label{sec: section1}}
Partial equilibrium (PE) models of trade policy focus on the direct effects of policy changes within a specific industry, while more complex general equilibrium models also try to capture indirect, or spillover, effects on the rest of the economy. The main advantages of PE models are that they have simpler data requirements and can be tailored to specific structural features of the industry of interest.\footnote{In contrast, general equilibrium models generally rely on a more generic representation of individual industries.} A disadvantage of PE models of trade are that they are missing effects on downstream industries.
This paper develops a middle ground between PE and general equilibrium models by constructing a PE model that links an upstream industry and a downstream industry within a single model. This upstream-downstream model tells a more nuanced story about the effects of different types of upstream trade shocks. In a simpler PE model, foreign production cost reductions and tariff reductions both increase imports and have similar effects on the domestic industry. In a linked upstream-downstream model, these trade shocks in the upstream industry have opposite effects on domestic production and employment in the downstream industry: downstream domestic employment is negatively correlated with upstream imports when the imports are driven by foreign production cost shocks and are positively correlated with upstream imports when the imports are driven by changes in tariff rates.\footnote{This is also the case in a general equilibrium model, but it is intermingled with many other effects.}
I demonstrate how the linked PE model works using 2020 data for the upstream rubber and plastic products industry and the downstream furniture industry. I simulate the effects of hypothetical tariff reductions and foreign productivity shocks in the rubber and plastic products industry that increase U.S. imports from China.
Beyond providing a practical tool for trade policy analysis, the model contributes an important distinction to the debate over the effects of trade on labor markets. The literature on this topic splits its focus between the \textit{effects of trade} on labor markets and the \textit{effects of trade policy}. For example, some models -- including \citeasnoun{Hakobyan2016}, \citeasnoun{Pierce2016} and \citeasnoun{Handley2017} -- focus on the impact of changes in imports due to changes in trade policy or uncertainty about trade policy. Other models -- including \citeasnoun{ADH2013} and \citeasnoun{CDP2019} -- focus on the impact of changes in imports due to foreign productivity shocks. In other models like \citeasnoun{Ebenstein2014} , the distinction between the two types of trade shocks is blurred. The distinction between the effects of trade and the effects of trade policy is also frequently blurred in popular discussions of the impact of trade.
The rest of the paper is organized into four parts. Section \ref{sec: section2} describes the modeling framework: first the structural equations, then the calibration strategy, and finally the data and parameter inputs of the model. Section \ref{sec: section3} contrasts the effects estimated in alternative model simulations, and Section \ref{sec: section4} provides further sensitivity analysis of the simulations. Section \ref{sec: section5} concludes.
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\section{Model \label{sec: section2}}
The model includes upstream and downstream production in three countries indexed by $i$, $j$, and $k$. The simulations focus on effects in the downstream market in country $i$.
\subsection{Structural Equations \label{subsec: subsection2.1}}
The prices of the upstream products from country $c \in \{i,j,k\}$ are $p_{uc}$. These upstream prices reflect constant marginal costs of production and are exogenous variables in the model. The tariff factor (i.e., one plus the tariff rate) for imports of the upstream and downstream products from country $c$ into country $i$ are $\tau_{uc}$ and $\tau_{dc}$. These tariff factors are also exogenous variables in the model.
Equation (\ref{eq:1}) relates the price of the domestic downstream product, $p_{di}$, to the prices of inputs from the upstream industry, wages, and tariff factors.
\begin{equation}\label{eq:1}
p_{di} = \left( (p_{ui})^{1 \ - \ \sigma_u} \ + \ (p_{uj} \ \tau_{uj})^{1 \ - \ \sigma_u} \ + \ (p_{uk} \ \tau_{uk})^{1 \ - \ \sigma_u} \right)^{\frac{\beta}{1 \ - \ \sigma_u}} \ (w_i)^{1 \ - \ \beta}
\end{equation}
\noindent $\sigma_u$ is the constant elasticity of substitution (CES) between domestic and foreign products in intermediate inputs of the upstream industry. $\beta$, the cost share of the upstream industry in downstream production, is a constant parameter in the model, reflecting a Cobb-Douglas production function that combines upstream inputs and labor in downstream production. $w_i$, the wage in country $i$, is also an exogenous variable in the PE model. The foreign downstream prices in equations (\ref{eq:2}) and (\ref{eq:3}) add the simplifying assumption that foreign downstream production uses only foreign-produced inputs.
\begin{equation}\label{eq:2}
p_{dj} = (p_{uj})^{\beta} \ (w_{j})^{1 \ - \ \beta}
\end{equation}
\begin{equation}\label{eq:3}
p_{dk} = (p_{uk})^{\beta} \ (w_{k})^{1 \ - \ \beta}
\end{equation}
\noindent Equation (\ref{eq:4}) is the CES price index for the downstream market in country $i$.
\begin{equation}\label{eq:4}
P_{i} = \left( (p_{di})^{1 \ - \ \sigma_d} \ + \ \alpha_j \ (p_{dj} \ \tau_{dj})^{1 \ - \ \sigma_d} \ + \ \alpha_k \ (p_{dk} \ \tau_{dk})^{1 \ - \ \sigma_d} \right)^{\frac{1}{1 \ - \ \sigma_d}}
\end{equation}
\noindent $\sigma_d$ is the CES between domestic and foreign products in downstream production. $\alpha_j$ and $\alpha_k$ are constant demand parameters. Equation (\ref{eq:5}) is the value of domestic shipments in the downstream industry in country $i$.
\begin{equation}\label{eq:5}
V_{di} = X_i \ \left(\frac{p_{di}}{P_i}\right)^{1 \ - \ \sigma_d}
\end{equation}
\noindent $X_i$ is the value of aggregate expenditure in country $i$ on the products of the downstream industry. Equation (\ref{eq:6}) is employment in the downstream industry in country $i$ that supports these domestic shipments.
\begin{equation}\label{eq:6}
L_{di} = \frac{V_{di} \ (1 \ - \ \beta)}{w_i}
\end{equation}
\noindent Finally, equation (\ref{eq:7}) is the value of domestic shipments in the upstream industry in country $i$.
\begin{equation}\label{eq:7}
V_{ui} = V_{di} \ \beta \ \left( \frac{(p_{ui})^{1 \ - \ \sigma_u}}{(p_{ui})^{1 \ - \ \sigma_u} \ + \ (p_{uj} \ \tau_{uj})^{1 \ - \ \sigma_u} \ + \ (p_{uk} \ \tau_{uk})^{1 \ - \ \sigma_u}} \right)
\end{equation}
Adopting the normalization that $p_{ui}=1$ and $w_i=1$ and defining $\gamma_j = \alpha_j \ (w_j)^{(1 \ - \ \beta)(1 \ - \ \sigma_d)}$ and $\gamma_k = \alpha_k \ (w_k)^{(1 \ - \ \beta)(1 \ - \ \sigma_d)}$, the equations of the PE model can be simplified as follows:
\begin{equation}\label{eq:8}
p_{di}= \left(1 \ + \ (p_{uj} \ \tau_{uj})^{1 \ - \ \sigma_u} \ + \ (p_{uk} \ \tau_{uk})^{1 \ - \ \sigma_u} \right)^{\frac{\beta}{1 \ - \ \sigma_u}}
\end{equation}
\begin{equation}\label{eq:9}
P_{i} = \left( (p_{dj}) \ ^{1 \ - \ \sigma_d} \ + \ \gamma_j \ ((p_{uj})^\beta \ \tau_{dj})^{1 \ - \ \sigma_d} \ + \ \gammaa_k \ ((p_{uk)}^\beta \ \tau_{dk})^{1 \ - \ \sigma_d} \right)^{\frac{1}{1 \ - \ \sigma_d}}
\end{equation}
\begin{equation}\label{eq:10}
V_{di} = X_i \ \left(\frac{p_{di}}{P_{i}}\right)^{1 \ - \ \sigma_d}
\end{equation}
\begin{equation}\label{eq:11}
L_{di} = V_{di} \ (1 \ - \ \beta)
\end{equation}
\begin{equation}\label{eq:12}
V_{ui} = V_{di} \ \beta \ \left( \frac{1}{1 \ + \ (p_{uj} \ \tau_{uj})^{1 \ - \ \sigma_u} \ + \ (p_{uk} \ \tau_{uk})^{1 \ - \ \sigma_u}} \right)
\end{equation}
\subsection{Calibration \label{subsec: subsection2.2}}
Equations (\ref{eq:13}) and (\ref{eq:14}) calibrate initial upstream prices $p_{uj}$ and $p_{uk}$ using functions of the initial import penetration rates in the upstream market in country $i$ ($\mu_{uj}$ and $\mu_{uk}$), the elasticity of substitution in the upstream market ($\sigma_u$), and the initial upstream tariff factors in country $i$ ($\tau_{uj}$ and $\tau_{uk}$).
\begin{equation}\label{eq:13}
p_{uj} = \left( \frac{\mu_{uj}}{1 \ - \ \mu_{uj} - \ \mu_{uk}} \right) ^{\frac{1}{1 \ - \ \sigma_u}} \ \frac{1}{\tau_{uj}}
\end{equation}
\begin{equation}\label{eq:14}
p_{uk} = \left( \frac{\mu_{uk}}{1 \ - \ \mu_{uj} - \ \mu_{uk}} \right) ^{\frac{1}{1 \ - \ \sigma_u}} \ \frac{1}{\tau_{uk}}
\end{equation}
\noindent Equations (\ref{eq:15}) and (\ref{eq:16}) calibrate $\gamma_j$ and $\gamma_k$ using functions of the initial import penetration rates in the downstream market in country $i$ ($\mu_{dj}$, and $\mu_{dk}$), the initial prices of foreign upstream production ($p_{uj}$ and $p_{uk}$), the cost share ($\beta$), the elasticity of substitution in the downstream market ($\sigma_d$), and the initial downstream tariff factors in country $i$ ($\tau_{dj}$ and $\tau_{dk}$).
\begin{equation}\label{eq:15}
\gamma_j = \left( \frac{\mu_{dj}}{1 \ - \ \mu_{dj} \ - \ \mu_{dk}} \right) \ \left( \frac{1}{(p_{uj})^\beta \ \tau_{dj}} \right)^{1 \ - \ \sigma_d}
\end{equation}
\begin{equation}\label{eq:16}
\gamma_k = \left( \frac{\mu_{dk}}{1 \ - \ \mu_{dj} \ - \ \mu_{dk}} \right) \ \left( \frac{1}{(p_{uk})^\beta\ \tau_{dk}} \right)^{1 \ - \ \sigma_d}
\end{equation}
\subsection{Data and Parameter Inputs \label{subsec: subsection2.3}}
The data requirements of the PE model are fairly limited, and so it is practical to apply the model. In this paper, I apply the model to 2020 data for the upstream rubber and plastic products industry (NAICS code 326) and the downstream furniture industry (NAICS code 337).
I calculate the values of import penetration rates, average tariff rates, and total industry expenditure using import and export data for 2020 from the USITC's Trade Dataweb and value of total shipments data from the Annual Survey of Manufactures (ASM) for 2020. The U.S. employment level in the downstream industry in 2020 is also from the ASM. The share of NAICS 326 shipments in the cost of NAICS 337 production is based on the BEA's Use Table for the U.S. economy in 2020. I calculate the elasticity of substitution values for the upstream and downstream industries from 2017 Economic Census data using the methodology in \citeasnoun{AhmadRiker2020}. Table 1 reports the data and parameter inputs for the model application.
\begin{table}[tbph]
\centering
\begin{threeparttable}
\caption{Model Inputs}
\begin{tabular}{p{11cm} r}
\textbf{Variable} & \textbf{Value} \\
\toprule
Total Expenditure in the Downstream Market & \$89.92 billion \\
\midrule
Elasticity of Substitution in the Upstream & 2.6 \\
Elasticity of Substitution in the Downstream & 2.5 \\
\midrule
China's Share of the Upstream Imports & 9.40\% \\
China's Share in the Downstream Imports & 23.36\% \\
\midrule
Initial Tariff Rate on Upstream Imports from China & 12.35\% \\
Initial Tariff Rate on Downstream Imports from China & 18.19\% \\
\midrule
Cost Share of Upstream in Downstream Production & 7.02\% \\
\midrule
Domestic Workers in the Downstream Industry & 349,925 \\
\bottomrule
\end{tabular}
\end{threeparttable}
\end{table}
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\newpage
\section{Comparison of Simulations \label{sec: section3}}
Table 2 reports simulation results for two different types of upstream trade shocks. The first simulation completely eliminates the tariff on U.S. imports of plastic and rubber products from China, while leaving the tariff on U.S. imports of furniture unchanged. The second simulation reduces production cost in China in the upstream rubber and plastic products industry by 10\%, due to an increase in productivity, with no changes in tariff rates.
\begin{table}[tbph]
\centering
\begin{threeparttable}
\caption{Simulations with Different Types of Upstream Trade Shocks}
\begin{tabular}{p{8cm} r r}
\ & \ & \textbf{Increase in} \\
\textbf{Modeled} & \textbf{Tariff} & \textbf{Foreign} \\
\textbf{Outcome} & \textbf{Elimination} & \textbf{Productivity} \\
\toprule
\textit{Upstream Domestic Industry} & \ \\
\ & \ & \ \\
\% Change in Domestic Shipments & -1.736\% & -1.696\% \\
Change in Domestic Shipments & -\$63.3 million & -\$61.8 million \\
\ & \ & \ \\
\midrule
\textit{Downstream Domestic Industry} & \ \\
\ & \ & \ \\
\% Change in Domestic Shipments & 0.045\% & -0.099\% \\
Change in Domestic Shipments & \$32.2 million & -\$70.4 million \\
\ & \ & \ \\
Change in Domestic Employment & 149 & -327 \\
\ & \ & \ \\
\% Change in the Industry Price Index & -0.049\% & -0.137\% \\
\ & \ & \ \\
\bottomrule
\end{tabular}
\end{threeparttable}
\end{table}
In both of the simulations reported in Table 2, the cost of the upstream product from China declines, and this increases upstream imports, reduces upstream domestic shipments, and reduces the industry price index that consumers face in the downstream market. However, while U.S. consumers benefit from both types of upstream trade shocks, the effects on downstream producers in the United States depends on the type of shock. Tariff elimination reduces the cost of imported upstream inputs of the domestic industry, and this leads to an expansion in the value of downstream domestic shipments. The increase in foreign productivity also reduces the cost of imported upstream inputs of the domestic industry, but it reduces the costs of producing downstream imports by even more, since downstream foreign production is especially intensive in foreign upstream inputs, and the net effect is a reduction in the value of domestic shipments of downstream producers. Domestic downstream employment is positively correlated with upstream imports if they are due to tariff elimination in the upstream industry but negatively correlated if they are due to increased foreign productivity in the upstream industry.
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\section{Sensitivity Analysis \label{sec: section4}}
To illustrate the sensitivity of the simulation results to parameter inputs, I repeat the simulation of tariff elimination on upstream imports from China and then rerun the model, first doubling the cost share of the upstream in the downstream ($\beta$) and then doubling the elasticity of substitution in the upstream market ($\sigma_u$). Table 3 reports simulated effects for these alternatives. Increasing $\beta$ and $\sigma_u$ both magnify the effects of tariff elimination on the downstream industry (compared to the simulation results in Table 2). Increasing $\beta$ dampens the effects on the upstream industry, while increasing $\sigma_u$ magnifies the upstream effect.
\begin{table}[tbph]
\centering
\begin{threeparttable}
\caption{Simulations of Tariff Elimination with Different Parameter Values}
\begin{tabular}{p{7cm} r r r}
\ & \ & \textbf{Doubled} & \textbf{Doubled} \\
\textbf{Modeled} & \textbf{Values in} & \textbf{the Value} & \textbf{the Value} \\
\textbf{Outcome} & \textbf{Table 2} & \textbf{of $\beta$} & \textbf{of $\sigma_u$} \\
\toprule
\textit{Upstream Domestic Industry} & \ & \ \\
\ & \ & \ & \ \\
\% Change in Domestic Shipments & -1.736\% & -1.693\% & -5.239\% \\
\ & \ & \ & \ \\
\midrule
\textit{Downstream Domestic Industry} & \ & \ \\
\ & \ & \ & \ \\
\% Change in Domestic Shipments & 0.045\% & 0.090\% & 0.052\% \\
\ & \ & \ \\
Change in Domestic Employment & 149 & 297 & 173 \\
\ & \ & \ & \ \\
\% Change in the Industry Price Index & -0.049\% & -0.098\% & -0.056\% \\
\bottomrule
\end{tabular}
\end{threeparttable}
\end{table}
Finally, to illustrate the importance of trade in both upstream and downstream products, I repeat the simulation of the 10\% increase in productivity in the Chinese upstream industry and then rerun the model, first eliminating all downstream trade but maintaining the upstream trade and then eliminating all upstream trade but maintaining the downstream trade. Table 4 reports simulated effects for these two hypothetical trade elimination scenarios. Without downstream trade, the increase in upstream foreign productivity still has a negative effect on the domestic upstream industry and no effect on the domestic downstream industry. In other words, the negative effect on the domestic downstream industry requires downstream trade. The last column reports the scenario with no upstream trade. In this final column, the negative effect on the domestic upstream industry is dampened (compared to the full-trade case in the first column of simulation results), the negative effects on the domestic downstream industry are magnified, and the negative effect on the industry price index is dampened.
\begin{table}[tbph]
\centering
\begin{threeparttable}
\caption{Simulations of Productivity Shocks with Different Restrictions on Trade}
\begin{tabular}{p{7cm} r r r}
\ & \textbf{Up and} & \textbf{No} & \textbf{No} \\
\textbf{Modeled} & \textbf{Downstream} & \textbf{Downstream} & \textbf{Upstream} \\
\textbf{Outcome} & \textbf{Trade} & \textbf{Trade} & \textbf{Trade} \\
\toprule
\textit{Upstream Domestic Industry} & \ & \ \\
\ & \ & \ & \ \\
\% Change in Domestic Shipments & -1.696\% & -1.599\% & -0.141\% \\
\ & \ & \ & \ \\
\midrule
\textit{Downstream Domestic Industry} & \ & \ \\
\ & \ & \ & \ \\
\% Change in Domestic Shipments & -0.099\% & 0.000\% & -0.141\% \\
\ & \ & \ \\
Change in Domestic Employment & -327 & 0 & -466 \\
\ & \ & \ & \ \\
\% Change in the Industry Price Index & -0.137\% & -0.071\% & -0.094\% \\
\bottomrule
\end{tabular}
\end{threeparttable}
\end{table}
\newpage
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\section{Conclusions \label{sec: section5}}
The upstream-downstream PE model illustrates, in a simple way, how changes in imports due to changes in trade policy or changes in foreign productivity can have very different effects on domestic downstream industries when there is significant international trade in downstream products. Domestic downstream employment is positively correlated with upstream imports if they are due to tariff elimination in the upstream industry but negatively correlated if they are due to increased foreign productivity in the upstream industry. To preserve this distinction, it is useful to try to link closely related industries, and the upstream-downstream PE model provides a practical way to do this with limited, industry-focused data.
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