\begin{document} \title{Practical PE Models of Trade and FDI Policy Uncertainty} \author{Patricia Mueller} \author{David Riker} \date{\vspace{1.5in}% \today} \thispagestyle{empty} { % set font to helvetica (arial) to make it 508-compliant \fontfamily{phv}\selectfont \begin{center} {\Large \textbf{PRACTICAL PE MODELS OF}} \\ \vspace{0.25in} {\Large \textbf{TRADE AND FDI POLICY UNCERTAINTY}} \\ \vspace{0.75in} {\Large Patricia Mueller} \\ \vspace{0.25in} {\Large David Riker} \\ \vspace{0.75in} {\large ECONOMICS WORKING PAPER SERIES}\\ Working Paper 2020--08--A \\ \vspace{0.5in} U.S. INTERNATIONAL TRADE COMMISSION \\ 500 E Street SW \\ Washington, DC 20436 \\ \vspace{0.5in} August 2020 \end{center} \vfill \noindent The authors are grateful to Nuno Lim{\~a}o for helpful comments on this working paper. \vspace{0.25in} \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. Working papers are circulated to promote the active exchange of ideas between USITC Staff and recognized experts outside the USITC and to promote professional development of Office Staff by encouraging outside professional critique of staff research. Please address correspondence to patricia.mueller@usitc.gov or david.riker@usitc.gov. \newpage \thispagestyle{empty} % remove headers, footers, and page numbers from cover page \begin{flushleft} Practical PE Models of Trade and FDI Policy Uncertainty \\ Patricia Mueller and David Riker\\ Office of Economics Working Paper 2020--08--A\\ August 2020 \\~\\ \end{flushleft} \vfill \begin{abstract} \noindent We convert the model of trade and investment under policy uncertainty in \citeasnoun{HandLim2015} into a simple spreadsheet model with limited data requirements that can be used in ex ante analysis of changes in policy regimes. We illustrate the model of exports and trade policy uncertainty in a series of simulations. Then we reconfigure the modeling framework to address the impact of tax policy uncertainty on horizontal foreign direct investment and foreign affiliate sales. \end{abstract} \vfill \begin{flushleft} Patricia Mueller, Research Division, Office of Economics\\ \href{mailto:david.riker@usitc.gov}{patricia.mueller@usitc.gov}\\ \vspace{0.5in} David Riker, Research Division, Office of Economics\\ \href{mailto:david.riker@usitc.gov}{david.riker@usitc.gov}\\ \vspace{0.5in} \end{flushleft} } % end of helvetica (arial) font \clearpage \newpage \doublespacing \setcounter{page}{1} \section{Introduction \label{sec: section1}} The recent economics literature on trade policy uncertainty sheds new light on the economic impact of trade agreements. Credible agreements increase trade even if tariff rates were already close to zero, because they lock in the low or zero rates. The firm heterogeneity models of trade and policy uncertainty in \citeasnoun{HandLim2015} and \citeasnoun{HandLim2017} are seminal contributions to this literature. They apply the models in retrospective analysis that quantifies the effects of past trade agreements on policy uncertainty and trade. Their models measure the extent of trade policy uncertainty, and they estimate the effects of this uncertainty on exporting decisions. \citeasnoun{HandLim2015} examines Portugal's accession to the European Community in 1986. They estimate that the reduction in uncertainty about future trade policies accounted for most new exporters and growth in the total volume of Portugal's exports in the late 1980s. \citeasnoun{HandLim2017} examines the reduction in trade policy uncertainty when China joined the WTO in 2001. They estimate that the reduction in trade policy uncertainty accounted for over one-third of the growth in China's exports to the United States between 2000 and 2005. The modeling framework of Handley and Lim{\~a}o can also be used in ex ante analysis.\footnote{\citeasnoun{HandLim2017} includes a series of simulations of hypothetical policy change scenarios, though most of the study focuses on retrospective econometric analysis.} However, in this case the user will need to specify the probability distribution of future policies, since the probabilities cannot be inferred from an historical record. Keeping in mind the challenges of collecting information about this probability distribution and other relevant economic factors, we develop a spreadsheet implementation of the Handley and Lim{\~a}o model with assumptions that significantly reduce the data requirements of the model and make it a practical tool for ex ante analysis. We adopt the partial equilibrium "small exporter" assumption in \citeasnoun{HandLim2015} and a specific probability distribution for the policy uncertainty with three possible tariff rates, the current tariff rate, a lower rate, or a higher rate. Section \ref{sec: section2} presents the simplified version of Handley and Lim{\~a}o's model of exports with trade policy uncertainty. We start by presenting the structural equations of the model and derive a reduced-form expression for the percent change in the value of exports from locking in current tariff rates. Then we present a series of simulations with hypothetical data inputs to illustrate how the model works. Section \ref{sec: section3} reconfigures the modeling framework to fit an industry in which cross-border trade is not feasible and foreign markets can only be supplied through horizontal foreign direct investment (FDI) and foreign affiliate sales (FAS). These sales are not subject to a tariff, since they do not cross national borders, but the operating profits of the foreign affiliate are taxed. Then we follow the same three steps: we present the structural equations, derive a reduced-form expression for the percent change in the value of FAS from locking in the tax rate, and report the results from illustrative simulations. Section \ref{sec: section4} concludes. \section{Model with Exports \label{sec: section2}} Our model closely follows the dynamic model of exporting in \citeasnoun{HandLim2015}.\footnote{They build on the trade with firm heterogeneity models in \citeasnoun{Melitz2003} and \citeasnoun{Chaney2008} and models of investment under uncertainty in \citeasnoun{Dixit1989}. \citeasnoun{HandLim2017} significantly extends the model to capture general equilibrium effects and upgrading in the technology for exporting.} There is Constant Elasticity of Substitution (CES) demand for the differentiated products of a specific industry in a specific export market, with elasticity of substitution $\sigma$. Firms take aggregate expenditure and the CES price index in the export market as exogenous.\footnote{This "small exporter" assumption is more reasonable if the exports account for only a small share of the foreign market.} This partial equilibrium assumption greatly simplifies the equations of the model. Each exporting firm incurs a one-time sunk cost of exporting $K_x$. The ad valorem tariff rate is $t$.\footnote{\citeasnoun{HandLim2015} represent tariffs as a factor $\tau$ that is equal to the one plus this tariff rate.} There is heterogeneity in the firms' marginal costs of production for export, represented by $c$. The constant discount factor $\beta$ reflects the probability that an exporting firm survives in the foreign market each period. There is an exogenous number of firms that supply their own domestic market, and an endogenous share of these firms also invest in exporting. On the policy side, the initial tariff rate $t_0$ is subject to change. The rate is reassessed with probability $\gamma$ each period. If policy uncertainty is eliminated as the rate is locked in by a trade agreement, then $\gamma$ is reduced to zero. Firms observe tariff rates before setting their prices but after deciding whether to invest in exporting. We assume that the probability distribution of tariff rates, conditional on policy reassessment, has three possible states.\footnote{The restriction to three potential states helps to limit the data requirements of the model. The framework can be easily extended to incorporate a more elaborate probability distribution.} If the tariff rate is reassessed, then it switches to a higher tariff rate $t_h \geq t_0$ with probability $\phi_h$, switches to a lower tariff rate $t_l \leq t_0$ with probability $\phi_l$, and stays the same at $t_0$ with probability $1 \ - \phi_h \ - \ \phi_l$. Equation (\ref{eq:1}) is the profits of a firm with marginal cost of production $c$ that faces tariff rate $t$. \begin{equation}\label{eq:1} \pi_x(c,t) = A \ \left( c \right)^{1 \ - \ \sigma} \ (1 \ + \ t)^{- \sigma} \end{equation} \noindent $A$ is a constant in the model that is equal to $\frac{1}{\sigma} \ E \ {P \ } ^{\sigma \ - \ 1} \ \left( \frac{\sigma}{\sigma \ - \ 1} \right)^{1-\sigma}$. $E$ is aggregate expenditure on the products of the industry in the export market, and $P$ is the industry price index in the market. Equation (\ref{eq:2}) is the value function for a firm with marginal cost $c$ if it enters into exporting in state $s$, facing tariff rate $t_s$. \begin{equation}\label{eq:2} V_x(c,t_s) = \pi_x(c, t_s) \ + \ \beta \ \left( (1 \ - \ \gamma ) + \gamma \ \phi_s) \right) \ V_x(c, t_s) \ + \ \beta \ \gamma \sum_{s'} \ \phi_{s'} \ V_x(c, t_{s'}) \end{equation} \noindent $s$ and $s'$ index the three states. Equation (\ref{eq:3}) is the value function for a firm with marginal cost $c$ if it waits when it faces tariff rate $t_0$ and then enters into exporting later if the tariff rate declines to $t_l \leq t_0$. \begin{equation}\label{eq:3} V_w(c, t_0) = \beta \ \left( (1 \ - \ \gamma ) \ + \ \gamma \left( 1 \ - \ \phi_l \right) \right) \ V_w(c, t_0) \ + \ \beta \ \gamma \ \phi_l \ \left( V_x(c, t_l) \ - \ K_x \right) \end{equation} \noindent There will be a cutoff marginal cost for each combination of $t_0$ and $\gamma_0$, below which a firm will choose to invest in exporting.\footnote{This is equivalent to a cutoff unit labor requirement, since the wage is normalized to one.} This cutoff, $c_x \ (\gamma, t_0)$, is implicitly defined in (\ref{eq:4}). \begin{equation}\label{eq:4} V_x(c_x \ (\gamma, t_0), \gamma) \ - \ K_x = V_w(c_x \ (\gamma, t_0), \gamma) \end{equation} \noindent It rises as $\gamma$ declines from $\gamma_0$ to zero. Next, we derive a reduced-form expression for the change in exports that results from locking in the tariff rate. Equation (\ref{eq:5}) is the ratio of the cutoff marginal cost of exporting when $\gamma = 0$ to the value of exports when $\gamma = \gamma_0$, in both cases evaluated at the initial tariff rate $t_0$.\footnote{This is equivalent to the expression in equation (40) in \citeasnoun{HandLim2017}, with differences in notations.} \begin{equation}\label{eq:5} \frac{c_x \ (0, t_0)}{c_x \ (\gamma_0, t_0)} = \left( 1 \ - \ \frac{\ \beta \ \gamma_0 \ \phi_h \ \left( 1 \ - \ \left( \frac{1 \ + \ t_{h}}{1 \ + t_{0}} \right)^{- \sigma} \right)}{1 \ - \ \beta \ (1 \ - \gamma_0)} \right) ^ {\frac{1}{1 \ - \ \sigma}} \end{equation} \noindent Assuming that marginal costs are heterogeneous across firms and Pareto-distributed with shape parameter $k$, equation (\ref{eq:6}) is the ratio of the value of exports for the two values of $\gamma$.\footnote{As long as $k > \sigma \ - \ 1$, the value of exports will increase as the elimination of uncertainty increases the cutoff for exporting. We assume that this condition holds.} \begin{equation}\label{eq:6} \frac{X \ (0, t_0)}{X \ (\gamma_0, t_0)} = \left( \frac{c_x \ (0, t_0)}{c_x \ (\gamma_0, t_0)} \right)^{k \ - \ (\sigma \ - \ 1)} \end{equation} \noindent Equation (\ref{eq:7}) is the percent change in the value of exports from locking in the tariff rate. \begin{equation}\label{eq:7} \frac{X \ (0, t_0) \ - \ X \ (\gamma_0, t_0)}{X \ (\gamma_0, t_0)} = \left( 1 \ - \ \frac{\ \beta \ \gamma_0 \ \phi_h \ \left( 1 \ - \left( \frac{1 \ + \ t_{h}}{1 \ + \ t_{0}}\right)^{-\sigma} \right) }{1 \ - \ \beta \ (1 \ - \gamma_0)} \right) ^ {\frac{k \ - \ (\sigma \ - \ 1)}{1 \ - \ \sigma }} \ - 1 \end{equation} \noindent Equation (\ref{eq:7}) calculates the effect of locking-in the tariff rate on the value of exports using only a few model parameters, without needing to observe the marginal costs of production or the fixed costs of becoming an exporter. We first focus on a restricted case in which the initial tariff rate is already at its lowest possible value. This is equivalent to setting $t_l = t_0$ or setting $\phi_l=0$. Given this restriction on the probability distribution, there is no reason for a firm to wait and then invest later in exporting, since profits only have the potential to decline. Table \ref{table:1} reports the percent change in the value of exports from seven simulations with alternative values of the parameter inputs. In addition to illustrating how the model works, these simulations can help the model user to identify which of the model inputs has the greatest effect on the simulated percent changes in the value of exports. The first simulation, labeled $v1.1$, defines the benchmark values of the model parameters. Each of the other simulations in Table 1 changes the value of one of the parameters and while leaving the others at their benchmark values. Exports grow by 8.8\% in the benchmark simulation, $v1.1$. When we double the high tariff rate in $v1.2$, it nearly doubles export growth, to 15.1\%. Simulation $v1.3$ increases the low initial tariff rate to 5\%, and this reduces the export growth rate to 4.5\%. The reduction in the probability of a high tariff in $v1.4$ reduces the growth rate to 2.7\%, while the reduction in the probability of a policy reassessment in $v1.5$ only reduces growth to 6.7\%. Lowering the value of $\sigma$ from 5 to 4 in $v1.6$ almost doubles the growth rate, while a lower $\beta$ in $v1.7$ has a small negative effect. \begin{table}[tbph] \centering \begin{threeparttable} \caption{Simulated Impact on Exports\label{table:1}} \begin{tabular}{l c c c c c c c} \toprule Model Runs & $v1.1$ & $v1.2$ & $v1.3$ & $v1.4$ & $v1.5$ & $v1.6$ & $v1.7$ \\ \midrule \textbf{Inputs} & \ & \ & \ & \ & \ & \ & \ \\ Elasticity of Substitution ($\sigma$) & 5 & 5 & 5 & 5 & 5 & \textbf{4} & 5\\ Pareto Shape Parameter ($k$) & 6 & 6 & 6 & 6 & 6 & 6 & 6 \\ Initial Prob. of Reassessment ($\gamma_0$) & 0.5 & 0.5 & 0.5 & 0.5 & \textbf{0.2} & 0.5 & 0.5 \\ Conditional Prob. of a High Tariff ($\phi_h$) & 0.5 & 0.5 & 0.5 & \textbf{0.2} & 0.5 & 0.5 & 0.5 \\ High Tariff Rate ($t_{h}$) & 10\% & \textbf{20\%} & 10\% & 10\% & 10\% & 10\% & 10\% \\ Initial Tariff Rate ($t_{0}$) & 0\% & 0\% & \textbf{5\%} & 0\% & 0\% & 0\% & 0\% \\ Discount Factor ($\beta$) & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & \textbf{0.8} \\ \midrule \textbf{Outputs} & \ & \ & \ & \ & \ & \ & \ \\ Percent Change in the Value of Exports & 8.8\% & 15.1\% & 4.5\% & 3.3\% & 6.7\% & 14.9\% & 7.0\% \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} Table 2 reports a second set of simulations of the effects on the value of exports under a less restrictive set of assumptions: $\phi_l >0$ and $t_l < t_0$. In this case, there is a possibility of a reduction in the tariff rate from $t_0$ (good news), as well as an increase in the tariff rate (bad news). Exports grow by 1.7\% in the benchmark simulation, $v2.1$. When we double the high tariff rate in $v2.2$, it more than doubles export growth, to 4.2\%. When we increase the low tariff rate to 2\% in $v2.3$, this has no effect on export growth relative to the benchmark simulation. The increase in the initial tariff rate in $v2.4$ reduces the growth rate to 1.1\%, while the reduction in the initial probability of a policy reassessment in $v2.5$ only reduces growth to 1.4\%. A lower value of $\sigma$ in $v2.6$ has a positive effect on the growth rate, while a lower $\beta$ in $v2.7$ has a negative effect. \begin{table}[tbph] \centering \begin{threeparttable} \caption{Additional Simulations of the Impact on Exports\label{table:2}} \begin{tabular}{l c c c c c c c} \toprule Model Runs & $v2.1$ & $v2.2$ & $v2.3$ & $v2.4$ & $v2.5$ & $v2.6$ & $v2.7$ \\ \midrule \textbf{Inputs} & \ & \ & \ & \ & \ & \ & \ \\ Elasticity of Substitution ($\sigma$) & 5 & 5 & 5 & 5 & 5 & \textbf{4} & 5\\ Pareto Shape Parameter ($k$) & 6 & 6 & 6 & 6 & 6 & 6 & 6 \\ Initial Prob. of Reassessment ($\gamma_0$) & 0.5 & 0.5 & 0.5 & 0.5 & \textbf{0.2} & 0.5 & 0.5 \\ Conditional Prob. of a High Tariff ($\phi_h$) & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ Conditional Prob. of a Medium Tariff ($\phi_m$) & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 \\ Conditional Prob. of a Low Tariff ($\phi_h$) & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ High Tariff Rate ($t_{h}$) & 10\% & \textbf{20\%} & 10\% & 10\% & 10\% & 10\% & 10\% \\ Initial Tariff Rate ($t_{0}$) & 5\% & 5\% & 5\% & \textbf{7\%} & 5\% & 5\% & 5\% \\ Low Tariff Rate ($t_{l}$) & 0\% & 0\% & \textbf{2\%} & 0\% & 0\% & 0\% & 0\% \\ Discount Factor ($\beta$) & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & \textbf{0.8} \\ \midrule \textbf{Outputs} & \ & \ & \ & \ & \ & \ & \ \\ Percent Change in the Value of Exports & 1.7\% & 4.2\% & 1.7\% & 1.1\% & 1.4\% & 2.9\% & 1.4\% \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} \newpage \section{Model with Horizontal FDI \label{sec: section3}} Next, we modify the modeling framework and reapply it to a setting where it is not feasible to serve the foreign market through cross-border exports. Firms can only supply the foreign market through horizontal FDI and FAS. For example, this describes the international supply of some service categories, like legal services, that are mostly limited to mode one trade in services (defined as supply through a foreign commercial presence). Each firm incurs a one-time sunk cost of establishing a foreign affiliate equal to $K_f$. In this reconfiguration of the model, the tariff rate does not matter since there are no cross-border exports. Instead, we focus on uncertainty about the taxation of the operating profits from FAS.\footnote{If they faced a tax on the sales of the foreign affiliate rather than its operating profits, then the equations of the model would be identical to the equations for the model with exporting in Section 2, and the variables would just have a slightly different interpretation. That case would also be mathematically equivalent to an ad valorem regulatory cost on those sales, since operating profits are proportional to revenue in the model.} Again, there are three potential policy states indexed by $s$. The tax rate is initially $t_0$. If the policy is reassessed, it switches to rate $t_h \geq t_0$ with probability $\lambda_h$, switches to $t_l \leq t_0$ with probability $\lambda_l$, and remains at the initial rate $t_0$ with probability $1 \ - \ \lambda_h \ - \ \lambda_l$. Equation (\ref{eq:8}) is the after-tax operating profits from the FAS of a firm with marginal cost $c$ and tax rate $t$. % \begin{equation}\label{eq:8} \pi_f(c,t) = A \ \left( c \right)^{1 \ - \ \sigma} \ \left (1 \ - \ t \right) \end{equation} \noindent Equations (\ref{eq:9}) is the value function for this firm if it enters the foreign market by investing in a foreign affiliate in state $s$, when the tax rate is $t_s$. % \begin{equation}\label{eq:9} V_f(c,t_s) = \pi_f(c, t_s) \ + \ \beta \ \left( (1 \ - \ \gamma ) + \gamma \ \lambda_s \right) \ V_f(c, t_s) \ + \ \beta \ \gamma \ \sum_{s'} \lambda_{s'} \ V_f(c, t_{s'}) \end{equation} % % \noindent Equation (\ref{eq:10}) is the value function for a firm with marginal cost $c$ if it waits when it faces tax rate $t_0$ and then later establishes a foreign affiliate if the tax rate declines to $t_l$. \begin{equation}\label{eq:10} V_w(c, t_0) = \ \beta \ \left( (1 \ - \ \gamma ) \ + \ \gamma \ \left(1 \ - \ \lambda_l \right) \right) \ V_w(c, t_0) \ + \ \beta \ \gamma \ \lambda_l \ \left( V_f(c, t_l) \ - \ K_f \right) \end{equation} \noindent There will be a cutoff marginal cost for each combination of $t_0$ and $\gamma_0$. This cutoff, $c_f \ (\gamma, t_0)$, is implicitly defined in (\ref{eq:11}). \begin{equation}\label{eq:11} V_f(c_f \ (\gamma, t_0), \gamma) \ - \ K_f = V_w(c_f \ (\gamma, t_0), \gamma) \end{equation} \noindent It rises as $\gamma$ declines from $\gamma_0$ to zero. Next, we derive a reduced-form expression for the percent change in the value of FAS from locking-in the tax rate. Again, it is straightforward to solve the model for the ratio of the value of foreign affiliate sales when $\gamma = 0$ to the value of sales when $\gamma = \gamma_0$, with the tax rate at its initial level. Equation (\ref{eq:12}) is the ratio of the cutoff marginal cost for FAS for the two values of $\gamma$. % \begin{equation}\label{eq:12} \frac{c_f (0, t_0)}{c_f (\gamma_0, t_0)} = \left( 1 \ - \ \frac{\ \beta \ \gamma_0 \ \lambda_h \ \left( 1 \ - \ \frac{1 \ - \ t_{h}}{1 \ - t_{0}} \right)}{1 \ - \ \beta \ (1 \ - \gamma_0)} \right) ^ {\frac{1}{1 \ - \ \sigma}} \end{equation} \noindent Assuming that marginal costs are heterogeneous across firms and Pareto-distributed with shape parameter $k$, equation (\ref{eq:13}) is the ratio of the value of FAS for the two values of $\gamma$. % \begin{equation}\label{eq:13} \frac{F(0, t_0)}{F(\gamma_0, t_0)} = \left( \frac{c_f \ (0,t_0)}{c_f \ (\gamma_0,t_0)} \right)^{k-(\sigma \ - \ 1)} \end{equation} \noindent Equation (\ref{eq:14}) is the percent change in the value of foreign affiliate sales from locking in the tax rate. % \begin{equation}\label{eq:14} \frac{F(0, t_0) \ - \ F(\gamma_0, t_0)}{F(\gamma_0, t_0)} = \left(1 \ - \ \frac{\beta \ \gamma_0 \ \lambda_h \ \left(1 \ - \ \frac{1 \ - \ t_{h}}{1 \ - \ t_{0}} \right)}{1 \ - \ \beta \ (1 \ - \gamma_0)} \right)^{\frac{k \ - \ (\sigma \ - \ 1)}{1 \ - \ \sigma}} \ - \ 1 \end{equation} \noindent This equation calculates the effect of locking in the tax rate on foreign affiliate sales without needing to observe the marginal or fixed costs of foreign affiliate production. As in our analysis of the exporting model, we focus first on a more restricted case in which the initial tax rate, $t_0$, is at the lowest possible value. This is equivalent to setting $t_l = t_0$ or setting $\lambda_l=0$. Given this restrictive assumption about the probability distribution, there is no reason for a firm to wait before investing in foreign affiliate sales, since profits only have the potential to decline. Table 3 reports the growth rate of FAS for alternative values of the parameter inputs. Like in Table 1, the first simulation, $v3.1$, defines the benchmark values of the model parameters, and each of the other simulations changes the value of one of the parameters and leaves the others at their benchmark values. Foreign affiliate sales grow by 4.4\% in the benchmark simulation, $v3.1$. When we increase the high tariff rate by 50\% in $v3.2$ it increases the growth of foreign affiliate sales by a little more than 50\%, to 6.8\%. Simulation $v3.3$ increases the initial tax rates to 10\%, and this reduces the growth rate to 2.4\%. The reduction in the probability of a high tax rate in $v3.4$ reduces the growth rate to 1.7\%, while the reduction in the probability of a policy reassessment in $v3.5$ only reduces growth to 3.4\%. A lower value of $\sigma$ in $v3.6$ has a positive effect on the growth rate, while a lower $\beta$ in $v3.7$ has a negative effect. \begin{table}[tbph] \centering \begin{threeparttable} \caption{Additional Simulations of the Impact on Foreign Affiliate Sales\label{table:3}} \begin{tabular}{l c c c c c c c} \toprule Model Runs & $v3.1$ & $v3.2$ & $v3.3$ & $v3.4$ & $v3.5$ & $v3.6$ & $v3.7$ \\ \midrule \textbf{Inputs} & \ & \ & \ & \ & \ & \ & \ \\ Elasticity of Substitution ($\sigma$) & 5 & 5 & 5 & 5 & 5 & \textbf{4} & 5\\ Pareto Shape Parameter ($k$) & 6 & 6 & 6 & 6 & 6 & 6 & 6 \\ Initial Prob. of Reassessment ($\gamma_0$) & 0.5 & 0.5 & 0.5 & 0.5 & \textbf{0.2} & 0.5 & 0.5 \\ Conditional Prob. of a High Tax ($\lambda$) & 0.5 & 0.5 & 0.5 & \textbf{0.2} & 0.5 & 0.5 & 0.5 \\ Initial Tax Rate ($t_{0}$) & 0\% & 0\% & \textbf{10\%} & 0\% & 0\% & 0\% & 0\% \\ High Tax Rate ($t_{h}$) & 20\% & \textbf{30\%} & 20\% & 20\% & 20\% & 20\% & 20\% \\ Discount Factor ($\beta$) & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & \textbf{0.8} \\ \midrule \textbf{Outputs} & \ & \ & \ & \ & \ & \ & \ \\ Percent Change in Foreign Affiliate Sales & 4.4\% & 6.8\% & 2.4\% & 1.7\% & 3.4\% & 8.9\% & 3.5\% \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} Table 4 reports a final set of simulations of the effects on the value of foreign affiliate sales under less restrictive assumptions: $\lambda_l >0$ and $t_l < t_0$. Foreign affiliate sales grow by 4.4\% in the benchmark simulation, $v4.1$. When we increase the high tax rate to 30\% in $v4.2$ it increases the growth of foreign affiliate sales to 2.2\%. When we increase the low of tax rate to 2\%, this has no effect on the growth rate relative to the benchmark case. The increase in the initial tax rate in $v4.4$ reduces the growth rate to 0.9\%, while the reduction in the probability of a policy reassessment in $v4.5$ only reduces growth to 1.0\%. The lower value of $\sigma$ in $v4.6$ increases the growth rate to 2.7\%, while the lower $\beta$ in $v4.7$ reduces the growth rate relative to the benchmark simulation. \begin{table}[tbph] \centering \begin{threeparttable} \caption{Additional Simulations of the Impact on Foreign Affiliate Sales\label{table:4}} \begin{tabular}{l c c c c c c c} \toprule Model Runs & $v4.1$ & $v4.2$\ & $v4.3$ & $v4.4$ & $v4.5$ & $v4.6$ & $v4.7$ \\ \midrule \textbf{Inputs} & \ & \ & \ & \ & \ & \ & \ \\ Elasticity of Substitution ($\sigma$) & 5 & 5 & 5 & 5 & 5 & \textbf{4} & 5\\ Pareto Shape Parameter ($k$) & 6 & 6 & 6 & 6 & 6 & 6 & 6 \\ Initial Prob. of Reassessment ($\gamma_0$) & 0.5 & 0.5 & 0.5 & 0.5 & \textbf{0.2} & 0.5 & 0.5 \\ Conditional Prob. of a High Tax ($\lambda_h$) & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ Conditional Prob. of a Medium Tax ($\lambda_m$) & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 & 0.6 \\ Conditional Prob. of a Low Tax ($\lambda_l$) & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 & 0.2 \\ High Tax Rate ($t_{h}$) & 20\% & \textbf{30\%} & 20\% & 20\% & 20\% & 20\% & 20\% \\ Initial Tax Rate ($t_{0}$) & 5\% & 5\% & 5\% & \textbf{10\%} & 5\% & 5\% & 5\% \\ Low Tax Rate ($t_{l}$) & 0\% & 0\% & \textbf{2\%} & 0\% & 0\% & 0\% & 0\% \\ Discount Factor ($\beta$) & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & 0.9 & \textbf{0.8} \\ \midrule \textbf{Outputs} & \ & \ & \ & \ & \ & \ & \ \\ Percent Change in Foreign Affiliate Sales & 1.3\% & 2.2\% & 1.3\% & 0.9\% & 1.0\% & 2.7\% & 1.1\% \\ \bottomrule \end{tabular} \end{threeparttable} \end{table} \newpage \section{Conclusions \label{sec: section4}} The simplified model is a practical tool for analyzing the impact of policy uncertainty on exports or foreign affiliate sales. It does not come close to capturing the richness and complexity of the more general models in \citeasnoun{HandLim2015} and \citeasnoun{HandLim2017}, but it can serve as a practical introduction to their modeling framework. The model has limited data requirements. Model simulations can be run in a spreadsheet, similar to the wide range of spreadsheet PE trade policy models available online at the U.S. International Trade Commission's Trade Policy PE Modeling Portal at \url{https://www.usitc.gov/data/pe_modeling/index.htm}. \bibliographystyle{dcu} \bibliography{biblio} \end{document}