\begin{document}

\title{Modeling the Upstream-Downstream Effects of Trade Policy Changes with Multiple Country Markets\vspace{0.5in}%
}
\author{Samantha Schreiber\thanks{U.S. International Trade Commission.\newline Contact emails: samantha.schreiber@usitc.gov}}
\date{\vspace{1.5in}%
\today}

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\begin{center}
{\Large \textbf{Modeling the Upstream-Downstream Effects  \\
\vspace{2mm}
of Trade Policy Changes with Multiple Country Markets\\}}
\vspace{0.75in}
{\Large Samantha Schreiber} \\
\vspace{0.75in}
{\large ECONOMICS WORKING PAPER SERIES}\\ 
Working Paper 2023--02--A 
\\ \vspace{0.5in}
U.S. INTERNATIONAL TRADE COMMISSION \\
500 E Street SW \\
Washington, DC 20436 \\
\vspace{0.25in}
February 2023
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\noindent The author thanks David Riker and Peter Herman for helpful comments on this paper. 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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Modeling the Upstream-Downstream Effects of Trade Policy Changes with Multiple Country Markets \\
Samantha Schreiber \\
February 2023\\~\\
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\begin{abstract}
\noindent This paper presents a partial equilibrium model of two closely related industries: an intermediate good in the upstream and a final good in the downstream. Unlike other partial equilibrium models that focus on one specific country, such as a model of the U.S. market, this model allows for more than one country market. The model can be used to analyze how a tariff on intermediate imports can affect final good domestic production. It can also be used to analyze how the removal of trade barriers on intermediates between two countries can affect both imports and exports in intermediate and final goods markets.
\end{abstract}

\vfill
\begin{flushleft}
Samantha Schreiber\\ 
Research Division, Office of Economics\\
\href{mailto:samantha.schreiber@usitc.gov}{samantha.schreiber@usitc.gov}\\
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\section{Introduction}

In recent years, there have been several significant trade disruptions that have impacted global supply chains. Semiconductor shortages, the COVID-19 pandemic, the war in Ukraine, and many others are impacting the supply of intermediate goods used in the production of final goods. To analyze the impact of supply chain disruptions and trade policy changes on related products, we present a partial equilibrium (PE) modeling framework that links together upstream and downstream products to analyze how changes in one affect the other. Departing from the standard PE model set-up that only models the market of one specific country, the approach in this paper has flexibility to model multiple countries that are linked by trade. This means that the model can analyze the effect of trade policy changes on both imports and exports between two countries.

Section \ref{sec:model} describes the model, first as a many-market model with $i$ origin countries and $j$ destination countries, and second as a two-country model. Then, we describe the data inputs required for the model and potential sources. In section \ref{sec:calibration}, we describe how the cost parameters in the model can be calibrated to available data. Section \ref{sec:illsims} then provides illustrative simulations to show how the model works. First, the model is run with a 10 percent tariff applied to one country's imports of another country. Second, tariff liberalization is illustrated by reducing a 10 percent tariff on trade in intermediates between two countries. Finally, section \ref{sec:concl} concludes.

\section{Model Description}\label{sec:model}

This partial equilibrium model is intended to be applied to analyze trade policy changes on two closely related industries: an intermediate good in the upstream and a final good in the downstream. Unlike other partial equilibrium models that focus on one specific country, such as a model of the U.S. market, this model allows for more than one country market.\footnote{The equations presented in this section are first written in general terms. We then set the number of country markets equal to two in the illustrative simulation described later in this paper.} The model can be used to analyze how a tariff or supply chain disruption on intermediate imports can affect final good domestic production. It can also be used to analyze how the removal of trade barriers on intermediates between two countries can affect both imports and exports in intermediate and final goods markets. 

\subsection{Many-Market Model}\label{sec:manymarket}

The index $i$ refers to the origin country and $j$ the destination market.\footnote{We describe the location of production as the origin country and the location of consumption as the destination market. The destination market could also be called destination country.} The price $p_{ui}$ is the producer price of the upstream good that is produced in country $i$. The tariff factor,  $1+\tau_{uij}$, is the tariff imposed by country $j$ on upstream imports from country $i$. Equation (\ref{eq:uppi}) is the upstream price index in country $j$, $z_j$, where $b_{uij}$ is a calibrated demand asymmetry parameter and $\sigma_u$ the upstream constant elasticity of substitution.

\begin{equation}\label{eq:uppi}
z_j = \left( \sum_i \ \ b_{uij} \ (p_{uij}(1+\tau_{uij}))^{1-\sigma_{u}}  \right)^{\frac{1}{1 \ - \ \sigma_{u}}}
\end{equation}

Equation (\ref{eq:downpi}) shows the downstream price index, $P_j$, where $p_{di}$ is the price of the downstream good produced in country $i$ and consumed in country $j$ and $1+\tau_{dij}$ is the tariff factor. 

\begin{equation}\label{eq:downpi}
P_j = \left( \sum_i \ \ b_{dij} \ (p_{di} \ (1+\tau_{dij}))^{1-\sigma_{d}}  \right)^{\frac{1}{1 \ - \ \sigma_{d}}}
\end{equation}

The price of the downstream domestically-produced good is a function of the upstream prices it uses as inputs. Equation (\ref{eq:downdp}) represents the price of the downstream domestic product in country $i$. The parameter $c_{i}$ is a calibrated cost parameter and $w_{i}$ is the price of all other production inputs, treated as exogenous in the model.\footnote{This assumption is appropriate when the trade policy shock is small. If the policy change is expected to have large effects on the market, impacting the cost of labor and other production inputs, it might not be feasible to make this assumption.} The upstream good and all other production inputs are consumed by the downstream in fixed proportions. 

\begin{equation}\label{eq:downdp}
p_{di}=(w_{i} \ + \ c_{i} \ z_i)
\end{equation}

Then the demand for the upstream good produced in country $i$ by all destinations $j$, $q_{ui}$, is represented by Equation (\ref{eq:downdem}). This equation is a modified version of a constant elasticity of substitution (CES) demand equation that incorporates upstream and downstream prices. Demand for the downstream good produced in country $i$ and consumed in $j$ is represented by Equation (\ref{eq:downimp}).

\begin{equation}\label{eq:downdem}
q_{ui} \ = \sum_j \left( \frac{k_j \ c_j \ b_{uij}}{p_{ui} \ (1+\tau_{uij})}\right) \left( \frac{p_{dj}}{P_j}\right) ^{1-\sigma_d} \left(  \frac{z_j}{p_{dj}} \right) \left( \frac{p_{ui} \ (1+\tau_{uij})}{z_j} \right)^{1-\sigma_u}
\end{equation}

\begin{equation}\label{eq:downimp}
q_{di} \ = \sum_{j} \ k_j \ b_{dij} \ P_j^{\sigma_d - 1} \ (p_{dj} \ (1+\tau_{dij}))^{-\sigma_d}
\end{equation}

Equation (\ref{eq:supplyup}) describes the supply curve for upstream imports and domestic production destined for all sources, where $a_{ui}$ is a supply parameter and $\epsilon_{ui}$ is the constant elasticity of supply for upstream goods from country $i$.\footnote{Note that $q_{ui}=\sum_j q_{uij}$.} Equation (\ref{eq:supplydown}) is the supply curve for downstream imports from countries outside of the model.

\begin{equation}\label{eq:supplyup}
q_{ui} \ = \ a_{ui} \ p_{ui} \ ^{\epsilon_{ui}}
\end{equation}

\begin{equation}\label{eq:supplydown}
q_{di} \ = \ a_{di} \ p_{di} \ ^{\epsilon_{di}}
\end{equation}

\subsection{Two-Market Model}\label{sec:2market}

In this section, we set $j$ equal to two and present the model with two countries that are both destinations and origins. We run illustrative simulations with hypothetical countries A and B to show how the model works. Figure \ref{fig:twocountry} illustrates the model design with two markets.

\begin{figure}[htbp]
\caption{Multi-Country Supply Chain Model with 2 Markets}
\begin{adjustwidth*}{}{-2em} 
\begin{tikzpicture}[node distance=3cm]
\node (udpA) [process] {Upstream Domestic Production};
\node (ddpA) [process, below of=udpA] {Downstream Domestic Production};
\node (cA) [io, below of=ddpA] {Country A Consumers};
\node (A) [startstop, above of=udpA, yshift=-1cm] {Country A};
\node (B) [startstop, right of=A, xshift=2cm] {Country B};
\node (udpB) [process, right of=udpA, xshift=2cm] {Upstream Domestic Production};
\node (ddpB) [process, right of=ddpA, xshift=2cm] {Downstream Domestic Production};
\node (cB) [io, right of=cA, xshift=2cm] {Country B Consumers};
\node (uiA) [process, left of=udpA, xshift=-1cm] {Other Upstream Imports};
\node (uiB) [process, right of=udpB, xshift=1cm] {Other Upstream Imports};
\node (diA) [process, left of=ddpA, xshift=-1cm] {Other Downstream Imports};
\node (diB) [process, right of=ddpB, xshift=1cm] {Other Downstream Imports};
\node (upstream)[left of=uiA,rotate=90]{Upstream};
\node (downstream)[left of=diA,rotate=90]{Downstream};
\draw [arrow] (udpA) -- (ddpA);
\draw [arrow] (ddpA) -- (cA);
\draw [arrow] (udpA) -- (ddpB);
\draw [arrow] (udpB) -- (ddpA);
\draw [arrow] (udpB) -- (ddpB);
\draw [arrow] (ddpB) -- (cB);
\draw [arrow] (ddpB) -- (cA);
\draw [arrow] (ddpA) -- (cB);
\draw [arrow] (uiA) -- (ddpA);
\draw [arrow] (uiB) -- (ddpB);
\draw [arrow] (diB) -- (cB);
\draw [arrow] (diA) -- (cA);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=teal!60] (-6.8,-1.49) -- (10.2,-1.49);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=teal!60] (2.5,-5.2) -- (2.5,2);
\end{tikzpicture}
\end{adjustwidth}
\label{fig:twocountry}
%Alt text: This figure shows an illustration of the two-country model in a flowchart. The figure has 4 quadrants: Country A upstream, Country B upstream, Country A downstream, and Country B downstream. All four quadrants are connected by trade. Each quadrant also has imports from other countries outside of the model.
\end{figure}

Equations (\ref{eq:A}) - (\ref{eq:F}) describe the price indices and equilibrium conditions for the two-market model.\footnote{The demand equations for imports from other countries are also omitted for brevity but follow equation (\ref{eq:downdem}) and (\ref{eq:downimp}).} 
\begin{equation}\label{eq:A}
z_A = \left( p_{uA}^{1-\sigma_{u}} + b_{uBA} \ (p_{uB}(1+\tau_{uBA}))^{1-\sigma_{u}} + b_{uCA} \ (p_{uCA}(1+\tau_{uCA}))^{1-\sigma_{u}}  \right)^{\frac{1}{1 \ - \ \sigma_{u}}}
\end{equation}
\begin{equation}\label{eq:B}
z_B = \left( p_{uB}^{1-\sigma_{u}} + b_{uAB} \ (p_{uA}(1+\tau_{uAB}))^{1-\sigma_{u}} + b_{uCB} \ (p_{uCB}(1+\tau_{uCB}))^{1-\sigma_{u}}  \right)^{\frac{1}{1 \ - \ \sigma_{u}}}
\end{equation}
\begin{equation}\label{eq:C}
P_A = \left( p_{dA}^{1-\sigma_{d}} + b_{dBA} \ (p_{dB}(1+\tau_{dBA}))^{1-\sigma_{d}} + b_{dCA} \ (p_{dCA}(1+\tau_{dCA}))^{1-\sigma_{d}} \right)^{\frac{1}{1 \ - \ \sigma_{d}}}
\end{equation}
\begin{equation}\label{eq:D}
P_B = \left( p_{dB}^{1-\sigma_{d}} + b_{dAB} \ (p_{dA}(1+\tau_{dAB}))^{1-\sigma_{d}} + b_{dCB} \ (p_{dCB}(1+\tau_{dCB}))^{1-\sigma_{d}} \right)^{\frac{1}{1 \ - \ \sigma_{d}}}
\end{equation}
\begin{equation}
p_{dA}=(w_{A} \ + \ c_{A} \ z_A)
\end{equation}
\begin{equation}
p_{dB}=(w_{B} \ + \ c_{B} \ z_B)
\end{equation}
\begin{multline}
a_{uA} \ p_{uA} \ ^{\epsilon_{uA}} \ =  \left( \frac{k_A \ c_A \ b_{uAA}}{p_{uA}}\right) \left( \frac{p_{dA}}{P_A}\right) ^{1-\sigma_d} \left(  \frac{z_A}{p_{dA}} \right) \left( \frac{p_{uA} }{z_A} \right)^{1-\sigma_u} + \\ \left( \frac{k_B \ c_B \ b_{uAB}}{p_{uA} \ (1+\tau_{uAB})}\right) \left( \frac{p_{dB}}{P_B}\right) ^{1-\sigma_d} \left(  \frac{z_B}{p_{dB}} \right) \left( \frac{p_{uA} \ (1+\tau_{uAB})}{z_B} \right)^{1-\sigma_u}
\end{multline}
\begin{multline}\label{eq:F}
a_{uB} \ p_{uB} \ ^{\epsilon_{uB}} \ \ =  \left( \frac{k_B \ c_B \ b_{uBB}}{p_{uB}}\right) \left( \frac{p_{dB}}{P_B}\right) ^{1-\sigma_d} \left(  \frac{z_B}{p_{dB}} \right) \left( \frac{p_{uB} }{z_B} \right)^{1-\sigma_u} + \\ \left( \frac{k_A \ c_A \ b_{uBA}}{p_{uB} \ (1+\tau_{uBA})}\right) \left( \frac{p_{dA}}{P_A}\right) ^{1-\sigma_d} \left(  \frac{z_A}{p_{dA}} \right) \left( \frac{p_{uB} \ (1+\tau_{uBA})}{z_A} \right)^{1-\sigma_u}
\end{multline}

\subsection{Data Inputs Required for the Model}

This model specification requires domestic production and trade data to calibrate model equations. For the two-market model described above, the data inputs are: 
\begin{itemize}
\item Total domestic production of upstream product produced in country $A$ and $B$
\item Total domestic production of downstream product produced in country $A$ and $B$
\item Country $A$ imports of upstream product from country $B$, country $B$ imports of upstream product from country $A$, country $A$ imports of upstream product from all other countries, country $B$ imports of upstream product from all other countries
\item Country $A$ imports of downstream product from country $B$, country $B$ imports of downstream product from country $A$, country $A$ imports of downstream product from all other countries, country $B$ imports of downstream product from all other countries
\item Share of total upstream domestic production and total imports used in downstream production in each country
\end{itemize}

\noindent In addition, this model specification also requires the following parameter estimates:
\begin{itemize}
\item Elasticity of substitution across upstream sources of supply
\item Elasticity of substitution across downstream sources of supply
\item Price elasticity of supply of upstream domestic production in both country $A$ and $B$
\item Price elasticity of supply of non-Country $A$ and $B$ upstream imports
\item Price elasticity of supply of non-Country $A$ and $B$ downstream imports
\item Policy change (e.g. pre- and post- tariff rates, change in quantity from supply disruption, etc.)
\end{itemize}

For the U.S. market, domestic production data by NAICS code can be obtained from the U.S. Census Annual Survey of Manufactures.\footnote{https://www.census.gov/programs-surveys/asm.html} Import data can be obtained from the USITC's DataWeb.\footnote{https://dataweb.usitc.gov/} The BEA's use tables and import matrices can be used to determine the share of production and imports that are used in the specific downstream industry modeled.\footnote{https://www.bea.gov/industry/input-output-accounts-data} Elasticity estimates can be obtained from a number of sources (including Ahmad and Riker, 2020). Data for non-U.S. countries may be difficult to find depending on the country.

\subsection{Calibration of Cost Parameters to Implicit Cost Shares}\label{sec:calibration}

A number of model parameters can be calibrated to data inputs described above. The demand asymmetry parameters ($b_{uij}$, $b_{dij}$) and supply parameters ($a_{ui}$, $a_{di}$) can be calibrated to upstream domestic production and import data by using the demand and supply equations specified in Section \ref{sec:manymarket} and \ref{sec:2market}. The cost parameters ($c_{i}$) can be calibrated to available cost share data, assuming perfect competition in the downstream. In equations (\ref{eq:cali1}) and (\ref{eq:cali2}), the left-hand side represents the upstream share of downstream production costs by country implied by the data inputs. The right-hand side re-writes the cost share using the demand equations, which are a function of observable inputs, calibrated parameters, and elasticities. Then the cost parameters ($c_{A}, c_{B}$) can be solved for analytically by using the following equations\footnote{The values variables $v_{uij}$ and $v_{dij}$ are data inputs. The prices \{$p_{uA}, p_{uB}, p_{uCA}, p_{uCB}$\} can be normalized to 1 if the researcher only wishes to estimate percent changes. The other prices can be solved for with the equations listed above.}: 
\begin{multline}\label{eq:cali1}
\frac{v_{uAA0}+v_{uBA0}+v_{uCA0}}{v_{dAA0}+v_{dAB0}+v_{dAC0}} = \\ \frac{1}{v_{dAA0}+v_{dAB0}+v_{dAC0}}  \left( \left( p_{uAA0} \ \frac{k_A \ c_A}{p_{uAA0}} \right) \left( \frac{p_{dA0}}{P_{A0}} \right)^{1-\sigma_d} \left( \frac{z_{A0}}{p_{dA0}}\right) \left( \frac{p_{uAA0}}{z_{A0}} \right)^{1-\sigma_u}\right)  \\ 
+ \ \left( \left( p_{uBA0}(1+\tau_{uBA0}) \ \frac{k_A \ c_A \ b_{uBA}}{p_{uBA0}(1+\tau_{uBA0})} \right) \left( \frac{p_{dA0}}{P_{A0}} \right)^{1-\sigma_d} \left( \frac{z_{A0}}{p_{dA0}}\right) \left( \frac{p_{uBA0}(1+\tau_{uBA0})}{z_{A0}} \right)^{1-\sigma_u}\right) \\
+ \ \left( \left( p_{uCA0}(1+\tau_{uCA0}) \ \frac{k_A \ c_A \ b_{uCA}}{p_{uCA0}(1+\tau_{uCA0})} \right) \left( \frac{p_{dA0}}{P_{A0}} \right)^{1-\sigma_d} \left( \frac{z_{A0}}{p_{dA0}}\right) \left( \frac{p_{uCA0}(1+\tau_{uCA0})}{z_{A0}} \right)^{1-\sigma_u}\right) 
\end{multline}
\begin{multline}\label{eq:cali2}
\frac{v_{uBB0}+v_{uAB0}+v_{uCB0}}{v_{dBB0}+v_{dBA0}+v_{dBC0}} = \\ \frac{1}{v_{dBB0}+v_{dBA0}+v_{dBC0}} \left( \left( p_{uBB0} \ \frac{k_B \ c_B}{p_{uBB0}} \right) \left( \frac{p_{dB0}}{P_{B0}} \right)^{1-\sigma_d} \left( \frac{z_{B0}}{p_{dB0}}\right) \left( \frac{p_{uBB0}}{z_{B0}} \right)^{1-\sigma_u}\right)  \\ 
+ \ \left( \left( p_{uAB0}(1+\tau_{uAB0}) \ \frac{k_B \ c_B \ b_{uAB}}{p_{uAB0}(1+\tau_{uAB0})} \right) \left( \frac{p_{dB0}}{P_{B0}} \right)^{1-\sigma_d} \left( \frac{z_{B0}}{p_{dB0}}\right) \left( \frac{p_{uAB0}(1+\tau_{uAB0})}{z_{B0}} \right)^{1-\sigma_u}\right) \\
+ \ \left( \left( p_{uCB0}(1+\tau_{uCB0}) \ \frac{k_B \ c_B \ b_{uCB}}{p_{uCB0}(1+\tau_{uCB0})} \right) \left( \frac{p_{dB0}}{P_{B0}} \right)^{1-\sigma_d} \left( \frac{z_{B0}}{p_{dB0}}\right) \left( \frac{p_{uCB0}(1+\tau_{uCB0})}{z_{B0}} \right)^{1-\sigma_u}\right) 
\end{multline}

\section{Illustrative Simulations}\label{sec:illsims}

In the next section, we run illustrative simulations to describe how the model works. First, a unilateral 10 percent tariff is applied to Country A imports of upstream products from country B. Second, we simulate a tariff liberalization by removing a 10 percent tariff on intermediate imports for both countries. We consider two cases: one where the markets are the same size, and one where one market is larger. 

Data and parameter inputs are held fixed throughout this section, with the exception of the last simulation that changes the market size for one of the countries. The elasticities of substitution and price elasticities of supply are all set to 5. Data inputs used are described in table \ref{tab:inputs}. 

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Illustrative Data Inputs}
\begin{tabular}{p{12cm} r }	
\toprule
\textbf{Upstream:} & \\
Country A production used in Country A downstream & 200 \\ 
Country A production used in Country B downstream & 200 \\ 
Country A production exported to other countries excluding B & 200 \\ 
Country A imports from other countries excluding B & 200 \\
Country B production used in Country B downstream & 200 \\ 
Country B production used in Country A downstream & 200 \\ 
Country B production exported to other countries excluding A & 200 \\ 
Country B imports from other countries excluding A & 200 \\
\midrule
\textbf{Downstream:} & \\
Country A production consumed in Country A & 2,000 \\ 
Country A production exported to Country B & 2,000 \\ 
Country A production exported to countries other than B & 2,000 \\ 
Country A imports from other countries excluding B & 1,000 \\
Country B production consumed in Country B & 2,000 \\ 
Country B production exported to Country A & 2,000 \\ 
Country B production exported to countries other than A & 2,000 \\ 
Country B imports from other countries excluding A & 1,000 \\
\bottomrule
	\end{tabular}\label{tab:inputs}
	 \end{threeparttable}
\end{table}

A tariff on intermediate goods affects the downstream industries that use the intermediate as a production input. The magnitude of the economic effects depends on the cost share of that intermediate input in domestic production, as well as the share of intermediates that are sourced from imports. Another important determinant is the amount of trade that is diverted to and from the other country in the model. Additionally, the elasticity of substitution parameter between intermediate sources is another important determinant; the easier it is to shift sourcing after a relative price change of inputs, the greater the economic effects. 

\subsection{Effects of a Unilateral Upstream Tariff}

In this first simulation, we apply a 10 percent tariff to intermediate inputs originating in Country B and used in the downstream production in Country A (figure \ref{fig:oneway}). Note that the current model specification estimates the effects of a tariff on intermediate goods on the downstream industry modeled, not the effects of the tariff on total upstream production. This means that the model does not estimate the effects of a tariff on intermediates sent to other downstream industries. The model could be extended to include all upstream production and imports of the intermediate product, and additional downstream industries that use the intermediate good as an input. 

\begin{figure}[tbph]
\caption{Unilateral 10 percent tariffs on intermediate goods}
\begin{adjustwidth*}{}{-2em} 
\begin{tikzpicture}[node distance=3cm]
\node (udpA) [processg] {Upstream Domestic Production};
\node (ddpA) [processg, below of=udpA] {Downstream Domestic Production};
\node (cA) [iog, below of=ddpA] {Country A Consumers};
\node (A) [startstopg, above of=udpA, yshift=-1cm] {Country A};
\node (B) [startstopg, right of=A, xshift=2cm] {Country B};
\node (udpB) [processg, right of=udpA, xshift=2cm] {Upstream Domestic Production};
\node (ddpB) [processg, right of=ddpA, xshift=2cm] {Downstream Domestic Production};
\node (cB) [iog, right of=cA, xshift=2cm] {Country B Consumers};
\node (uiA) [processg, left of=udpA, xshift=-1cm] {Other Upstream Imports};
\node (uiB) [processg, right of=udpB, xshift=1cm] {Other Upstream Imports};
\node (diA) [processg, left of=ddpA, xshift=-1cm] {Other Downstream Imports};
\node (diB) [processg, right of=ddpB, xshift=1cm] {Other Downstream Imports};
\node (upstream)[left of=uiA,rotate=90]{Upstream};
\node (downstream)[left of=diA,rotate=90]{Downstream};
\draw [arrow] (udpA) -- (ddpA);
\draw [arrow] (ddpA) -- (cA);
\draw [arrow] (udpA) -- node[above=-0.8cm]{\textcolor{red}{tariff}}(ddpB);
\draw [->, red, line width=1.6mm] (udpB) -- node[below=-1cm]{+10\%} (ddpA);
\draw [arrow] (udpB) -- (ddpB);
\draw [arrow] (ddpB) -- (cB);
\draw [arrow] (ddpB) -- (cA);
\draw [arrow] (ddpA) -- (cB);
\draw [arrow] (uiA) -- (ddpA);
\draw [arrow] (uiB) -- (ddpB);
\draw [arrow] (diB) -- (cB);
\draw [arrow] (diA) -- (cA);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (-6.8,-1.49) -- (10.2,-1.49);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (2.5,-5.2) -- (2.5,2);
\end{tikzpicture}\label{fig:oneway}
\end{adjustwidth}
%Alt text: This figure shows an illustration of the two-country model in a flowchart. The figure has 4 quadrants: Country A upstream, Country B upstream, Country A downstream, and Country B downstream. All four quadrants are connected by trade. Each quadrant also has imports from other countries outside of the model. The figure shows a 10 percent tariff applied in the Country A upstream to imports from Country B.
\end{figure}

\begin{figure}[tbph]
\caption{Change in Quantity after Unilateral 10\% Tariff}
\begin{adjustwidth*}{}{-2em} 
\begin{tikzpicture}[node distance=3cm]
\node (udpA) [processg] {Upstream Domestic Production};
\node (ddpA) [processg, below of=udpA] {Downstream Domestic Production};
\node (cA) [iog, below of=ddpA] {Country A Consumers};
\node (A) [startstopg, above of=udpA, yshift=-1cm] {Country A};
\node (B) [startstopg, right of=A, xshift=2cm] {Country B};
\node (udpB) [processg, right of=udpA, xshift=2cm] {Upstream Domestic Production};
\node (ddpB) [processg, right of=ddpA, xshift=2cm] {Downstream Domestic Production};
\node (cB) [iog, right of=cA, xshift=2cm] {Country B Consumers};
\node (uiA) [processg, left of=udpA, xshift=-1cm] {Other Upstream Imports};
\node (uiB) [processg, right of=udpB, xshift=1cm] {Other Upstream Imports};
\node (diA) [processg, left of=ddpA, xshift=-1cm] {Other Downstream Imports};
\node (diB) [processg, right of=ddpB, xshift=1cm] {Other Downstream Imports};
\node (upstream)[left of=uiA,rotate=90]{Upstream};
\node (downstream)[left of=diA,rotate=90]{Downstream};
\draw [->, green, line width=1mm] (udpA) -- node[right=-0.2cm]{+10.2\%} (ddpA);
\draw [->, red, ultra thick] (ddpA) -- node[right=-0.1cm]{-3.2\%}(cA);
\draw [->, red, ultra thick] (udpA) -- node[above=-0.9cm]{-3.2\%} (ddpB);
\draw [->, red, line width=1.6mm] (udpB) -- node[below=-1cm]{-25.2\%} (ddpA);
\draw [->, green, ultra thick] (udpB) -- node[right=-0.2cm]{+1.9\%}(ddpB);
\draw [->, green, ultra thick] (ddpB) -- node[right=-0.2cm]{+1.9\%}(cB);
\draw [->, green, ultra thick] (ddpB) -- node[above=0.35cm]{+1.9\%}(cA);
\draw [->, red, ultra thick] (ddpA) -- node[right=0.2cm]{-3.2\%}(cB);
\draw [->, green, ultra thick] (uiA) -- node[below=0.2cm]{+6.4\%}(ddpA);
\draw [->, green, ultra thick] (uiB) -- node[below=0.2cm]{+0.4\%} (ddpB);
\draw [->, green, ultra thick] (diB) -- node[right=-0.1cm]{+0.8\%}(cB);
\draw [->, green, ultra thick] (diA) -- node[right=-0.1cm]{+0.8\%}(cA);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (-6.8,-1.49) -- (10.2,-1.49);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (2.5,-5.2) -- (2.5,2);
\end{tikzpicture}\label{fig:results}
\end{adjustwidth}
%Alt text: This figure shows an illustration of the two-country model in a flowchart. The figure has 4 quadrants: Country A upstream, Country B upstream, Country A downstream, and Country B downstream. All four quadrants are connected by trade. Each quadrant also has imports from other countries outside of the model. The figure shows the percent change in quantity after a 10 percent tariff is applied in the Country A upstream to imports from Country B.
\end{figure}

Economic effects are reported in figure \ref{fig:results} and table \ref{tab:oneway}. Country A adds a 10 percent tariff on the intermediate goods imported from Country B. The consumer price of Country B-originating imports increases by 8.6 percent after the tariff application, decreasing intermediate imports from Country B by 25.2 percent. Downstream production in Country A demand more upstream production in Country A as the relative price of imports increases after the tariff. This raises the price of domestically produced intermediates by half a percent, and increases the use of domestic intermediates in the downstream by 10.2 percent. Intermediate imports in Country A from countries not subject to the tariff also increase by 6.4 percent.

The increase in prices in the upstream translates to an increase in costs per unit of production in the downstream of Country A. This lowers Country A output of the final good modeled. The consumer price of downstream production increases by just less than one percent, and domestic production of the final good decreases by 3.2 percent. 

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Effects of a Unilateral 10\% Tariff}
\begin{tabular}{p{12cm} r }	
& \% Change  \\
\toprule
\textbf{Upstream results:} & \\
Producer price, country A domestic production & 0.54 \\
Delivered price, country B imports of country A & 0.54 \\ 
Producer price, country B domestic production & -1.23 \\
Delivered price, country A imports of country B & 8.64 \\ 
Quantity, produced and consumed in country A  & 10.16 \\
Quantity, produced and consumed in country B & 7.19 \\
Quantity, country A imports of country B & -25.23 \\ 
Quantity, country B imports of country A & -1.94 \\
Total quantity of country A domestic production & 2.74\\
Total quantity of country B domestic production & -6.01\\
\midrule
\textbf{Downstream results:} & \\
Price, country A domestic production & 0.95  \\
Price, country B domestic production & -0.07 \\
Quantity, country A domestic production  & -3.17 \\
Quantity, country B domestic production & 1.86 \\
\bottomrule
	\end{tabular}\label{tab:oneway}
	 \end{threeparttable}
\end{table}

As described in the previous paragraph, the amount of intermediates exported from Country B to Country A decreased after the Country A tariff. The producer price of the Country B intermediate good decreased by 1.2 percent. The relatively lower price of Country B intermediates leads Country B downstream purchasers to buy more domestic intermediates. In other words, the intermediates sent to Country A are now being used in Country B downstream production. This leads to an increase of domestic intermediates in Country B of 7.2 percent, and an increase in quantity of downstream production by 1.9 percent. 

The pass-through of upstream tariffs into downstream prices depends on the cost share of the intermediate good in production and the fraction of intermediates that are imported. The cost share of the intermediate in downstream production of Country A is 10 percent. Of that 10 percent, one third originates in country B that is subject to the policy change. Quantifying the pass-through into the downstream, a 10 percent tariff in the upstream on Country B translates to about a 1 percent increase in the price of Country A domestic production and about a 3 percent decline in production quantity. 

\subsection{Effects of Bilateral Tariff Liberalization}

In this next set of simulations, tariff rates are reduced between the two closely-related countries. This illustration is akin to tariff liberalization following a new free-trade agreement. In the simulations, Country A removes a 10 percent tariff on intermediate imports from Country B, and Country B removes a 10 percent tariff on intermediate imports from Country A. Figure \ref{fig:2way} illustrates the import flows with the tariff reductions.    

\begin{figure}
\caption{Bilateral 10 percent tariff reduction on intermediate goods}
\begin{adjustwidth*}{}{-2em} 
\begin{tikzpicture}[node distance=3cm]
\node (udpA) [processg] {Upstream Domestic Production};
\node (ddpA) [processg, below of=udpA] {Downstream Domestic Production};
\node (cA) [iog, below of=ddpA] {Country A Consumers};
\node (A) [startstopg, above of=udpA, yshift=-1cm] {Country A};
\node (B) [startstopg, right of=A, xshift=2cm] {Country B};
\node (udpB) [processg, right of=udpA, xshift=2cm] {Upstream Domestic Production};
\node (ddpB) [processg, right of=ddpA, xshift=2cm] {Downstream Domestic Production};
\node (cB) [iog, right of=cA, xshift=2cm] {Country B Consumers};
\node (uiA) [processg, left of=udpA, xshift=-1cm] {Other Upstream Imports};
\node (uiB) [processg, right of=udpB, xshift=1cm] {Other Upstream Imports};
\node (diA) [processg, left of=ddpA, xshift=-1cm] {Other Downstream Imports};
\node (diB) [processg, right of=ddpB, xshift=1cm] {Other Downstream Imports};
\node (upstream)[left of=uiA,rotate=90]{Upstream};
\node (downstream)[left of=diA,rotate=90]{Downstream};
\draw [arrow] (udpA) -- (ddpA);
\draw [arrow] (ddpA) -- (cA);
\draw [->, green, line width=1.6mm] (udpA) -- node[below=-0.9cm]{-10\%}(ddpB);
\draw [->, green, line width=1.6mm] (udpB) --  node[above=-0.9cm]{\textcolor{green}tariffs} (ddpA);
\draw [arrow] (udpB) -- (ddpB);
\draw [arrow] (ddpB) -- (cB);
\draw [arrow] (ddpB) -- (cA);
\draw [arrow] (ddpA) -- (cB);
\draw [arrow] (uiA) -- (ddpA);
\draw [arrow] (uiB) -- (ddpB);
\draw [arrow] (diB) -- (cB);
\draw [arrow] (diA) -- (cA);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (-6.8,-1.49) -- (10.2,-1.49);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (2.5,-5.2) -- (2.5,2);
\end{tikzpicture}\label{fig:2way}
\end{adjustwidth}
%Alt text: This figure shows an illustration of the two-country model in a flowchart. The figure has 4 quadrants: Country A upstream, Country B upstream, Country A downstream, and Country B downstream. All four quadrants are connected by trade. Each quadrant also has imports from other countries outside of the model. The figure shows a 10 percent tariff reduction on upstream imports between Country A and Country B.
\end{figure}

\begin{figure}
\caption{Change in Quantity after Bilateral 10\% Tariff Liberalization with Symmetric Markets}
\begin{adjustwidth*}{}{-2em} 
\begin{tikzpicture}[node distance=3cm]
\node (udpA) [processg] {Upstream Domestic Production};
\node (ddpA) [processg, below of=udpA] {Downstream Domestic Production};
\node (cA) [iog, below of=ddpA] {Country A Consumers};
\node (A) [startstopg, above of=udpA, yshift=-1cm] {Country A};
\node (B) [startstopg, right of=A, xshift=2cm] {Country B};
\node (udpB) [processg, right of=udpA, xshift=2cm] {Upstream Domestic Production};
\node (ddpB) [processg, right of=ddpA, xshift=2cm] {Downstream Domestic Production};
\node (cB) [iog, right of=cA, xshift=2cm] {Country B Consumers};
\node (uiA) [processg, left of=udpA, xshift=-1cm] {Other Upstream Imports};
\node (uiB) [processg, right of=udpB, xshift=1cm] {Other Upstream Imports};
\node (diA) [processg, left of=ddpA, xshift=-1cm] {Other Downstream Imports};
\node (diB) [processg, right of=ddpB, xshift=1cm] {Other Downstream Imports};
\node (upstream)[left of=uiA,rotate=90]{Upstream};
\node (downstream)[left of=diA,rotate=90]{Downstream};
\draw [->, red, line width=1mm] (udpA) -- node[right=-0.1cm]{-18.1\%} (ddpA);
\draw [->, green, ultra thick] (ddpA) -- node[right=-0.1cm]{+1.6\%}(cA);
\draw [->, green, line width=1.6mm] (udpA) -- node[above=-0.9cm]{+31.9\%} (ddpB);
\draw [->, green, line width=1.6mm] (udpB) -- node[below=-1cm]{+31.9\%} (ddpA);
\draw [->, red, line width=1mm] (udpB) -- node[right=-0.1cm]{-18.1\%}(ddpB);
\draw [->, green, ultra thick] (ddpB) -- node[right=-0.2cm]{+1.6\%}(cB);
\draw [->, green, ultra thick] (ddpB) -- node[above=0.35cm]{+1.6\%}(cA);
\draw [->, green, ultra thick] (ddpA) -- node[right=0.2cm]{+1.6\%}(cB);
\draw [->, red, ultra thick] (uiA) -- node[below=0.2cm]{-7.8\%}(ddpA);
\draw [->, red, ultra thick] (uiB) -- node[below=0.2cm]{-7.8\%} (ddpB);
\draw [->, red, ultra thick] (diB) -- node[right=0.1cm]{-1.8\%}(cB);
\draw [->, red, ultra thick] (diA) -- node[right=0.1cm]{-1.8\%}(cA);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (-6.8,-1.49) -- (10.2,-1.49);
\draw [thick,dash pattern={on 10pt off 2pt on 10pt off 2pt}, color=gray!60] (2.5,-5.2) -- (2.5,2);
\end{tikzpicture}\label{fig:results2way}
\end{adjustwidth}
%Alt text: This figure shows an illustration of the two-country model in a flowchart. The figure has 4 quadrants: Country A upstream, Country B upstream, Country A downstream, and Country B downstream. All four quadrants are connected by trade. Each quadrant also has imports from other countries outside of the model. The figure shows the quantity changes after a 10 percent tariff reduction is applied to upstream imports between Country A and Country B.
\end{figure}

Model results are shown in figure \ref{fig:results2way} and table \ref{tab:2way}. In the second column, country A and B are symmetric so economic effects are symmetric. In the third column, country A intermediate production is three times larger than country B intermediate production so economic effects differ by country. Consumer prices of the intermediate good decrease when the tariff is reduced in both Country A and B. There is a shift in use of domestic production of the intermediate good, as the price of exporting becomes relatively more advantageous for upstream producers than shipping their products to downstream domestic producers. The total quantity of domestic production increases after the tariff reduction. 

The downstream results differ based on whether the markets are symmetric or asymmetric. In the symmetric markets case, where Country A and B are the same size in terms of domestic production of the intermediate, the lower tariff on intermediates lowers production costs and downstream production increases by about 1.6 percent. In the asymmetric markets case, downstream production increases in Country B but decreases in Country A. This is because there are multiple opposing effects. Country B subject imports from Country A are larger, so removing a tariff will have a larger positive impact on Country B production. Because more of Country A intermediates are being sent to the downstream in Country B, Country A benefits less from the tariff liberalization. Additionally, Country A consumers are purchasing relatively more from Country B and less from Country A domestic production because downstream domestic production in B is now relatively cheaper.

\begin{table}[tbph]
\centering
\begin{threeparttable}
	\caption{Effects of Tariff Liberalization on Intermediate Inputs}
\begin{tabular}{ p{0.6\textwidth}
      >{\centering}p{0.15\textwidth}
      >{\centering\arraybackslash}p{0.15\textwidth}}	
& Symmetric Markets, & Asymmetric Markets, \\
& \% Change & \% Change \\
\toprule
\textbf{Upstream results:} & &\\
Producer price, country A domestic production & 0.75 & 1.89\\
Consumer price, country B imports of country A & -8.41 & -7.37\\ 
Producer price, country B domestic production & 0.75 & 1.80\\
Consumer price, country A imports of country B & -8.41 & -7.45\\ 
Quantity, produced and consumed in country A  & -18.05 & -13.81\\
Quantity, produced and consumed in country B & -18.05 & -8.59\\
Quantity, country A imports of country B & 31.98 & 39.38\\ 
Quantity, country B imports of country A & 31.98 & 46.61\\
Total quantity of country A domestic production & 3.79 & 9.81\\
Total quantity of country B domestic production & 3.79 & 9.35\\
\midrule
\textbf{Downstream results:} & &\\
Price, country A domestic production & -1.05 & -0.23\\ 
Quantity, country A domestic production & 1.61 & -1.57\\
Price, country B domestic production & -1.05 & -1.33\\ 
Quantity, country B domestic production & 1.61 & 4.02\\
\bottomrule
	\end{tabular}\label{tab:2way}
	 \end{threeparttable}
\end{table}

\section{Conclusion}\label{sec:concl}

This paper presents a model that analyzes the supply chain effects of a new trade policy between closely-related countries. It can be used to analyze how a tariff change on intermediates may affect downstream industries. It can also be used to estimate the effects of tariff liberalization on imports, exports, and domestic production in both upstream and downstream industries. The model specification is designed for narrowly-defined industries. It is not suitable for aggregate industries or industries with complex supply chain linkages. The model analyzes a specific upstream-downstream linkage and does not compute general equilibrium effects. 

\end{document}